General Mathematics
[1]
vixra:2410.0064 [
pdf]
A Dynamical Systems Model for Population and Depleting Resources
We investigate a coupled, non-linear dynamical systems model for the relationship between population and depleting resources inspired by limits to growth. The model is determined by logistic growth in population with carrying capacity determined by resources. The rate of decline of resources is determined linearly by the population. The model produces an initial exponential increase in population followed by a decrease to the fixed point while congruently resources decrease in a sigmoidal fashion to the fixed point. We fit the model to world population over the period 10000 BC to 2021 in different time intervals corresponding to different growth rates. We show a number of projections to 2500 based on fitting to the time period of 1950 to 2021 with various parameter constraints.
[2]
vixra:2410.0046 [
pdf]
Computational Complexity Analysis using Negation Negation Normal Form Circuit
概要. This paper describes about analyzing method for computational complexity using Negation Normal Form Circuit. Although Negation Normal Form Circuit can emulate Turing machines, most of the circuits are monotonic. In this paper, Negation Normal Form Circuit is further divided into a monotonic subcircuit consisting of AND and OR gate (Rating Circuit) and a subcircuit consisting of NOT elements, and the analysis focuses on the Rating Circuit. From the viewpoint of the Rating Circuit, the NOT gate is constraint on the input of the Rating Circuit. We can use another input constraints. By changing the constraints of the inputs of Rating Circuit, We can analyse complexity detail. In this paper, we use this method to analyze the complexity of the clique problem.
[3]
vixra:2410.0035 [
pdf]
Cournot's Principle Revisited
Cournot's principle states that a typical event (i.e., an event with probability very close to 1) occurs nearly certainly in a single trial of an experiment. This principle has been considered by various authors as the only connection between mathematical probability and the real world of experiments. To make the logical structure of the principle clearer, in this paper a reformulation of the principle is proposed. This reformulation is based on the following three elements: (1) The explicit definition of the empirical property of practical certainty, (2) the clear separation between probability measure and experiment, including the remark that typicality is a mathematical property defined by the probability measure while practical certainty is an empirical property defined by the experiment, and (3) the explicit formulation of the product rule for independent trials. The novel formulation then states that a probability measure P "governs" an experiment E if the events that are typical according to P^n are practically certain according to E^n for all n >= 1, where P^n is the n-fold product of P and E^n is the experiment whose trials are composed of n trials of E. The novel formulation highlights the possible existence of two ambiguities in the principle, namely: (i) that different probability measures govern the same experiment and (ii) that the same probability measure governs different experiments. In this paper the first ambiguity is rigorously disproved, while the second is disproved provided that a suitable property characterizing the empirical equivalence of experiments is assumed.
[4]
vixra:2409.0136 [
pdf]
Problem of Principal Axis and DBZC: Tan(pi/2)=0
In this note, we would like to see the fundamental result $tan(pi/2)=0$ from the famous problem of principal axis in connection with the division by zero calculus $frac{f(x)}{(x - a)^n}|_{x =a} : = frac{f^{(n)}(a)}{n!}.$
[5]
vixra:2409.0123 [
pdf]
Resonance Phenomena May be Interpreted by DBZC: $(f(x)/x )(x=0):= F^prime(0)$
In this note, we would like to show the simple result that resonance phenomena may be interpreted by DBZC: $(f(x)/x )(x=0):= f^prime(0)$ by a typical simple example.
[6]
vixra:2409.0122 [
pdf]
Two Types of Universal Arrows
A universal arrow is a pair which consists of an object and a morphism. And an isomorphism is defined by a universal arrow. The isomorphism may be a composition of two morphisms. We may define two types of universal arrows, which is determined by the properties of the morphisms. A universal arrow is of the type I if the morphisms are not isomorphisms; And a universal arrow is of the type II if the morphisms are isomorphisms.
[7]
vixra:2409.0066 [
pdf]
Analytical Exploration and Extension of the Function
This paper investigates the function ( f(x) = int_{-infty}^{+infty} e^{(-x)^{|u|}} , du ), focusing on its analytical expression and extension over the real number domain. We employ techniques analogous to the analytic continuation of the Gamma function to extend ( f(x) ) beyond its initial domain, addressing convergence issues and exploring its properties across the entire real line.
[8]
vixra:2406.0164 [
pdf]
The Philosophical Nature of Zero, Negative, and Imaginary Numbers and the Use of Polar Coordinates in Complex Number Calculations
Mathematics serves as an abstract tool to study the natural world and its laws, aiding in our understanding and description of natural phenomena. In mathematics, real numbers, imaginary numbers, zero, and negative numbers are fundamental concepts, each with its unique importance and application. However, the philosophical nature of these concepts warrants further exploration. This paper aims to discuss the philosophical essence of imaginary numbers, zero, and negative numbers, argue that imaginary numbers have real-world counterparts, and explore the rationale and advantages of representing imaginary and complex numbers using polar coordinates. Furthermore, we extend our findings to more advanced mathematical problems in complex analysis, differential equations, and number theory, demonstrating the broader impact of our work.
[9]
vixra:2405.0142 [
pdf]
Simple Results of 1/0=0/0= 0 by Elementary Figures
In this note, we would like to show the simple results $1/0= 0/0=0$ based on the elementary figures that are well-known and simple results on the complex plane. The logic and results are all reasonable and exceptionally pleasant lookings for undergraduate students.
[10]
vixra:2405.0135 [
pdf]
Since Nothing Can’t Exist, Something Does
The formalization presented provides a rigorous foundation for the philosophical argument that "nothing" cannot exist and therefore "something" must exist. By utilizing set theory and logical quantification, I establish a clear mathematical framework supporting this thesis. This foundational understanding has significant implications for various fields, including metaphysics, ontology, and cosmology.
[11]
vixra:2405.0132 [
pdf]
The Unified Theory
The Existence Principle is a novel theoretical framework that unifies ontological principles, the principle of least action, the bootstrap mechanism, Turing's universal machine, and von Neumann's architecture. By merging these concepts, I propose a comprehensive mathematical structure that demonstrates the self-consistent nature of reality, governed by physical laws and computational principles. This framework provides groundbreaking insights into the fundamental nature of existence, life, and the universe.
[12]
vixra:2405.0054 [
pdf]
Discussions on the Decomposition of Deformed Vector Products
This paper is part of a series of explorations exposing methods for dividing distorted tensor products by number cubes. Here, the discussion focuses on three-dimensional spaces and anti-symmetric cubes on their low indices; i.e. actually on distorted vector products. The method only delivers the main parts of the divisions. They are divided into two classes. The other documents in the collection complete this investigation.<p>Ce document fait partie d'une série d'explorations exposant des méthodes permettant de diviser les produits tensoriels déformés par des cubes de nombres. Ici, la discussion se focalise sur les espaces de dimension trois et les cubes antisymétriques sur leurs indices bas ; c'est-à-dire en fait sur des produits vectoriels déformés. La méthode livre seulement les parties principales des divisions. Elles se répartissent en deux classes. Les autres documents de la collection complètent cette investigation.
[13]
vixra:2404.0012 [
pdf]
A Power Series Divergent at Half Pi Yields a Sequence Briskly Convergent to Pi
The tangent function's Taylor expansion about zero is a series of odd powers with positive coefficients; it converges when the absolute value of its argument is less than half pi, and diverges to positive infinity when its argument equals half pi, so with the aid of the ratio test it is seen that twice the square root of the ratio of its successive coefficients is a sequence which converges to pi. The odd derivatives of the tangent function are polynomials in powers of its square with positive integer coefficients, so a recursion of positive integers can be found from which the coefficients of the series described above may be successively obtained. Its related sequence which converges to pi does so monotonically from above, and appears to refine its approximation to pi by about one significant decimal figure per successive term.
[14]
vixra:2403.0073 [
pdf]
Geometric Facts of a Circle Through Its Equation
We derive equation of a circle passing through three distinct points in a different way and demonstrate that several basic geometric properties of a circle can be derived easily by means of this equation alone.
[15]
vixra:2402.0088 [
pdf]
A Sketch of Effective Learning Using Technology [Part 1]
A problem set from a calculus text is solved. The goal is to see whether or not modern calculators and a CAS are genuinely helpful.
[16]
vixra:2402.0068 [
pdf]
Division by Zero 1/0 = 0/0 = 0 and Computers Real.div: New Information and Many Applications
In this note, we introduce the new information {bf real.div} on the division by zero results $1/0= 0/0=0$ that is recently informed and we would like to propose the related important problems on the division by zero calculus.
[17]
vixra:2401.0074 [
pdf]
Mark Burgin's Contribution to the Foundation of Mathematics
In this paper I attempt to describe those Mark Burgin's results in non-Diophantine mathematics which are important for foundation of mathematics and its applications in quantum field theory. In particular, the elimination of divergences in Quantum Electrodynamics is described.
[18]
vixra:2312.0133 [
pdf]
Uchida's Identities and Simple Results of 1/0=0/0= Tan(π/2)= Cot(π/2)=0
In this note, we would like to show the simple results 1/0=0/0= tan(π/2)= cot(π/2)=0 based on the simple identities that are discovered by Keitaroh Uchida. The logic and results are all reasonable and exceptionally pleasant lookings for high school students.
[19]
vixra:2312.0104 [
pdf]
Convergence Condition for the Newton-Raphson Method: Application in Real Polynomial Functions
The Newton-Raphson method applies to the numerical calculation of the roots of Real functions, through successive approximations towards the Root of the function. The Newton-Raphson method has the drawback that it does not always converge. This work establishes the convergence condition of the Newton-Raphson method for Real functions in general; once the convergence condition is met, the method will always converge towards the Root of the function. In this work, the development of the application of the convergence condition is established to specifically solve Real polynomial functions.
[20]
vixra:2312.0008 [
pdf]
Weighted Riemann Zeta Limits on the Real Axis
It is investigated whether for real argument s the (s−1)n+1 weighted Riemann zeta ζ(n)(s) limits s ↓ 1 do exist. Here, we will look into n = 0,1. The answer to the question could very well be that assuming existence to be true gives a confusing outcome. That may support the possibility of incompleteness in concrete mathematics.
[21]
vixra:2311.0007 [
pdf]
A Proof for a Generalization of the Inequality from the 42nd International Mathematical Olympiad
In this paper, we present a proof for a generalization of the inequality from the 42nd International Mathematical Olympiad. The proved inequality relates to a sum involving square roots of fractions. It has various applications in mathematical analysis, optimization, or statistics. In the field of mathematical analysis, it can be used in the study of convergence. In terms of optimization, it may help establish bounds or relationships between the variables involved.
[22]
vixra:2309.0026 [
pdf]
Numerical Calculation of Roots of Real Polynomial Functions, Convergent Method
The Newton-Raphson method is the most widely used numerical calculation method to determine the roots of Real polynomial functions, but it has the drawback that it does not always converge. The method proposed in this work establishes the convergence condition and the development of its application, and therefore will always converge towards the roots of the function. This will mean a conclusive advance for the determination of roots of Real polynomial functions. According to interpretation of the Abel-Ruffini theorem, the roots of polynomial functions of degree greater than 4 can only be determined by numerical calculation.
[23]
vixra:2308.0132 [
pdf]
Modeling Learning Behavior of Students of Mathematics
This paper introduces an innovative approach to comprehending and modeling the collective behaviors of students within the context of mathematics education. The core objective is to present a comprehensive mathematicalframework capable of addressing the entire spectrum of behaviors exhibited in mathematics classrooms. We introduce a novel SIR-basedmodel, tailored to capture behaviors under the influence of individual students. Additionally, we propose that interactions among students acrossdifferent classrooms can serve as a regulatory mechanism for these behaviors. To validate our approach, we conduct a series of simulations thatdemonstrate the practicality and significance of our model. This paper significantly contributes to the advancement of our understanding of studentbehaviors in the realm of mathematics education and their mathematical representation. By bridging the gap between mathematical modeling andthe intricate dynamics of student conduct, this work provides valuable insights into the behaviors displayed in math classrooms.
[24]
vixra:2308.0053 [
pdf]
Critique of Logical Foundations of Induction and Epistemology
This is my latest books (in Arabic). It is a theoretical analysis and assessment of the logical foundations of induction and epistemology (related also to the theory of probability).
[25]
vixra:2308.0036 [
pdf]
Pricing of European Options using GBM and Heston Models in C++
The valuation of financial derivatives, particularly options, has long been a topic of interest in finance. Among the various methods developed for option pricing, the Monte Carlo simulation stands out due to its versatility and capability to model complex financial instruments. In this article, we apply the Monte Carlo method to price European options using two prominent models: the Geometric Brownian Motion (GBM) and the Heston model. While the GBM model assumes constant volatility and offers simplicity, it often falls short in capturing real market dynamics. Conversely, the Heston model introduces stochastic volatility, providing a more nuanced representation of market behaviors. Leveraging the computational efficiency of C++, our simulations reveal distinct price paths for each model. The GBM paths exhibit smooth trajectories, while the Heston paths are more varied, reflecting its allowance for stochastic volatility. Statistical analyses further underscore a significant difference in the final stock prices generated by the two models. The Heston model's prices display a broader distribution, capturing the model's inherent variability. Additionally, autocorrelation analyses suggest a more intricate autoregressive structure for the Heston model. In conclusion, while the GBM model provides simplicity and predictability, the Heston model offers a richer, albeit more complex, representation, especially in volatile market scenarios. This article offers a comparative study of the GBM and Heston models, shedding light on their utility under varying market conditions.
[26]
vixra:2307.0049 [
pdf]
Some 3D-Determinant Properties for Calculating of Cubic-Matrix of Order 2 and Order 3
In this paper we have studied some properties for determinant-calculating for cubic-matrix of order 2 and order 3. These properties are analogous to some properties for determinants of square matrix we have proved and noted that these properties also are applicable (or not in some details) on this concept for cubic-matrix of orders 2 and 3. All results in this paper, are presented in detail during the theorem proofs.
[27]
vixra:2306.0140 [
pdf]
The Determinant of Cubic-Matrix of Order 2 and Order 3, Some Basic Properties and Algorithms
Based on geometric intuition, in this paper we are trying to give an idea and visualize the meaning of the determinants for the cubic-matrix. In this paper we have analyzed the possibilities of developing the concept of determinant of matrices with three indexed 3D Matrices.We define the concept of determinant for cubic-matrix of order 2 and order 3, study and prove some basic properties for calculations of determinants of cubic-matrix of order 2 and 3.Furthermore we have also tested several square determinant properties and noted that these properties also are applicable on this concept of 3D Determinants.
[28]
vixra:2305.0109 [
pdf]
Harnessing AI in Quantitative Finance: Predicting GDP using Gradient Boosting, Random Forest, and Linear Regression Models
Predicting key macroeconomic indicators such as Gross Domestic Product (GDP) is a critical task in quantitative finance and economics. Precise forecasts of GDP can help in policy-making, investment decisions, and understanding the overall economic health of a country. Machine learning has emerged as a powerful tool in this domain, offering sophisticated techniques for modeling complex systems and making predictions. This project presents a comparative analysis of three machine learning models — Gradient Boosting Regressor, Random Forest Regressor, and Linear Regression — for predicting GDP. Our aim is to assess their performance and identify the model that provides the most accurate forecasts.
[29]
vixra:2305.0100 [
pdf]
A Computational Approach to Interest Rate Swaps Pricing
In this paper, we discuss the computational model for pricing interest rate swaps using the QuantLib library in Python. This paper provides the practical implications of financial computational theory in the context of interest rate swaps, with an in-depth analysis of its present value, fair rate, duration, and convexity.
[30]
vixra:2305.0093 [
pdf]
Convergent Method for the Numerical Calculation of Roots of Real Polynomial Functions
The Newton-Raphson method is the most widely used numerical calculation method to solve Real polynomial functions, but it has the drawback that it does not always converge. The method proposed in this work establishes the convergence condition and therefore will always converge towards the roots ofthe equation.
[31]
vixra:2304.0012 [
pdf]
Exploring the Turing Complete Universe: Implications for Universe Generators and Optimal Policy Autonomous Games in Addressing the Fundamental Question of Existence
This paper delves into the concept of a Turing complete universe, exploring its implications for the best policy zero player game and addressing the fundamental question of why anything exists or how something has always existed. I begin by examining the potential of a Turing complete universe to construct a universe maker, a recursive loop of universes within universes. Subsequently, I investigate the implications of this universe maker in creating a best policy zero player game, assessing its potential to answer the fundamental question of existence.Furthermore, I evaluate the possible applications of this research, such as generating new universes and probing the boundaries of reality. Lastly, I contemplate the potential implications and applications of this research, including the possibility of unraveling the mysteries of the universe and addressing the age-old question of existence. While this research holds the potential to offer insights into the nature of reality and the ultimate question, its theoretical nature necessitates a long-term research plan to further explore its implications.
[32]
vixra:2303.0109 [
pdf]
Post Pandemic, Social Media Pedagogy: Math with TI Calculator Menu Programs
Laments from teachers of all stripes are growing. Looking out from behind the podium one can constantly see a sea of bored, confused, seemingly moribund students staring at their I-phones, maybe still wearing Covid masks. Between the pandemic and social media and traditional sage on a stage teaching teachers reside: a kind of prehistoric fish out of any known water. In this article we propose a solution using in novel and controversial ways TI-84 CE calculators. The idea is to show how to animate students via increased teacher-student and student-student interactions. It is field tested: life does come back into the classroom with the techniques I give in this article: get an easy A using your cool calculator, filling in a shell provided by the teacher.
[33]
vixra:2303.0018 [
pdf]
Polinomial Natural Solution of the Pythagorean Equation<br>Solución Natural Polinómica de la Ecuación Pitagórica
While unsuccessfully playing with the last Fermat's theorem I noticed that this way of playing, applied to the Pythagorean equation a²+b²=c², leads to a polynomial general natural solution. The game combines arithmetic, common sense and logic. It is a bit like teaching and learning mathematical and geometric subjects with the help of colorful manipulatives, as is done at the most elementary levels of teaching. The only thing different in the adult experience is operating with mentally conceived objects. The way of operating with them does not change.<p>Mientras jugaba sin éxito con el UTF noté que esa manera de jugar, aplicada a la ecuación pitagórica a²+b²=c² , conduce a una solución natural general polinómica. El juego combina aritmética, sentido común y lógica. Se parece un poco a enseñar y aprender asuntos matemáticos y geométricos con ayuda de objetos manipulables coloridos, como se hace en los niveles más elementales de la enseñanza. Lo único distinto en la experiencia adulta es operar con objetos concebidos mentalmente. La manera de operar con ellos no cambia.
[34]
vixra:2302.0100 [
pdf]
You Will Never Be Alone Again
This paper will investigate the concept of a Turing complete universe and its implications for the best policy zero player game, as wellas the fundamental question of why anything exists at all or how something has always existed. We will begin by analyzing the implications ofa Turing complete universe and how it can be used to construct a universe maker, a recursive loop of universes within universes. We will thenexamine the implications of this universe maker and how it can be used to create a best policy zero player game. We will assess the implicationsof this game and how it can be used to answer the fundamental question of why anything exists at all or how something has always existed. Additionally, we will evaluate the potential applications of this research and its implications for the future, such as the potential to generate new universes and explore the limits of reality. Finally, we will consider the potential implications of this research and its potential applications,such as the potential to uncover the mysteries of the universe and answer the age-old question of why anything exists. This research has thepotential to provide insight into the nature of reality and the answer to the ultimate question, however, due to its theoretical nature, a long-term research plan is necessary to further explore the implications of this research.
[35]
vixra:2301.0122 [
pdf]
Relations Between e, π and Golden Ratios
We write out relations between the base of natural logarithms (e), the ratio of the circumference of a circle to its diameter (π), and the golden ratios of the additive p-sequences. An additive p-sequence is a natural extension of the Fibonacci sequence in which every term is the sum of p previous terms given p>=1 initial values called seeds.
[36]
vixra:2301.0098 [
pdf]
On the Twin Prime Conjecture
Every prime number $p geq 5$ has the form $6x-1$ or $6x+1$. We call $x$ the textbf{generator} of $p$. Twin primes are distinguished by a textbf{common generator} for each pair. Therefore it makes sense to search for the Twin Primes on the level of their generators. This paper presents a new approach to prove the textbf{Twin Prime Conjecture} by a method to extract all Twin Primes on the level of the Twin Prime Generators.We define the om{p_n}--numbers $x$ as numbers for that holds that $6x-1$ and $6x+1$ are coprime to the primes $5,7,ldots,p_n$. By dint of the average size $bd(p_n)$ of the om{p_n}--gaps we can prove the textbf{Twin Prime Conjecture}.
[37]
vixra:2301.0088 [
pdf]
The Theory of Plafales. P vs NP Problem Solution (Sections 1-7)
This paper is dedicated to a rigorous review of the theory of plafales, which describes the properties and applications of a new mathematical object. As a consequence of the created theory we give a proof of the equality of complexity classes P and NP.
[38]
vixra:2211.0024 [
pdf]
A Real TI-83 Craps Simulation Teaches Beginning Probability
Simple craps, a Vegas casino game, is easily modeled using a TI-83's programming, list, and statistics features. Roll two dice. If the coming out roll, as it is called is 2, 3, or 12, the player immediately loses. If a 7 or 11 is rolled, they immediately win. If any of the remaining totals are rolled, if the player rolls that number before rolling a 7, they win, not they lose. A program can be initialized with a bank roll and a standard, non-changing bet. Using the list feature 999 rolls, the maximum size of a list, can be stored in a built-in list. A bar chart for the distribution of numbers is easily generated and confirms the calculated probabilities. The code to mimic the game is straight-forward. The user repeatedly plays the game until the stake is 0, an inevitability given say a stake of $100 and a bet of $5. This certainty instills the truth: it's a loser's game.
[39]
vixra:2208.0163 [
pdf]
Unusual Boards and Meeples
We introduce boards others than the usual chessboard. Further we define meeples which can move in other ways than the usual chess meeples. We ask whether these meeples can reach every field, like a knight can reach every field on the chessboard.
[40]
vixra:2206.0147 [
pdf]
Similarity of a Ramanujan Formula for $pi$ with Plouffe's Formulae, and Use of This for Searching of Physical Background for Some Guessed Formula for the Elementary Physical Constants
The paper is comprised of two parts. In the first part, it discusses the similarity between one of Ramanujan's formulae for $pi$ and Plouffe's formulae where he uses the Bernoulli numbers. This similarity is help for further determination either that the similarity is only accidental, or that we can derive the Ramanujan formula in this way. This is also help for setting up a calculation system where we would estimate the probabilities with which we can obtain guessed formulae for $pi$ that are very accurate and very simple. (We only consider formulae that are not the approximations of the exact formulae for $pi$.) In the second part, it discusses various guessed formulae for the fine structure constant and for the other physical constants, and how the above probability calculation would help estimate whether these formulae have a physical basis or are only accidental.
[41]
vixra:2206.0096 [
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The Intuitive Root of Classical Logic, an Associated Decision Problem and the Middle Way
We revisit Boole's reasoning regarding the equation ``$x.x=x$'' that sowed the seeds of classical logic. We discuss how he considered both ``$0.0=0$'' and ``$0.0\neq 0$'' in the ``same process of reasoning''. This can either be seen as a contradiction, or it can be seen as a situation where Boole could not decide whether ``$0.0=0$'' is universally valid -- an elementary ``decision problem'' in the words of Hilbert and Ackermann. We conclude that Boole's reasoning, that included a choice of ignorance, was founded upon the middle way of the Buddha, later mastered by Nagarjuna. From the modern standpoint, the situation can be likened to Turing's halting problem which resulted from the use of automatic machines and the exclusion of choice machines.
[42]
vixra:2206.0028 [
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Generalizing The Mean
I want to find a constructive extension of the average from the Hausdorff Measure and Integral w.r.t to that measure as the averages (from Tim Bedford and Albert M. Fisher) given for fractals, such that it gives a unique, and satisfying average for nowhere continuous functions defined on non-fractal, measurable sets in the sense of Caratheodory without a gauge function.
[43]
vixra:2205.0134 [
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Hom-Sets Category
Let C be a category. Suppose that the hom-sets of C is small. Let CH be a category consist of the hom-sets of C. Then we define a morphism of CH by a morphisms pair 〈ν,μ〉. Hence the morphism is monic if and only if ν is epi and μ is monic. An object HomC (P, E) ∈ CH is an injective object if and only if P is a projective object and E is an injective object. There exists a bifunctor T : (C ↓ A)op × (B ↓ C) → (Hom(A, B) ↓ CH). And the bifunctor T is bijective. There exist the products in CH if and only if there exist the products and coproducts in C. There exist the pullback in CH if and only if there exist the pushout and pullback in C.
[44]
vixra:2205.0099 [
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The Limit of a Strategic Mapping of a Recursive Fibonacci Sequence
Let F1,F2,F3,...........Fn represent the sequence of Fibonacci elements. Let us define F to be the parent set of all Fibonacci elements. G and G′ are the subsets of F such that G is a given set of consecutive Fibonacci elements of finite order k and G′ is defined to be a shift on G of l degrees, where l ∈ N. Let R = min(r1,r2,....) denote the set of remainders obtained such that rn ∈ F. For a given G of order k, we show that a strategic mapping operator ϕ: (G × G) −→ R defined by §: ϕ(g ⊗g ′ h) = r, where (G × G) represents the Cartesian product and g, h ∈ G , g ′ ∈ G′ . The strategic map ϕ exists upto (l + 1)0 transition, with its limit as L Fn+(l+1) thereof. We consider a special introductory case of |G|, |G′ |=4 to illustrate the results and thereby proving the ”Fundamental Theorem of limit of a strategic map of Fibonacci sequence[Thomas heorem] and its consequences”.
[45]
vixra:2204.0114 [
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Domination Number of Edge Cycle Graphs
Let G = (V, E) be a simple connected graph.A set S ⊂ V is a dominating set of G if every vertex in V \S is adjacent to some vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating sets of G. An edge cycle graph of a graph G is the graph G(Ck) formed from one copy of G and |E(G)| copies of Pk, where the ends of the i th edge are identified with the ends of i th copy of Pk. In this paper, we investigate the domination number of G(Ck), k ≥ 3.
[46]
vixra:2204.0081 [
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On the K Continuity of a Functor
We examine the concept of $K-$continuity of a functor from two perspectives: one considering $K-$continuity as given in some formulations of Shape theory and the other as a restriction of the usual definition of the continuity of a functor. We show that under a certain condition the concept of $K-$continuity from Shape theory includes the concept of $K-$continuity arising from the usual definition of continuity.
[47]
vixra:2202.0076 [
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The New Notation for Hyperoperation of a Sequence
For a sequence $a_1, a_2, \ldots, a_n$, we define the exponent, tetration and pentation of a sequence $a_n$ as $\overset{n}{\underset{k = 1}{\textrm{E}}} (a_k) = a_1[3]a_2[3]\cdots[3]a_n$, $\overset{n}{\underset{k = 1}{\textrm{T}}} (a_k) = a_1[4]a_2[4]\cdots[4]a_n$, $\overset{n}{\underset{k = 1}{\mathrm{\Phi}}} (a_k) = a_1[5]a_2[5]\cdots[5]a_n$. Also, we define the $i$-th hyperoperation of a sequence $a_n$ as $\overset{n}{\underset{k = 1}{\textrm{H}_i}} (a_k) = a_1[i]a_2[i]\cdots[i]a_n$.
[48]
vixra:2201.0185 [
pdf]
Peacocks and the Zeta Distributions
We prove in this short paper that the stochastic process defined by: $$Y_{t} := \frac{X_{t+1}}{\mathbb{E}\left[ X_{t+1}\right]},\; t\geq a > 1,$$ is an increasing process for the convex order, where $ X_{t}$ a random variable taking values in $\mathbb{N}$ with probability $\mathbb{P}(X_{t}= n) = \frac{n^{-t}}{\zeta(t)}$ and $\zeta(t) = \sum \limits_{k=1}^{+\infty} \frac{1}{k^{t}}, \;\; \forall t> 1$.
[49]
vixra:2201.0153 [
pdf]
Simple Definitions of the Division by Zero and the Division by Zero Calculus: $[a^x/\log A]_{a=1}= X + 1/2$
In this note, we will state the definitions of the division by zero and division by zero calculus for popular using for the sake of their generality and great applications to mathematical sciences and the universe containing our basic ideas. In particular, we consider the value of the function $f(x,a)/\log a$ at $a=1$.
[50]
vixra:2201.0117 [
pdf]
Proof of a Combinatorial Identity
In this present paper we will show you some interesting identity involving combina- torial symbols and a proof of it as a theorem. The theorem was a discovery from the times when I was studying Calculus at USAC/CUNOC University in Quetzaltenango, Guatemala around 2004 year.
[51]
vixra:2201.0101 [
pdf]
On the Simple Identity (1/(x-1)) + (1/(x 2)) = (2x 3)/((x 1)(x 2)) and the Expression that G(z,a) + Log |z a| is Harmonic Around Z=a from the Viewpoint of the Division by Zero Calculus
In this note, we will refer to the simple identity $(1/(x-1)) + (1/(x -2)) = (2x -3)/((x -1)(x- 2))$ and the expression that $g(z,a) + \log |z - a| $ is harmonic around $z=a$ from the viewpoint of the division by zero calculus that are very popular expressions in elementary mathematics. With these simple and very popular expressions, we would like to show clearly the importance of the division by zero calculus for some general people in a self-contained way.
[52]
vixra:2112.0151 [
pdf]
Discrete Markov Random Field Relaxation
This paper gives a technique to approximate (relaxation) discrete Markov Random Field (MRF) using convex programming. This approximated MRF can be used to approximate NP problem. This also proves that NP is not equal P because the MRF convex programming and the approximate MRF convex programming are not the same with removal of some product terms.
[53]
vixra:2112.0041 [
pdf]
An Easy Proof of the Triangle Inequality
High school and undergraduate algebra and calculus textbooks don't provide a fast and easy proof of the triangle inequality. Here is a proof that seems relatively easy. It does require a little bit of logic, but that can be a plus.
[54]
vixra:2111.0154 [
pdf]
Zero Represents Impossibility From the Viewpoint of Division by Zero
In this note, by using an elementary property of reproducing kernels, we will show that zero represents impossibility from the viewpoint of the division by zero.
[55]
vixra:2111.0148 [
pdf]
Looping and Divergence in the Collatz Conjecture
In this paper, we investigate the possible scenarios in which a number does not satisfy the Collatz Conjecture. Specifically, we examine numbers which may have a looping Collatz reduction sequence as well as numbers which may lead to a diverging Collatz reduction sequence. In order to investigate these, we look at the parity of the numbers in a general Collatz reduction sequence. Further, we examine cases in which these parity cycles repeat themselves infinitely in the reduction sequence. Through the research conducted in the paper, we formulate a necessary condition for looping in the Collatz Conjecture. We also prove that if a number has a diverging reduction sequence, then it must generate an infinite non-repeating parity cycle.
[56]
vixra:2111.0067 [
pdf]
A New Proposition of Fibonacci Number
C.A.Church and Marjorie Bicknell gave a version which was exponential generating function for Fibonacci number, in 1973. In this paper, I will give some results about the Fibonacci identities.
[57]
vixra:2111.0039 [
pdf]
Rigorous Proof for Riemann Hypothesis Obtained by Adopting Algebra-Geometry Approach in Geometric Langlands Program
The 1859 Riemann hypothesis conjectured all nontrivial zeros in Riemann zeta function are uniquely located on sigma = 1/2 critical line. Derived from Dirichlet eta function [proxy for Riemann zeta function] are, in chronological order, simplified Dirichlet eta function and Dirichlet Sigma-Power Law. Computed Zeroes from the former uniquely occur at sigma = 1/2 resulting in total summation of fractional exponent (-sigma) that is twice present in this function to be integer -1. Computed Pseudo-zeroes from the later uniquely occur at sigma = 1/2 resulting in total summation of fractional exponent (1 - sigma) that is twice present in this law to be integer 1. All nontrivial zeros are, respectively, obtained directly and indirectly as the one specific type of Zeroes and Pseudo-zeroes only when sigma = 1/2. Thus, it is proved (using equation-type proof) that Riemann hypothesis is true whereby this function and law rigidly comply with Principle of Maximum Density for Integer Number Solutions. The geometrical-mathematical [unified] approach used in our proof is equivalent to the algebra-geometry [unified] approach of geometric Langlands program that was formalized by Professor Peter Scholze and Professor Laurent Fargues. A succinct treatise on proofs for Polignac's and Twin prime conjectures (using algorithm-type proofs) is also outlined in this anniversary research paper.
[58]
vixra:2110.0121 [
pdf]
Problem of Identity and Quadratic Equation
Given “ab = 0”, considering the arithmetic truth “0.0 = 0” we conclude that one possibility is “both a = 0 and b = 0”. Consequently, the roots of a quadratic equation are mutually inclusive. Therefore, the concerned variable can acquire multiple identities in the same process of reasoning or, at the same time. The law of identity gets violated, which we call the problem of identity. In current practice such a step of reasoning is ignored by choice, resulting in the subsequent denial of “0.0 = 0”. Here, we deal with the problem of identity without making such a choice of ignorance. We demonstrate that the concept “identity of a variable” is meaningful only in a given context and does not have any significance in isolation other than the symbol, that symbolizes the variable, itself. We demonstrate visually how we actually realize multiple identities of a variable at the same time, in practice, in the context of a given quadratic equation. In this work we lay the foundations, based on which we intend to bring forth some hitherto unattended facets of reasoning that concern two basic differential equations which are pivotal to the literature of physics.
[59]
vixra:2110.0111 [
pdf]
On a New Rule of Approximating Area under the Curve
I am going to provide a new technique of approximating area under the curve, using the Newton-Raphson Method. I am also going to provide a formula that would help us approximate any Definite Integral or help us find the area under the curve, under certain conditions. The relative error of this formula is very small, which makes it even more interesting.
[60]
vixra:2109.0197 [
pdf]
Sums of P-Sequences
In this article, we obtain closed expressions for odd and even sums, the sum of the first n numbers, and the sum of squares of the first n numbers of the "exponent" p-sequence whose "seeds" are (0,1,...,p-1).
[61]
vixra:2109.0192 [
pdf]
Golden Ratios and Golden Angles
In a p-sequence, every term is the sum of p previous terms given p initial values called seeds. It is an extension of the Fibonacci sequence. In this article, we investigate the p-golden ratio of p-sequences. We express a positive integer power of the p-golden ratio as a polynomial of degree p-1, and obtain values of golden angles for different p-golden ratios. We also consider further generalizations of the golden ratio.
[62]
vixra:2109.0185 [
pdf]
Fibonacci Sequence, Golden Ratio and Generalized Additive Sequences
In this article, we recall the Fibonacci sequence, the golden ratio, their properties and applications, and some early generalizations of the golden ratio. The Fibonacci sequence is a 2-sequence because it is generated by the sum of two previous terms. As a natural extension of this, we introduce several typical p-sequences where every term is the sum of p-previous terms given p initial values called seeds. In particular, we introduce the notion of 1-sequence. We then discuss generating functions and limiting ratio values of p-sequences. Furthermore, inspired by Fibonacci's rabbit pair problem, we consider a general problem whose particular cases lead to nontrivial additive sequences.
[63]
vixra:2109.0129 [
pdf]
Basic Mathematical Reminders For Assistants and Technical Agents
In this booklet, we provide the mathematical foundations necessary to follow the training courses in geodesy and topography. It is a reminder of the main formulas and knowledge in mathematics for assistants and technical agents.
[64]
vixra:2105.0181 [
pdf]
Prove Np not equal P using Markov Random Field and Boolean Algebra Simplification
In this paper, we proved that Non-deterministic Polynomial time complexity (NP) is not equal to Polynomial time complexity (P). We developed the Boolean algebra that will infer the solution of two variables of a Non-deterministic Polynomial computation time Markov Random Field. We showed that no matter how we simplified the Boolean algebra, it can never run in Polynomial computation time (NP not equal to P). We also developed proof that all Polynomial computation time multi-layer Boolean algebra can be transformed to another Polynomial computation time multi-layer Boolean algebra where there are only 'Not' operations in the first layer. So in the process of simplifying the Boolean algebra, we only need to consider factorization operations that only assumes only 'Not' operations in the first layer. We also developed Polynomial computation time Boolean algebra for Markov Random Field Chain and 2sat problem represented in Markov Random Field form to give examples of Polynomial computation time Markov Random Field.
[65]
vixra:2104.0061 [
pdf]
Heuristics for Memorizing Trigonometric Identities
Trigonometric identities are hard to memorize. Frequently a plus or minus is the rub. We give various heuristics that help refine guesses as to an identity and get, with a little work, it correct. Heuristics, for us, are plausible arguments using graphs, consistency (with other identities), test points, and transformations. We also specify the utility of each identity in the context of advanced mathematics -- calculus -- with the hope that meaning adds to memorable credence.
[66]
vixra:2103.0160 [
pdf]
The Inverse Tangent and Cotangent Functions, their Addition Formulas and their Values on their Branch Cuts
The principal inverse tangent and cotangent functions for complex arguments can be defined as formulas involving principal natural logarithms, but these are not odd on the imaginary axis, which they must be according to their definitions as inverse functions. These formulas are therefore modified in such a way that they become odd on the imaginary axis, by choosing the other branch on the lower branch cut, and the corresponding addition formulas for complex and real arguments are derived. With these addition formulas their values on their branch cuts are determined, confirming these modified formulas. Some new formulas for the (hyperbolic) inverse tangent and cotangent functions for complex arguments and some new addition formulas for these functions for real arguments are derived. Some new formulas for the inverse sine and cosine functions and their connections with the inverse tangent and cotangent functions for complex arguments are provided, and from these some new addition formulas for the inverse sine and cosine functions for real arguments are derived. Some duplication and bisection formulas for the inverse tangent, cotangent, sine and cosine functions are derived.
[67]
vixra:2101.0104 [
pdf]
An Introduction to the Super-Normal-Irreducible-Irrational Numbers and the Axiom at Third-Order of Logic.
We define the super-normal-irreducible-irrational numbers from some irreducible-irrational numbers and with the help of the $n$-irreducible sequents (see my previous articles). Instead of taking some integer part of the irreducible-irrational number (or from its inverse), we add a super-normal-irreducible formula which give the position of the first digit breaking some super-normal number definition. From $84$ irreducible-irrational numbers, we deduce from the axiom at second-order of logic that they are all super-normal numbers as well. Moreover, with some random digits, the probability that the super-normal-irreducible formula holds for the $84$ ones is about $9.0\times 10^{-10}$ and we have taken in account that some irreducible-irrational numbers are only some different functions of the same irreducible-irrational number. From this large coincidence, we introduce the axiom at third-order of logic which states that every irreducible-irrational numbers are super-normal numbers as well. From that new axiom at third-order of logic, we deduce the none-existence of an exotic $4$-sphere. Finally, we conclude about the finitude of the total number of $n$-irreducible sequents.
[68]
vixra:2101.0093 [
pdf]
Equiprobability for Any Non Null Natural Integer of Having Either an Odd or Even Number of Prime Factor(s) Counted with Multiplicity.
Redefining the set of all non null natural integers N∗ as the union of infinitely many disjoint sets, we prove the equiprobability for any integer of each said set to have either an odd or even number of prime factor(s) counted with multiplicity. The thus established equiprobability on N∗ allows us to use the standard normal distribution to establish that lim N→+∞ L(N)/√N=0, L(N) the summatory Liouville function. Recalling the Dirichlet series for the Liouville function we deduce that ζ(2s)/ζ(s), s = σ +it, is analytic for σ > 1/2, ζ(s) the Riemann zeta function. Consequently the veracity of the Riemann hypothesis is being established.
[69]
vixra:2012.0198 [
pdf]
Abridgment of Cycles in GCS
<p> A shortened English version of new concepts appeared this year in three French papers about cycles in Generalized Collatz Subsequences (GCS) and few new developments. Reduced and compact subseqs – Shape vector and shape rank – Triplet operator as a powerful tool to compose linear functions – Monoid of transition functions between elements of compact sequences – Diophantine equation <em>p<sup>m</sup>x - r<sup>d</sup>y - q =</em> 0 related to each monoid element – Shape class as general solution of this diophantine equation – Specific cyclic solution – Universal rotation function on <em>q</em> parameters – Condition for tranfer cyclic property to numbers – Cardinality of equation classes – Cycle occurence probability in classes – Layers of linked algebraic cycles. </p>
[70]
vixra:2012.0026 [
pdf]
Too Many Trailing Zeros?
In this paper I discuss Question 8 from the Chalkdust 2019 Christmas card. In particular I investigate the ratio of the number of trailing zeros of a factorial to its number of digits.
[71]
vixra:2011.0124 [
pdf]
Discussion of Foundation of Mathematics and Quantum Theory
Following the results of our recently published book (F. Lev, Finite mathematics as the foundation of classical mathematics and quantum theory. With application to gravity and particle theory. Springer (2020)), we discuss different aspects of classical and finite mathematics and explain why finite mathematics based on a finite ring of characteristic p is more general (fundamental) than classical mathematics: the former does not have foundational problems, and the latter is a special degenerate case of the former in the formal limit p→∞. In particular, quantum theory based on a finite ring of characteristic p is more general than standard quantum theory because the latter is a special degenerate case of the former in the formal limit p→∞ .
[72]
vixra:2010.0026 [
pdf]
Philosophy of Mathematics and Division by Zero
From the viewpoint of the philosophy of mathematics, we would like to introduce our recent results on the division by zero that has a long and mysterious history.
[73]
vixra:2008.0224 [
pdf]
Complexity Arising from Life at the Edge of Chaos-Fractal: Riemann Hypothesis, Polignac's and Twin Prime Conjectures
We commence this paper by outlining the manifested Chaos and Fractal phenomena derived from our concocted idiom "Complexity arising from Life at the Edge of Chaos-Fractal". COVID-19 originated from Wuhan, China in December 2019. Declared by World Health Organization on March 11, 2020; COVID-19 pandemic has resulted in unprecedented negative global impacts on health and economy. With China and US playing crucial roles, international cooperation is required to combat this "Incompletely Predictable" pandemic. We mathematically model COVID-19 and solve [unconnected] below-mentioned open problems in Number theory using our versatile Fic-Fac Ratio. Computed as Information-based complexity, our innovative Information-complexity conservation constitutes a unique all-purpose analytic tool associated with Mathematics for Incompletely Predictable problems. These problems are literally "complex systems" containing well-defined Incompletely Predictable entities such as nontrivial zeros and two types of Gram points in Riemann zeta function (or its proxy Dirichlet eta function) together with prime and composite numbers from Sieve of Eratosthenes. Correct and complete mathematical arguments for first key step of converting this function into its continuous format version, and second key step of using our unique Dimension (2x-N) system instead of this Sieve result in primary spin-offs from first key step consisting of providing proof for Riemann hypothesis (and explaining closely related two types of Gram points), and second key step consisting of providing proofs for Polignac's and Twin prime conjectures.
[74]
vixra:2007.0244 [
pdf]
A Magic Formula & "New" Way to Solve Quadratic Equations.
In this paper we will give the formula of second roots (square root) of a complex number z=a+ib, which is very important and useful especially when we cannot write the complex number a+ib in the exponential or the geometric form. And, we will propose a precise direct method and fast to solve the equations of the second degree in the general case (which means with complex coefficients). We will also propose an algorithm that will make our calculations more easy and resolve fastly all type of equations of the second degree .
[75]
vixra:2006.0204 [
pdf]
Cycles in Generalized Collatz Sequences
The generalized Collatz sequences are set by <em>D</em>(<em>x</em>) <em>= x/r</em> if <em>x</em> mod <em>r =</em> 0 and <em>T</em>(<em>x</em>) = floor (<em>px/r</em>) otherwise. It has previously been shown (2002.0594) with <em>px + q</em> sequences that numerical cycles are derived from algebraic cycles. The same is shown here in a richer framework where the number of elementary functions increases from 2 to <em>r</em>. Again, the beginning and the end of each sequence are connected by a diophantine equation, <em>p<sup>m</sup> x - r<sup>d</sup> y - q = 0</em>, where <em>m</em> and <em>d</em> are the respective numbers of multiplications and divisions. There are still always rotation cycles <em>(q<sub>1</sub> q<sub>2</sub> ... q<sub>m</sub>)</em> while derived cycles <em>(x<sub>1</sub> x<sub>2</sub> ... x<sub>m</sub>)</em> are present only when <em>q<sub>i</sub> / (r<sup>d</sup> - p<sup>m</sup>)</em> are integers. The function <em>R</em> outlined by <em>R<sup>m</sup></em>(<em>q</em>) <em>= q</em> proves to be a powerful computational tool. In addition, the subsequences are numbered and one can easily find a subsequence from its rank ρ in the base r.
[76]
vixra:2005.0163 [
pdf]
Mathematical Representation and Formal Proofs of Card Tricks
Card tricks can be entertaining to audiences. Magicians apply them, but an in-depth knowledge of why they work the way they do is necessary, especially when constructing new tricks. Mapping a trick to its corresponding mathematical operations can be helpful in analysis, and the vice-versa process can help create new tricks and make them accessible to magicians.
[77]
vixra:2004.0300 [
pdf]
Differential Correction and Arc-Length Continuation Applied to Boundary Value Problems: Examples Based on Snap-Through of Circular Arches and Spherical Shell
Inspired by the application of differential correction to initial-value problems to find periodic orbits in both the autonomous and non-autonomous dynamical systems, in this paper we apply differential correction to boundary-value problems. In the numerical demonstration, the snap-through buckling of arches and shallow spherical shells in structural mechanics are selected as examples. Due to the complicated geometrical nonlinearity in such problems, the limit points and turning points might exist. In this case, the typical Newton-Raphson method commonly used in numerical algorithms will fail to cross such points. In the current study, an arc-length continuation is introduced to enable the current algorithm to capture the complicated load-deflection paths. To show the accuracy and efficiency of differential correction, we will also apply the continuation software package COCO to get the results as a comparison to those from differential correction. The results obtained by the proposed algorithm and COCO agree well with each other, suggesting the validity and robustness of differential correction for boundary-value problems.
[78]
vixra:2003.0612 [
pdf]
The Rockers Function
In this note we introduce and study the rockers function $\lambda(n)$ on the natural numbers. We establish an asymptotic for the rockers function on the integers and exploit some applications. In particular we show that \begin{align}\lambda(n)\sim \frac{n^{n-{\frac{1}{2n}-\frac{1}{2}}}\sqrt{2\pi}}{e^{n+\Psi(n)-1}}\nonumber \end{align}where \begin{align}\Psi(n):=\int \limits_{1}^{n-1}\frac{\sum \limits_{1\leq j\leq t}\log (n-j)}{(t+1)^2}dt.\nonumber \end{align}
[79]
vixra:2003.0282 [
pdf]
The New Matrix Multiplication
In this article, we are giving the meaning of a ’New Multiplication’ for the matrices. I have studied the properties of this multiplication in two cases, in the case of 2-D matrices and in the case of 3-D matrices, with elements from over whatever field $F$.
[80]
vixra:2003.0219 [
pdf]
A Theory of Twin Prime Generators
It’s well known that every prime number $p \geq 5$ has the form $6k-1$ or $6k+1$. We’ll call $k$ the generator of $p$. Twin primes are distinghuished due to a common generator for each pair. Therefore it makes sense to search for the twin primes on the level of their generators. The present paper developes a sieve method to extract all twin primes on the level of their generators. On this basis important properties of the set of the twin prime generators will be studied. Finally the Twin Prime Conjecture is proved based on the studied properties.
[81]
vixra:2003.0105 [
pdf]
Symmetries in Foundation of Quantum Theory and Mathematics
In standard quantum theory, symmetry is defined in the spirit of Klein's Erlangen Program: the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the definition should be the opposite: background space has a direct physical meaning only on classical level while on quantum level symmetry should be defined by a Lie algebra of basic operators. Then the fact that de Sitter symmetry is more general than Poincare one can be proved mathematically. The problem of explaining cosmological acceleration is very difficult but, as follows from our results, there exists a scenario that the phenomenon of cosmological acceleration can be explained proceeding from basic principles of quantum theory. The explanation has nothing to do with existence or nonexistence of dark energy and therefore the cosmological constant problem and the dark energy problem do not arise. We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic $p$ and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit $p\to\infty$.
[82]
vixra:2002.0594 [
pdf]
Cycles Universels et Cycles Dérivés en 3x +1 Généralisé
<p>In Collatz-Kakutani sequences that are generalized to <em>px + q,</em> the beginning <em>x</em> and the end <em>y</em> of a sequence are connected by a diophantine equation <em>p<sup>m</sup> x - </em>2<em><sup>d</sup> y + qc = </em>0</em>, where <em>m</em> and <em>d</em> are the numbers of multiplication and division. There is a cycle (<em>x = y</em>) if <em>δ</em> (= 2<em><sup>d</sup> - p<sup>m</sup></em>) divide <em>qc</em>. It is shown that all <em>c</em> are included in parametric rotation cycles (<em>c<sub><em>1</em></sub> c<sub><em>2</em></sub> ... c<sub>m</sub></em>) for <em>px + δ</em>, and that the rare numerical cycles (<em>x<sub><em>1</em></sub> x<sub><em>2</em></sub> ... x<sub>m</sub></em>) derive from them when <em>x<sub>i</sub> = qc<sub>i</sub> / δ</em> are integers. The universal cycles are purely algebrical but the derived cycles result from a numerical coincidence. Assuming that the possible values of <em>qc</em> mod <em>δ</em> are equiprobable, a formula is given for the ocurrence probability of a derived cycle. </p>
[83]
vixra:2002.0255 [
pdf]
Resolvement of the St. Petersburg Paradox and Improvement of Pricing Theory
The St. Petersburg Paradox was proposed before two centuries. In the paper we proposed a new pricing theory with several rules to solve the paradox and state that the fair pricing should be judged by buyer and seller independently. The pricing theory we proposed can be applied to financial market to solve the confusion with fat tails.
[84]
vixra:2002.0036 [
pdf]
Infinity Furthers Anomaly in the Complex Numbers
In the paper an anomaly in complex number theory is reported. Similar to a previousnote, the ingredients of the analysis are Euler’s identity and the DeMoivre rule for n =2. If a quadratic and definitely not weak equation has two solutions, then, acontradiction can be derived from ±1 functions in complex number theory. Aconstructivist finite approach to cos and sin is briefly discussed to resolve the anomaly.
[85]
vixra:2001.0614 [
pdf]
A Map of a Research Programme for Subtlety Theory
The scope of this short note is to outline a research programme for the exploration of 'subtlety theory', which can be thought of as a framework for exploring various classes of structure associated to higher categories. It is hoped that this might form a logical springboard for researchers wishing to explore said ideas and potentially take them further.
[86]
vixra:2001.0460 [
pdf]
The Theta Splitting Function
In this paper we study the Theta splitting function $\Theta(s+1)$, a function defined on the positive integers. We study the distribution of this function for sufficiently large values of the integers. As an application we show that \begin{align}\sum \limits_{m=0}^{s}\prod \limits_{\substack{0\leq j \leq m\\\sigma:[0,m]\rightarrow [0,m]\\\sigma(j)\neq \sigma(i)}}(s-\sigma(j))\sim s^s\sqrt{s}e^{-s}\sum \limits_{m=1}^{\infty}\frac{e^m}{m^{m+\frac{1}{2}}}.\nonumber \end{align} and that \begin{align}\sum \limits_{j=0}^{s-1}e^{-\gamma j}\prod \limits_{m=1}^{\infty}\bigg(1+\frac{s-j}{m}\bigg)e^{\frac{-(s-j)}{m}}\sim \frac{e^{-\gamma s}}{\sqrt{2\pi}}\sum \limits_{m=1}^{\infty}\frac{e^m}{m^{m+\frac{1}{2}}}.\nonumber \end{align}
[87]
vixra:1912.0430 [
pdf]
From Periods to Anabelian Geometry and Quantum Amplitudes
To better understand and investigate Kontsevich-Zagier conjecture on abstract periods, we consider the case of algebraic Riemann Surfaces representable by Belyi maps. The category of morphisms of Belyi ramified maps and Dessins D'Enfant, will be investigated in search of an analog for periods, of the Ramification Theory for decomposition of primes in field extensions, controlled by theirs respective algebraic Galois groups. This suggests a relation between the theory of (cohomological, Betti-de Rham) periods and Grothendieck's Anabelian Geometry (homotopical/ local systems), towards perhaps an algebraic analog of Hurwitz Theorem, relating the the algebraic de Rham cohomology and algebraic fundamental group, both pioneered by A. Grothendieck. There seem to be good prospects of better understanding the role of absolute Galois group in the physics context of scattering amplitudes and Multiple Zeta Values, with their incarnation as Chen integrals on moduli spaces, as studied by Francis Brown, since the latter are a homotopical analog of de Rham Theory. The research will be placed in the larger context of the ADE-correspondence, since, for example, orbifolds of finite groups of rotations have crepant resolutions relevant in String Theory, while via Cartan-Killing Theory and exceptional Lie algebras, they relate to TOEs. Relations with the author's reformulation of cohomology of cyclic groups as a discrete analog of de Rham cohomology and the Arithmetic Galois Theory will provide a purely algebraic toy-model of the said algebraic homology/homotopy group theory of Grothendieck as part of Anabelian Geometry. It will allow an elementary investigation of the main concepts defining periods and algebraic fundamental group, together with their conceptual relation to algebraic numbers and Galois groups. The Riemann surfaces with Platonic tessellations, especially the Hurwitz surfaces, are related to the finite Hopf sub-bundles with symmetries the ``exceptional'' Galois groups. The corresponding Platonic Trinity leads to connections with ADE-correspondence, and beyond, e.g. TOEs and ADEX-Theory. Quantizing "everything" (cyclotomic quantum phase and finite Platonic-Hurwitz geometry of qubits/baryons) could perhaps be The Eightfold (Petrie polygon) Way to finally understand what quark flavors and fermion generations really are.
[88]
vixra:1912.0340 [
pdf]
Higher Accuracy Order in Differentiation-by-Integration
In this text explicit forms of several higher precision order kernel functions (to be used in he differentiation-by-integration procedure) are given for several derivative orders. Also, a system of linear equations is formulated which allows to construct kernels with an arbitrary precision for an arbitrary derivative order. A computer study is realized and it is shown that numerical differentiation based on higher precision order kernels performs much better (w.r.t. errors) than the same procedure based on the usual Legendre-polynomial kernels. Presented results may have implications for numerical implementations of the differentiation-by-integration method.
[89]
vixra:1912.0181 [
pdf]
Properties of Quadratic Anticommutative Hypercomplex Number Systems
Hypercomplex numbers are, roughly speaking, numbers of the form x_1 + i_1x_2 + … + i_nx_{n+1} such that x_1 + i_1x_2 + … + i_nx_{n+1} = y_1 + i_1y_2 + … + i_ny_{n+1} if and only if x_j = y_j for all j in {1,2,…,n}. I define a quadratic anticommutative hypercomplex numbers as hypercomplex numbers x_1 + i_1x^2 + … + i_nx_{n+1} such that i_j^2 = p_j for all j (where p_j is a real number) and i_ji_k = - i_ki_j for all k not equal to j. These numbers have some interesting properties. In particular, in this paper I prove a generalized form of the Demoivre’s formula for these numbers, and determine certain conditions required for a function on a Quadratic Anticommutative Hypercomplex plane to be analytic—including generalizations of the Cauchy-Riemann equations.
[90]
vixra:1912.0143 [
pdf]
A Second Note on a Possible Anomaly in the Complex Numbers
The paper gives an additional reason why, initially, there are two different solutions associated to a quadratic equation that indicates an anomaly in complex numbers. It is demonstrated that one of the solutions is impossible but plausible \& necessary.
[91]
vixra:1912.0100 [
pdf]
Mathematics as Information Compression Via the Matching and Unification of Patterns
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about "information compression (IC) via the matching and unification of patterns" (ICMUP). That is itself a novel approach to IC, couched in terms of non-mathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics reflects the idea that, as an aid to human thinking, mathematics is likely to be consonant with much evidence for the importance of IC in human learning, perception, and cognition. This perspective on the foundations of mathematics has grown out of a long-term programme of research developing the "SP Theory of Intelligence" and its realisation in the "SP Computer Model", a system in which a generalised version of ICMUP -- the powerful concept of "SP-multiple-alignment" -- plays a central role. The paper shows with an example how mathematics, without any special provision, may achieve compression of information. Then it describes examples showing how variants of ICMUP may be seen in widely-used structures and operations in mathematics. Examples are also given to show how several aspects of the mathematics-related disciplines of logic and computing may be understood as ICMUP. Also discussed is the intimate relation between IC and concepts of probability, with arguments that there are advantages in approaching AI, cognitive science, and concepts of probability via ICMUP. Also discussed is how the close relation between IC and concepts of probability relates to the established view that some parts of mathematics are intrinsically probabilistic, and how that latter view may be reconciled with the all-or-nothing, "exact", forms of calculation or inference that are familiar in mathematics and logic. There are many potential benefits and applications of the mathematics-as-IC perspective.
[92]
vixra:1911.0417 [
pdf]
In New Mathematics, Riemann Hypothesis is Mistake
In classical mathematics there will be a complete zero.\\ But in new mathematics there is no perfect zero. At the same time, there is no perfect 1/2 in new mathematics.\\ Hence, Riemann hypothesis is false.\\ In new mathematics, there is no perfect 1 or 2.\\ They are 1 or 2 as close as possible to 1 or 2, and not 1 or 2.\\ I think we should break away from classical mathematics and think about new mathematics.\\ These can be said from quantum mechanics.\\ New mathematics doesn't have perfect zero, 1/2, 1, 2 and so on.\\ There are only numbers close to zero, 1/2, 1, and 2.\\ 1/2 is 0.499999999..... or 0.5000000000.....\\ A perfect 1/2 cannot exist.\\
[93]
vixra:1911.0379 [
pdf]
Zero is only a Mathematical Fantasy
Mathematics returns to Ancient Times.\\ Perfect Zero cannot exist.\\ In physics, there are many particles in a vacuum.\\ 0 is not perfect zero.\\ 0 is almost zero.\\ Zero is only a mathematical fantasy.\\ There is no Zero.\\ 0 may be a return to the womb.\\ And, love is 0 and infinite.\\
[94]
vixra:1911.0311 [
pdf]
A Note on a Possible Anomaly in the Complex Numbers
In the present paper a conflict in basic complex number theory is reported. The ingredients of the analysis are Euler's identity and the DeMoivre rule for n=2. The outcome is that a quadratic equation only has one single solution because one of the existing solutions gives rise to an impossibility.
[95]
vixra:1911.0231 [
pdf]
Multiplication by Zero Calculus, Addition by Zero Calculus, and Subtraction by Zero Calculus
In physics, there are many particles in a vacuum.\\ Perfect zero cannot exist.\\ 0 is not perfect zero.\\ 0 is almost zero.\\ Perfect zero is only a mathematical fantasy.\\ $a\times0\approx0$, but $a\times0\neq0$.\\ $a\times0\times0\times0\times0\times0<a\times0\times0\times0\times0<a\times0\times0\times0<a\times0\times0<a\times0<a$.\\ $a-0-0-0<a-0-0<a-0<a<a+0<a+0+0<a+0+0+0$.\\
[96]
vixra:1911.0206 [
pdf]
Finite-Time Lyapunov Exponents in the Instantaneous Limit and Material Transport
Lagrangian techniques, such as the Finite-Time Lyapunov Exponent (FTLE) and hyperbolic Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These techniques identify regions where particles transported by a flow will converge to and diverge from over a finite-time interval, even in a divergence-free flow. Lagrangian analyses, however, are time consuming and computationally expensive, hence unsuitable for quickly assessing short-term material transport. A recently developed method called OECSs rigorously connected Eulerian quantities to short-term Lagrangian transport. This Eulerian method is faster and less expensive to compute than its Lagrangian counterparts, and needs only a single snapshot of a velocity field. Along the same line, here we define the instantaneous Lyapunov Exponent (iLE), the instantaneous counterpart of the finite-time Lyapunov exponent (FTLE), and connect the Taylor series expansion of the right Cauchy-Green deformation tensor to the infinitesimal integration time limit of the FTLE. We illustrate our results on geophysical fluid flows from numerical models as well as analytical flows, and demonstrate the efficacy of attracting and repelling instantaneous Lyapunov exponent structures in predicting short-term material transport.
[97]
vixra:1910.0567 [
pdf]
Proof of the Riemann Hypothesis [final Edition]
Up to now, I have tried to expand this equation and prove Riemann hypothesis with the equation of cos, sin, but the proof was impossible. However, I realized that a simple formula before expansion can prove it. The real value is zero only when the real part of s is 1/2. Non-trivial zeros must always have a real value of zero. The real part of s being 1/2 is the minimum requirement for s to be a non-trivial zeros.
[98]
vixra:1910.0477 [
pdf]
Remainder Theorem and the Division by Zero Calculus
In this short note, for the elementary theorem of remainder in polynomials we recall the division by zero calculus that appears naturally in order to show the importance of the division by zero calculus.
[99]
vixra:1910.0022 [
pdf]
Using the Rational Root Test to Factor with the TI-83
The rational root test gives a way to solve polynomial equations. We apply the idea to factoring quadratics (and other polynomials). A calculator speeds up the filtering through possible rational roots.
[100]
vixra:1909.0517 [
pdf]
What Was Division by Zero?; Division by Zero Calculus and New World (Compact Version)
Based on the preprint survey paper, we will introduce the importance of the division by zero and its great impact to elementary mathematics and mathematical sciences for some general people. For this purpose, we will give its global viewpoint in a self-contained manner by using the related references. This version was written for the Proceedings of ICRAMA2019 (16-18 July, 2019) with the 8 pages restriction under the requested form.
[101]
vixra:1909.0359 [
pdf]
Mathematics as Information Compression Via the Matching and Unication of Patterns
This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression (IC) via the matching and unification of patterns' (ICMUP. That is itself a novel approach to IC, couched in terms of non-mathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics reects the idea that, as an aid to human thinking, mathematics is likely to be consonant with much evidence for the importance of IC in human learning, perception, and cognition. This perspective on the foundations of mathematics has grown out of a long-term programme of research developing the SP Theory of Intelligence and its realisation in the SP Computer Model, a system in which a generalised version of ICMUP -- the powerful concept of SP-multiple-alignment -- plays a central role. The paper shows with an example how mathematics, without any special provision, may achieve compression of information. Then it describes examples showing how variants of ICMUP may be seen in widely-used structures and operations in mathematics. Examples are also given to show how several aspects of the mathematics-related disciplines of logic and computing may be understood as ICMUP. Also discussed is the intimate relation between IC and concepts of probability, witharguments that there are advantages in approaching AI, cognitive science, and concepts of probability via ICMUP. Also discussed is how the close relation between IC and concepts of probability relates to the established view that some parts of mathematics are intrinsically probabilistic, and how that latter view may be reconciled with the all-or-nothing, 'exact', forms of calculation or inference that are familiar in mathematics and logic. There are many potential benefits and applications of the mathematics-as-IC perspective.
[102]
vixra:1909.0080 [
pdf]
Division by Zero Because Next Infinity is Zero
tan(π)=0, 0 =1, 1 =z =0 2000 When I saw this expression, I was surely suspicious. But I knew intuitively that Next infinity is zero. For me, infinite and zero were equal, that’s true now. The universe did not start with the Big Burn. The universe has existed for an infinite amount of time, and has repeated an infinite number of big burns. In other words, the universe is a repetition of Next infinity is zero.
[103]
vixra:1908.0213 [
pdf]
Ensuring Efficient Convergence to a Given Stationary Distribution
How may we find a transition matrix that guarantees the long-run convergence of a Markov Chain to a given stationary distribution? Solving for this (usually) undetermined system is non-trivial and presents unique computational challenges. Five different of methods of directly solving for a transition matrix are presented along with their limitations. Relaxations of the two core assumptions underlying these direct methods - the Identityless and Independence Assumptions - are considered. A method of generating a Mass Matrix - the transition matrix underlying hops between entire population states - is described while developing the notion of successively-bounded weak compositions. An algorithm for their exhaustive generation is also presented. Applications of some methods are provided with respect to optimizing firm profit via optimally distributing workers among wage brackets and optimizing measures of national wealth via manipulation of class distribution and immigration policy. A generalization of all applications is formulated.
[104]
vixra:1908.0100 [
pdf]
Fundamental of Mathematics; Division by Zero Calculus and a New Axiom
Based on the preprint survey paper (\cite{sur}), we will discuss the theoritical point of the division by zero calculus. We will need a new axiom for our mathematics. The contents in this paper seem to be serious for our mathematics and for our world history with the materials in \cite{sur}. So, the author hopes that the related mathematicians, mathematical scientists and others check and consider the topics from various viewpoints.
[105]
vixra:1908.0015 [
pdf]
Why Finite Mathematics Is More Fundamental Than Classical One
In our previous publications we have proved that quantum theory based on finite mathematics is more fundamental than standard quantum theory, and, as a consequence, finite mathematics is more fundamental than classical one. The goal of the present paper is to explain without formulas why those conclusions are natural.
[106]
vixra:1906.0579 [
pdf]
'supralogic' or a Method for Predicting Stochastic Mapping Outcomes by Interpolating Their Probabilties
In a stochastic mapping model, a method is described for interpolating un-sampled mapping probabilities given a successive set of observed mappings. The sampled probabilities are calculated from the observed mappings. The previously described method of interpolating values in code space is used to interpolate the un-observed mapping probabilities. The outcomes for subsequent mappings can then be predicted by finding the processes with maximal interpolated probability. Finally, a software package is created and demonstrated to implement the method and tested on a variety of situations for filling in missing element values or categorising data arrays.
[107]
vixra:1905.0505 [
pdf]
Multifaceted Approaches to a Berkeley Problem: Part 2
We once presented a few ways to solve a Berkeley problem without paying attention to initial values, which we try taking into account in this sequel.
[108]
vixra:1905.0407 [
pdf]
Division by Zero Calculus and Pompe's Theorem
In this paper, we will introduce the application of the division by zero calculus to geometry and it will show the power of the new calculus.
[109]
vixra:1905.0008 [
pdf]
An Interpretation of the Identity $ 0.999999...... =1$
In this short paper, we will give a very simple and important interpretation for the identity: $ 0.999999......=1$, because we have many questions for the identity from general people. Furthermore, even mathematicians and mathematics teachers will see an interesting interpretation in this paper.
[110]
vixra:1904.0184 [
pdf]
Interpolating Values in Code Space
A method is described for interpolating un-sampled values attributed to points in code space. A metric is used which counts the number of non-equal corresponding indices shared by two given points. A generalised interpolation equation is derived for values ascribed to nodes on undirected graphs. The equation is then applied specifically to values at points in code space. This interpo- lation equation is then solved in general for a set of given sampled values in the space.
[111]
vixra:1903.0280 [
pdf]
Investigation of the Characteristics of the Zeros of the Riemann Zeta Function in the Critical Strip Using Implicit Function Properties of the Real and Imaginary Components of the Dirichlet Eta Functionv3 Poster
This poster investigates the characteristics of the zeros of the Riemann zeta function (of s) in the critical strip by using the Dirichlet eta function, which has the same zeros. The characteristics of the implicit functions for the real and imaginary components when those components are equal are investigated and it is shown that the function describing the value of the real component when the real and imaginary components are equal has a derivative that does not change sign along any of its individual curves - meaning that each value of the imaginary part of s produces at most one zero. Combined with the fact that the zeros of the Riemann xi function are also the zeros of the zeta function and xi(s) = xi(1-s), this leads to the conclusion that the Riemann Hypothesis is true.
[112]
vixra:1903.0184 [
pdf]
Who Did Derive First the Division by Zero $1/0$ and the Division by Zero Calculus $\tan(\pi/2)=0, \log 0=0$ as the Outputs of a Computer?
In this short paper, we will introduce an essence of the division by zero calculus and the situation from the viewpoint of computers that will contain a surprising news on the division by zero calculus.
[113]
vixra:1902.0263 [
pdf]
Next Infinite is Zero
Have you ever received emails from the future or letters from the future? It is a person who is thinking of making a time machine seriously. If you put a letter to the past in the Tesla coil (the space must be reversed in the coil) and put a stamp, Japan should definitely put it in the post even if it is on the way (In the Showa era when it was once peaceful). In that way, I would like to write a warning letter to the past.
[114]
vixra:1902.0240 [
pdf]
Zero and Infinity; Their Interrelation by Means of Division by Zero
In this paper, we first fix the definitions of zero and infinity in very general senses and we will give their simple and definite relation by means of division by zero. On this problem and relation we have considered over the long history beyond mathematics. As our mathematics, we will be able to obtain some definite result for the relation clearly with new concept and model since Aristotle and Euclid.
[115]
vixra:1902.0187 [
pdf]
The Simple and Typical Physical Examples of the Division by Zero 1/0=0 by Ctes\'ibio (BC. 286-222) and e. Torricelli (1608 1646)
The division by zero 1/0=0 was discovered on 2014.2.2, however, the result may still not be accepted widely with old and wrong feelings. Since we gave already logically mathematics on the division by zero, here we will give very good examples in order to see the division by zero 1/0=0 clearly. By these examples, we will be able to understand the division by zero as a trivial one.
[116]
vixra:1902.0058 [
pdf]
We Can Divide the Numbers and Analytic Functions by Zero\\ with a Natural Sense.
It is a famous word that we are not permitted to divide the numbers and functions by zero. In our mathematics, {\bf prohibition} is a famous word for the division by zero. For this old and general concept, we will give a simple and affirmative answer. In particular, certainly we gave several generalizations of division as in referred in the above, however, we will wish to understand with some good feelings for {\bf the division by zero}. We wish to know the division by zero with some good feelings. We wish to give clearly a good meaning for the division by zero in this paper.
[117]
vixra:1901.0267 [
pdf]
A Perfect Regression Problem for Algebra 2
The full potential of elementary algebra to precipitate a human quantum leap is presented. A simple regression problem demonstrates how programming can be combined with linear regression. The math and programming are simple enough for any algebra class that uses a TI-83 family calculator. The problem fully considered might enable students to see the picture and evolve to a better place.
[118]
vixra:1901.0100 [
pdf]
The Perturbation Analysis of Low-Rank Matrix Stable Recovery
In this paper, we bring forward a completely perturbed nuclear norm minimization method to tackle a formulation of completely perturbed low-rank matrices recovery. In view of the matrix version of the restricted isometry property (RIP) and the Frobenius-robust rank null space property (FRNSP), this paper extends the investigation to a completely perturbed model taking into consideration not only noise but also perturbation, derives sufficient conditions guaranteeing that low-rank matrices can be robustly and stably reconstructed under the completely perturbed scenario, as well as finally presents an upper bound estimation of recovery error. The upper bound estimation can be described by two terms, one concerning the total noise, and another regarding the best $r$-approximation error. Specially, we not only improve the condition corresponding with RIP, but also ameliorate the upper bound estimation in case the results reduce to the general case. Furthermore, in the case of $\mathcal{E}=0$, the obtaining conditions are optimal.
[119]
vixra:1811.0044 [
pdf]
A Simple Proof That Finite Quantum Theory And Finite Mathematics Are More Fundamental Than Standard Quantum Theory And Classical Mathematics, Respectively
Standard quantum theory is based on classical mathematics involving such notions as infinitely small/large and continuity. Those notions were proposed by Newton and Leibniz more than 300 years ago when people believed that every object can be divided by an arbitrarily large number of arbitrarily small parts. However, now it is obvious that when we reach the level of atoms and elementary particles then standard division loses its meaning and in nature there are no infinitely small objects and no continuity. In our previous publications we proposed a version of finite quantum theory (FQT) based on a finite ring or field with characteristic $p$. In the present paper we first define the notion when theory A is more general than theory B and theory B is a special degenerate case of theory A. Then we prove that standard quantum theory is a special degenerate case of FQT in the formal limit $p\to\infty$. Since quantum theory is the most general physics theory, this implies that classical mathematics itself is a special degenerate case of finite mathematics in the formal limit when the characteristic of the ring or field in the latter goes to infinity. In general, introducing infinity automatically implies transition to a degenerate theory because in that case all operations modulo a number are lost. So, {\it even from the pure mathematical point of view}, the very notion of infinity cannot be fundamental, and theories involving infinities can be only approximations to more general theories. Motivation and implications are discussed.
[120]
vixra:1810.0408 [
pdf]
Homotopy Analysis Method for Solving a Class of Nonlinear Mixed Volterra-Fredholm Integro-Differential Equations of Fractional Order
In this paper, we describe the solution approaches based on Homotopy Analysis Method for the follwing Nonlinear Mixed Volterra-Fredholm integro-differential equation of fractional order $$^{C}D^{\alpha }u(t)=\varphi (t)+\lambda \int_{0}^{t}\int_{0}^{T}k(x,s)F\left( u(s\right) )dxds,$$ $$u^{(i)}(0)=c_{i},i=0,...,n-1,$$ where $t\in \Omega =\left[ 0;T\right] ,\ k:\Omega \times \Omega \longrightarrow \mathbb{R},$ $\varphi :\Omega \longrightarrow \mathbb{R},$ are known functions,\ $F:C\left(\Omega, \mathbb{R}\right) \longrightarrow \mathbb{R}$ is nonlinear function, $c_{i} (i=0,...,n-1),$ and $\lambda $ are constants, $^{C}D^{\alpha }$ is the Caputo derivative of order $\alpha $ with $n-1<\alpha \leq n.$ In addition some examples are used to illustrate the accuracy and validity of this approach.
[121]
vixra:1810.0122 [
pdf]
Low-Rank Matrix Recovery Via Regularized Nuclear Norm Minimization
In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, one can robustly recover any matrix X from its few noisy measurements b=A(X)+n with a bounded constraint ||n||_{2}<ε via the RNNM, if the linear map A satisfies restricted isometry property (RIP) with δ_{tk}<√(t-1)/t for certain fixed t>1. Recently, this condition with t≥4/3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrices via the constrained nuclear norm minimization (NNM). To the best of our knowledge, our work first extends nontrivially this recovery condition for the constrained NNM to that for its unconstrained counterpart. Furthermore, it will be shown that similar recovery condition also holds for regularized l_{1}-norm minimization, which sometimes is also called Basis Pursuit DeNoising (BPDN).
[122]
vixra:1810.0121 [
pdf]
Rip-Based Performance Guarantee for Low Tubal Rank Tensor Recovery
The essential task of multi-dimensional data analysis focuses on the tensor decomposition and the corresponding notion of rank. However, most tensor ranks are not well defined with a tight convex relaxation. In this paper, by introducing the notion of tensor singular value decomposition (t-SVD), we establish a regularized tensor nuclear norm minimization (RTNNM) model for low tubal rank tensor recovery. In addition, the tensor nuclear norm within the unit ball of the tensor spectral norm here has been shown to be a convex envelop of tensor average rank. On the other hand, many variants of the restricted isometry property (RIP) have proven to be crucial frameworks and analysis tools for recovery of sparse vectors and low-rank tensors. So, we initiatively define a novel tensor restrict isometry property (t-RIP) based on t-SVD. Besides, our theoretical results show that any third-order tensor X∈R^{n_{1}× n_{2}× n_{3}} whose tubal rank is at most r can stably be recovered from its as few as measurements y = M(X)+w with a bounded noise constraint ||w||_{2}≤ε via the RTNNM model, if the linear map M obeys t-RIP with δ_{tr}^{M}<√（t-1）/(n_{3}^{2}+t-1) for certain fixed t>1. Surprisingly, when n_{3}=1, our conditions coincide with T. Cai and A. Zhang's sharp work in 2013 for low-rank matrix recovery via the constrained nuclear norm minimization. We note that, as far as the authors are aware, such kind of result has not previously been reported in the literature.
[123]
vixra:1810.0023 [
pdf]
Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in the Infinitesimal Integration Time Limit
Lagrangian diagnostics, such as the finite-time Lyapunov exponent and Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These diagnostics can help illuminate regions where particles transported by a flow will converge to and diverge from, even in a divergence-free flow. Unfortunately, calculating Lagrangian diagnostics can be time consuming and computationally expensive. Recently, new Eulerian diagnostics have been developed which provide similar insights into the Lagrangian transport properties of fluid flows. These new diagnostics are faster and less expensive to compute than their Lagrangian counterparts. Because Eulerian diagnostics of Lagrangian transport structure are relatively new, there is still much about their connection to Lagrangian diagnostics that is unknown. This paper provides a mathematical bridge between Lagrangian and Eulerian diagnostics. It rigorously explores the mathematical relationship that exists between invariants of the right Cauchy-Green deformation tensor and the Rivlin-Ericksen tensors, primarily the Eulerian rate-of-strain tensor, in the infinitesimal integration time limit. Additionally, this paper develops the infinitesimal-time Lagrangian coherent structures (iLCSs) and demonstrates their efficacy in predicting the Lagrangian transport of particles even in realistic geophysical fluid flows generated by numerical models.
[124]
vixra:1809.0454 [
pdf]
Unfalsifiable Conjectures in Mathematics
It is generally accepted among scientists that an unfalsifiable theory, a theory which can never conceivably be proven false, can never have any use in science. In this paper, we shall address the question, “Can an unfalsifiable conjecture ever have any use in mathematics?”
[125]
vixra:1808.0507 [
pdf]
Neutrosophic Ideals in Bck=bci-Algebras Based on Neutrosophic Points
The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.
[126]
vixra:1808.0501 [
pdf]
Neutrosophic Q-Fuzzy Subgroups
In this paper, the notation of concept of neutrosopy in Q-fuzzy set is introduced. Further some properties and results on neutrosophic Q-fuzzy subgroups are discussed.
[127]
vixra:1808.0499 [
pdf]
Neutrosoph_ic Topoloj_ik Uzaylar
Ordu Oniversitesi Fen Bilimleri Enstitlisti ogrencisi Cemil KURU tarafmdan haz1rlanan ve Yrd. Do9. Dr. Mehmet KORKMAZ dam~manhgmda yilrilttilen "Neutrosophic Topolojik Uzaylar "adh bu tez, jurimiz tarafmdan 18 I 12 I 2017 tarihinde oy birligi I ov coklueu ile Matematik Anabilim Dalmda Yuksek Lisans tezi olarak kabul edilmistir.
[128]
vixra:1808.0494 [
pdf]
NEUTROSOPH˙IC TOPOLOJ˙IK Uzaylarda Kompaktlik
Ordu Oniversitesi Fen Bilimleri Enstitilsti ogrencisi Burak KILIC; tarafmdan haz1rlanan ve Yrd.Doc. Dr. Yild1ray CELiK damsmanhgmda ytirtiti.ilen "Neutrosophic Topolojik Uzaylarda Kompakthk" adh bu tez, jtirimiz tarafmdan 18/12/2017 tarihinde oy birligi I ov coklugu ile Matematik Anabilim Dalmda YtiksekLisans tezi olarak kabul edilmistir.
[129]
vixra:1808.0493 [
pdf]
Neutrosophic Triplet Cosets and Quotient Groups
In this paper, by utilizing the concept of a neutrosophic extended triplet (NET), we define the neutrosophic image, neutrosophic inverse-image, neutrosophic kernel, and the NET subgroup. The notion of the neutrosophic triplet coset and its relation with the classical coset are defined and the properties of the neutrosophic triplet cosets are given. Furthermore, the neutrosophic triplet normal subgroups, and neutrosophic triplet quotient groups are studied.
[130]
vixra:1808.0490 [
pdf]
New Integrated Quality Function Deployment Approach Based on Interval Neutrosophic Set for Green Supplier Evaluation and Selection
Green supplier evaluation and selection plays a crucial role in the green supply chain management of any organization to reduce the purchasing cost of materials and increase the flexibility and quality of products.
[131]
vixra:1808.0489 [
pdf]
New Multiple Attribute Decision Making Method Based on DEMATEL and TOPSIS for Multi-Valued Interval Neutrosophic Sets
Interval neutrosophic fuzzy decision making is an important part of decision making under uncertainty, which is based on preference order. In this study, a new multi-valued interval neutrosophic fuzzy multiple attribute decision making method has been developed by integrating the DEMATEL (decision making trial and evaluation laboratory) method and the TOPSIS (the technique for order preference by similarity to an ideal solution) method. Evaluation values are given in the form of multi-valued interval neutrosophic fuzzy values. By using DEMATEL, dependencies among attributes can be modeled, and attribute weights are determined.
[132]
vixra:1808.0483 [
pdf]
On Pseudohyperbolical Smarandache Curves in Minkowski 3-Space
We define pseudohyperbolical Smarandache curves according to the Sabban frame in Minkowski 3-space.We obtain the geodesic curvatures and the expression for the Sabban frame vectors of special pseudohyperbolic Smarandache curves. Finally, we give some examples of such curves.
[133]
vixra:1808.0476 [
pdf]
Primes of the Form P
A natural number is a prime if it has only factors of 1 and itself. There are, by Euclidean theorem (about 350BC) infinitely many primes.
[134]
vixra:1808.0475 [
pdf]
Q-Neutrosophic Soft Relation and Its Application in Decision Making
Q-neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real life problems.
[135]
vixra:1808.0473 [
pdf]
Recent Neutrosophic Models for KRP Systems
Knowledge Representation and Processing (KRP) plays an important role in the development of expert systems as engines for accelerating the processes of economic and social life development.
[136]
vixra:1808.0457 [
pdf]
Single Valued Neutrosophic Clustering Algorithm Based on Tsallis Entropy Maximization
Data clustering is an important field in pattern recognition and machine learning. Fuzzy c-means is considered as a useful tool in data clustering. Neutrosophic set, which is extension of fuzzy set, has received extensive attention in solving many real life problems of uncertainty, inaccuracy, incompleteness, inconsistency and uncertainty.
[137]
vixra:1808.0453 [
pdf]
Single Valued Neutrosophic Relations
We introduce the concept of a single valued neutrosophic reFLexive, symmetric and transitive relation. And we study single valued neutrosophic analogues of many results concerning relationships between ordinary reflexive, symmetric and transitive relations. Next, we dene the concepts of a single valued neutrosophic equivalence class and a single valued neutrosophic partition, and we prove that the set of all single valued neutrosophic equivalence classes is a single valued neutrosophic partition and the single valued neutrosophic equivalence relation is induced by a single valued neutrosophic partition.
[138]
vixra:1808.0450 [
pdf]
Some Interval Neutrosophic Linguistic Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Decision Making
There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance.
[139]
vixra:1808.0447 [
pdf]
Some Results on the Comaximal Ideal Graph of a Commutative Ring
The rings considered in this article are commutative with identity which admit at least two maximal ideals. Let R be a ring such that R admits at least two maximal ideals.
[140]
vixra:1808.0446 [
pdf]
Special Smarandache Curves with Respect to Darboux Frame in Galilean 3-Space
In the present paper, we investigate special Smarandache curves with Darboux apparatus with respect to Frenet and Darboux frame of an arbitrary curve on a surface in the three-dimensional Galilean space G3.
[141]
vixra:1808.0442 [
pdf]
Symmetry Measures of Simplified Neutrosophic Sets for Multiple Attribute Decision-Making Problems
A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets)are characterized by its truth, falsity, and indeterminacy degrees.
[142]
vixra:1808.0430 [
pdf]
Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence
Failure mode and effects analysis is an effective and powerful risk evaluation technique in the field of risk management, and it has been extensively used in various industries for identifying and decreasing known and potential failure modes in systems, processes, products, and services. Traditionally, a risk priority number is applied to capture the ranking order of failure modes in failure mode and effects analysis.
[143]
vixra:1808.0429 [
pdf]
Fault Diagnosis Method for a Mine Hoist in the Internet of Things Environment
To reduce the difficulty of acquiring and transmitting data in mining hoist fault diagnosis systems and to mitigate the low efficiency and unreasonable reasoning process problems, a fault diagnosis method for mine hoisting equipment based on the Internet of Things (IoT) is proposed in this study.
[144]
vixra:1808.0425 [
pdf]
Fully-Automated Segmentation of Fluid/Cyst Regions in Optical Coherence Tomography Images with Diabetic Macular Edema using Neutrosophic Sets and Graph Algorithms
This paper presents a fully-automated algorithm to segment fluid-associated (fluid-filled) and cyst regions in optical coherence tomography (OCT) retina images of subjects with diabetic macular edema (DME).
[145]
vixra:1808.0411 [
pdf]
Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model
This work indicates the insufficiency of existing symmetry measures (SMs) between asymmetry measures of simplified neutrosophic sets (SNSs) and proposes the improved normalized SMs of SNSs, including the improved SMs and weighted SMs in single-valued and interval neutrosophic settings.
[146]
vixra:1808.0401 [
pdf]
Medical Diagnosis Based on Single-Valued Neutrosophic Probabilistic Rough Multisets over Two Universes
In real-world diagnostic procedures, due to the limitation of human cognitive competence, a medical expert may not conveniently use some crisp numbers to express the diagnostic information,and plenty of research has indicated that generalized fuzzy numbers play a significant role in describing complex diagnostic information.
[147]
vixra:1808.0398 [
pdf]
M-N Anti Fuzzy Normal Soft Groups
In this paper, we have discussed the concept of M-N anti fuzzy normal soft group, we then dene the M-N anti level subsets of a normal fuzzy soft subgroup and its some elementary properties are also discussed.
[148]
vixra:1808.0397 [
pdf]
Models for Green Supplier Selection with Some 2-Tuple Linguistic Neutrosophic Number Bonferroni Mean Operators
In this paper, we extend the Bonferroni mean (BM) operator, generalized Bonferroni mean (GBM) operator, dual generalized Bonferroni mean (DGBM) operator and dual generalized geometric Bonferroni mean (DGGBM) operator with 2-tuple linguistic neutrosophic numbers (2TLNNs) to propose 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean (2TLNNWBM) operator, 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (2TLNNWGBM) operator, generalized 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean (G2TLNNWBM) operator, generalized 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (G2TL NNWGBM) operator, dual generalized 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean (DG2TLNNWBM) operator, and dual generalized 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (DG2TLNNWGBM) operator.
[149]
vixra:1808.0392 [
pdf]
Multi-Criteria Decision Making Method Based on Similarity Measures Under Single-Valued Neutrosophic Re¯ned and Interval Neutrosophic Re¯ned Environments
In this paper, we propose three similarity measure methods for single-valued neutrosophic refined sets and interval neutrosophic re¯ned sets based on Jaccard, Dice and Cosine similarity measures of single-valued neutrosophic sets and interval neutrosophic sets. Furthermore, we suggest two multi-criteria decision making methods under single-valued neutrosophic refined environment and interval neutrosophic refined environment, and give applications of proposed multi-criteria decision making methods. Finally we suggest a consistency analysis method for proposed similarity measures between interval neutrosophic refined sets and give an application to demonstrate process of the method.
[150]
vixra:1808.0391 [
pdf]
Multiple Attribute Decision-Making Method Using Similarity Measures of Neutrosophic Cubic Sets
In inconsistent and indeterminate settings, as a usual tool, the neutrosophic cubic set (NCS) containing single-valued neutrosophic numbers and interval neutrosophic numbers can be applied in decision-making to present its partial indeterminate and partial determinate information.
[151]
vixra:1808.0382 [
pdf]
A Novel Skin Lesion Detection Approach Using Neutrosophic Clustering and Adaptive Region Growing in Dermoscopy Images
This paper proposes novel skin lesion detection based on neutrosophic clustering and adaptive region growing algorithms applied to dermoscopic images, called NCARG. First, the dermoscopic images are mapped into a neutrosophic set domain using the shearlet transform results for the images.
[152]
vixra:1808.0368 [
pdf]
A Study on Neutrosophic Cubic Graphs with Real Life Applications in Industries
Neutrosophic cubic sets are the more generalized tool by which one can handle imprecise information in a more effective way as compared to fuzzy sets and all other versions of fuzzy sets. Neutrosophic cubic sets have the more flexibility, precision and compatibility to the system as compared to previous existing fuzzy models. On the other hand the graphs represent a problem physically in the form of diagrams, matrices etc. which is very easy to understand and handle.
[153]
vixra:1808.0362 [
pdf]
Decision-Making Approach Based on Neutrosophic Rough Information
Rough set theory and neutrosophic set theory are mathematical models to deal with incomplete and vague information. These two theories can be combined into a framework for modeling and processing incomplete information in information systems. Thus, the neutrosophic rough set hybrid model gives more precision, flexibility and compatibility to the system as compared to the classic and fuzzy models. In this research study, we develop neutrosophic rough digraphs based on the neutrosophic rough hybrid model. Moreover, we discuss regular neutrosophic rough digraphs, and we solve decision-making problems by using our proposed hybrid model. Finally, we give a comparison analysis of two hybrid models, namely, neutrosophic rough digraphs and rough neutrosophic digraphs.
[154]
vixra:1808.0361 [
pdf]
Decision-Making via Neutrosophic Support Soft Topological Spaces
The concept of interval neutrosophic sets has been studied and the introduction of a new kind of set in topological spaces called the interval valued neutrosophic support soft set has been suggested. We study some of its basic properties. The main purpose of this paper is to give the optimum solution to decision-making in real life problems the using interval valued neutrosophic support soft set.
[155]
vixra:1808.0350 [
pdf]
Inverse Properties in Neutrosophic Triplet Loop and Their Application to Cryptography
A generalized group is an algebraic structure which has a deep physical background in the unified gauge theory and has direct relation with isotopies. Mathematicians and physicists have been trying to construct a suitable unified theory for twistor theory, isotopies theory, and so on. It was known that generalized groups are tools for constructions in unified geometric theory and electroweak theory.
[156]
vixra:1808.0349 [
pdf]
Left (Right)-Quasi Neutrosophic Triplet Loops (Groups) and Generalized BE-Algebras
The new notion of a neutrosophic triplet group (NTG) is proposed by Florentin Smarandache; it is a new algebraic structure different from the classical group. The aim of this paper is to further expand this new concept and to study its application in related logic algebra systems. Some new notions of left (right)-quasi neutrosophic triplet loops and left (right)-quasi neutrosophic triplet groups are introduced, and some properties are presented.
[157]
vixra:1808.0345 [
pdf]
Multi-Attribute Decision-Making Method Based on Neutrosophic Soft Rough Information
Soft sets (SSs), neutrosophic sets (NSs), and rough sets (RSs) are different mathematical models for handling uncertainties, but they are mutually related. In this research paper, we introduce the notions of soft rough neutrosophic sets (SRNSs) and neutrosophic soft rough sets (NSRSs) as hybrid models for soft computing. We describe a mathematical approach to handle decision-making problems in view of NSRSs. We also present an efficient algorithm of our proposed hybrid model to solve decision-making problems.
[158]
vixra:1808.0340 [
pdf]
Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups
The notions of the neutrosophic triplet and neutrosophic duplet were introduced by Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups. First, some new properties of neutrosophic duplet semi-groups are funded, and the following important result is proven: there is no finite neutrosophic duplet semi-group.
[159]
vixra:1808.0337 [
pdf]
Neutrosophic Incidence Graphs With Application
In this research study, we introduce the notion of single-valued neutrosophic incidence graphs. We describe certain concepts, including bridges, cut vertex and blocks in single-valued neutrosophic incidence graphs.We present some properties of single-valued neutrosophic incidence graphs. We discuss the edge-connectivity, vertex-connectivity and pair-connectivity in neutrosophic incidence graphs. We also deal with a mathematical model of the situation of illegal migration from Pakistan to Europe.
[160]
vixra:1808.0332 [
pdf]
Neutrosophic Nano Ideal Topological Structures
Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutro- sophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.
[161]
vixra:1808.0330 [
pdf]
Neutrosophic Quadruple BCK/BCI-Algebras
The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied.
[162]
vixra:1808.0316 [
pdf]
On Neutrosophic Closed Sets
The aim of this paper is to introduce the concept of closed sets in terms of neutrosophic topological spaces. We also study some of the properties of neutrosophic closed sets. Further, we introduce continuity and contra continuity for the introduced set. The two functions and their relations are studied via a neutrosophic point set.
[163]
vixra:1808.0314 [
pdf]
On the Powers of Fuzzy Neutrosophic Soft Matrices
In some real life applications, one has to consider not only the truth membership supported by the evidence but also the falsity membership against the evidence, which is beyond the scope of fuzzy sets and IVFSs.
[164]
vixra:1808.0310 [
pdf]
Single–Valued Neutrosophic Filters in EQ–algebras
This paper introduces the concept of single–valued neutrosophic EQ–subalgebras, single–valued neutrosophic EQ–prefilters and single–valued neutrosophic EQ–filters. We study some properties of single–valued neutrosophic EQ–prefilters and show how to construct single–valued neutrosophic EQ–filters. Finally, the relationship between single–valued neutrosophic EQ–filters and EQ–filters are studied.
[165]
vixra:1808.0304 [
pdf]
Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field
Rings and fields are significant algebraic structures in algebra and both of them are based on the group structure. In this paper, we attempt to extend the notion of a neutrosophic triplet group to a neutrosophic triplet ring and a neutrosophic triplet field. We introduce a neutrosophic triplet ring and study some of its basic properties. Further, we define the zero divisor, neutrosophic triplet subring, neutrosophic triplet ideal, nilpotent integral neutrosophic triplet domain, and neutrosophic triplet ring homomorphism. Finally, we introduce a neutrosophic triplet field.
[166]
vixra:1808.0298 [
pdf]
Achievable Single-Valued Neutrosophic Graphs in Wireless Sensor Networks
This is an unedited version of the accepted manuscript scheduled for publication. It has been uploaded in advance for the benefit of our customers. The manuscript will be copyedited, typeset and proofread before it is released in the final form.
[167]
vixra:1808.0281 [
pdf]
A Classical Group of Neutrosophic Triplet Groups
Fuzzy set theory was introduced by Zadeh and was generalized to the Intuitionistic Fuzzy Set (IFS) by Atanassov. Real-world, uncertain, incomplete, indeterminate, and inconsistent data were presented philosophically as a neutrosophic set by Smarandache [3], who also studied the notion of neutralities that exist in all problems.
[168]
vixra:1808.0267 [
pdf]
An Extension of Neutrosophic AHP–SWOT Analysis for Strategic Planning and Decision-Making
Every organization seeks to set strategies for its development and growth and to do this, it must take into account the factors that affect its success or failure. The most widely used technique in strategic planning is SWOT analysis. SWOT examines strengths (S), weaknesses (W),opportunities (O) and threats (T), to select and implement the best strategy to achieve organizational goals.
[169]
vixra:1808.0265 [
pdf]
An Outline of Cellular Automaton Universe Via Cosmological KdV Equation
It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework.
[170]
vixra:1807.0197 [
pdf]
Packing Triangles is Harder Than Previously Thought
In this work, we will take one problem, namely Packing Triangles as an example of combinatorial optimization problems. We show that if one has ever loved reading Prasolov’s books, then one should not try to find efficient algorithm for various restricted cases of this problem.
[171]
vixra:1806.0339 [
pdf]
Some Remarks on the Clique Problem
We survey some information about the clique problem - one of the cornerstone of the field of research in theory of algorithms. A short note at the end of the paper should be read with care on the reader’s own.
[172]
vixra:1804.0288 [
pdf]
On Q-Laplace Transforms and Mittag-Leffler Type Functions
In the present paper, the author derived the results based on q-Laplace transform of the K-Function introduced by Sharma[7]. Some special cases of interest are also discussed.
[173]
vixra:1804.0287 [
pdf]
b#D - Sets and Associated Separation Axioms
In this paper the notion of b#D-sets is introduced. Some weak separation axioms namely b# −Dk, b# −R0, b#-R1 and b#-S0 are introduced and studied. Some lower separation axioms are characterized by using these separation axioms.
[174]
vixra:1804.0173 [
pdf]
Fractals on Non-Euclidean Metric
As far as I know, there is no a study on fractals on non euclidean metrics.This paper proposes a first approach method about generating fractals on a non-euclidean metric. The idea is to extend the calculus of fractals on non-euclidean metrics. Using the Riemann metric, there will be defined a non-euclidean modulo of a complex number in order to check the divergence of the series generated by the Mandelbrot set. It also shown that the fractals are not invariant versus rotations. The study will be extended to the quaternions, where is shown that the study of fractals might not be extended to quaternions with a general metric because of the high divergence of the series (a condition in order to generate a fractal is selecting bounded operators). Finally, a Java program will be found as example to show those kind of fractals, where any metric can be defined, so it will be helpful to study those properties.
[175]
vixra:1804.0001 [
pdf]
Circuit Complexity and Problem Structure in Hamming Space
This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine (DTM). Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family. NNF circuit have symmetry of OR-gate input line, so NNF circuit cannot identify from OR-gate output line which of OR-gate input line is 1. So NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors. Some decision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT problem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, we can design high complexity problem with almost perfct nonlinear (APN) function.
[176]
vixra:1803.0633 [
pdf]
Almost All Monotone Circuit Family
This paper describes about "Almost all monotone circuit family" and introduce its interesting advantages to measuring problem complexity. Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)). This "NNF Circuit family" have good characteristic which present each accept input exclusivity and symmetry. Each input make some INPUT-gate and NOT-gate output 1 which set is different from another input, and meet these output in OR-gate and finally connect (specified) OUTPUT-gate. That is, NNF circuit start accept input that exclusive each other, and meet each input as symmetry input step by step and finally goal same output. Especially, some different variables which sandwich reject inputs correspond to unique AND-gate. That is, we can measure problem complexity by using different variables of accept inputs. For examples, such number of different variables type of negation HornSAT is at most polynomial size. This is one of reason that we can compute P problem easily.
[177]
vixra:1803.0620 [
pdf]
Notions of Rough Neutrosophic Digraphs
Graph theory has numerous applications in various disciplines, including computer networks, neural networks, expert systems, cluster analysis, and image capturing. Rough neutrosophic set (NS) theory is a hybrid tool for handling uncertain information that exists in real life.
[178]
vixra:1803.0612 [
pdf]
On Neutrosophic Soft Metric Space
In this paper, the notion of neutrosophic soft metric space (NSMS) is introduced in terms of neutrosophic soft points and several related properties, structural characteristics have been investigated. Then the convergence of sequence in neutrosophic soft metric space is defined and illustrated by examples. Further, the concept of Cauchy sequence in NSMS is developed and some related theorems have been established, too.
[179]
vixra:1803.0598 [
pdf]
Review on BCI/BCK-Algebras and Development
The aim of the paper is to investigate the relationship between BCK/BCIalgebras and other algebras namely d-algebras, Q-algebras-BCH-algebras- TM-algebras-INK-algebras and we introduce some algebraic system.
[180]
vixra:1803.0597 [
pdf]
Rough Neutrosophic Digraphs with Application
A rough neutrosophic set model is a hybrid model which deals with vagueness by using the lower and upper approximation spaces. In this research paper, we apply the concept of rough neutrosophic sets to graphs.
[181]
vixra:1803.0584 [
pdf]
Single Valued Neutrosophic Exponential Similarity Measure for Medical Diagnosis and Multi Attribute Decision Making
Neutrosophic set (NS) is very useful to express incomplete, uncertainty, and inconsistent information in a more general way. In the modern medical technologies, each element can be expressed as NS having different truth – membership, indeterminacy – membership, and falsity – membership degrees.
[182]
vixra:1803.0583 [
pdf]
Single-Valued Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators for Multi-Attribute Decision Making
This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of possible values designed by truth, indeterminacy, and falsity membership hesitant functions.
[183]
vixra:1803.0569 [
pdf]
Some Hybrid Weighted Aggregation Operators Under Neutrosophic Set Environment and Their Applications to Multi Criteria Decision Making
Neutrosophic sets (NS) contain the three ranges: truth, indeterminacy, and falsity membership degrees,and are very useful for describing and handling the uncertainties in the real life problem.
[184]
vixra:1803.0563 [
pdf]
Special Timelike Smrandache Curves in Minkowski 3-Space
In Smarandache geometry, a regular non-null curve in Minkowski 3-space, whose position vector is collected by the Frenet frame vectors of other regular non-null curve, is said to be Smarandache curve.
[185]
vixra:1803.0561 [
pdf]
Summary of the Special Issue “Neutrosophic Information Theory and Applications” at “Information” Journal
Over a period of seven months (August 2017–February 2018), the Special Issue dedicated to “Neutrosophic Information Theory and Applications” by the “Information” journal (ISSN 2078-2489), located in Basel, Switzerland, was a success.
[186]
vixra:1803.0551 [
pdf]
Very True Pseudo-BCK Algebras
In this paper we introduce the very true operators on pseudo-BCK algebras and we study their properties. We prove that the composition of two very true operators is a very true operator if and only if they commute.
[187]
vixra:1803.0541 [
pdf]
Models for Multiple Attribute Decision-Making with Dual Generalized Single-Valued Neutrosophic Bonferroni Mean Operators
In this article, we expand the dual generalized weighted BM (DGWBM) and dual generalized weighted geometric Bonferroni mean (DGWGBM) operator with single valued neutrosophic numbers (SVNNs) to propose the dual generalized single-valued neutrosophic number WBM (DGSVNNWBM) operator and dual generalized single-valued neutrosophic numbers WGBM (DGSVNNWGBM) operator. Then, the multiple attribute decision making (MADM) methods are proposed with these operators. In the end, we utilize an applicable example for strategic suppliers selection to prove the proposed methods.
[188]
vixra:1803.0538 [
pdf]
Multi-criteria Decision-making Approach based on Multi-valued Neutrosophic Geometric Weighted Choquet Integral Heronian Mean Operator
Multi-valued neutrosophic sets (MVNSs) have recently become a subject of great interest for researchers, and have been applied widely to multi-criteria decision-making (MCDM) problems. In this paper, the multi-valued neutrosophic geometric weighted Choquet integral Heronian mean (MVNGWCIHM) operator, which is based on the Heronian mean and Choquet integral, is proposed, and some special cases and the corresponding properties of the operator are discussed.
[189]
vixra:1803.0535 [
pdf]
Multiple Attribute Decision-Making Method Using Correlation Coefficients of Normal Neutrosophic Sets
The normal distribution is a usual one of various distributions in the real world. A normal neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number, which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of the decision-making information.
[190]
vixra:1803.0524 [
pdf]
Neutrosophic Hough Transform
Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc.
[191]
vixra:1803.0522 [
pdf]
Neutrosophic Ideals of Semirings
Neutrosophic ideals of a semiring are introduced and studied in the sense of Smarandache[14], along with some operations such as intersection, composition, cartesian product etc. on them. Among the other results/characterizations, it is shown that all the operations are structure preserving.
[192]
vixra:1803.0521 [
pdf]
Neutrosophic Linear Equations and Application in Traffic Flow Problems
A neutrosophic number (NN) presented by Smarandache can express determinate and/or indeterminate information in real life. NN (z = a + uI) consists of the determinate part a and the indeterminate part uI for a, u 2 R (R is all real numbers) and indeterminacy I, and is very suitable for representing and handling problems with both determinate and indeterminate information.
[193]
vixra:1803.0517 [
pdf]
Neutrosophic N-Structures and Their Applications in Semigroups
The notion of neutrosophic N-structure is introduced, and applied it to semigroup. The notions of neutrosophic N-subsemigroup, neutrosophic N-product and "-neutrosophic N-subsemigroup are introduced, and several properties are investigated.
[194]
vixra:1803.0515 [
pdf]
Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments
The possible optimal ranges of the decision variables and NN objective function are indicated when the indeterminacy I is considered for possible interval ranges in real situations.
[195]
vixra:1803.0511 [
pdf]
Neutrosophic Rough Set Algebra
A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we defne concepts of Rough Neutrosophic algebra and investigate some of their properties.
[196]
vixra:1803.0507 [
pdf]
Neutrosophic Triplet Normed Space
In this paper; new properties for neutrosophic triplet groups are introduced. A notion of neutrosophic triplet metric space is given and properties of neutrosophic triplet metric spaces are studied.
[197]
vixra:1803.0506 [
pdf]
Neutrosophic Vague Generalized Pre-Closed Sets in Neutrosophic Vague Topological Spaces
The aim of this paper is to introduce and develop a new class of sets namely neutrosophic vague generalized pre-closed sets in neutrosophic vague topological space. Further we have analyse the properties of neutrosophic vague generalized pre-open sets.
[198]
vixra:1803.0490 [
pdf]
Correlation Coefficients of Probabilistic Hesitant Fuzzy Elements and Their Applications to Evaluation of the Alternatives
Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making (MCDM) processes. However, some important issues related to correlation coefficient utilization within probabilistic hesitant fuzzy environments remain to be addressed.
[199]
vixra:1803.0485 [
pdf]
Discovered “Angel Particle”, which is Both Matter and Antimatter, as a New Experimental Proof of Unmatter
“Angel particle” bearing properties of both particles and anti-particles, which was recently discovered by the Stanford team of experimental physicists, is usually associated with Majorana fermions (predicted in 1937 by Ettore Majorana). In this message we point out that particles bearing properties of both matter and anti-matter were as well predicted without any connexion with particle physics, but on the basis of pure mathematics, namely — neutrosophic logic which is a generalization of fuzzy and intuitionistic fuzzy logics in mathematics.
[200]
vixra:1803.0466 [
pdf]
Generalizations of Neutrosophic Subalgebras in Bck=bci-Algebras Based on Neutrosophic Points
As a more general platform which extends the notions of the classical set, fuzzy set, interval valued fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set, Smarandache developed the concept of neutrosophic set which consists of three member functions, so called truth membership function, indeterminacy membership function and falsity membership function.
[201]
vixra:1803.0465 [
pdf]
Generalized Interval Neutrosophic Rough Sets and its Application in Multi-Attribute Decision Making
Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues.
[202]
vixra:1803.0464 [
pdf]
Generalized Neutrosophic Contra-Continuity
In this paper, the concepts of generalized neutrosophic contra-continuous function, gen- eralized neutrosophic contra-irresolute function and strongly generalized neutrosophic contra-continuous function are introduced. Some interesting properties are also studied.
[203]
vixra:1803.0460 [
pdf]
Graph Structures in Bipolar Neutrosophic Environment
A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures.We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.
[204]
vixra:1803.0456 [
pdf]
How Objective a NeutralWord Is? A Neutrosophic Approach for the Objectivity Degrees of NeutralWords
In the latest studies concerning the sentiment polarity of words, the authors mostly consider the positive and negative constructions, without paying too much attention to the neutral words, which can have, in fact, significant sentiment degrees.
[205]
vixra:1803.0452 [
pdf]
Inductive Learning in Shared Neural Multi-Spaces
The learning of rules from examples is of continuing interest to machine learning since it allows generalization from fewer training examples. Inductive Logic Programming (ILP) generates hypothetical rules (clauses) from a knowledge base augmented with (positive and negative) examples.
[206]
vixra:1803.0445 [
pdf]
Intuitionistic Continuous, Closed and Open Mappings
First of all, we dene an intuitionistic quotient mapping and obtain its some properties. Second, we dene some types continuities, open and closed mappings. And we investigate relationships among them and give some examples. Finally, we introduce the notions of an intuitionistic subspace and the heredity, and obtain some properties of each concept.
[207]
vixra:1803.0443 [
pdf]
Intuitionistic Topological Spaces
First of all, we list some concepts and results introduced by[10, 15]. Second, we give some examples related to intuitionistic topologies and intuitionistic bases, and obtain two properties of an intuitionistic base and an intuitionistic subbase. And we dene intuitionistic intervals in R.Finally, we dene some types of intuitionistic closures and interiors, and obtain their some properties.
[208]
vixra:1803.0440 [
pdf]
Logarithmic Similarity Measure Between Interval-Valued Fuzzy Sets and Its Fault Diagnosis Method
Fault diagnosis is an important task for the normal operation and maintenance of equipment. In many real situations, the diagnosis data cannot provide deterministic values and are usually imprecise or uncertain.
[209]
vixra:1803.0406 [
pdf]
Computing the Greatest X-eigenvector of Fuzzy Neutrosophic Soft Matrix
Uncertainty forms have a very important part in our daily life. During the time we handle real life problems involving uncertainty like Medical elds, Engineering, Industry and Economics and so on.
[210]
vixra:1803.0392 [
pdf]
A Retinal Vessel Detection Approach Based on Shearlet Transform and Indeterminacy Filtering on Fundus Images
A fundus image is an effective tool for ophthalmologists studying eye diseases. Retinal vessel detection is a significant task in the identification of retinal disease regions. This study presents a retinal vessel detection approach using shearlet transform and indeterminacy filtering.
[211]
vixra:1803.0390 [
pdf]
A Side Scan Sonar Image Target Detection Algorithm Based on a Neutrosophic Set and Diffusion Maps
To accurately achieve side scan sonar (SSS) image target detection, a novel target detection algorithm based on a neutrosophic set (NS) and diffusion maps (DMs) is proposed in this paper. Firstly, the neutrosophic subset images were obtained by transforming the input SSS image into the NS domain. Secondly, the shadowed areas of the SSS image were detected using the single gray value threshold method before the diffusion map was calculated.
[212]
vixra:1803.0367 [
pdf]
Algorithms for Interval Neutrosophic Multiple Attribute Decision-Making Based on Mabac, Similarity Measure, and Edas
In this paper, we define a new axiomatic definition of interval neutrosophic similarity measure, which is presented by interval neutrosophic number (INN). Later, the objective weights of various attributes are determined via Shannon entropy theory; meanwhile, we develop the combined weights, which can show both subjective information and objective information.
[213]
vixra:1803.0320 [
pdf]
A Novel Triangular Interval Type-2 Intuitionistic Fuzzy Sets and Their Aggregation Operators
The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws.
[214]
vixra:1803.0085 [
pdf]
Input Relation and Computational Complexity
This paper describes about complexity of PH problems by using "Almost all monotone circuit family" and "Accept input pair that sandwich reject inputs". Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)). Therefore, we can find out DTM limitation by using this "NNF Circuit family". To clarify NNF circuit family limitation, we pay attention to AND-gate and OR-gate relation. If two accept "Neighbor input" pair that sandwich reject "Boundary input" in Hamming distance, NNF circuit have to meet these different variables of neighbor inputs in AND-gate to differentiate boundary inputs. NNF circuit have to use unique AND-gate to identify such neighbor input. The other hand, we can make neighbor input problem "Neighbor Tautology DNF problem (NTD)" in PH. NTD is subset of tautology DNF that do not become tautology if proper subset of one variable permutate positive / negative. NTD include many different variables which number is over polynomial size of input length. Therefore NNF circuit family that compute NTD are over polynomial size of length, and NTD that include PH is not in P.
[215]
vixra:1802.0392 [
pdf]
NS-Cross Entropy-Based MAGDM under Single-Valued Neutrosophic Set Environment
A single-valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties.
[216]
vixra:1802.0391 [
pdf]
Neutrosophic CommutativeN-Ideals in BCK-Algebras
The notion of a neutrosophic commutative N-ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N-ideal and a neutrosophic commutative N-ideal are discussed. Characterizations of a neutrosophic commutative N-ideal are considered.
[217]
vixra:1802.0390 [
pdf]
Neutrosophic N-Structures Applied to BCK/BCI-Algebras
Neutrosophic N-structures with applications in BCK/BCI-algebras is discussed. The notions of a neutrosophic N-subalgebra and a (closed) neutrosophic N-ideal in a BCK/BCI-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N-subalgebra and a neutrosophic N-ideal are considered, and relations between a neutrosophic N-subalgebra and a neutrosophic N-ideal are stated. Conditions for a neutrosophic N-ideal to be a closed neutrosophic N-ideal are provided.
[218]
vixra:1802.0388 [
pdf]
Generalized Single-Valued Neutrosophic Hesitant Fuzzy Prioritized Aggregation Operators and Their Applications to Multiple Criteria Decision-Making
Single-valued neutrosophic hesitant fuzzy set (SVNHFS) is a combination of single-valued neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the multiple criteria decision-making (MCDM) process. This paper investigates the MCDM problems in which the criteria under SVNHF environment are in different priority levels.
[219]
vixra:1802.0387 [
pdf]
Some New Biparametric Distance Measures on Single-Valued Neutrosophic Sets with Applications to Pattern Recognition and Medical Diagnosis
Single-valued neutrosophic sets (SVNSs) handling the uncertainties characterized by truth, indeterminacy, and falsity membership degrees, are a more flexible way to capture uncertainty. In this paper, some new types of distance measures, overcoming the shortcomings of the existing measures, for SVNSs with two parameters are proposed along with their proofs.
[220]
vixra:1802.0386 [
pdf]
Certain Concepts in Intuitionistic Neutrosophic Graph Structures
A graph structure is a generalization of simple graphs. Graph structures are very useful tools for the study of different domains of computational intelligence and computer science. In this research paper, we introduce certain notions of intuitionistic neutrosophic graph structures. We illustrate these notions by several examples. We investigate some related properties of intuitionistic neutrosophic graph structures. We also present an application of intuitionistic neutrosophic graph structures.
[221]
vixra:1802.0385 [
pdf]
NC-TODIM-Based MAGDM under a Neutrosophic Cubic Set Environment
A neutrosophic cubic set is the hybridization of the concept of a neutrosophic set and an interval neutrosophic set. A neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets has been reported in the current literature.
[222]
vixra:1802.0384 [
pdf]
VIKOR Method for Interval Neutrosophic Multiple Attribute Group Decision-Making
In this paper, we will extend the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to multiple attribute group decision-making (MAGDM) with interval neutrosophic numbers (INNs). Firstly, the basic concepts of INNs are briefly presented.
[223]
vixra:1802.0382 [
pdf]
TODIM Method for Single-Valued Neutrosophic Multiple Attribute Decision Making
Recently, the TODIM has been used to solve multiple attribute decision making (MADM) problems. The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the single-valued neutrosophic numbers (SVNNs).
[224]
vixra:1802.0124 [
pdf]
Investigation of the Characteristics of the Zeros of the Riemann Zeta Function in the Critical Strip Using Implicit Function Properties of the Real and Imaginary Components of the Dirichlet Eta Function v5
This paper investigates the characteristics of the zeros of the Riemann zeta function (of s) in the critical strip by using the Dirichlet eta function, which has the same zeros. The characteristics of the implicit functions for the real and imaginary components when those components are equal are investigated and it is shown that the function describing the value of the real component when the real and imaginary components are equal has a derivative that does not change sign along any of its individual curves - meaning that each value of the imaginary part of s produces at most one zero. Combined with the fact that the zeros of the Riemann xi function are also the zeros of the zeta function and xi(s) = xi(1-s), this leads to the conclusion that the Riemann Hypothesis is true.
[225]
vixra:1801.0211 [
pdf]
Smarandache Fresh and Clean Ideals of Smarandache Bci Algebras
The notion of Smarandache fresh and clean ideals is introduced, examples are given, and related properties are investigated. Relations between Q-Smarandache fresh ideals and Q-Smarandache clean ideals are given. Extension properties for Q-Smarandache fresh ideals and Q-Smarandache clean ideals are established.
[226]
vixra:1711.0185 [
pdf]
An Improved Dempster-Shafer Algorithm Using a Partial Conflict Measurement
Multiple evidences based decision making is an important functionality for computers and robots. To combine multiple evidences, mathematical theory of evidence has been developed, and it involves the most vital part called Dempster’s rule of combination. The rule is used for combining multiple evidences.
[227]
vixra:1711.0184 [
pdf]
An Internet of Things Approach for Extracting Featured Data Using AIS Database: An Application Based on the Viewpoint of Connected Ships
Automatic Identification System (AIS), as a major data source of navigational data, is widely used in the application of connected ships for the purpose of implementing maritime situation awareness and evaluating maritime transportation.
[228]
vixra:1711.0175 [
pdf]
A View on Intuitionistic Smarandache Topological Semigroup Structure Spaces
The purpose of this paper is to introduce the concepts of intuitionistic Smarandache topological semigroups, intuitionistic Smarandache topological semigroup structure spaces, intuitionistic SG exteriors and intuitionistic SG semi exteriors.
[229]
vixra:1711.0174 [
pdf]
Contributions to Differential Geometry of Spacelike Curves in Lorentzian Plane L2
In this work, first the differential equation characterizing position vector of spacelike curve is obtained in Lorentzian plane L2: Then the special curves mentioned above are studied in Lorentzian plane L2: Finally some characterizations of these special curves are given in L2.
[230]
vixra:1711.0154 [
pdf]
Another Note on Paraconsistent Neutrosophic Sets
In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s intuitionistic fuzzy topology. Here, we study this new definition and its relation to Smarandache’s paraconsistent neutrosophic sets.
[231]
vixra:1711.0106 [
pdf]
A Novel Single-Valued Neutrosophic Set Similarity Measure and Its Application in Multicriteria Decision-Making
The single-valued neutrosophic set is a subclass of neutrosophic set, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems.
[232]
vixra:1711.0099 [
pdf]
Certain Competition Graphs Based on Intuitionistic Neutrosophic Environment
The concept of intuitionistic neutrosophic sets provides an additional possibility to represent imprecise, uncertain, inconsistent and incomplete information, which exists in real situations. This research article first presents the notion of intuitionistic neutrosophic competition graphs.
[233]
vixra:1711.0097 [
pdf]
Content-based Image Retrieval with Color and Texture Features in Neutrosophic Domain
In this paper, a new content-based image retrieval (CBIR) scheme is proposed in neutrosophic (NS) domain. For this task, RGB images are first transformed to three subsets in NS domain and then segmented.
[234]
vixra:1711.0093 [
pdf]
Domestic Violence Against Women Using Induced Linked Bidirectional Associative Memories (ILBAM)
Domestic violence is an abusive behaviour perpetrated by intimate partner and other members in the family. Traditionally women were expected to married soon and settle down in her life.
[235]
vixra:1711.0090 [
pdf]
Evaluating Investment Risks of Metallic Mines Using an Extended TOPSIS Method with Linguistic Neutrosophic Numbers
The investment in and development of mineral resources play an important role in the national economy. A good mining project investment can improve economic efficiency and increase social wealth.
[236]
vixra:1711.0089 [
pdf]
Exponential Operations and an Aggregation Method for Single-Valued Neutrosophic Numbers in Decision Making
As an extension of an intuitionistic fuzzy set, a single-valued neutrosophic set is described independently by the membership functions of its truth, indeterminacy, and falsity, which is a subclass of a neutrosophic set (NS).
[237]
vixra:1711.0088 [
pdf]
Expression and Analysis of Joint Roughness Coefficient Using Neutrosophic Number Functions
In nature, the mechanical properties of geological bodies are very complex, and its various mechanical parameters are vague, incomplete, imprecise, and indeterminate. In these cases, we cannot always compute or provide exact/crisp values for the joint roughness coefficient (JRC),which is a quite crucial parameter for determining the shear strength in rock mechanics, but we need to approximate them.
[238]
vixra:1711.0087 [
pdf]
Expressions of Rock Joint Roughness Coefficient Using Neutrosophic Interval Statistical Numbers
In nature, the mechanical properties of geological bodies are very complex, and their various mechanical parameters are vague, incomplete, imprecise, and indeterminate. However, we cannot express them by the crisp values in classical probability and statistics.
[239]
vixra:1711.0083 [
pdf]
Green Supplier Evaluation and Selection Using Cloud Model Theory and the QUALIFLEX Method
Nowadays, companies have to improve their practices in the management of green supply chain with increased awareness of environmental issues worldwide. Selecting the optimum green supplier is crucial for green supply chain management, which is a challenging multi-criteria decision making (MCDM) problem.
[240]
vixra:1711.0082 [
pdf]
Group Decision Making Method Based on Single Valued Neutrosophic Choquet Integral Operator
Single valued neutrosophic set (SVNS) depicts not only the incomplete information, but also the indeterminate information and inconsistent information which exist commonly in belief systems.
[241]
vixra:1711.0077 [
pdf]
Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems
As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world.
[242]
vixra:1711.0072 [
pdf]
Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method
To describe both certain linguistic neutrosophic information and uncertain linguistic neutrosophic information simultaneously in the real world, this paper originally proposes the concept of a linguistic neutrosophic cubic number (LNCN), including an internal LNCN and external LNCN.
[243]
vixra:1711.0070 [
pdf]
Merger and Acquisition Target Selection Based on Interval Neutrosophic Multigranulation Rough Sets over Two Universes
As a significant business activity, merger and acquisition (M&A) generally means transactions in which the ownership of companies, other business organizations or their operating units are transferred or combined.
[244]
vixra:1711.0069 [
pdf]
Minimal Solution of Fuzzy Neutrosophic Soft Matrix
The aim of this article is to study the concept of unique solvability of max-min fuzzy neutrosophic soft matrix equation and strong regularity of fuzzy neutrosophic soft matrices over Fuzzy Neutrosophic Soft Algebra (FNSA).
[245]
vixra:1711.0060 [
pdf]
Multiple Attribute Group Decision-Making Method Based on Linguistic Neutrosophic Numbers
Existing intuitionistic linguistic variables can describe the linguistic information of both the truth/membership and falsity/non-membership degrees, but it cannot represent the indeterminate and inconsistent linguistic information.
[246]
vixra:1711.0049 [
pdf]
Neutrosophic Subalgebras of Bck=bci-Algebras Based on Neutrosophic Points
The concept of neutrosophic set (NS) developed by Smarandacheis a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.
[247]
vixra:1711.0048 [
pdf]
Neutrosophic Subalgebras of Several Types in Bck=bci-Algebras
The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.
[248]
vixra:1711.0036 [
pdf]
Representation of Graph Structure Based on I-V Neutrosophic Sets
In this research article, we apply the concept of interval-valued neutrosophic sets to graph structures. We present the concept of interval-valued neutrosophic graph structures. We describe certain operations on interval-valued neutrosophic graph structures and elaborate them with appropriate examples. Further,we investigate some relevant properties of these operators. Moreover,we propose some open problems on interval-valued neutrosophic line graph structures.
[249]
vixra:1711.0031 [
pdf]
Selecting Project Delivery Systems Based on Simplified Neutrosophic Linguistic Preference Relations
Project delivery system selection is an essential part of project management. In the process of choosing appropriate transaction model, many factors should be under consideration, such as the capability and experience of proprietors, project implementation risk, and so on. How to make their comprehensive evaluations and select the optimal delivery system?
[250]
vixra:1711.0027 [
pdf]
Shortest Path Problem by Minimal Spanning Tree Algorithm Using Bipolar Neutrosophic Numbers
Normally, Minimal Spanning Tree algorithm is used to nd the shortest route in a network. Neutrosophic set theory is used when incomplete, inconsistancy and indeterminacy occurs. In this paper, Bipolar Neutrosophic Numbers are used in Minimal Spanning Tree algorithm for finding the shortest path on a network when the distances are inconsistant and indeterminate and it is illustrated by a numerical example.
[251]
vixra:1711.0019 [
pdf]
Some Single-Valued Neutrosophic DombiWeighted Aggregation Operators for Multiple Attribute Decision-Making
The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets.
[252]
vixra:1711.0018 [
pdf]
Subtraction and Division Operations of Simplified Neutrosophic Sets
A simplified neutrosophic set is characterized by a truth-membership function, an indeterminacy-membership function, and a falsity-membership function, which is a subclass of the neutrosophic set and contains the concepts of an interval neutrosophic set and a single valued neutrosophic set.
[253]
vixra:1711.0011 [
pdf]
Vector Similarity Measures Between Refined Simplified Neutrosophic Sets and Their Multiple Attribute Decision-Making Method
A refined single-valued/interval neutrosophic set is very suitable for the expression and application of decision-making problems with both attributes and sub-attributes since it is described by its refined truth, indeterminacy, and falsity degrees.
[254]
vixra:1711.0010 [
pdf]
Vector Similarity Measures for Simplified Neutrosophic Hesitant Fuzzy Set and Their Applications
In this article we present three similarity measures between simplied neutrosophic hesitant fuzzy sets, which contain the concept of single valued neutrosophic hesitant fuzzy sets and interval valued neutrosophic hesitant fuzzy sets, based on the extension of Jaccard similarity measure, Dice similarity measure and Cosine similarity in the vector space.
[255]
vixra:1709.0289 [
pdf]
Selected Papers de L'Ingénieur Abdelmajid Ben Hadj Salem
This book concerns the tome III of the selected papers of the Senior Engineer Abdelmajid Ben Hadj Salem that contains papers about: - the robust estimators, - the coordinates Fuseaux in Tunisia, - the problem of the movement of n body.
[256]
vixra:1709.0203 [
pdf]
A Lattice Theoretic Look: A Negated Approach to Adjectival (Intersective, Neutrosophic and Private) Phrases
The aim of this paper is to provide a contribution to Natural Logic and Neutrosophic Theory. This paper considers lattice structures built on noun phrases. Firstly, we present some new negations of intersective adjectival phrases and their settheoretic semantics such as non-red non-cars and red non-cars. Secondly, a lattice structure is built on positive and negative nouns and their positive and negative intersective adjectival phrases. Thirdly, a richer lattice is obtained from previous one by adding neutrosophic prefixes neut and anti to intersective adjectival phrases. Finally, the richest lattice is constructed via extending the previous lattice structures by private adjectives (fake, counterfeit). We call these lattice classes Neutrosophic Linguistic Lattices (NLL).
[257]
vixra:1709.0202 [
pdf]
An Efficient Image Segmentation Algorithm Using Neutrosophic Graph Cut
Segmentation is considered as an important step in image processing and computer vision applications, which divides an input image into various non-overlapping homogenous regions and helps to interpret the image more conveniently. This paper presents an efficient image segmentation algorithm using neutrosophic graph cut (NGC).
[258]
vixra:1709.0201 [
pdf]
A Novel NeutrosophicWeighted Extreme Learning Machine for Imbalanced Data Set
Extreme learning machine (ELM) is known as a kind of single-hidden layer feedforward network (SLFN), and has obtained considerable attention within the machine learning community and achieved various real-world applications.
[259]
vixra:1709.0185 [
pdf]
Neutrosophic Quadruple Algebraic Hyperstructures
The objective of this paper is to develop neutro- sophic quadruple algebraic hyperstructures. Specically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.
[260]
vixra:1709.0184 [
pdf]
NS-K-NN: Neutrosophic Set-Based K-Nearest Neighbors Classifier
k-nearest neighbors (k-NN), which is known to be a simple and efficient approach,is a non-parametric supervised classifier. It aims to determine the class label of an unknown sample by its k-nearest neighbors that are stored in a training set.
[261]
vixra:1709.0173 [
pdf]
Special Types of Bipolar Single Valued Neutrosophic Graphs
Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs,total BSVNGs and BSVNLGs.
[262]
vixra:1708.0240 [
pdf]
Counting Complexity by Using Partial Circuit Independency
This paper describes about complexity of NP problems by using “Effective circuit” independency, and apply SAT problem. Inputs of circuit family that compute P problem have some explicit symmetry that indicated circuit structure. To clarify this explict symmetry, we define “Effective circuit” as partial circuit which are necessary to compute target inputs. Effective circuit set divide problem to some symmetric partial problems. The other hand, inputs of NTM that compute NP problem have extra implicit symmetry that indicated nondeterministic transition functions. To clarify this implicit symmetry, we define special DTM “Concrete DTM”which index i correspond to selection of nondeterministic transition functions. That is, NTM split many different asymmetry DTM and compute all DTM in same time. Consider concrete DTM and effective circuit set, circuit family [SAT] that solve SAT problem have to include all effective circuit set [CVPi] that correspond to concrete DTM as Circuit Value Problem. [CVPi] have unique gate and [SAT] must include all [CVPi]. Number of [CVPi] is over polynomial size of input. Therefore, [SAT] is over polynomial size.
[263]
vixra:1706.0361 [
pdf]
Entropy Measures on Neutrosophic Soft Sets and Its Application in Multi Attribute Decision Making
The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems.
[264]
vixra:1706.0356 [
pdf]
Further Research of Single Valued Neutrosophic Rough Set Model
Neutrosophic sets (NSs), as a new mathematical tool for dealing with problems involving incomplete, indeterminant and inconsistent knowledge, were proposed by Smarandache. By simplifying NSs, Wang et al. proposed the concept of single valued neutrosophic sets (SVNSs) and studied some properties of SVNSs. In this paper, we mainly investigate the topological structures of single valued neutrosophic rough sets which is constructed by combining SVNSs and rough sets. Firstly, we introduce the concept of single valued neutrosophic topological spaces.
[265]
vixra:1706.0346 [
pdf]
Generalized Inverse of Fuzzy Neutrosophic Soft Matrix
Aim of this article is to find the maximum and minimum solution of the fuzzy neutrosophic soft relational equation = and = , where and are fuzzy neutrosophic soft vector and is a fuzzy neutrosophic soft matrix.
[266]
vixra:1706.0342 [
pdf]
Information Fusion of Conflicting Input Data
Sensors, and also actuators or external sources such as databases, serve as data sources in order to realise condition monitoring of industrial applications or the acquisition of characteristic parameters like production speed or reject rate. Modern facilities create such a large amount of complex data that a machine operator is unable to comprehend and process the information contained in the data.
[267]
vixra:1706.0336 [
pdf]
Interval-Valued Neutrosophic Competition Graphs
We first introduce the concept of interval-valued neutrosophic competition graphs. We then discuss certain types, including k-competition interval-valued neutrosophic graphs, p-competition interval-valued neutrosophic graphs and m-step interval-valued neutrosophic competition graphs. Moreover, we present the concept of m-step interval-valued neutrosophic neighbouhood graphs.
[268]
vixra:1706.0334 [
pdf]
Introduction to Neutrosophic Nnearrings
The objective of this paper is to introduce the concept of neutrosophic nearrings. The concept of neutrosophic N-group of a neutrosophic nearring is introduced. We study neutrosophic subnearrings of neutrosophic nearrings and also neutrosophic N-subgroups of neutrosophic N- groups. The notions of neutrosophic ideals in neutrosophic nearrings and neutrosophic N-groups are introduced and their elementary properties are presented. In addition, we introduce the concepts of neutrosophic homomorphisms of neutrosophic nearrings and neutrosophic N-homomorphisms of neutrosophic N-groups and also, we present neutrosophic quotient nearrings and quotient N-groups.
[269]
vixra:1706.0333 [
pdf]
Jaccard Vector Similarity Measure of Bipolar Neutrosophic Set Based on Multi-Criteria Decision Making
The main aim of this study is to present a novel method based on multi-criteria decision making for bipolar neutrosophic sets. Therefore, Jaccard vector similarity and weighted Jaccard vector similarity measure is defined to develop the bipolar neutrosophic decision making method. In addition, the method is applied to a numerical example in order to confirm the practicality and accuracy of the proposed method.
[270]
vixra:1706.0329 [
pdf]
Measure Distance Between Neutrosophic Sets: an Evidential Approach
Due to the efficiency to handle uncertainty information, the single valued neutrosophic set is widely used in multicriteria decision-making. In MCDM, it is inevitable to measure the distance between two single valued neutrosophic sets. In this paper, an evidence distance for neutrosophic sets is proposed. There are two main contributions of this work. One is a new method to transform the single valued neutrosophic set into basic probability assignment. The other is evidence distance function between two single valued neutrosophic sets. The application in MCDM is illustrated the efficiency of the proposed distance.
[271]
vixra:1706.0282 [
pdf]
Neutrosophic Subalgebras of Bck/bci-Algebras Based on Neutrosophic Points
The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.
[272]
vixra:1706.0275 [
pdf]
Novel Single-Valued Neutrosophic Aggregated Operators Under Frank Norm Operation and Its Application to Decision-Making Process
Uncertainties play a dominant role during the aggregation process and hence their corresponding decisions are made fuzzier. Single-value neutrosophic numbers (SVNNs) contain the three ranges: truth, indeterminacy, and falsity membership degrees, and are very useful for describing and handling the uncertainties in the day-to-day life situations. In this study, some operations of SVNNs such as sum, product, and scalar multiplication are defined under Frank norm operations and, based on it, some averaging and geometric aggregation operators have been developed. We further establish some of its properties. Moreover, a decision-making method based on the proposed operators is established and illustrated with a numerical example.
[273]
vixra:1706.0267 [
pdf]
Operations on Complex Multi-Fuzzy Sets
In this paper, we introduce the concept of complex multi-fuzzy sets (CMkFSs) as a generalization of the concept of multi-fuzzy sets by adding the phase term to the definition of multi-fuzzy sets. In other words, we extend the range of multi-membership function from the interval [0,1] to unit circle in the complex plane. The novelty of CMkFSs lies in the ability of complex multi- membership functions to achieve more range of values while handling uncertainty of data that is periodic in nature. The basic operations on CMkFSs, namely complement, union, intersection, product and Cartesian product are studied along with accompanying examples. Properties of these operations are derived. Finally, we introduce the intuitive definition of the distance measure between two complex multi-fuzzy sets which are used to define δ-equalities of complex multi-fuzzy sets.
[274]
vixra:1706.0260 [
pdf]
Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making
The simplified neutrosophic set (SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging (SNNPWA) operator, simplified neutrosophic number power weighted geometric (SNNPWG) operator, simplified neutrosophic number power ordered weighted averaging (SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric (SNNPOWG) operator.
[275]
vixra:1706.0259 [
pdf]
Proposal for the Formalization of Dialectical Logic
Classical logic is typically concerned with abstract analysis. The problem for a synthetic logic is to transcend and unify available data to reconstruct the object as a totality. Three rules are proposed to pass from classic logic to synthetic logic. We present the category logic of qualitative opposition using examples from various sciences. This logic has been defined to include the neuter as part of qualitative opposition. The application of these rules to qualitative opposition, and, in particular, its neuter, demonstrated that a synthetic logic allows the truth of some contradictions. This synthetic logic is dialectical with a multi-valued logic, which gives every proposition a truth value in the interval [0,1] that is the square of the modulus of a complex number. In this dialectical logic, contradictions of the neuter of an opposition may be true.
[276]
vixra:1706.0254 [
pdf]
Representation of Graphs Using Intuitionistic Neutrosophic Soft Sets
The concept of intuitionistic neutrosophic soft sets can be utilized as a mathematical tool to deal with imprecise and unspecified information. In this paper, we apply the concept of intuitionistic neutrosophic soft sets to graphs. We introduce the concept of intuitionistic neutrosophic soft graphs, and present applications of intuitionistic neutrosophic soft graphs in multiple-attribute decision-making problems. We also present an algorithm of our proposed method.
[277]
vixra:1706.0241 [
pdf]
Single-Valued Neutrosophic Planar Graphs
We apply the concept of single-valued neutrosophic sets to multigraphs, planar graphs and dual graphs. We introduce the notions of single-valued neutrosophic multigraphs, single-valued neutrosophic planar graphs, and single-valued neutrosophic dual graphs. We illustrate these concepts with examples. We also investigate some of their properties.
[278]
vixra:1706.0231 [
pdf]
Supervised Pattern Recognition Using Similarity Measure Between Two Interval
F. Smarandache introduced the concept of neutrosophic set in 1995 and P. K. Maji introduced the notion of neutrosophic soft set in 2013, which is a hybridization of neutrosophic set and soft set. Irfan Deli introduced the concept of interval valued neutrosophic soft sets. Interval valued neutrosophic soft sets are most efficient tools to deals with problems that contain uncertainty such as problem in social, economic system, medical diagnosis, pattern recognition, game theory, coding theory and so on. In this article we introduce similarity measure between two interval valued neutrosophic soft sets and study some basic properties of similarity measure. An algorithm is developed in interval valued neutrosophic soft set setting using similarity measure. Using this algorithm a model is constructed for supervised pattern recognition problem using similarity measure.
[279]
vixra:1706.0224 [
pdf]
The Category of Neutrosophic Crisp Sets
We introduce the category NCSet consisting of neutrosophic crisp sets and morphisms between them. And we study NCSet in the sense of a topological universe and prove that it is Cartesian closed over Set, where Set denotes the category consisting of ordinary sets and ordinary mappings between them.
[280]
vixra:1706.0212 [
pdf]
Unification of Evidence Theoretic Fusion Algorithms: A Case Study in Level-2 and Level-3 Fingerprint Features
This paper formulates an evidence-theoretic multimodal unification approach using belief functions that takes into account the variability in biometric image characteristics. While processing non-ideal images the variation in the quality of features at different levels of abstraction may cause individual classifiers to generate conflicting genuine-impostor decisions.
[281]
vixra:1706.0210 [
pdf]
Statistic-Based Approach for Highest Precision Numerical Differentiation
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution, interpreted as the value of the quantity of interest, can be determined with much better precision than what is the precision provided by a single algorithm. Many practical algorithms introduce a bias using a parameter, e.g. a small but finite number to compute a limit or a large but finite number (cutoff) to approximate infinity. One may vary such parameter of a single algorithm, interpret the resulting numbers as generated by several algorithms and compute the average. A numerical evidence for the validity of this approach is, in the context of a fixed machine epsilon, shown for differentiation: the method greatly improves the precision and leads, presumably, to the most precise numerical differentiation nowadays known.
[282]
vixra:1706.0180 [
pdf]
Alliance Based Evidential Reasoning Approach with Unknown Evidence Weights
In the evidential reasoning approach of decision theory, different evidence weights can generate different combined results. Consequently, evidence weights can significantly influence solutions. In terms of the “psychology of economic man,” decision-makers may tend to seek similar pieces of evidence to support their own evidence and thereby form alliances.
[283]
vixra:1706.0174 [
pdf]
A Multi-Valued Neutrosophic Qualitative flexible Approach Based on Likelihood for Multi-Criteria Decision-Making Problems
In this paper, multi-criteria decision-making (MCDM) problems based on the qualitative flexible multiple criteria method (QUALIFLEX), in which the criteria values are expressed by multi-valued neutrosophic information, are investigated. First,multi-valued neutrosophic sets(MVNSs),which allow the truth-membership function,indeterminacy-membership function and falsity-membership function to have a set of crisp values between zeroand one, are introduced.
[284]
vixra:1706.0149 [
pdf]
An Improved Score Function for Ranking Neutrosophic Sets and Its Application to Decision-Making Process
The neutrosophic set (NS) is a more general platform which generalizes the concept of crisp, fuzzy, and intuitionistic fuzzy sets to describe the membership functions in terms of truth, indeterminacy, and false degree. Under this environment, the present paper proposes an improved score function for ranking the single as well as interval-valued NSs by incorporating the idea of hesitation degree between the truth and false degrees. Shortcomings of the existing function have been highlighted in it. Further, the decision-making method has been presented based on proposed function and illustrates it with a numerical example to demonstrate its practicality and effectiveness.
[285]
vixra:1706.0090 [
pdf]
An Holomorphic Study Of Smarandache Automorphic and Cross Inverse Property Loops
By studying the holomorphic structure of automorphic inverse property quasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop if and only if its Smarandache automorphism group is trivial and the loop is itself is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop.
[286]
vixra:1706.0089 [
pdf]
A Pair of Smarandachely Isotopic Quasigroups and Loops Of The Same Variety
The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past. A variety of quasigroups(loops) that are not universal have been found to be isotopic invariant relative to a special type of isotopism or the other. Presently, there are two outstanding open problems on universality of loops: semi automorphic inverse property loops(1999) and Osborn loops(2005). Smarandache isotopism(S-isotopism) was originally introduced by Vasantha Kandasamy in 2002.
[287]
vixra:1706.0080 [
pdf]
Generalized Fibonacci Sequences in Groupoids
In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents. Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci sequences.
[288]
vixra:1706.0066 [
pdf]
On the Smarandache-Pascal Derived Sequences of Generalized Tribonacci Numbers
The main purpose of this paper is, using the elementary method and the properties of the third-order linear recurrence sequence, to unify the above results by proving the following theorem.
[289]
vixra:1706.0065 [
pdf]
On the Universality of Some Smarandache Loops of Bol-Moufang Type
A Smarandache quasigroup(loop) is shown to be universal if all its f; g-principal isotopes are Smarandache f; g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol, Moufang and extra loops are shown to be universal if all their f; g-principal isotopes are Smarandache f; g-principal isotopes.
[290]
vixra:1706.0061 [
pdf]
Shared Multi-Space Representation for Neural-Symbolic Reasoning
This paper presents a new neural-symbolic reasoning approach based on a sharing of neural multi-space representation for coded fractions of first-order logic. A multi-space is the union of spaces with different dimensions, each one for a different set of distinct features.
[291]
vixra:1706.0056 [
pdf]
Smarandache Isotopy Of Second Smarandache Bol Loops
The study of the Smarandache concept in groupoids was initiated by W. B. Vasantha Kandasamy. In her book and first paper on Smarandache concept in loops,she defined a Smarandache loop(S-loop) as a loop with at least a subloop which forms a subgroup under the binary operation of the loop.
[292]
vixra:1705.0446 [
pdf]
Uniform and Partially Uniform Redistribution Rules
This paper introduces two new fusion rules for combining quantitative basic belief assignments. These rules although very simple have not been proposed in literature so far and could serve as useful alternatives because of their low computation cost with respect to the recent advanced Proportional Conflict Redistribution rules developed in the DSmT framework.
[293]
vixra:1705.0437 [
pdf]
Neutrosophic Filters in be-Algebras
In this paper, we introduce the notion of (implicative) neutrosophic filters in BE-algebras. The relation between implicative neutrosophic filters and neutrosophic filters is investigated and we show that in self distributive BEalgebras these notions are equivalent.
[294]
vixra:1705.0430 [
pdf]
Triple Refined Indeterminate Neutrosophic Sets for Personality Classification
Personality tests are most commonly objective type, where the users rate their behaviour. Instead of providing a single forced choice, they can be provided with more options. A person may not be in general capable to judge his/her behaviour very precisely and categorize it into a single category. Since it is self rating there is a lot of uncertain and indeterminate feelings involved.
[295]
vixra:1703.0160 [
pdf]
Logarithmic Extension of Real Numbers and Hyperbolic Representation of Generalized Lorentz Transforms
We construct the logarithmic extension for real numbers in which the numbers, less then $-\infty$ exist. Using this logarithmic extension we give the single formula for hyperbolic representation of generalized tachyon Lorentz transforms.
[296]
vixra:1703.0073 [
pdf]
On The Riemann Zeta Function
We discuss the Riemann zeta function, the topology of its domain, and make an argument against the Riemann hypothesis. While making the argument in the classical formalism, we discuss the material as it relates to the theory of infinite complexity (TOIC). We extend Riemann's own (planar) analytic continuation $\mathbb{R}\to\mathbb{C}$ into (bulk) hypercomplexity with $\mathbb{C}\to\,^\star\mathbb{C}$. We propose a solution to the Banach--Tarski paradox.
[297]
vixra:1702.0324 [
pdf]
Why Finite Mathematics Is The Most Fundamental and Ultimate Quantum Theory Will Be Based on Finite Mathematics
Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the situation is the opposite: classical mathematics is only a degenerate special case of finite one and finite mathematics is more pertinent for describing nature than standard one. Then we describe results of a quantum theory based on finite mathematics. Implications for foundation of mathematics are discussed.
[298]
vixra:1702.0238 [
pdf]
Certain Types of Graphs in Interval-Valued Intuitionistic Fuzzy Setting
Interval-valued intuitionistic fuzzy set (IVIFS) as a generalization of intuitionistic fuzzy set (IFS) increase its elasticity drastically. In this paper, some important types of interval-valued intuitionistic fuzzy graphs (IVIFGs) such as regular, irregular, neighbourly irregular, highly irregular and strongly irregular IVIFGs are discussed. The relation among neighbourly irregular, highly irregular and strongly irregular IVIFGs is proved. The notion of interval-valued intuitionistic fuzzy clique (IVIFC) is introduced. A complete characterization of the structure of the IVIFC is presented.
[299]
vixra:1702.0237 [
pdf]
Measurement of Planarity in Product Bipolar Fuzzy Graphs
Bipolar fuzzy set theory provides a basis for bipolar cognitive modeling and multiagent decision analysis, where in some situations, the product operator may be preferred to the min operator, from theoretical and experimental aspects. In this paper, the definition of product bipolar fuzzy graphs (PBFGs) is modified. The concepts of product bipolar fuzzy multigraphs (PBFMGs), product bipolar fuzzy planar graphs (PBFPGs) and product bipolar fuzzy dual graphs (PBFDGs) are introduced and investigated. Product bipolar fuzzy planarity value of PBFPG is introduced. The relation between PBFPG and PBFDG is also established. Isomorphism between PBFPGs is discussed. Finally, an application of the proposed concepts is provided.
[300]
vixra:1701.0616 [
pdf]
Bipolar Neutrosophic Planar Graphs
Fuzzy graph theory is used for solving real-world problems in different fields, including theoretical computer science, engineering, physics, combinatorics and medical sciences. In this paper, we present conepts of bipolar neutrosophic multigraphs, bipolar neutrosophic planar graphs, bipolar neutrosophic dual graphs, and study some of their related properties. We also describe applications of bipolar neutrosophic graphs in road network and electrical connections.
[301]
vixra:1701.0597 [
pdf]
Certain Single-Valued Neutrosophic Graphs
Neutrosophic sets are the generalization of the concept of fuzzy sets and intuitionistic fuzzy sets. Neutrosophic models give more flexibility, precisions and compatibility to the system as compared to the classical, fuzzy and intuitionistic fuzzy models. In this research paper, we present certain types of single-valued neutrosophic graphs, including regular single-valued neutrosophic graphs, totally regular single-valued neutrosophic graphs, edge regular single-valued neutrosophic graphs and totally edge regular single-valued neutrosophic graphs. We also investigate some of their related properties
[302]
vixra:1701.0452 [
pdf]
Relations on Neutrosophic Multi Sets with Properties
In this paper, we first give the cartesian product of two neutrosophic multi sets(NMS). Then, we define relations on neutrosophic multi sets to extend the intuitionistic fuzzy multi relations to neutrosophic multi relations. The relations allows to compose two neutrosophic sets. Also, various properties like reflexivity, symmetry and transitivity are studied.
[303]
vixra:1701.0433 [
pdf]
The 3n±p Conjecture: A Generalization of Collatz Conjecture
The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n + 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo Kakutani) and so on. Several various generalization of the Collatz conjecture has been carried.
[304]
vixra:1701.0423 [
pdf]
Triple Refined Indeterminate Neutrosophic Sets for Personality Classification
Personality tests are most commonly objective type where the users rate their behaviour. Instead of providing a single forced choice, they can be provided with more options. A person may not be in general capable to judge his/her behaviour very precisely and categorize it into a single category. Since it is self rating there is a lot of uncertain and indeterminate feelings involved. The results of the test depend a lot on the circumstances under which the test is taken, the amount of time that is spent, the past experience of the person, the emotion the person is feeling and the person’s self image at that time and so on.
[305]
vixra:1701.0419 [
pdf]
α-D MCDM-Topsis Multi-Criteria Decision Making Method for N-Wise Criteria Comparisons and Inconsistent Problems
The purpose of this paper is to present an extension and alternative of the hybrid approach using Saaty’s Analytical Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method (AHP-TOPSIS), that based on the AHP and its use of pairwise comparisons, to a new method called α-D MCDM-TOPSIS(α-Discounting Method for Multi-Criteria Decision Making-TOPSIS). The proposed method works not only for preferences that are pairwise comparisons of criteria as AHP does, but for preferences of any n-wise (with n ≥ 2) comparisons of criteria. Finally the α-D MCDM-TOPSIS methodology is verified by some examples to demonstrate how it might be applied in different types of matrices and is how it allwos for consistency, inconsistent, weak inconsistent, and strong inconsistent problems.
[306]
vixra:1701.0413 [
pdf]
NeutrosophicfiltersinBE-Algebras
In this paper, we introduce the notion of (implicative)neutrosophic filters in BE-algebras. The relation between implicative neutrosophic filters and neutrosophic filters is investigated and we show that in self distributive BEalgebras these notions are equivalent.
[307]
vixra:1701.0406 [
pdf]
Neutrosophic Set Approch for Characterizations of Left Almost Semigroups
In this paper we have dened neutrosophic ideals, neutrosophic interior ideals, netrosophic quasi-ideals and neutrosophic bi-ideals (neutrosophic generalized bi-ideals) and proved some results related to them.
[308]
vixra:1701.0392 [
pdf]
A New 3n−1 Conjecture Akin to Collatz Conjecture
The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n + 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutani’s problem (after Shizuo Kakutani) and so on.
[309]
vixra:1701.0373 [
pdf]
Clustering Algorithm of Triple Refined Indeterminate Neutrosophic Set for Personality Grouping
Triple Refined Indeterminate Neutrosophic Set (TRINS) which is a case of the refined neutrosophic set was introduced. It provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world.
[310]
vixra:1701.0371 [
pdf]
Clustering of Personality using Indeterminacy Based Personality Test
Triple Refined Indeterminate Neutrosophic Set (TRINS) a case of the refined neutrosophic set was introduced in [8]. The uncertain and inconsistent information which are available in real world is represented with sensitivity and accuracy by TRINS.
[311]
vixra:1701.0354 [
pdf]
Interval-Valued Neutrosophic Soft Rough Sets
We first defined interval-valued neutrosophic soft rough sets (IVN-soft rough sets for short) which combine interval-valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of interval-valued intuitionistic fuzzy soft rough sets(IVIF-soft rough sets).
[312]
vixra:1701.0278 [
pdf]
Structural Properties of Neutrosophic Abel-Grassmanns Groupoids
In this paper, we have introduced the notion of neutrosophic (2;2)regular, neutrosophic strongly regular neutrosophic AG-groupoids and investigated these structures. We have shown that neutrosophic regular, neutrosophic intraregular and neutrosophic strongly regular AG-groupoid are the only generalized classes of an AG-groupoid.
[313]
vixra:1701.0275 [
pdf]
Supervised Pattern Recognition Using Similarity Measure Between Two Interval Valued Neutrosophic Soft Sets
F. Smarandache introduced the concept of neutrosophic set in 1995 and P. K. Maji introduced the notion of neutrosophic soft set in 2013, which is a hybridization of neutrosophic set and soft set.
[314]
vixra:1701.0272 [
pdf]
Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant by Applying WASPAS Method with Single-Valued Neutrosophic Set
The principles of sustainability have become particularly important in the construction, real estate maintenance sector, and all areas of life in recent years. The one of the major problem of urban territories that domestic and construction waste of generated products cannot be removed automatically.
[315]
vixra:1701.0263 [
pdf]
The Smarandache Bryant Schneider Group Of A Smarandache Loop
The concept of Smarandache Bryant Schneider Group of a Smarandache loop is introduced. Relationship(s) between the Bryant Schneider Group and the Smarandache Bryant Schneider Group of an S-loop are discovered and the later is found to be useful in finding Smarandache isotopy-isomorphy condition(s) in S-loops just like the formal is useful in finding isotopy-isomorphy condition(s) inloops.
[316]
vixra:1701.0255 [
pdf]
The Weighted Distance Measure Based Method to Neutrosophic Multi-Attribute Group Decision Making
Neutrosophic set (NS) is a generalization of fuzzy set (FS) that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function.
[317]
vixra:1701.0244 [
pdf]
Vector Similarity Measures for Simplied Neutrosophic Hesitant Fuzzy Set and Their Applications
In this article we present three similarity measures between simplied neutrosophic hesitant fuzzy sets, which contain the concept of single valued neutrosophic hesitant fuzzy sets and interval valued neutrosophic hesitant fuzzy sets, based on the extension of Jaccard similarity measure, Dice similarity measure and Cosine similarity in the vector space.
[318]
vixra:1701.0238 [
pdf]
Liar Liar, Pants on fire; or How to Use Subjective Logic and Argumentation to Evaluate Information from Untrustworthy Sources
This paper presents a non-prioritized belief change operator, designed specifically for incorporating new information from many heterogeneous sources in an uncertain environment. We take into account that sources may be untrustworthy and provide a principled method for dealing with the reception of contradictory information.
[319]
vixra:1701.0230 [
pdf]
Multi-Criteria Decision Making Method Based on Similarity Measures Under Single Valued Neutrosophic Refined and Interval Neutrosophic Refined Environments
In this paper, we propose three similarity measure methods for single valued neutrosophic refined sets and interval neutrosophic refined sets based on Jaccard, Dice and Cosine similarity measures of single valued neutrosophic sets and interval neutrosophic sets.
[320]
vixra:1701.0217 [
pdf]
Neutrosophic Complex N Continuity
In this paper, the concept of N-open set in neutrosophic complex topological space is introduced. Some of the interesting properties of neutrosophic complex N-open sets are studied. The idea of neutrosophic complex N-continuous function and its characterization are discussed. Also the interrelation among the sets and continuity are established.
[321]
vixra:1701.0216 [
pdf]
Neutrosophic Cubic Ideals
Operational properties of neutrosophic cubic sets are investigated.The notion of neutrosophic cubic subsemigroups and neutrosophic cubic left (resp.right) ideals are introduced, and several properties are investigated.
[322]
vixra:1701.0214 [
pdf]
Neutrosophic Hypergraphs
In this paper, we introduce certain concepts, including neutrosophic hypergraph, line graph of neutrosophic hypergraph, dual neutrosophic hypergraph, tempered neutrosophic hypergraph and transversal neutrosophic hypergraph. We illustrate these concepts by several examples and investigate some of interesting properties.
[323]
vixra:1701.0213 [
pdf]
Neutrosophic Hyperideals of Γ-Semihyperrings
Hyperstructures, in particular hypergroups, were introduced in 1934 by Marty [12] at the eighth congress of Scandinavian Mathematicians. The notion of algebraic hyperstructure has been developed in the following decades and nowadays by many authors, especially Corsini [2, 3], Davvaz [5, 6, 7, 8, 9], Mittas [13], Spartalis [16], Stratigopoulos [17] and Vougiouklis [20]. Basic definitions and notions concerning hyperstructure theory can be found in [2].
[324]
vixra:1701.0199 [
pdf]
Neutrsophic Complex N-Continuity
In this paper, the concept of N-open set in neutrosophic complex topological space is introduced. Some of the interesting properties of neutrosophic complex N-open sets are studied. The idea of neutrosophic complex N-continuous function and its characterization are discussed. Also the interrelation among the sets and continuity are established.
[325]
vixra:1701.0197 [
pdf]
New Distance Measure of Single-Valued Neutrosophic Sets and Its Application
A single-valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which can be used to handle uncertainty, imprecise, indeterminate, and inconsistent information in real life. In this paper, a new distance measure between two SVNSs is defined by the full consideration of truthmembership function, indeterminacy-membership function, and falsity-membership function for the forward and backward differences.
[326]
vixra:1701.0195 [
pdf]
N-Fold Filters in Smarandache Residuated Lattices, Part (I)
In this paper we introduce the notions of n-fold BL-Smarandache positive implicateve filter and n-fold BL-Smarandache implicateve filter in Smarandache residuated lattices and study the relations among them.
[327]
vixra:1701.0194 [
pdf]
N-Fold Filters in Smarandache Residuated Lattices, Part (Ii)
In this paper we introduce the notions of n-fold BL-Smarandache n-fold BL-Smarandache fantastic filter and n-fold BL-Smarandache easy filter in Smarandache residuated lattices and study the relations among them.
[328]
vixra:1701.0193 [
pdf]
Non-Overlapping Matrices
Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the k-generalized Fibonacci numbers. Moreover, the generating function for the enumerating sequence is easily seen to be rational.
[329]
vixra:1701.0190 [
pdf]
Novel Multiple Criteria Decision Making Methods Based on Bipolar Neutrosophic Sets and Bipolar Neutrosophic Graphs
In this research article, we present certain notions of bipolar neutrosophic graphs. We study the dominating and independent sets of bipolar neutrosophic graphs. We describe novel multiple criteria decision making methods based on bipolar neutro- sophic sets and bipolar neutrosophic graphs. We develop an algorithm for computing domination in bipolar neutrosophic graphs. We also show that there are some flaws in Broumi et al. [11]’s definition.
[330]
vixra:1701.0189 [
pdf]
N-Valued Refined Neutrosophic Soft Set Theory
In this paper as a generalization of neutrosophic soft set we introduce the concept of n-valued refined neutrosophic soft set and study some of its properties. We also, define its basic operations, complement, union intersection, "AND" and "OR" and study their properties.
[331]
vixra:1701.0188 [
pdf]
N-Valued Refined Neutrosophic Soft Sets and Its Applications in Decision Making Problems and Medical Diagnosis
In this work we use the concept of a n-valued refined neutrosophic soft sets and its properties to solve decision making problems, Also a similarity measure between two n-valued refined neutrosophic soft sets are proposed.
[332]
vixra:1701.0187 [
pdf]
On a Q-Smarandache Fuzzy Commutative Ideal of a Q-Smarandache BH-algebra
In this paper, the notions of Q-Smarandache fuzzy commutative ideal and Q-Smarandache fuzzy sub-commutative ideal of a Q-Smarandache BH-Algebra are introduced, examples and related properties are investigated. Also, the relationships among these notions and other types of Q-Smarandache fuzzy ideal of a Q-Smarandache BH-Algebra are studied.
[333]
vixra:1701.0183 [
pdf]
On Neutrosophic Soft Function
In this paper, the cartesian product and the relations on neutrosophic soft sets have been defined in a new approach. Some properties of this concept have been discussed and verified with suitable real life examples.
[334]
vixra:1701.0182 [
pdf]
On Neutrosophic Submodules of a Module
The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept.
[335]
vixra:1701.0181 [
pdf]
On Parallel Curves Via Parallel Transport Frame in Euclidean 3-Space
In this paper, we study the parallel curve of a space curve according to parallel transport frame. Then, we obtain new results according to some cases of this curve by using parallel transport frame in Euclidean 3-space. Additionally, we give new examples for this characterizations and we illustrate this examples in gures.
[336]
vixra:1701.0180 [
pdf]
On Pseudospherical Smarandache Curves in Minkowski 3-Space
In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space.
[337]
vixra:1701.0178 [
pdf]
On The Darboux Vector Belonging To Involute Curve A Different View
In this paper, we investigated special Smarandache curves in terms of Sabban frame drawn on the surface of the sphere by the unit Darboux vector of involute curve. We created Sabban frame belonging to this curve. It was explained Smarandache curves position vector is composed by Sabban vectors belonging to this curve. Then, we calculated geodesic curvatures of this Smarandache curves. Found results were expressed depending on the base curve. We also gave example belonging to the results found.
[338]
vixra:1701.0169 [
pdf]
Quantitative Analysis of Particles Segregation
Segregation is a popular phenomenon. It has considerable effects on material performance. To the author’s knowledge, there is still no automated objective Quantitative indicator for segregation. In order to full fill this task, segregation of particles is analyzed. Edges of the particles are extracted from the digital picture. Then, the whole picture of particles is splintered to small rectangles with the same shape.
[339]
vixra:1701.0155 [
pdf]
Single-Valued Neutrosophic Graph Structures
A graph structure is a generalization of undirected graph which is quite useful in studying some structures, including graphs and signed graphs. In this research paper, we apply the idea of single-valued neutrosophic sets to graph structure, and explore some interesting properties of single-valued neutrosophic graph structure. We also discuss the concept of φ-complement of single-valued neutrosophic graph structure.
[340]
vixra:1701.0151 [
pdf]
Smarandache Curves According to Sabban Frame of Fixed Pole Curve Belonging to the Bertrand Curves Pair
In this paper, we investigate the Smarandache curves according to Sabban frame of fixed pole curve which drawn by the unit Darboux vector of the Bertrand partner curve. Some results have been obtained. These results were expressed as the depends Bertrand curve.
[341]
vixra:1701.0141 [
pdf]
Special Smarandache Curves in R
In differential geometry, there are many important consequences and properties of curves studied by some authors [1, 2, 3]. Researchers always introduce some new curves by using the existing studies.
[342]
vixra:1701.0129 [
pdf]
Basic Properties Of Second Smarandache Bol Loops
The basic properties of S2ndBLs are studied. These properties are all Smarandache in nature. The results in this work generalize the basic properties of Bol loops, found in the Ph.D. thesis of D. A. Robinson. Some questions for further studies are raised.
[343]
vixra:1701.0127 [
pdf]
Bipolar Neutrosophic Refined Sets and Their Applications in Medical Diagnosis
This paper proposes concept of bipolar neutrosophic refined set and its some operations. Firstly, a score certainty and accuracy function to compare the bipolar neutrosophic refined information is defined. Secondly, to aggregate the bipolar neutrosophic refined information, a bipolar neutrosophic refined weighted average operator and a bipolar neutrosophic refined weighted geometric operator is developed.
[344]
vixra:1701.0122 [
pdf]
Certain Networks Models Using Single-valued Neutrosophic Directed Hypergraphs
A directed hypergraph is powerful tool to solve the problems that arises in different fields, including computer networks, social networks and collaboration networks. In this research paper, we apply the concept of single-valued neutrosophic sets to directed hypergraphs.
[345]
vixra:1701.0121 [
pdf]
Change Detection by New DSmT Decision Rule and Icm with Constraints :Application to Argan Land Cover
The objective of this work is, in the first place, the integration in a fusion process using hybrid DSmT model, both, the contextual information obtained from a supervised ICM classification with constraints and the temporal information with the use of two images taken at two different dates.
[346]
vixra:1701.0111 [
pdf]
Context-dependent Combination of Sensor Information in Dempster-Shafer Theory for BDI
There has been much interest in the Belief-Desire-Intention (BDI) agentbased model for developing scalable intelligent systems, e.g. using the AgentSpeak framework. However, reasoning from sensor information in these large-scale systems remains a significant challenge.
[347]
vixra:1701.0103 [
pdf]
Cosine Similarity Measures of Neutrosophic Soft Set
In this paper we have introduced the concept of cosine similarity measures for neutrosophic soft set and interval valued neutrosophic soft set.An application is given to show its practicality and effectiveness.
[348]
vixra:1701.0101 [
pdf]
Decision-Making with Belief Interval Distance
In this paper we propose a new general method for decisionmaking under uncertainty based on the belief interval distance. We show through several simple illustrative examples how this method works and its ability to provide reasonable results.
[349]
vixra:1701.0093 [
pdf]
Dual Curves of Constant Breadth According to Bishop Frame in Dual Euclidean Space
In this work, curves of constant breadth are defined and some characterizations of closed dual curves of constant breadth according to Bishop frame are presented in dual Euclidean space. Also, it has been obtained that a third order vectorial differential equation in dual Euclidean 3-space.
[350]
vixra:1701.0082 [
pdf]
Fingerprint Quality Assessment: Matching Performanceand Image Quality
This article chiefly focuses on Fingerprint Quality Assessment(FQA)applied to the Automatic Fingerprint Identification System (AFIS). In our research work, different FQA solutions proposed so far are compared by using several quality metrics selected from the existing studies.
[351]
vixra:1701.0071 [
pdf]
Generalizedfibonaccisequencesin Groupoids
In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents.Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci sequences.
[352]
vixra:1701.0066 [
pdf]
A Clustering-Based Evidence Reasoning Method
Aiming at the counterintuitive phenomena of the Dempster–Shafer method in combining the highly conflictive evidences, a combination method of evidences based on the clustering analysis is proposed in this paper. At first, the cause of conflicts is disclosed from the point of view of the internal and external contradiction. Andthen,a new similarity measure based on it is proposed by comprehensively considering the Pignistic distance and the sequence according to the size of the basic belief assignments over focal elements.
[353]
vixra:1701.0065 [
pdf]
A Double Cryptography Using The Smarandache Keedwell Cross Inverse Quasigroup
The present study further strengthens the use of the Keedwell CIPQ against attack on a system by the use of the Smarandache Keedwell CIPQ for cryptography in a similar spirit in which the cross inverse property has been used by Keedwell. This is done as follows. By constructing two S-isotopic S-quasigroups(loops) U and V such that their Smarandache automorphism groups are not trivial, it is shown that U is a SCIPQ(SCIPL) if and only if V is a SCIPQ(SCIPL). Explanations and procedures are given on how these SCIPQs can be used to double encrypt information.
[354]
vixra:1701.0062 [
pdf]
Algorithms for Neutrosophic Soft Decision Making Based on Edas and New Similarity Measure
This paper presents two novel single-valued neutrosophic soft set (SVNSS) methods. First,we initiate a new axiomatic definition of single-valued neutrosophic simlarity measure, which is expressed by single-valued neutrosophic number (SVNN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via grey system theory. Combining objective weights with subjective weights, we present the combined weights, which can reflect both the subjective considerations of the decision maker and the objective information. Later, we present two algorithms to solve decision making problem based on Evaluation based on Distance from Average Solution (EDAS) and similarity measure. Finally, the effectiveness and feasibility of approaches are demonstrated by a numerical example.
[355]
vixra:1701.0059 [
pdf]
A Model for Medical Diagnosis Via Fuzzy Neutrosophic Soft Sets
The concept of neutrosophic soft set is a new mathematical tool for dealing with uncertainties that is free from the difficulties affecting existing methods. The theory has rich potential for applications in several directions. In this paper, a new approach is proposed to construct the decision method for medical diagnosis by using fuzzy neutrosophic soft sets. Also, we develop a technique to diagnose which patient is suffering from what disease. Our data with respect to the case study has been provided by the a medical center in Ordu, Turkey.
[356]
vixra:1701.0056 [
pdf]
AnAlgorithmforMedicalMagneticResonanceImage Non-LocalMeansDenoising
Digital images and digital image processing were widely researched in the past decades and special place in this field have medical images. Magnetic resonance images are a very important class of medical images and their enhancement is very significant for diagnostic process.
[357]
vixra:1701.0044 [
pdf]
A New Definition of Entropy of Belief Functions in the Dempster-Shafer Theory
We propose a new definition of entropy for basic probability assignments (BPA) in the Dempster-Shafer (D-S) theory of belief functions, which is interpreted as a measure of total uncertainty in the BPA. Our definition is different from the definitions proposed by H¨ohle, Smets, Yager, Nguyen, Dubois-Prade, Lamata-Moral, Klir-Ramer, Klir-Parviz, Pal et al., MaedaIchihashi, Harmanec-Klir, Jousselme et al., and Pouly et al. We state a list of five desired properties of entropy for D-S belief functions theory that are motivated by Shannon’s definition of entropy for probability functions together with the requirement that any definition should be consistent with the semantics of D-S belief functions theory.
[358]
vixra:1701.0038 [
pdf]
A New Similarity Measure on Npn-Soft Set Theory and Its Application
In this paper, we give a new similarity measure on npn-soft set theory which is the extension of correlation measure of neutrosophic refined sets. By using the similarity measure we propose a new method for decision making problem. Finally, we give an example for diagnosis of diseases could be improved by incorporating clinical results and other competing diagnosis in npn-soft environment.
[359]
vixra:1701.0021 [
pdf]
Application of DSmT-Icm with Adaptive Decision Rule to Supervised Classification in Multisource Remote Sensing
In this paper, we introduce a new procedure called DSmT-ICM with adaptive decision rule, which is an alternative and extension of Multisource Classification Using ICM (Iterated conditional mode) and DempsterShafer theory (DST).
[360]
vixra:1610.0149 [
pdf]
Introduction to Tensor Calculus
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is presumed.
[361]
vixra:1610.0148 [
pdf]
Tensor Calculus
These notes are the second part of the tensor calculus documents which started with the previous set of introductory notes. In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when necessary, some topics and developing further concepts and techniques. Unlike the previous notes which are largely based on a Cartesian approach, the present notes are essentially based on assuming an underlying general curvilinear coordinate system.
[362]
vixra:1610.0147 [
pdf]
Principles of Differential Geometry
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on tensor calculus as they are based on the materials and conventions given in those documents. They can be used as a reference for a first course on the subject or as part of a course on tensor calculus.
[363]
vixra:1610.0121 [
pdf]
On Complex Interval Linear System
Linear system of equations with crisp values are crucial filed of research. Several different technique are available to solve this type of equations. The parameter values are actually uncertain in nature because data are collected from experiment. Another aspect is error in calculation. To avoid errors and uncertain nature of the parameter values, we use interval analysis. In this work, we are addressed solution methods for complex interval linear system. We propose a new method for finding solution of complex linear system of equations (CLSE). Moreover we study the numerical experiments using the proposed different methods.
[364]
vixra:1609.0318 [
pdf]
Mechanical Behaviors of Banana Fibres with Different Mechanical Properties
World is as of now concentrating on alternate material sources that are environment agreeable and biodegradable in nature. Because of the expanding natural concerns, bio composite produced out of regular fiber and polymeric resin, is one of the late advancements in the business and constitutes the present extent of experimental work. The use of composite materials field is increasing gradually in engineering. The composite consists of mainly two phases i.e. matrix and fiber. The accessibility of characteristic fiber and simplicity of assembling have enticed scientists worldwide to attempt by regional standards accessible inexpensive fiber and to learning their achievability of fortification determinations and to what degree they fulfill the obliged particulars of great strengthened polymer composite aimed at structural requisition. Fiber reinforced polymer composites has numerous preferences, for example, generally minimal effort of creation, simple to create and better quality contrast than perfect polymer tars due with this reason fiber strengthened polymer composite utilized within an assortment of provision as class of structure material. This work describe the fabrication and the mechanical behavior of banana fiber reinforced polymer composite at varying composition (25\%, 30\%, 35\%) with that of silicon carbide at 4\%, 8\%, 12\% respectively. Also the test such as the tensile test, hardness test and the bending test are carried out and the mechanical properties of the composite material are studied.
[365]
vixra:1608.0263 [
pdf]
Cercurile Apollonius de Rangul K
In this paper, the notion of Apollonius circle of rank k is introduced and a number of results related to the classical Apollonius circles are generalized.
[366]
vixra:1605.0148 [
pdf]
On the a-Posteriori Fourier Method for Solving Ill-Posed Problems
The Fourier method is a convenient regularization method for solving a class of ill-posed problems. This class of ill-posed problems can be also formulated as the problem of ill-posed multiplication operator equation in the frequency domain. A recent work on the Morozov's discrepancy principle for the Fourier method are discussed in [2]. In this paper, we investigate the Fourier method within the framework of regularization theory thoroughly for solving the severely ill-posed problems. Many ill-posed examples are provided.
[367]
vixra:1605.0146 [
pdf]
Intuitionistic Fuzzy Hypermodules
The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using this new idea, the concept of interval-valued (α, β) - intuitionistic fuzzy sub - hypermodule of a hypermodule is defined. This newly defined interval-valued (α, β) - intuitionistic fuzzy sub - hypermodule is a generalization of the usual intuitionistic fuzzy sub - hypermodule.
[368]
vixra:1605.0145 [
pdf]
Solving Coupled Hirota System by Using Reduced Differential Transform Method
In this paper, Reduced Differential TransformMethod (RDTM) has been successively used to find the numerical solutions of the coupled Hirota system (CHS). The results obtained by RDTM are compared with exact solutions to reveal that the RDTM is very accurate and effective. In our work, Maple 13 has been used for computations.
[369]
vixra:1604.0080 [
pdf]
On Neutrosophic Refined Sets and Their Applications in Medical Diagnosis
In this paper, we present some definitions of neutrosophic re¯ned sets such as; union, intersection, convex and strongly convex in a new way to handle the indeterminate information and inconsistent information. Also we have examined some desired properties of neutrosophic refined sets based on these definitions. Then, we give distance measures of neutrosophic refined sets with properties. Finally, an application of neutrosophic re¯ned set is given in medical diagnosis problem (heart disease diagnosis problem) to illustrate the advantage of the proposed approach.
[370]
vixra:1604.0079 [
pdf]
Neutrosophic Cubic Sets
The aim of this paper is to extend the concept of cubic sets to the neutrosophic sets. The notions of truth-internal (indeterminacy-internal, falsity-internal) neutrosophic cu- bic sets and truth-external (indeterminacy-external, falsity-external) neutrosophic cubic sets are introduced, and related properties are investigated.
[371]
vixra:1604.0048 [
pdf]
Soft Neutrosophic Semigroup and Their Generalization
Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly dened objects. In this paper we introduced soft neutrosophic semigroup,soft neutosophic bisemigroup, soft neutrosophic N-semigroup with the discuissionf of some of their characteristics.
[372]
vixra:1603.0178 [
pdf]
He's Variational Iteration Method for the Solution of Nonlinear Newell-Whitehead-Segel Equation
In this paper, we apply He's Variational iteration method (VIM) for solving nonlinear Newell-Whitehead-Segel equation. By using this method three dierent cases of Newell-Whitehead-Segel equation have been discussed. Comparison of the obtained result with exact solutions shows that the method used is an eective and highly promising method for solving dierent cases of nonlinear Newell-Whitehead-Segel equation.
[373]
vixra:1602.0334 [
pdf]
The P Versus NP Problem. Refutation.
In the article we provides an response to the problem of equality of P and NP classes, which is also called the Millennium problem. As a result, given the complete result of equality. For theory of refutation we use method of "reductio ad absurdum". We use tensor analysis which for define objects, such considered relatively to the Turing machine computation. The goal was to give an answer to a proble that has affected to degree of the proof calculation's details. The result can be obtained relative to the current problems of equality P and NP classes, but other than that give an opportunity to explore the computational process more.
[374]
vixra:1601.0354 [
pdf]
Numerical Solution for Solving fuzzy Fredholm Integro-Differential Equations by Euler Method
Numerical algorithms for solving Fuzzy Integro-Differential Equations (FIDEs) are considered. A scheme based on the classical Euler method is discussed in detail and this is followed by a complete error analysis. The algorithm is illustrated by solving linear first-order fuzzy integro-differential equations.
[375]
vixra:1601.0351 [
pdf]
Unsteady Non-Darciancouette ow in Porous Medium with Heat Transfer Subject to Uniform Suction or Injection
The unsteady non-DarcianCouette ow through a porous medium of a viscous incompressible uid bounded by two parallel porous plates is studied with heat transfer. A non-Darcy model that obeys the Forchheimer extension is assumed for the characteristics of the porous medium. A uniform suction and injection are applied perpendicular to the plates while the uid motion is subjected to a constant pressure gradient. The two plates are kept at dierent but constant temperatures while the viscous dissipation is included in the energy equation. The eects of the porosity of the medium, inertial eects and the uniform suction and injection velocity on both the velocity and temperature distributions are investigated.
[376]
vixra:1601.0350 [
pdf]
Quasi-Interpolation Method for Numerical Solution of Volterra Integral Equations
In this article, a numerical method based on quasi-interpolation method is used for the numerical solution of the linear Volterra integral equations of the second kind. Also, we approximate the solution of Volterra integral equations by Nystrom's method. Some examples are given and the errors are obtained for the sake of comparison.
[377]
vixra:1601.0349 [
pdf]
A Fixed-Size Fragment Approach to Graph Mining
Many practical computing problems concern large graphs. Some examples include the Web graphs, various social networks and molecular datasets. The scale of these graphs introduces challenges to their ecient processing. One of the main issues in such problems is that most of the mentioned datasets cannot be t in the memory. In this paper, we present a new data fragment framework for graph mining. The original dataset is divided into a xed number of fragments, associated with the number of the graphs in each dataset. Then each fragment is mined individually using a well-known graph mining algorithm (i.e. FSG or gSpan) and the results are combined to generate global results. A major problem in fragmenting graphs is concerning on similarity or dissimilarity of them. Another problem corresponds to the completeness of the output which will be discussed in this paper.
[378]
vixra:1601.0348 [
pdf]
Laplace Decomposition and Semigroup Decomposition Methods to Solve Glycolysis System in One Dimension
In this article, we formulate two methods to get approximate solution of Glycolysis system. The first is Laplace decomposition methods (is a method combined Lplace transform and Adomian polynomial) and the second is semigroup decomposition method (is a method combined semigroup approach and Adomian polynomial), In both methods the nonlinear terms in Glycolysis system treated with help Adomian polynomial. One example are presented to illustrate the efficiency of the methods, this is done by writing a computer programs with the aid of Maple 13.
[379]
vixra:1601.0347 [
pdf]
Numerical Solutions of the Time Fractional Diffusion Equations by Using Quarter-Sweep Sor Iterative Method
The main objective of this paper is to describe the formulation of Quarter-Sweep Successive Over-Relaxation (QSSOR) iterative method using the Caputos time fractional derivative together with Quarter-Sweep implicit nite dierence approximation equation for solving one-dimensional linear time-fractional diusion equations. To solve the problems, a linear system will be constructed via discretization of the one-dimensional linear time fractional diusion equations by using the Caputos time fractional derivative. Then the generated linear system has been solved by using the proposed QSSOR iterative method. Computational results are provided to demonstrate the eectiveness of the proposed methods as compared with the FSSOR and HSSOR methods.
[380]
vixra:1601.0345 [
pdf]
B-Spline Collocation Method for Numerical Solution of the Nonlinear Two-Point Boundary Value Problems with Applications to Chemical Reactor Theory
In this article, the cubic B-spline collocation method is implemented to nd numerical solution of the problem arising from chemical reactor theory. The method is tested on some model problems from the literature, and the numerical results are compared with other methods.
[381]
vixra:1601.0344 [
pdf]
Application of Complex Analysis on Solving Some Definite Integrals
This paper studies two types of denite integrals and uses Maple for verication. The closed forms of the two types of denite integrals can be obtained mainly using Cauchy integral theorem and Cauchy integral formula. In addition, some examples are used to demonstrate the calculations.
[382]
vixra:1601.0342 [
pdf]
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
The standard harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in which the conservative force is additionally expanded as a Fourier sine series in space. As a result, the steady-state oscillation frequency can be expressed in terms of a Bessel series, and the sums of many such series are known or can be developed. The method is illustrated for five different physical situations, including a ball rolling inside a V-shaped ramp, an electron attracted to a charged filament, a large-amplitude pendulum, and a During oscillator. As an example of the results, the predicted period of a simple pendulum swinging between -90° and +90° is found to be only 0.4% larger than the exact value. Even better, the predicted frequency for the V-ramp case turns out to be exact.
[383]
vixra:1601.0341 [
pdf]
Comparison of Two Finite Difference Methods for Solving the Damped Wave Equation
In this work we present two finite-difference schemes for solving this equation with one initial and boundary conditions. We study stability and consistency of these methods. Two methods are explicit and they approximates the solutions of the wave equation with consistency of order O, for examining the accuracy of the results , we compare the results with the solution obtained by the methods of separation of variable, also a numerical example for each methods is presented and compared with each other. Finally, the graphs of the error have been plotted to show the methods work with high accuracy.
[384]
vixra:1601.0340 [
pdf]
A Reconstruction Method for the Gradient of a Function in Two-Dimensional Space
Numerical differentiation is a classical ill-posed problem. In image processing, sometimes we have to compute the gradient of an image. This involves a problem of numerical differentiation. In this paper we present a truncation method to compute the gradient of a two-variables function which can be considered as an image. A H¨older-type stability estimate is obtained. Numerical examples show that the proposed method is effective and stable.
[385]
vixra:1601.0339 [
pdf]
An O(h^10) Methods For Numerical Solutions Of Some Differential Equations Occurring In Plate Deflection Theory
A tenth-order non-polynomial spline method for the solutions of two-point boundary value problem u(4)(x) + f(x; u(x)) = 0; u(a) = 1; u00(a) = 2; u(b) = 3; u00(b) = 4; is constructed. Numerical method of tenth-order with end conditions of the order 10 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications of method, and to compare the computed results with other known methods.
[386]
vixra:1601.0338 [
pdf]
Trapezoidal Method for Solving the First Order Stiff Systems on a Piecewise Uniform Mesh
In this paper, we introduce a method based on the modification of the Trapezoidal Method with a Piecewise Uniform Mesh proposed in Sumithra and Tamilselvan [1] for a numerical solution of stiff Ordinary Differential Equations (ODEs) of the first order system. Using this modification, the stiff ODEs were successfully solved and it resulted in good solutions.
[387]
vixra:1601.0337 [
pdf]
A New Method for Solving Fuzzy Linear Fractional Programs with Triangular Fuzzy Numbers
Several methods currently exist for solving fuzzy linear and non-linear programming problems. In this paper an efficient method for FLFP has been proposed, in order to obtain the fuzzy optimal solution. This proposed method based on crisp linear programming and has a simple structure. It is easy to apply the proposed method compare to exiting method for solving FLFP problems in real life situations. To show the efficiency of our proposed method a numerical example has been illustrated with a practical problem.
[388]
vixra:1601.0324 [
pdf]
Numerical Solution for Hybrid Fuzzy System by Adams Fourth Order Predictor-Corrector Method
In this paper three numerical methods to solve for hybrid fuzzy differential equations are discussed. These methods are Adams-Bashforth, Adams-Moulton and Predictor-Correctormethod is obtained by combining Adams-Bashforth and Adams-Moulton methods. Convergence and stability of the proposed methods are also proved in detail. In addition, these methods are illustrated by solving two Cauchy problems.
[389]
vixra:1601.0302 [
pdf]
A Mathematical Approach to Simple Bulls and Cows
This document describes the game of Bulls and Cows and the research previously done on it. We then proceed to discuss our simplified algorithm which can be used practically by humans during course of play. An extended version of the algorithm, which leverages computational power to guess the code quickly and more efficiently, has also been explored. Lastly, extensive human trials have been conducted to study the effectiveness of the algorithm, and it has been shown that the algorithm results in a marked decrease in the average number of guesses in which a code is guessed by the code-breaker.
[390]
vixra:1512.0211 [
pdf]
Human Integration of Motion and Texture Information in Visual Slant Estimation
The present research is aimed to: (i) characterize the ability of human visual system to define the objects’ slant on the base of combination of visual stimulus characteristics, that in general are uncertain and even conflicting. (ii) evaluate the influence of human age on visual cues assessment and processing; (iii) estimate the process of human visual cue integration based on the well known Normalized Conjunctive Consensus and Averaging fusion rules, as well on the base of more efficient probabilistic Proportional Conflict Redistribution rule no.5 defined within Dezert-Smarandache Theory for plausible and paradoxical reasoning.
[391]
vixra:1512.0204 [
pdf]
Intelligent Alarm Classification Based on DSmT
In this paper the critical issue of alarms’ classification and prioritization (in terms of degree of danger) is considered and realized on the base of Proportional Conflict Redistribution rule no.5, defined in Dezert-Smarandache Theory of plausible and paradoxical reasoning. The results obtained show the strong ability of this rule to take care in a coherent and stable way for the evolution of all possible degrees of danger, relating to a set of a priori defined, out of the ordinary dangerous directions.
[392]
vixra:1512.0186 [
pdf]
Multiple Camera Fusion Based on DSmT for Tracking Objects on Ground Plane
This paper presents comparative results of a model for multiple camera fusion, which is based on Dezert-Smarandache theory of evidence. Our architecture works at the decision level to track objects on a ground plane using predefined zones, producing useful information for surveillance tasks such as behavior recognition. Decisions from cameras are generated by applying a perspective-based basic belief assignment function, which represent uncertainty derived from cameras perspective while tracking objects on ground plane.
[393]
vixra:1512.0167 [
pdf]
P-Union and P-Intersection of Neutrosophic Cubic Sets
Conditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truth- external) neutrosophic cubic set are provided.
[394]
vixra:1512.0157 [
pdf]
Rough sets in Neutrosophic Approximation Space
A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we introduce the concepts of neutrosophic rough Sets and investigate some of its properties. Further as the characterisation of neutrosophic rough approxi- mation operators, we introduce various notions of cut sets of neutrosophic rough sets.
[395]
vixra:1512.0153 [
pdf]
Simulating Human Decision Making for Testing Soft and Hard/Soft Fusion Algorithms
Current methods for evaluating the effects of human opinions in data fusion systems are often dependent on human testing (which is logistically hard and difficult to arrange for repeated tests of the same population).
[396]
vixra:1512.0147 [
pdf]
Smarandache-Lattice and Algorithms
In this paper we introduced algorithms for constructing Smarandache-lattice from the Boolean algebra through Atomic lattice, weakly atomic modular lattice, Normal ideals, Minimal subspaces, Structural matrix algebra, Residuated lattice. We also obtained algorithms for Smarandache-lattice from the Boolean algebra.
[397]
vixra:1512.0136 [
pdf]
The Improvement of DS Evidence Theory and its Application in IR/MMW Target Recognition
ATR system has a broad application prospect in military, especially in the field of modern defense technology. When paradoxes are existence in ATR system due to adverse battlefield environment, integration cannot be effectively and reliably carried out only by traditional DS evidence theory.
[398]
vixra:1512.0103 [
pdf]
DSmT Based Scheduling Algorithm in Opportunistic Beamforming Systems
A novel approach based on Dezert-Smarandache Theory (DSmT) is proposed for scheduling in opportunistic beamforming (OBF) systems. By jointly optimizing among system throughput, fairness and time delay of each user, the proposed algorithm can achieve larger system throughput and lower average time delay with approximately the same fairness and acceptable complexity, as compared with the proportional fair scheduler PFS).
[399]
vixra:1512.0049 [
pdf]
Applying Extensions of Evidence Theory to Detect Frauds in Nancial Infrastructures
The Dempster-Shafer (DS) theory of evidence has signicant weaknesses when dealing with confflicting information sources, as demonstrated by preeminent mathematicians. This problem may invalidate its eectiveness when it is used to implement decision making tools that monitor a great number of parameters and metrics.
[400]
vixra:1512.0036 [
pdf]
Cautious OWA and Evidential Reasoning for Decision Making under Uncertainty
To make a decision under certainty, multicriteria decision methods aims to choose, rank or sort alternatives on the basis of quantitative or qualitative criteria and preferences expressed by the decision-makers. However, decision is often done under uncertainty: choosing alternatives can have different consequences depending on the external context (or state of the word). In this paper, a new methodology called Cautious Ordered Weighted Averaging with Evidential Reasoning (COWA-ER) is proposed for decision making under uncertainty to take into account imperfect evaluations of the alternatives and unknown beliefs about groups of the possible states of the world (scenarii). COWA-ER mixes cautiously the principle of Yager’s Ordered Weighted Averaging (OWA) approach with the efficient fusion of belief functions proposed in Dezert-Smarandache Theory DSmT).
[401]
vixra:1512.0035 [
pdf]
Change Detection by New DSmT Decision Rule and Icm with Constraints :Application to Argan Land Cover
The objective of this work is, in the first place, the integration in a fusion process using hybrid DSmT model, both, the contextual information obtained from a supervised ICM classification with constraints and the temporal information with the use of two images taken at two different dates. Secondly, we have proposed a new decision rule based on the DSmP transformation to overcome the inherent limitations of the decision rules thus use the maximum of generalized belief functions.The approach is evaluated on two LANDSAT ETM+ images, the results are promising.
[402]
vixra:1512.0033 [
pdf]
Change Detection in Heterogeneous Remote Sensing Images Based on Multidimensional Evidential Reasoning
We present a multidimensional evidential reasoning (MDER) approach to estimate change detection from the fusion of heterogeneous remote sensing images. MDER is based on a multidimensional (M-D) frame of discernment composed by the Cartesian product of the separate frames of discernment used for the classification of each image.
[403]
vixra:1512.0032 [
pdf]
Characterizations of Normal Parameter Reductions of Soft Sets
In 2014, Wang et. al gave the reduct denition for fuzzy information system. We observe that the reduct denition given by Wang et. al does not retain the optimal choice of objects. In this paper, we give the drawbacks of the reduct denition of Wang et. al and give some characterizations of normal parameter reduction of soft sets. Also, we prove that the image and inverse image of a normal parameter reduction is a normal parameter reduction under consistency map.
[404]
vixra:1512.0029 [
pdf]
Comparing Performance of Interval Neutrosophic Sets and Neural Networks with Support Vector Machines for Binary Classification Problems
In this paper, the classification results obtained from several kinds of support vector machines (SVM) and neural networks (NN) are compared with our proposed classifier. Our approach is based on neural networks and interval neutrosophic sets which are used to classify the input patterns into one of the two binary class outputs.
[405]
vixra:1510.0316 [
pdf]
A Note on Q-Analogue of SANDOR’S Functions
The additive analogues of Pseudo-Smarandache, Smarandache-simple functions and their duals have been recently studied by J. S´andor. In this note, we obtain q-analogues of S´andor’s theorems.
[406]
vixra:1510.0315 [
pdf]
A Pair Of Smarandachely Isotopic Quasigroups And Loops Of The Same Variety
The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past.
[407]
vixra:1510.0312 [
pdf]
Comparative Review of Some Properties of Fuzzy and Anti Fuzzy Subgroups
This paper is to comparatively review some works in fuzzy and anti fuzzy group theory. The aim is to provide anti fuzzy versions of some existing theorems in fuzzy group theory and see how much similar they are to their fuzzy versions. The research therefore focuses on the properties of fuzzy subgroup, fuzzy cosets, fuzzy conjugacy and fuzzy normal subgroups of a group which are mimicked in anti fuzzy group theory.
[408]
vixra:1510.0309 [
pdf]
Contributii in Dezvoltarea Sistemelor de Control Neuronal al Miscarii Robotilor Mobili Autonomi
Robotica reprezinta in prezent unul din cele mai mari realizari ale omenirii si este cea mai mare incercare de a produce o inta articiala capabila sa simta si sa transmita emotii, producatorii de roboti realizand in ultimii ani modele de serie extrem de complexe disponibile pentru publicul larg.
[409]
vixra:1510.0302 [
pdf]
Fuzzy Crossed Product Algebras
We introduce fuzzy groupoid graded rings and, as a particular case, fuzzy crossed product algebras. We show that there is a bijection between the set of fuzzy graded isomorphism equivalence classes of fuzzy crossed product algebras and the associated second cohomology group.
[410]
vixra:1510.0278 [
pdf]
Smarandache Curves of Some Special Curves in the Galilean 3-Space
In the present paper, we consider a position vector of an arbitrary curve in the three-dimensional Galilean space G3. Furthermore, we give some conditions on the curvatures of this arbitrary curve to study special curves and their Smarandache curves. Finally, in the light of this study, some related examples of these curves are provided and plotted.
[411]
vixra:1510.0275 [
pdf]
Smarandache Isotopy Theory Of Smarandache: Quasigroups And Loops
The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops. The exploration includes: Smarandache; isotopy and isomorphy classes, Smarandache f, g principal isotopes and G-Smarandache loops.
[412]
vixra:1510.0272 [
pdf]
Smarandache Multi-¸ Space Theory(III)
A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics
[413]
vixra:1510.0271 [
pdf]
Smarandache Multi-¸ Space Theory(IV)
A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics.
[414]
vixra:1510.0266 [
pdf]
Special Smarandache Curves According To Darboux Frame In E3
In this study, we determine some special Smarandache curves according to Darboux frame in E3 . We give some characterizations and consequences of Smarandache curves.
[415]
vixra:1510.0260 [
pdf]
A Two-Step Fusion Process for Multi-Criteria Decision Applied to Natural Hazards in Mountains
Mountain river torrents and snow avalanches generate human and material damages with dramatic consequences. Knowledge about natural phenomenona is often lacking and expertise is required for decision and risk management purposes using multi-disciplinary quantitative or qualitative approaches. Expertise is considered as a decision process based on imperfect information coming from more or less reliable and conflicting sources.
[416]
vixra:1510.0247 [
pdf]
Human Experts Fusion for Image Classification
In image classification, merging the opinion of several human experts is very important for different tasks such as the evaluation or the training. Indeed, the ground truth is rarely known before the scene imaging.
[417]
vixra:1510.0244 [
pdf]
Inductive Classification Through Evidence-Based Models and Their Ensembles
In the context of Semantic Web, one of the most important issues related to the class-membership prediction task (through inductive models) on ontological knowledge bases concerns the imbalance of the training examples distribution, mostly due to the heterogeneous nature and the incompleteness of the knowledge bases.
[418]
vixra:1510.0241 [
pdf]
New Ahp Methods for Handling Uncertainty Within the Belief Function Theory
As society becomes more complex, people are faced with many situations in which they have to make a decision among different alternatives. However, the most preferable one is not always easily selected.
[419]
vixra:1510.0239 [
pdf]
Order in DSmT; Definition of Continuous DSm Models
When implementing the DSmT, a difficulty may arise from the possible huge dimension of hyperpower sets, which are indeed free structures.However, it is possible to reduce the dimension of these structures by involving logical constraints.
[420]
vixra:1510.0238 [
pdf]
Probabilistische Fahrzeugumfeldschätzung Für Fahrerassistenzsysteme
Viele aktuelle Fahrerassistenzsysteme wie beispielsweise die adaptive Geschwindigkeitsregelung, purwechselassistenten und Systeme zur Anhaltewegverkürzung sind auf eine verlässliche Detektion anderer Verkehrsteilnehmer und Hindernisse angewiesen. Zukünftige Assistenzsysteme wie beispielsweise Systeme für das Automatische Fahren erhöhen diese Zuverlässigkeitsanforderung weiter.
[421]
vixra:1510.0211 [
pdf]
A Study on Symptoms of Stress on College Students Using Combined Disjoint Block Fuzzy Cognitive Maps (CDBFCM)
Going through college is stressful for everybody. Caused by many reasons, the stress is present whether one is in their first year of college or their last. However, most seniors have an easier time dealing with stress because they have experience handling it. Most of the reasons for so much stress fall into one of three categories: academic stress, that is, anything to do with studying for classes, financial stress, which has to do with paying for school, and personal stress, which is stress associated with personal problems in college. College students experience many effects of stress and depression.
[422]
vixra:1510.0207 [
pdf]
Correlated Aggregating Operators for Simplied Neutrosophic Set and their Application in Multi-attribute Group Decision Making
The simplied neutrosophic set (SNS) is a generalization of the fuzzy set that is designed for some incomplete, uncertain and inconsistent situations in which each element has dierent truth membership, indeterminacy membership and falsity membership functions.
[423]
vixra:1510.0196 [
pdf]
Interval Neutrosophic Sets
Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra.
[424]
vixra:1510.0195 [
pdf]
Interval-Valued Neutrosophic Soft Sets and Its Decision Making
In this paper, the notion of the interval valued neutrosophic soft sets (ivn−soft sets) is defined which is a combination of an interval valued neutrosophic sets and a soft sets.
[425]
vixra:1510.0183 [
pdf]
On Some Similarity Measures and Entropy on Quadripartitioned Single Valued Neutrosophic Sets
A notion of Quadripartitioned Single Valued Neutrosophic Sets (QSVNS) is introduced and a theoretical study on various set-theoretic operations on them has been carried out.
[426]
vixra:1510.0169 [
pdf]
A Double Cryptography Using The Smarandache Keedwell Cross Inverse Quasigroup
The present study further strengthens the use of the Keedwell CIPQ against attack on a system by the use of the Smarandache Keedwell CIPQ for cryptography in a similar spirit in which the cross inverse property has been used by Keedwell. This is done as follows.
[427]
vixra:1510.0166 [
pdf]
A New View of Co¸mbinatorial Maps by Smaranda¸che’s Notion
On a geometrical view, the conception of map geometries is introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surfaces. Some open problems related combinatorial maps with the Riemann geometry and Smarandache geometries are presented.
[428]
vixra:1510.0165 [
pdf]
An Holomorphic Study Of Smarandache Automorphic and Cross Inverse Property Loops
By studying the holomorphic structure of automorphic inverse property quasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop if and only if its Smarandache automorphism group is trivial and the loop is itself is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop.
[429]
vixra:1510.0164 [
pdf]
An Holomorphic Study of the Smarandache Concept in Loops
If two loops are isomorphic, then it is shown that their holomorphs are also isomorphic. Conversely, it is shown that if their holomorphs are isomorphic, then the loops are isotopic. It is shown that a loop is a Smarandache loop if and only if its holomorph is a Smarandache loop.
[430]
vixra:1509.0025 [
pdf]
An Application According to Spatial Quaternionic Smarandache Curve
In this paper, we found the Darboux vector of the spatial quaternionic curve according to the Frenet frame. Then, the curvature and torsion of the spatial quaternionic smarandache curve formed by the unit Darboux vector with the normal vector was calculated. Finally; these values are expressed depending upon the spatial quaternionic curve.
[431]
vixra:1509.0019 [
pdf]
Extended Banach G Flow Spaces on Differential Equations with Applications
The main purpose of this paper is to extend Banach spaces on topological graphs with operator actions and show all of these extensions are also Banach space with a bijection with a bijection between linear continuous functionals and elements, which enables one to solve linear functional equations in such extended space, particularly, solve algebraic, differential or integral equations on a topological graph, find multi-space solutions on equations, for instance, the Einstein’s gravitational equations.
[432]
vixra:1509.0014 [
pdf]
Parameters for Minimal Unsatisfiability: Smarandache Primitive Numbers and Full Clauses
We establish a new bridge between propositional logic and elementary number theory. A full clause contains all variables, and we study them in minimally unsatisfiable clause-sets (MU); such clauses are strong structural anchors, when combined with other restrictions.
[433]
vixra:1508.0427 [
pdf]
Surfaces Family With Common Smarandache Asymptotic Curve According To Bishop Frame In Euclidean Space
In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Bishop frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache asymptotic curve.
[434]
vixra:1508.0425 [
pdf]
Fusing Uncertain Knowledge and Evidence for Maritime Situational Awareness Via Markov Logic Networks
The concepts of event and anomaly are important building blocks for developing a situational picture of the observed environment. We here relate these concepts to the JDL fusion model and demonstrate the power of Markov Logic Networks (MLNs) for encoding uncertain knowledge and compute inferences according to observed evidence.
[435]
vixra:1508.0422 [
pdf]
Grid Occupancy Estimation for Environment Perception Based on Belief Functions and PCR6
In this contribution, we propose to improve the grid map occupancy estimation method developed so far based on belief function modeling and the classical Dempster’s rule of combination. Grid map offers a useful representation of the perceived world for mobile robotics navigation.
[436]
vixra:1508.0421 [
pdf]
Performance Evaluation of Fuzzy-Based Fusion Rules for Tracking Applications
Abstract: The objective of this paper is to present and to evaluate the performance of particular fusion rules based on fuzzy T-Conorm/T-Norm operators for two tracking applications: (1) Tracking object's type changes, supporting the process of objects' identication (e.g. ghter against cargo, friendly aircraft against hostile ones), which, consequently is essential for improving the quality of generalized data association for targets' tracking; (2) Alarms identication and prioritization in terms of degree of danger relating to a set of a priori dened, out of the ordinary dangerous directions.
[437]
vixra:1508.0420 [
pdf]
Dual-Complex Numbers and Their Holomorphic Functions
The purpose of this paper is to contribute to development a general theory of dual-complex numbers. We start by de…ne the notion of dual- complex and their algebraic properties. In addition, we develop a simple mathematical method based on matrices, simplifying manipulation of dual-complex numbers. Inspired from complex analysis, we generalize the concept of holo- morphicity to dual-complex functions. Moreover, a general representation of holomorphic dual-complex functions has been obtained. Finally and as concrete examples, some usual complex functions have been generalized to the algebra of dual-complex numbers.
[438]
vixra:1508.0408 [
pdf]
Correlation Measure for Neutrosophic Re¯ned Sets and Its Application in Medical Diagnosis
In this paper, the correlation measure of neutrosophic refined(multi-) sets is proposed. The concept of this correlation measure of neutrosophic refined sets is the extension of correlation measure of neutrosophic sets and intuitionistic fuzzy multi sets. Finally, using the correlation of neutrosophic refined set measure, the application of medical diagnosis and pattern recognition are presented.
[439]
vixra:1508.0399 [
pdf]
Some Weighted Geometric Operators with SVTrN-Numbers and Their Application to Multi-Criteria Decision Making Problems
The single valued triangular neutrosophic number (SVTrN-number) is simply an ordinary number whose precise value is somewhat uncertain from a philosophical point of view, which is a generalization of triangular fuzzy numbers and triangular intuitionistic fuzzy numbers.
[440]
vixra:1508.0389 [
pdf]
Comparative Study of Intuitionistic and Generalized Neutrosophic Soft Sets
The aim of this paper is to define several operations such as Intersection, Union, OR, AND operations of intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Maji and compare these with intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Said et al via examples.
[441]
vixra:1508.0388 [
pdf]
Correlation Measure for Neutrosophic Refined Sets and Its Application in Medical Diagnosis
In this paper, the correlation measure of neutrosophic refined(multi-) sets is proposed. The concept of this correlation measure of neutrosophic refined sets is the extension of correlation measure of neutrosophic sets and intuitionistic fuzzy multi-sets. Finally, using the correlation of neutrosophic refined set measure, the application of medical diagnosis and pattern recognition are presented.
[442]
vixra:1508.0360 [
pdf]
Introduction to Neutrosophic Nearrings
The objective of this paper is to introduce the concept of neutrosophic near-rings. The concept of neutrosophic N-group of a neutrosophic nearring is introduced. We studied neutrosophic subnearrings of neutrosophic nearrings and also neutrosophic N-subgroups of neutrosophic N- groups.
[443]
vixra:1508.0358 [
pdf]
On Single Valued Neutrosophic Relations
Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al.
[444]
vixra:1508.0351 [
pdf]
Simplified Neutrosophic Linguistic Normalized Weighted Bonferroni Mean Operator and Its Application to Multi-Criteria Decision-Making Problems
The main purpose of this paper is to provide a method of multi-criteria decision-making that combines simplified neutrosophic linguistic sets and normalized Bonferroni mean operator to address the situations where the criterion values take the form of simplified neutrosophic linguistic numbers and the criterion weights are known.
[445]
vixra:1508.0330 [
pdf]
Smarandache Curves and Spherical Indicatrices in the Galilean 3-Space
In the present paper, Smarandache curves for some special curves in the threedimensional Galilean space G3are investigated. Moreover, spherical indicatrices for the helix as well as circular helix are introduced. Furthermore, some properties for these curves are given. Finally, in the light of this study, some related examples of these curves are provided.
[446]
vixra:1508.0329 [
pdf]
Spinor Darboux Equations of Curves in Euclidean 3-Space
In this paper, the spinor formulation of Darboux frame on an oriented surface is given. Also, the relation between spinor formulation of Frenet frame and Darboux frame is obtained.
[447]
vixra:1508.0328 [
pdf]
Smarandache Curves In Terms of Sabban Frame of Fixed Pole Curve
In this paper, we study the special Smarandache curve in terms of Sabban frame of Fixed Pole curve and we give some characterization of Smarandache curves. Besides, we illustrate examples of our results.
[448]
vixra:1508.0313 [
pdf]
DSmH Evidential Network for Target Identication
This paper proposes a model of evidential network based on Hybrid Dezert-Smarandache theory (DSmH) to improve target identication of multi-sensors. In the classication simulation, we compared the results obtained at the Target Type node and Foe-Ally node in evidential network by using Dempster-Shafer theory (DS) and using DSmH. The comparisons show that, when we use DSmH in the evidential network, we can assign more Basic Belief Assignments (BBA) to the focal element the target belongs to. Experiments conrm that the model of evidential network using DSmH is better than the one using DS.
[449]
vixra:1508.0258 [
pdf]
Critical Review
In this paper we initiated the concept of neutrosophic codes which are better codes than other type of codes. We first construct linear neutrosophic codes and gave illustrative examples. This neutrosophic algebriac structure is more rich for codes and also we found the containement of corresponding code in neutrosophic code. We also found new types of codes and these are pseudo neutrosophic codes and strong or pure neutrosophic codes. By the help of examples, we illustrated in a simple way. We established the basic results for neutosophic codes. At the end, we developed the decoding proceedures for neutrosophic codes.
[450]
vixra:1508.0252 [
pdf]
Fuzzy Abel Grassmann Groupoids, Second Updated and Enlarged Version
Usually the models of real world problems in almost all disciplines like engineering, medical sciences, mathematics, physics, computer science, management sciences, operations research and arti…cial intelligence are mostly full of complexities and consist of several types of uncertainties while dealing them in several occasion.
[451]
vixra:1508.0238 [
pdf]
Neutrosophic Code
The idea of neutrosophic code came into my mind at that time when i was reading the literature about linear codes and i saw that, if there is data transfremation between a sender and a reciever. They want to send 11and 00 as codewords. They suppose 11 for true and 00 for false. When the sender sends the these two codewords and the error occures. As a result the reciever recieved 01 or 10 instead of 11 and 00. This story give a way to the neutrosophic codes and thus we introduced neutrosophic codes over finite field in this paper
[452]
vixra:1507.0058 [
pdf]
An Algorithm for Producing Benjamin Franklin's Magic Squares
An algorithm is presented that produces, in six steps, Benjamin Franklin's best known magic squares, one 8 x 8, and one 16 x 16. This same algorithm is then used to produce three related magic squares, dimensioned 4 x 4, 32 x 32, and 64 x 64.
[453]
vixra:1506.0213 [
pdf]
The Psychology of The Two Envelope Problem
This article concerns the psychology of the paradoxical Two Envelope Problem. The goal is to find instructive variants of the envelope switching problem that are capable of clear-cut resolution, while still retaining paradoxical features. By relocating the original problem into different contexts involving commutes and playing cards the reader is presented with a succession of resolved paradoxes that reduce the confusion arising from the parent paradox. The goal is to reduce confusion by understanding how we sometimes misread mathematical statements; or, to completely avoid confusion, either by reforming language, or adopting an unambiguous notation for switching problems. This article also suggests that an illusion close in character to the figure/ground illusion hampers our understanding of switching problems in general and helps account for the intense confusion that switching problems sometimes generate.
[454]
vixra:1506.0114 [
pdf]
Games People Play: an Overview of Strategic Decision-Making Theory in Conflict Situations
In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and nonzero-sum games. Several elements of cooperaive gaming, coalitions, voting ensembles, voting power and collective efficiency are described in brief. Analytical (matrix) and extended (tree-graph) forms of game representation is illustrated as the basic tools for identifying optimal strategies and “solutions” in games of any kind. Next, a typology of four standard nonzero-sum games is investigated, analyzing the Nash equilibria and the optimal strategies in each case. Signaling, stance and third-party intermediates are described as very important properties when analyzing strategic moves, while credibility and reputation is described as crucial factors when signaling promises or threats. Utility is introduced as a generalization of typical cost/gain functions and it is used to explain the incentives of irrational players under the scope of “rational irrationality”. Finally, a brief reference is presented for several other more advanced concepts of gaming, including emergence of cooperation, evolutionary stable strategies, two-level games, metagames, hypergames and the Harsanyi transformation.
[455]
vixra:1502.0122 [
pdf]
Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 1 Gossamer Numbers
The discovery of what we call the gossamer number system ∗G, as an extension of the real numbers includes an infinitesimal and infinitary number system; by using ‘infinite integers’, an isomorphic construction to the reals by solving algebraic equations is given. We believe this is a total ordered field. This could be an equivalent construction of the hyperreals. The continuum is partitioned: 0 < Φ+ < R+ + Φ < +Φ−1 < ∞.
[456]
vixra:1502.0121 [
pdf]
Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 2 the Much Greater Than Relations
An infinitesimal and infinitary number system the Gossamer numbers is fitted to du Bois-Reymond’s infinitary calculus, redefining the magnitude relations. We connect the past symbol relations much-less-than and much-less-than or equal to with the present little-o and big-O notation, which have identical definitions. As these definitions are extended, hence we also extend little-o and big-O, which are defined in Gossamer numbers. Notation for an reformed infinitary calculus, calculation at a point is developed. We proceed with the introduction of an extended infinitary calculus.
[457]
vixra:1502.0120 [
pdf]
Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 3 Comparing Functions
An algebra for comparing functions at infinity with infinireals, comprising of infinitesimals and infinities, is developed: where the unknown relation is solved for. Generally, we consider positive monotonic functions f and g, arbitrarily small or large, with relation z: f z g. In general we require f, g, f − g and f/g to be ultimately monotonic.
[458]
vixra:1502.0119 [
pdf]
Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 4 the Transfer Principle
Between gossamer numbers and the reals, an extended transfer principle founded on approximation is described, with transference between different number systems in both directions, and within the number systems themselves. As a great variety of transfers are possible, hence a mapping notation is given. In ∗G we find equivalence with a limit with division and comparison to a transfer ∗G → R with comparison.
[459]
vixra:1502.0118 [
pdf]
Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 5 Non-Reversible Arithmetic and Limits
Investigate and define non-reversible arithmetic in ∗G and the real numbers. That approximation of an argument of magnitude, is arithmetic. For non-reversible multiplication we define a logarithmic magnitude relation. Apply the much-greater-than relation in the evaluation of limits. Consider L’Hopital’s rule with infinitesimals and infinities, and in a comparison f (z) g form.
[460]
vixra:1502.0117 [
pdf]
Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 6 Sequences and Calculus in ∗G
With the partition of positive integers and positive infinite integers, it follows naturally that sequences are also similarly partitioned, as sequences are indexed on integers. General convergence of a sequence at infinity is investigated. Monotonic sequence testing by comparison. Promotion of a ratio of infinite integers to non-rational numbers is conjectured. Primitive calculus definitions with infinitary calculus, epsilon-delta proof involving arguments of magnitude are considered.
[461]
vixra:1502.0115 [
pdf]
Convergence Sums at Infinity with New Convergence Criteria
Development of sum and integral convergence criteria, leading to a representation of the sum or integral as a point at infinity. Application of du Bois-Reymond’s comparison of functions theory, when it was thought that there were none. Known convergence tests are alternatively stated and some are reformed. Several new convergence tests are developed, including an adaption of L’Hopital’s rule. The most general, the boundary test is stated. Thereby we give an overview of a new field we call ‘Convergence sums’. A convergence sum is essentially a strictly monotonic sum or integral where one of the end points after integrating is deleted resulting in a sum or integral at a point.
[462]
vixra:1502.0112 [
pdf]
Rearrangements of Convergence Sums at Infinity
Convergence sums theory is concerned with monotonic series testing. On face value, this may seem a limitation but, by applying rearrangement theorems at infinity, non-monotonic sequences can be rearranged into monotonic sequences. The resultant monotonic series are convergence sums. The classes of convergence sums are greatly increased by the additional versatility applied to the theory.
[463]
vixra:1502.0111 [
pdf]
Ratio Test and a Generalization with Convergence Sums
For positive series convergence sums we generalize the ratio test in ∗G the gossamer numbers. Via a transfer principle, within the tests we construct variations. However, most significantly we connect and show the generalization to be equivalent to the boundary test. Hence, the boundary test includes the generalized tests: the ratio test, Raabe’s test, Bertrand’s test and others.
[464]
vixra:1502.0110 [
pdf]
The Boundary Test for Positive Series
With convergence sums, a universal comparison test for positive series is developed, which compares a positive monotonic series with an infinity of generalized p-series. The boundary between convergence and divergence is an infinity of generalized p-series. This is a rediscovery and reformation of a 175 year old convergence/divergence test.
[465]
vixra:1501.0223 [
pdf]
Finite and Infinite Basis in P and NP
This article provide new approach to solve P vs NP problem by using cardinality of bases function. About NP-Complete problems, we can divide to infinite disjunction of P-Complete problems. These P-Complete problems are independent of each other in disjunction. That is, NP-Complete problem is in infinite dimension function space that bases are P-Complete. The other hand, any P-Complete problem have at most a finite number of P-Complete basis. The reason is that each P problems have at most finite number of Least fixed point operator. Therefore, we cannot describe NP-Complete problems in P. We can also prove this result from incompleteness of P.
[466]
vixra:1501.0004 [
pdf]
Open Letter on Hilbert's Fifth Problem
Hilbert's Fifth Problem, in English translation, [1], is as follows : ``How far Lie's concept of continuous groups of transformations is approachable in our investigations without the assumption of the differentiability of the functions ?" followed by : ``In how far are the assertions which we can make in the case of differentiable functions true under proper modifications without this assumptions ?" Lately, in the American mathematical literature, due to unclear reasons, it has often been distorted and truncated as follows, [3] : ``Hilbert's fifth problem, like many of Hilbert's problems, does not have a unique interpretation, but one of the most commonly accepted accepted interpretations ..." A recent letter in this regard, sent to Terence Tao, and the editors of [3], Dan Abramovich, Daniel S Freed, Rafe Mazzeo and Gigliola Staffilani can be found below.
[467]
vixra:1412.0029 [
pdf]
Consecutive, Reversed, Mirror, and Symmetric Smarandache Sequences of Triangular Numbers
We use the Maple system to check the investigations of S. S. Gupta regarding the Smarandache consecutive and the reversed Smarandache sequences of triangular numbers [Smarandache Notions Journal, Vol. 14, 2004, pp. 366–368]. Furthermore, we extend previous investigations to the mirror and symmetric Smarandache sequences of triangular numbers.
[468]
vixra:1412.0023 [
pdf]
Menelaus’s Theorem for Hyperbolic Quadrilaterals in The Einstein Relativistic Velocity Model of Hyperbolic Geometry
In this study, we present (i) a proof of the Menelaus theorem for quadrilaterals in hyperbolic geometry, (ii) and a proof for the transversal theorem for triangles, and (iii) the Menelaus*s theorem~for n-gons.
[469]
vixra:1412.0020 [
pdf]
Smarandache Filters in Smarandache Residuated Lattice
In this paper we dene the Smarandache residuated lattice, Smarandache lter, Smarandache implicative lter and Smarandache positive implicative lter, we obtain some related results. Then we determine relationships between Smarandache lters in Smarandache residuated lattices.
[470]
vixra:1411.0513 [
pdf]
Automatic Aircraft Recognition using DSmT and HMM
In this paper we propose a new method for solving the Automatic Aircraft Recognition (AAR) problem from a sequence of images of an unknown observed aircraft. Our method exploits the knowledge extracted from a training image data set (a set of binary images of different aircrafts observed under three different poses) with the fusion of information of multiple features drawn from the image sequence using Dezert-Smarandache Theory (DSmT) coupled with Hidden Markov Models (HMM).
[471]
vixra:1411.0479 [
pdf]
On Sub-Implicative (; )-Fuzzy Ideals of BCH-Algebras
The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real analysis, measure theory etc.
[472]
vixra:1411.0478 [
pdf]
Surfaces Family With Common Smarandache Asymptotic Curve
In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.
[473]
vixra:1411.0408 [
pdf]
Determinarea Solut, Iilor Ecuat, Iilor Diofantice 2069-2080
Functia care asociaza fiecarui numar natural n pe cel mai mic numar natural m care are proprietatea ca m! este multiplu lui n a fostconsiderata de prima data de Lucas in anul 1883.
[474]
vixra:1411.0402 [
pdf]
An Introduction to the Theory of Algebraic Multi-Hyperring Spaces
A Smarandache multi-space is a union of n dierent spaces equipped with some dierent structures for an integer n 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space and initiate a study of multi-hyperring theory. Some characterizations and properties of multi-hyperring spaces are investigated and obtained. Some open problems are suggested for further study and investigation.
[475]
vixra:1411.0389 [
pdf]
Smarandache Curves According to Curves on a Spacelike Surface in Minkowski 3-Space R31
In this paper, we introduce Smarandache curves according to the Lorentzian Darboux frame of a curve on spacelike surface in Minkowski 3-space R 3 1. Also, we obtain the Sabban frame and the geodesic curvature of the Smarandache curves and give some characterizations on the curves when the curve is an asymptotic curve or a principal curve. And, we give an example to illustrate these curves.
[476]
vixra:1411.0388 [
pdf]
Smarandache Curves According to Bishop Frame in Euclidean 3-Space
In this paper, we investigate special Smarandache curves according to Bishop frame in Euclidean 3-space and we give some differential geometric properties of Smarandache curves. Also we find the centers of the osculating spheres and curvature spheres of Smarandache curves.
[477]
vixra:1411.0387 [
pdf]
Smarandache Curves According to Sabban Frame on S2
In this paper, we introduce special Smarandache curves according to Sabban frame on S2 and we give some characterization of Smarandache curves. Besides, we illustrate examples of our results
[478]
vixra:1411.0384 [
pdf]
Smarandache Lattice and Pseudo Complement
In this paper, we have introduced smarandache - 2 - Algebraic structure of lattice namely smarandache lattice. A smarandache 2- algebraic structure on a set N means a weak algebraic structure Ao on N such that there exists a proper subset M of N which is embedded with a stronger algebraic structure A1. Stronger algebraic structure means a structure which satises more axioms, by proper subset one can understand a subset dierent from the empty set, by the unit element if any, and from the whole set. We have dened smarandache lattice and obtained some of its characterization through Pseudo complemented .For the basic concept, we referred the PadilaRaul [4].
[479]
vixra:1411.0383 [
pdf]
Smarandache N-Structure on ci-Algebras
The Smarandache algebraic structures theory was introduced in 1998 by Padilla [11]. In [6], Kandasamy studied of Smarandache groupoids, sub-groupoids, ideal of groupoids, seminormal sub groupoids, Smarandache Bol groupoids, and strong Bol groupoids and obtained many interesting results about them.
[480]
vixra:1411.0382 [
pdf]
Smarandache R Module and Morita Context
In this paper we introduced Smarandache - 2 - algebraic structure of R-Module namely Smarandache - R - Module. A Smarandache - 2 - algebraic structure on a set N means a weak algebraic structure A0 on N such that there exist a proper subset M of N, which is embedded with a stronger algebraic structure A1, stronger algebraic structure means satisfying more axioms, by proper subset one understands a subset from the empty set, from the unit element if any , from the whole set. We dene Smarandache - R - Module and obtain some of its characterization through S - algebra and Morita context. For basic concept we refer to Raul Padilla.
[481]
vixra:1411.0378 [
pdf]
Some Normal Congruences in Quasigroups Determined by Linear-Bivariate Polynomials Over the Ring ZN
In this work, two normal congruences are built on two quasigroups with underlining set Z2 n relative to the linear-bivariate polynomial P(x; y) = a + bx + cy that generates a quasigroup over the ring Zn. Four quasigroups are built using the normal congruences and these are shown to be homomorphic to the quasigroups with underlining set Z2 n. Some subquasigroups of the quasigroups with underlining set Z2 n are also found.
[482]
vixra:1411.0377 [
pdf]
On Some Smarandache Determinant Sequences
Murthy introduced the concept of the Smarandache Cyclic Determinant Natural Sequence, the Smarandache Cyclic Arithmetic Determinant Sequence, the Smarandache Bisymmetric Determinant Natural Sequence, and the Smarandache Bisymmetric Arithmetic Determinant Sequence and in [2], Majumdar derived the n-th terms of these four sequences. In this paper, we present some of the results found by Majumdar in [2] but of different approach..
[483]
vixra:1411.0376 [
pdf]
Bi-Strong Smarandache BL-Algebras
A Smarandache structure on a set A means a weak structureW on A such that there exists a proper subset B of A which is embedded with a strong structure S.
[484]
vixra:1411.0266 [
pdf]
Eccentricity, Space Bending, Dimension
The main goal of this paper is to present new transformations, previously non-existent in traditional mathematics, that we call centric mathematics (CM) but that became possible due to the new born eccentric mathematics, and, implicitly, to the supermathematics (SM).
[485]
vixra:1411.0257 [
pdf]
A New Proof of Menelaus’s Theorem of Hyperbolic Quadrilaterals in the Poincaré Model of Hyperbolic Geometry
Hyperbolic geometry appeared in the …rst half of the 19th century as an attempt to understand Euclids axiomatic basis of geometry. It is also known as a type of non-euclidean geometry, being in many respects similar to euclidean geometry. Hyperbolic geometry includes similar concepts as distance and angle.
[486]
vixra:1409.0120 [
pdf]
Examples of Solving PDEs by Order Completion
So far, the order completion method for solving PDEs, introduced in 1990, can solve by far the most general linear and nonlinear systems of PDEs, with possible initial and/or boundary data. Examples of solving various PDEs with the order completion method are presented. Some of such PDEs do not have global solutions by any other known methods, or are even proved not to have such global solutions. The presentation next aims to be as summary, and in fact, sketchy as possible, even if by that it may create some difficulty. However, nowadays, being subjected to an ever growing ``information overload", that approach may turn out to be not the worst among two bad alternatives. Details can be found in [1], while on the other hand, alternative longer "short presentations" are in [6-8].
[487]
vixra:1405.0184 [
pdf]
A New Class of LRS Bianchi Type VI0 Universes with Free Gravitational Field and Decaying Vacuum Energy Density
A new class of LRS Bianchi type VI0 cosmological models with free gravitational elds and a variable cosmological term is investigated in presence of perfect uid as well as bulk viscous uid. To get the deterministic solution we have imposed the two dierent conditions over the free gravitational elds. In rst case we consider the free gravitational eld as magnetic type whereas in second case `gravitational wrench' of unit `pitch" is supposed to be present in free gravitational eld. The viscosity coecient of bulk viscous uid is assumed to be a power function of mass density. The eect of bulk viscous uid distribution in the universe is compared with perfect uid model. The cosmological constant is found to be a positive decreasing function of time which is corroborated by results from recent observations. The physical and geometric aspects of the models are discussed.
[488]
vixra:1405.0154 [
pdf]
A Study of Finite Length Thermoelastic Problem of Hollow Cylinder with Radiation
In this paper, in hollow cylinders it is to be noticed that all possible prob- lems on boundary conditions can be solved by particularizing the method described here. A new finite integral transformation an extension of those given by Sneddon [11] whose kernel is given by cylindrical functions, is used to solve the problem of finding the temperature at any point of a hollow cylin- der of any height, with boundary conditions of radiation type on the outside and inside surfaces with independent radiation constants.
[489]
vixra:1405.0151 [
pdf]
Second Order Parallel Tensors on Generalized Sasakian Spaceforms
The object of present paper is to study the symmetric and skew symmetric properties of a second order parallel tensor in a generalized Sasakian space-form.
[490]
vixra:1405.0144 [
pdf]
A Hybrid Iterative Scheme for a General System of Variational Inequalities Based on Mixed Nonlinear Mappings
The purpose of this paper is to study the strong convergence of a hybrid iterative scheme for finding a common element of the set of a general system of variational inequalities for α-inverse- strongly monotone mapping and relaxed (c,d)- cocoercive mapping, the set of solutions of a mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Using the demi-closedness principle for nonexpansive mapping, we prove that the iterative sequence converges strongly to a common element of these three sets under some control conditions. Our results extend recent results announced by many others.
[491]
vixra:1405.0135 [
pdf]
Coprime Factorization of Singular Linear Systems. a Stein Matritial Equation Approach
In this work immersed in the field of control theory on a Given a singular linear dynamic time invariant represented by Ex+(t) = Ax(t)Bu(t), y(t) = Cx(t). We want to classify singular systems such that by means a feedback and an output injection, the transfer ma- trix of the system is a polynomial, for that we analyze conditions for obtention of a coprime factorization of transfer matrices of singular lin- ear systems defined over commutative rings R with element unit. The problem presented is related to the existence of solutions of a Stein matritial equation XE − NXA = Z.
[492]
vixra:1405.0133 [
pdf]
Numerical Solution of Fuzzy Differential Equations Under Generalized Differentiability by Modified Euler Method
In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a nu- merical approximation of solutions. The Modified Euler approximation method is implemented and its error analysis, which guarantees point- wise convergence, is given. The method applicability is illustrated by solving a linear first-order fuzzy differential equation.
[493]
vixra:1404.0400 [
pdf]
Numerical Solution of Time-Dependent Gravitational Schr ¨odinger Equation
In recent years, there are attempts to describe quantization of planetary distance based on time-independent gravitational Schr¨odinger equation, including Rubcic & Rubcic’s method and also Nottale’s Scale Relativity method. Nonetheless, there is no solution yet for time-dependent gravitational Schr ¨odinger equation (TDGSE). In the present paper, a numerical solution of time-dependent gravitational Schrodinger equation is presented, apparently for the first time. This numerical solution leads to gravitational Bohr-radius, as expected. In the subsequent section, we also discuss plausible extension of this gravitational Schr¨odinger equation to include the effect of phion condensate via Gross-Pitaevskii equation, as described recently by Moffat. Alternatively one can consider this condensate from the viewpoint of Bogoliubov de Gennes theory, which can be approximated with coupled time-independent gravitational Schr¨odinger equation. Further observation is of course recommended in order to refute or verify this proposition.
[494]
vixra:1404.0355 [
pdf]
Schr¨odinger Equation and the Quantization of Celestial Systems
In the present article, we argue that it is possible to generalize Schr ¨odinger equation to describe quantization of celestial systems. While this hypothesis has been described by some authors, including Nottale, here we argue that such a macroquantization was formed by topological superfluid vortice. We also provide derivation of Schr¨odinger equation from Gross-Pitaevskii-Ginzburg equation, which supports this superfluid dynamics interpretation.
[495]
vixra:1404.0354 [
pdf]
Schr¨odinger-Langevin Equation with PT-Symmetric Periodic Potential and its Application to Deuteron Cluster
In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schr¨odinger equation.
[496]
vixra:1404.0295 [
pdf]
A New Form of Matter—Unmatter, Composed of Particles and Anti-Particles
This article is an improved version of an old manuscript. This is a theoretical assumption about the possible existence of a new form of matter. Up to day the unmatter was not checked in the lab.
[497]
vixra:1404.0256 [
pdf]
Generalizations of the Distance and Dependent Function in Extenics to 2D, 3D, and N−D
Extension Theory (or Extenics) was developed by Professor Cai Wen in 1983 by publishing a paper called Extension Set and Non-Compatible Problems. Its goal is to solve contradictory problems and also nonconventional, nontraditional ideas in many fields.
[498]
vixra:1404.0158 [
pdf]
Declaration de la Liberte Academique
Le debut du 21eme siecle reflete, plus qu’aucun autre temps de l’histoire, la profondeur et l’importance de la science et la technologie dans les affaires humaines.
[499]
vixra:1404.0140 [
pdf]
An Exact Mapping from Navier-Stokes Equation to Schr¨odinger Equation via Riccati Equation
In the present article we argue that it is possible to write down Schr¨odinger representation of Navier-Stokes equation via Riccati equation. The proposed approach, while diers appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko’s and Gibbon’s route. Further observation is of course recommended in order to refute or verify this proposition
[500]
vixra:1404.0129 [
pdf]
Five Paradoxes and a General Question on Time Traveling
Traveling to the past Joe40, who is 40 years old, travels 10 years back to the past when he was 30 years old. He meets himself when he was 30 years old, let’s call this Joe30. Joe40 kills Joe30. If so, we mean if Joe died at age 30 (because Joe30 was killed), how could he live up to age 40?
[501]
vixra:1403.0628 [
pdf]
On the Hybrid Mean Value of the Smarandache kn Digital Sequence with SL(n) Function and Divisor Function D(n)1
The main purpose of this paper is using the elementary method to study the hybrid mean value properties of the Smarandache kn digital sequence with SL(n) function and divisor function d(n), then give two interesting asymptotic formulae for it.
[502]
vixra:1403.0482 [
pdf]
Singed Total Domatic Number of a Graph
In this paper, some properties related signed total domatic number and signed total domination number of a graph are studied and found the sign total domatic number of certain class of graphs such as fans, wheels and generalized Petersen graph.
[503]
vixra:1403.0476 [
pdf]
Smarandache V−Connected Spaces
In this paper Smarandache V−connectedness and Smarandache locally−connectedness in topological space are introduced, obtained some of its basic properties and interrelations are verified with other types of connectedness.
[504]
vixra:1403.0395 [
pdf]
Smarandache U-Liberal Semigroup Structure
In this paper, Smarandache U-liberal semigroup structure is given. It is shown that a semigroup S is Smarandache U-liberal semigroup if and only if it is a strong semilattice of some rectangular monoids.
[505]
vixra:1403.0367 [
pdf]
A Note on Path Signed Digraphs
For standard terminology and notion in digraph theory, we refer the reader to the classic text- books of Bondy and Murty [2]and Harary et al. [4]; the non-standard will be given in this paper as and when required.
[506]
vixra:1403.0252 [
pdf]
Euler-Savary's Formula for the Planar Curves in Two Dimensional Lightlike Cone
In this paper, we study the Euler-Savary's formula for the planar curves in the lightlike cone. We ¯rst de¯ne the associated curve of a curve in the two dimensional lightlike cone Q2:Then we give the relation between the curvatures of a base curve, a rolling curve and a roulette which lie on two dimensional lightlike cone Q2.
[507]
vixra:1403.0234 [
pdf]
A New Additive Function and the Smarandache Divisor Product Sequences
For any positive integer n, we define the arithmetical function G(n) as G(1) = 0. The main purpose of this paper is using the elementary method and the prime distribution theory to study the mean value properties of G(n) in Smarandache divisor product sequences fpd(n)g and fqd(n)g, and give two sharper asymptotic formulae for them.
[508]
vixra:1403.0209 [
pdf]
The Fulfilled Euclidean Plane
The fulfilled euclidean plane is the real projective plane completed with the infinite point of its infinite line denoted c. This new incidence structure is a structure with neighbouring elements, in which the unicity of the line through two distinct points is not assured. This new Geometry is a Smarandacheian structure introduced in [10] and [11], which generalizes and unites in the same time: Euclid, Bolyai Lobacewski Gauss and Riemann Geometries.
[509]
vixra:1403.0186 [
pdf]
On the Smarandache Function and the Divisor Product Sequences
Let n be any positive integer, Pd(n) denotes the product of all positive divisors of n. The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of a new arithmetical function S (Pd(n)), and give an interesting asymptotic formula for it.
[510]
vixra:1403.0165 [
pdf]
A Note on Smarandache BL-Algebras
Using some new characterizations of ideals in BL-algebras, we revisit the paper of A. Borumand, and al.[1] recently published in this Journal. Using the concept of MV-center of a BL-algebra, we give a very simple characterization of Smarandache BL-algebra. We also restate some of the results and provide much simpler proofs. Among other things, we notice that Theorem 3.17 and Theorem 3.18 of [1] are not true and they aect a good portion of the paper. Since Deni- tion 3.19, Examples 3.20, 3.21, Theorem 3.22, Remark 3.23 and Remark 3.24 are based on a wrong Theorem, they are completely irrelevant.
[511]
vixra:1403.0127 [
pdf]
A Note on Q-Analogue of S´ANDOR’S Functions
The additive analogues of Pseudo-Smarandache, Smarandache-simple func-tions and their duals have been recently studied by J. S´andor. In this note, we obtain q-analogues of S´andor’s theorems
[512]
vixra:1403.0126 [
pdf]
Pseudo-Manifold Geometries ¸ with Applications
A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a nmanifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equilateral triangular disks on a plane and a more general way for Smarandache 2-manifolds on surfaces, called map geome- tries was presented by the author in [9]−[10] and [12]. However, few observations for cases of n ≥ 3 are found on the journals. As a kind of Smarandache geometries, a general way for constructing dimensional n pseudo-manifolds are presented for any integer n ≥ 2 in this paper. Connection and principal fiber bundles are also defined on these manifolds. Following these constructions, nearly all existent geometries, such as those of Euclid geometry, Lobachevshy- Bolyai geometry, Riemann geometry, Weyl geometry, K¨ahler geometry and Finsler geometry, ...,etc., are their sub-geometries.
[513]
vixra:1403.0125 [
pdf]
On the Universality of Some Smarandache Loops of Bol-Moufang Type
Smarandache quasigroup(loop) is shown to be universal if all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol, Moufang and extra loops are shown to be universal if all their f, g-principal isotopes are Smarandache f, g- principal isotopes. Conversely, it is shown that if these weak Smarandache loops of Bol-Moufang type are universal, then some autotopisms are true in the weak Smaran- dache sub-loops of the weak Smarandache loops of Bol-Moufang type relative to some Smarandache elements. Futhermore, a S in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes is shown to be universal if and only if it is a Smarandache left(right) Bol loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, it is established that a Smarandache inverse property loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes is universal if and only if it is a Smarandache Moufang loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Hence, some of the autotopisms earlier mentioned are found to be true in the Smarandache sub-loops of universal Smarandache: left(right) inverse property loops and inverse property loops.
[514]
vixra:1403.0123 [
pdf]
A Multi-Space Model for Chinese Bids Evalua¸tion with Analyzing
A tendering is a negotiating process for a contract through by a tenderer issuing an invitation, bidders submitting bidding documents and the tenderer accepting a bidding by sending out a notification of award. As a useful way of purchasing, there are many norms and rulers for it in the purchasing guides of the World Bank, the Asian Development Bank, · · ·, also in contract conditions of various consultant associations. In China, there is a law and regulation system for tendering and bidding. However, few works on the mathematical model of a tendering and its evaluation can be found in publication. The main purpose of this paper is to construct a Smarandache multi-space model for a tendering, establish an evaluation system for bidding based on those ideas in the references [7] and [8] and analyze its solution by applying the decision approach for multiple objectives and value engineering. Open problems for pseudo-multi-spaces are also presented in the final section.
[515]
vixra:1403.0107 [
pdf]
Palindromic Permutations and Generalized Smarandache Palindromic Permutations
The idea of left(right) palindromic permutations(LPPs,RPPs) and left(right) gen- eralized Smarandache palindromic permutations(LGSPPs,RGSPPs) are introduced in symmetric groups Sn of degree n. It is shown that in Sn, there exist a LPP and a RPP and they are unique(this fact is demonstrated using S2 and S3). The dihedral group Dn is shown to be generated by a RGSPP and a LGSPP(this is observed to be true in S3) but the geometric interpretations of a RGSPP and a LGSPP are found not to be rotation and reflection respectively. In S3, each permutation is at least a RGSPP or a LGSPP. There are 4 RGSPPs and 4 LGSPPs in S3, while 2 permutations are both RGSPPs and LGSPPs. A permutation in Sn is shown to be a LPP or RPP(LGSPP or RGSPP) if and only if its inverse is a LPP or RPP(LGSPP or RGSPP) respectively. Problems for future studies are raised.
[516]
vixra:1303.0147 [
pdf]
Syntactic - Semantic Axiomatic Theories in Mathematics
A more careful consideration of the recently introduced "Grossone Theory" of Yaroslav Sergeev, [1], leads to a considerable enlargement of what can constitute possible legitimate mathematical theories by the introduction here of what we may call the {\it Syntactic - Semantic Axiomatic Theories in Mathematics}. The usual theories of mathematics, ever since the ancient times of Euclid, are in fact axiomatic, [1,2], which means that they are {\it syntactic} logical consequences of certain assumed axioms. In these usual mathematical theories {\it semantics} can only play an {\it indirect} role which is restricted to the inspiration and motivation that may lead to the formulation of axioms, definitions, and of the proofs of theorems. In a significant contradistinction to that, and as manifestly inspired and motivated by the mentioned Grossone Theory, here a {\it direct} involvement of {\it semantics} in the construction of axiomatic mathematical theories is presented, an involvement which gives semantics the possibility to act explicitly, effectively, and altogether directly upon the usual syntactic process of constructing the logical consequences of axioms. Two immediate objections to what appears to be an unprecedented and massive expansion of what may now become legitimate mathematical theories given by the {\it syntactic - semantic axiomatic theories} introduced here can be the following : the mentioned direct role of semantics may, willingly or not, introduce in mathematical theories one, or both of the "eternal taboo-s" of {\it inconsistency} and {\it self-reference}. Fortunately however, such concerns can be alleviated due to recent developments in both inconsistent and self-referential mathematics, [1,2]. Grateful recognition is acknowledged here for long and most useful ongoing related disccussions with Yaroslav Sergeev.
[517]
vixra:1303.0136 [
pdf]
Five Departures in Logic, Mathematics, and Thus Either We Like It, or not in Physics as Well ...
Physics depends on ”physical intuition”, much of which is formulated in terms of Mathematics. Mathematics itself depends on Logic. The paper presents three latest novelties in Logic which have major consequences in Mathematics. Further, it presents two possible significant departures in Mathematics itself. These five departures can have major implications in Physics. Some of them are indicated, among them in Quantum Mechanics and Relativity.
[518]
vixra:1203.0051 [
pdf]
Vertex-Only Bifurcation Diagrams Are Deceptively Simple
By plotting the polynomials corresponding to several iterations of the logistic map, it is found that the entropy of a branching path can be larger than what is intuitively expected.
[519]
vixra:1011.0054 [
pdf]
Four Comments on "The Road to Reality" by R Penrose
Four comments are presented on the book of Roger Penrose entitled "The Road to Reality, A Complete Guide to the Laws of the Universe". The first comment answers a concern raised in the book. The last three point to important omissions in the book.