Skip to main content
SHOW DETAILS
eye
Title
Date Archived
Creator
Project Gutenberg
by David Hume; Hannaford Bennett
texts

eye 135

favorite 0

comment 0

Book from Project Gutenberg: Essays
Topics: Political science, B, Philosophy
Source: https://www.gutenberg.org/ebooks/36120
Project Gutenberg
texts

eye 52

favorite 0

comment 0

Book from Project Gutenberg: Illustrations of Universal Progress: A Series of Discussions
Topics: Philosophy, B, Political science, Science
Source: https://www.gutenberg.org/ebooks/39977
Arxiv.org
texts

eye 6

favorite 0

comment 0

In this study, we present an original theoretical approach to prove $\pi (n)-li(n)=o(M(n)\sqrt{li(n)})$, where $M(n)$ is an arbitrary function such that $M(n)\rightarrow+\infty$. This implies that the Riemann Hypothesis almost certainly stands without any assumptions. To prove this, we apply Turing computability to probability theory and the distribution of arbitrarily large prime numbers. We prove that for any Turing machine prime numbers require an arbitrarily large number of computational...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1403.8075
Arxiv.org
by Agha Kashif; M. Aslam
texts

eye 11

favorite 0

comment 0

In this paper, we introduce the notion of a BCK-topological module in a natural way and establish that every decreasing sequence of submodules on a BCK-module M over bounded commutative BCK-algebra X is indeed a BCK- topological module. We have defined the notion of compatible and strict BCK- module homomorphisms, and establish that a strict BCK-module homomorphism is an open as well as a continuous mapping. Also, we establish the necessary and sufficient condition for a compatible mapping to...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1509.01234
Arxiv.org
texts

eye 6

favorite 0

comment 0

We keep the definition of intra-regularity (left regularity) of $po$-$\Gamma$-semigroups introduced in arXiv: 1511.00679 which is absolutely necessary for the investigation. Being able to describe the form of the elements of the principal filter by using this definition, we study the decomposition of an intra-regular $po$-$\Gamma$-semigroup into simple components. Then we prove that a $po$-$\Gamma$-semigroup $M$ is intra-regular and the ideals of $M$ form a chain if and only if $M$ is a chain...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1512.00404
Arxiv.org
texts

eye 6

favorite 0

comment 0

The purpose of this paper is to emulate the process used in defining and learning about the algebraic structure known as a Field in order to create a new algebraic structure which contains numbers that can be used to define Division By Zero, just as $i$ can be used to define $\sqrt{-1}$. This method of Division By Zero is different from other previous attempts in that each ${\alpha\over 0}$ has a different unique, numerical solution for every possible $\alpha$, albeit these numerical solutions...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1611.06838
Arxiv.org
by S. M. Abrarov; B. M. Quine
texts

eye 5

favorite 0

comment 0

We present a generalized $\text{Vi\'ete's}$-like formula for pi with rapid convergence. This formula is based on the arctangent function identity with argument $x=\sqrt{2-{{a}_{K-1}}}/{{a}_{K}}$, where \[ {{a}_{K}}=\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}}_{K\,\,\text{square}\,\,\text{roots}} \] is a radical consisting of $K$ nested square roots of twos. The computational test we performed reveals that the generalized $\text{Vi\'ete's}$-like formula provides a significant...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1610.07713
Arxiv.org
by S. M. Abrarov; B. M. Quine
texts

eye 6

favorite 0

comment 0

In our recent publication we obtained a series expansion of the arctangent function involving complex numbers. In this work we show that this formula can also be expressed as a real rational function.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1701.05098
Arxiv.org
by Niovi Kehayopulu; Michael Tsingelis
texts

eye 6

favorite 0

comment 0

A fuzzy subset $f$ of an ordered semigroup (or semigroup) $S$ is called fuzzy semiprime if $f(x)\ge f(x^2)$ for every $x\in S$ (Definition 1). Following the terminology of semiprime subsets of ordered semigroups (semigroups), the terminology of ideal elements of $poe$-semigroups (: ordered semigroups possessing a greatest element), and the terminology of ordered semigroups, in general, a fuzzy subset $f$ of an ordered semigroups (semigroup) should be called fuzzy semiprime if for every fuzzy...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1404.5875
Arxiv.org
by N. K. Sudev; K. P. Chithra; K. A. Germina
texts

eye 9

favorite 0

comment 0

Let $\mathbb{N}_0$ be the set of all non-negative integers, let $X\subset \mathbb{N}_0$ and $\mathcal{P}(X)$ be the the power set of $X$. An integer additive set-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$. An IASL $f$ is said to be an integer additive set-indexer (IASI) of a graph...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1503.07843
Arxiv.org
by Niovi Kehayopulu
texts

eye 6

favorite 0

comment 0

The aim is to correct part of the Remark 3 of my paper "On regular, intra-regular ordered semigroups" in Pure Math. Appl. (PU.M.A.) 4, no. 4 (1993), 447--461. On this occasion, some further results and the similarity between the $po$-semigroups and the $le$-semigroups is discussed.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1407.7483
Arxiv.org
texts

eye 4

favorite 0

comment 0

Four-Color Theorem has secret in its logical proof and actual operating. In this paper we will give a proof of Four-Color Theorem based on Kuratowski's Theorem using some induction argument and give a description of the most complicated coloring map, a simple proof of Kuratowski's Theorem using Euler charateristic is also presented. We also conjecture the higher dimensional generalization of Four-Color Theorem.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1408.1927
Arxiv.org
by Marcoen J. T. F. Cabbolet
texts

eye 8

favorite 0

comment 0

Recently Feferman (Rev. Symb. Logic 6: 6-15, 2013) has outlined a program for the development of a foundation for naive category theory. While Ernst (ibid. 8: 306-327, 2015) has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1509.08814
Arxiv.org
by Bülent Altunkaya; Ferdağ Kahraman Aksoyak; Levent Kula; Cahit Aytekin
texts

eye 3

favorite 0

comment 0

In this paper, we study the position vectors of rectifying slant helices in $E^3$. First, we have found the general equations of the curvature and the torsion of rectifying slant helices. After that, we have constructed a second order linear differential equation and by solving the equation, we have obtained a family of rectifying slant helices which lie on cones.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1602.03413
Arxiv.org
by Jan Kristian Haugland
texts

eye 4

favorite 0

comment 0

For a given partition of (1, 2, ..., 2n) into two disjoint subsets A and B with n elements in each, consider the maximum number of times any integer occurs as the difference between an element of A and an element of B. The minimum value of this maximum (over all partitions) is denoted by M(n). By a result of Swinnerton-Dyer, one way to estimate lim M(n)/n from above is to give step functions that describe the density of A, say, throughout the interval [1, 2n] for a large n rather than looking...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1609.08000
Arxiv.org
by E. Ostrovsky; L. Sirota
texts

eye 7

favorite 0

comment 0

We investigate in this short report the rate of increase of positive numerical recursion with quadratic non-linearity. More exactly, we intent to calculate the logarithmic index of its increasing. We present also the possible application in the theory of the Navier-Stokes equations.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1406.6044
Arxiv.org
by N. K. Sudev; K. P. Chithra; K. A. Germina
texts

eye 18

favorite 0

comment 0

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ is defined by $f^+ (uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. In this paper, we introduce the notion of a particular type of integer additive set-indexers called...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1507.02173
Arxiv.org
by Alex Goldvard; Lavi Karp
texts

eye 14

favorite 0

comment 0

We achieve compositions rules for the geometric parameters of the composed rotations, which is in a certain sense analogous to the well known Rodrigues formula. We also obtain a necessary and sufficient condition for a composition of two simple rotations in $\mathbb{E}^4$ to be a simple rotation.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1504.03717
Arxiv.org
by Mamuka Meskhishvili
texts

eye 29

favorite 0

comment 0

By using pairs of nontrivial rational solutions of congruent number equation $$ C_N:\;\;y^2=x^3-N^2x, $$ constructed are pairs of rational right (Pythagorean) triangles with one common side and the other sides equal to the sum and difference of the squares of the same rational numbers. The parametrizations are found for following Diophantine systems: \begin{align*} (p^2\pm q^2)^2-a^2 & =\square_{1,2}\,, \\[0.2cm] c^2-(p^2\pm q^2)^2 & =\square_{1,2}\,, \\[0.2cm] a^2+(p^2\pm q^2)^2 &...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1504.04584
Arxiv.org
by Tulay Erisir; Mehmet Ali Gungor; Soley Ersoy
texts

eye 11

favorite 0

comment 0

In this paper, one-parameter planar motion in the generalised complex plane (or p-complex plane) ${C_p} = \left\{ {x + iy: x,y \in R, {i^2} = p} \right\}$ which is defined as a system of generalised complex numbers is studied. Firstly, generalised Bobillier formula is obtained by using the geometric interpretation of generalised Euler-Savary formula in the p-complex plane. Moreover, it is shown that the Bobillier formula may be obtained by an alternative method without the use of Euler-Savary...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1503.01616
Arxiv.org
texts

eye 4

favorite 0

comment 0

We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [Choban, M., Berinde, V., {\it A general concept of multiple fixed point for mappings defined on spaces with a distance} (submitted)] and also simplifies some concepts of multiple fixed point considered by...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1701.00518
Arxiv.org
by Ricardo Almeida; Nuno R. O. Bastos; M. Teresa T. Monteiro
texts

eye 6

favorite 0

comment 0

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1511.06202
Arxiv.org
by Niovi Kehayopulu; Michael Tsingelis
texts

eye 4

favorite 0

comment 0

We characterize the intra-regular $\Gamma$-semigroups and the left regular $\Gamma$-semigroups $M$ in which $x\Gamma M\subseteq M\Gamma x$ for every $x\in M$ in terms of filters and we prove, among others, that every intra-regular $\Gamma$-semigroup is decomposable into simple components, and every $\Gamma$-semigroup $M$ for which $x\Gamma M\subseteq M\Gamma x$ is left regular, is decomposable into left simple components.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1511.07783
Arxiv.org
by Niovi Kehayopulu; Michael Tsingelis
texts

eye 5

favorite 0

comment 0

Concerning the paper in the title by K. Hila and E. Pisha in Commun. Korean Math. Soc. Volume 26, Issue 3 (2011), 373--384, we give our results and make the main corrections.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1402.3455
Arxiv.org
by J. Mahanta; D. Das
texts

eye 4

favorite 0

comment 0

In this paper, we introduce and study the concepts of semi open SOM) and semi closed (SCM) M-sets in multiset topological spaces.With this generalization of the notions of open and closed sets in M-topology, we generalize the concept of compactness in M-topology as semi compactness. Further semi compactness is generalized as semi whole compactness, semi partial whole compactness and semi full compactness. Some characterizations of these compact spaces are studied in the setting of multiset...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1403.5642
Arxiv.org
texts

eye 4

favorite 0

comment 0

Maji\cite{maj-13}, firstly proposed neutrosophic soft sets can handle the indeterminate information and inconsistent information which exists commonly in belief systems. In this paper, we have firstly redefined complement, union and compared our definitions of neutrosophic soft with the definitions given by Maji. Then, we have introduced the concept of neutrosophic soft matrix and their operators which are more functional to make theoretical studies in the neutrosophic soft set theory. The...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1404.0673
Arxiv.org
by Latif Ahmad; Muhammad Farooq; Saleem Abdullah
texts

eye 5

favorite 0

comment 0

In this paper, we generalize the fuzzy Laplace transformation (FLT) for the nth derivative of a fuzzy-valued function named as nth derivative theorem and under the strongly generalized differentiability concept, we use it in an analytical solution method for the solution of an nth order fuzzy initial value problem (FIVP). This is a simple approach toward the solution of nth order fuzzy initial value problem (FIVP) by the nth generalized (FLT) form, and then we can use it to solve any order of...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1403.0242
Arxiv.org
texts

eye 4

favorite 0

comment 0

The general abstract arbitrary order (N) Cauchy problem was solved in a closed form as a sum of exponential propagator functions. The infinite sparse exponential series was solved with the aid of a homogeneous differential equation. It generated a linear combination of exponential functions. The Cauchy problem solution was formed with N linear combinations of N exponential propagators.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1411.6890
Arxiv.org
by Mårten Wadenbäck
texts

eye 4

favorite 0

comment 0

In this paper the sum of an orthogonal matrix and an outer product is studied, and a relation between the norms of the vectors forming the outer product and the singular values of the resulting matrix is presented. The main result may be found in Theorem 1.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1512.03715
Arxiv.org
by Mayeul Arminjon
texts

eye 3

favorite 0

comment 0

A global vector field $v$ on a "spacetime" differentiable manifold $\mathrm{V}$, of dimension $N+1$, defines a congruence of world lines: the maximal integral curves of $v$, or orbits. The associated global space $\mathrm{N}\_v$ is the set of these orbits. A "$v$-adapted" chart on $\mathrm{V}$ is one for which the $\mathbb{R}^N$ vector ${\bf x}\equiv (x^j)\ (j=1,...,N)$ of the "spatial" coordinates remains constant on any orbit $l$. We consider non-vanishing vector...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1512.08718
Arxiv.org
texts

eye 4

favorite 0

comment 0

We give a proof of a mean value asymptotic formula for the number of representations of an integer as sum of two squares known as the Gauss circle problem.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1601.02890
Arxiv.org
by U. M. Pirzada; D. C. Vakaskar
texts

eye 7

favorite 0

comment 0

In this paper, we find a non-dominated solution of a fuzzy maximum-return problem ( unconstrained single-variable fuzzy optimization problem ) . We establish Newton method to find the solution of the unconstrained single-variable fuzzy optimization problem using the differentiability of $\alpha$-level functions of a fuzzy-valued function and partial order relation on a set of fuzzy numbers.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1610.01565
Arxiv.org
by Melek Erdogdu; Mustafa Ozdemir
texts

eye 27

favorite 0

comment 0

In this paper, real matrix representations of split quaternions are examined in terms of the casual character of quaternion. Then, we give De-Moivre' s formula for real matrices of timelike and spacelike split quaternions, separately. Finally, we state the Euler theorem for real matrices of pure split quaternions.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1503.05413
Arxiv.org
by Johan Kok; Naduvath Sudev
texts

eye 11

favorite 0

comment 0

Consider a network $D$ of pipes which have to be cleaned using some cleaning agents, called brushes, assigned to some vertices. The minimum number of brushes required for cleaning the network $D$ is called its brush number. The tattooing of a simple connected directed graph $D$ is a particular type of the cleaning in which an arc are coloured by the colour of the colour-brush transiting it and the tattoo number of $D$ is a corresponding derivative of brush numbers in it. Tattooing along an...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1603.00303
We solve some famous conjectures on the distribution of primes. These conjectures are to be listed as Legendre's, Andrica's, Oppermann's, Brocard's, Cram\'{e}r's, Shanks', and five Smarandache's conjectures. We make use of both Firoozbakht's conjecture (which recently proved by the author) and Kourbatov's theorem on the distribution of and gaps between consecutive primes. These latter conjecture and theorem play an essential role in our methods for proving these famous conjectures. In order to...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1605.01722
Arxiv.org
texts

eye 3

favorite 0

comment 0

We present a function that tests for primality, factorizes composites and builds a closed form expression of $\pi(n^2)$ in terms of $\sum_{3 \leq p \leq n} \frac{1}{p}$ and a weaker version of $\omega(n)$.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1701.05591
Arxiv.org
texts

eye 3

favorite 0

comment 0

We examine the prime gaps using a statistical approach. It is first shown that the Andrica's conjecture is true for half or more cases. Using the arguments of averages, it is further shown that Andrica's conjecture is true. We further obtain a precise bound for the Andrica's expression.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1702.08547
Arxiv.org
by James A. Tilley
texts

eye 6

favorite 0

comment 0

No proof of the 4-color conjecture reveals why it is true; the goal has not been to go beyond proving the conjecture. The standard approach involves constructing an unavoidable finite set of reducible configurations to demonstrate that a minimal counterexample cannot exist. We study the 4-color problem from a different perspective. Instead of planar triangulations, we consider near-triangulations of the plane with a face of size 4; we call any such graph an a-graph. We state an a-graph coloring...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1511.06872
Arxiv.org
by Vineet Kumar
texts

eye 9

favorite 0

comment 0

We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the number line. Generally the different categories of prime numbers found till date, satisfy the form of this function. We present some absolute and probabilistic conditions for the primality of the number generated by this method. This function is capable of...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1411.3356
Arxiv.org
texts

eye 47

favorite 0

comment 0

We give synthetic proofs of many new results in triangle geometry, focusing especially on fixed points of certain affine maps which are defined in terms of the cevian triangle $DEF$ of a point $P$ with respect to a given triangle $ABC$, as well as the cevian triangle of the isotomic conjugate $P'$ of $P$ with respect to $ABC$. We prove a formula for the cyclocevian map in terms of the isotomic and isogonal maps using an entirely synthetic argument, and show that the complement $Q$ of the...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1504.00210
Arxiv.org
by N. A. Carella
texts

eye 33

favorite 0

comment 0

This note generalizes the Fibonacci primitive roots to the set of integers. An asymptotic formula for counting the number of integers with such primitive root is introduced here.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1505.05519
Arxiv.org
by Henrik Stenlund
texts

eye 19

favorite 0

comment 0

This paper is about a method for solving infinite series in closed form by using inverse and forward Laplace transforms. The resulting integral is to be solved instead. The method is extended by parametrizing the series. A further Laplace transform with respect to it will offer more options for solving a series.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1405.7633
Arxiv.org
by John Washburn
texts

eye 31

favorite 0

comment 0

Building on the earlier works of Gadiyar and Padma, the main result of this paper is to prove: \begin{equation} \lim_{n \to \infty} \frac{1}{N} \sum_{n=1}^{N} \frac{\phi(n) \Lambda\left(n \right)}{n} \frac{\phi(n+h) \Lambda\left(n +h\right)}{n+h} = \sum\limits_{q=1}^{\infty} \left\Vert \frac{\mu(q)}{\phi(q)} \right\Vert^2 c_q(h) \end{equation} This sieve with Ramanujan-Fourier expansions is the the central relationship to be proven in within the works of H. G. Gadiyar and R. Padma, as related...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1506.07822
Arxiv.org
texts

eye 17

favorite 0

comment 0

In this paper, we present characterizations of totally bounded sets, relatively compact sets and compact sets in the fuzzy sets spaces $F_B(\mathbb{R}^m)$ and $F_B(\mathbb{R}^m)^p$ equipped with $L_p$ metric, where $F_B(\mathbb{R}^m)$ and $F_B(\mathbb{R}^m)^p$ are two kinds of general fuzzy sets on $\mathbb{R}^m$ which do not have any assumptions of convexity or star-shapedness. Subsets of $F_B(\mathbb{R}^m)^p$ include common fuzzy sets such as fuzzy numbers, fuzzy star-shaped numbers with...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1509.00447
Arxiv.org
by Octavian Cira; Florentin Smarandache
texts

eye 41

favorite 0

comment 0

In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation {\eta}({\pi}(x)) = {\pi}({\eta}(x)), where {\eta} is the Smarandache function and {\pi} is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and then...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1604.01760
Arxiv.org
by Chelton D. Evans; William K. Pattinson
texts

eye 25

favorite 0

comment 0

The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and little-o/big-O defined with the Gossamer number system, and the relations algebra is explored. A comparison of function algebra is developed. A transfer principle more general than Non-Standard-Analysis is developed, hence a two-tier system of calculus is described....
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1502.06936
Arxiv.org
by Giuliano G. La Guardia; Ana Lucia Pereira Baccon
texts

eye 46

favorite 0

comment 0

A magic square of order n is an nxn square (matrix) whose entries are distinct nonnegative integers such that the sum of the numbers of any row and column is the same number, the magic constant. In this paper we introduce the concept of pseudo magic squares, i.e., magic squares defined over the ring of integers, without the restriction of distinct numbers. Additionally, we generalize this new concept by introducing a group (ring) structure over it. This new approach can provide useful tools in...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1504.05642
Arxiv.org
by Manash Jyoti Borah; Bipan Hazarika
texts

eye 45

favorite 0

comment 0

In this paper, we introduce notion of fuzzy soft number. Here defined fuzzy soft number and four arithmetric operations $ \tilde{+}, \tilde{-}, \tilde{\times}, \tilde{\div} $ and related properties. Also introduce Hausdorff distance, Fuzzy soft metric space, convergence sequence, Cauchy sequence, Continuity and uniform continuity of fuzzy soft numbers. At starting of this paper, we study convex and concave fuzzy soft sets and some of their properties.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1611.06556
Arxiv.org
texts

eye 4

favorite 0

comment 0

In this paper, we introduce semiopen and semiclosed fuzzy soft sets in fuzzy soft topological spaces. Various properties of these sets are studied alongwith some characterizations. Further, we generalize the structures like interior and closure via semiopen and semiclosed fuzzy soft sets and study their various properties.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1403.3622
Arxiv.org
by Naduvath Sudev; Augustine Germina
texts

eye 10

favorite 0

comment 0

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) of a given graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. An IASI $f$ of a graph $G$ is said to be a weak IASI of $G$ if $|f^+(uv)|=\max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. A graph which...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1505.03841
Arxiv.org
texts

eye 5

favorite 0

comment 0

We show that it is possible to decide whether a given planar diagram correctly depicts the spatial figure consisting of a planar quadrangle together with its shadow in another plane.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1403.3621
Arxiv.org
by Johan Kok; Naduvath Sudev
texts

eye 3

favorite 0

comment 0

The studies on $b$-chromatic number attracted much interest since its introduction. In this paper, we discuss the $b$-chromatic number of certain classes of graphs and digraphs. The notion of a new general family of graphs called the Chithra graphs of a graph $G$ are also introduced.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1511.00680
Arxiv.org
by Airton von Sohsten de Medeiros; Ráderson Rodrigues da Silva
texts

eye 4

favorite 0

comment 0

We show essentially that the differential equation $\frac{\partial (P,Q)}{\partial (x,y)} =c \in {\mathbb C}$, for $P,\,Q \in {\mathbb C}[x,y]$, may be "integrated", in the sense that it is equivalent to an algebraic system of equations involving the homogeneous components of $P$ and $Q$. Furthermore, the first equations in this system give explicitly the homogeneous components of $Q$ in terms of those of $P$. The remaining equations involve only the homogeneous components of $P$.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1409.7059
Arxiv.org
by Hirokazu Nishimura; Hirowaki Takamiya
texts

eye 21

favorite 0

comment 0

We have studied the infinitesimal Baker-Campbell-Hausdorff formula up to n=4 (Math. Appl. 2 (2013), 61-91). In this note we correct some errors in our calculation for n=4 and presents the calculation for n=5 by using Mathematica.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1507.01453
Arxiv.org
texts

eye 12

favorite 0

comment 0

Objective of this paper is to introduce a new type of calculus which will be called G-Calculus based on non-Newtonian calculus introduced by Grossman and Katz \cite{GrossmanKatz}. The basic difference between geometric calculus defined by Grossman and Katz and the present G-calculus is that Grossman took the values of the argument as $x, x+ h, x+2h,...$ but here in G-calculus we take the values as $x, x\oplus h, x\oplus e^2\odot h, x\oplus e^3\odot h....$ This calculus will have great deal with...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1607.07749
Arxiv.org
texts

eye 10

favorite 0

comment 0

In this paper we propose a new method for determination of the two-term Machin-like formula for pi with arbitrarily small arguments of the arctangent function. This approach excludes irrational numbers in computation and leads to a significant improvement in convergence with decreasing arguments of the arctangent function.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1704.02875
Arxiv.org
by Niovi Kehayopulu
texts

eye 6

favorite 0

comment 0

This is about the paper by Thawhat Changphas and Nawamin Phaipong in Quasigroups and Related Systems 22 (2014), 193--200.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1510.02326
Arxiv.org
by Raymond Boute
texts

eye 31

favorite 0

comment 0

Engineering needs mathematics, but the converse is also increasingly evident. Indeed, mathematics is still recovering from the drawbacks of several "reforms". Encouraging is the revived interest in proofs indicated by various recent "introduction to proof"-type textbooks. Yet, many of these texts defeat their own purpose by self-conflicting definitions. Most affected are fundamental concepts such as relations and functions, despite flawless accounts 50 years ago. We take the...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1601.00989
Arxiv.org
texts

eye 5

favorite 0

comment 0

This research paper presents the results of a study on the application of extended analytic continuation to locate the non-trivial zeros of the Riemann Hypothesis.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1608.08082
Arxiv.org
texts

eye 16

favorite 0

comment 0

We characterize the fuzzy left (resp. right) ideals, the fuzzy ideals and the fuzzy prime (resp. semiprime) ideals of an ordered $\Gamma$-groupoid $M$ in terms of level subsets and we prove that the cartesian product of two fuzzy left (resp. right) ideals of $M$ is a fuzzy left (resp. right) ideal of $M\times M$, and the cartesian product of two fuzzy prime (resp. semiprime) ideals of $M$ is a fuzzy prime (resp. semiprime) ideal of $M\times M$. As a result, if $\mu$ and $\sigma$ are fuzzy left...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1501.03955
W. B. Jordan's conclusion that the quadruple principal value integral in problem 89-2 vanishes does not hold. The error sneaks in through a contribution of a subintegral which impedes some sign symmetry with respect to the master parameter (the Fermi radius) and which was overlooked in the published solution. In summary, the original problem of solving the quadruple integral remains unsolved.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1412.0032
Arxiv.org
by Ahmedou Yahya Ould Mohameden; Mohamed Vall Ould Moustapha
texts

eye 6

favorite 0

comment 0

In this article, we give the explicit solutions to the Laplace equations associated to the Dirac operator, Euler operator and the harmonic oscillator in R.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1703.01242
Arxiv.org
by Giuliano G. La Guardia
texts

eye 5

favorite 0

comment 0

It is well-known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose an alternative definition of Lyapunov exponent in terms of Lipschitz maps, which are not necessarily differentiable. We show that the results which are valid to standard discrete dynamical systems are also valid in this new context. Therefore, this novel approach expands the range of applications of the dynamical systems theory.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1704.04986
Arxiv.org
texts

eye 5

favorite 0

comment 0

The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this second part we show some arithmetically constructible examples of FQ operations ($n=2$), concentrating on monoaxiality, related extensions, and (hyper)scaling.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1512.03716
Arxiv.org
by V. Lakshmana Gomathi Nayagam; Jeevaraj. S; Geetha Sivaraman
texts

eye 7

favorite 0

comment 0

L.A.Zadeh introduced the concept of fuzzy set theory as the generalization of classical set theory in 1965 and further it has been generalized to intuitionistic fuzzy sets (IFSs) by Atanassov in 1983 to model information by the membership, nonmembership and hesitancy degree more accurately than the theory of fuzzy logic. The notions of intuitionistic fuzzy numbers in different contexts were studied in literature and applied in real life applications. Problems in different fields involving...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1601.01621
Arxiv.org
by Ravi Goyal; Mahipal Jadeja; Rahul Muthu
texts

eye 6

favorite 0

comment 0

Graphs constructed to translate some graph problem into another graph problem are usually called auxiliary graphs. Specifically total graphs of simple graphs are used to translate the total colouring problem of the original graph into a vertex colouring problem of the transformed graph. In this paper, we obtain a new characterisation of total graphs of simple graphs. We also design algorithms to compute the inverse total graphs when the input graph is a total graph. These results improve over...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1602.04698
Arxiv.org
by J. F. Peters; A. Tozzi
texts

eye 6

favorite 0

comment 0

This paper introduces a string-based extension of the Borsuk-Ulam Theorem (denoted by strBUT). A string is a region with zero width and either bounded or unbounded length on the surface of an $n$-sphere or a region of a normed linear space. In this work, an $n$-sphere surface is covered by a collection of strings. For a strongly proximal continuous function on an $n$-sphere into $n$-dimensional Euclidean space, there exists a pair of antipodal $n$-sphere strings with matching descriptions that...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1606.04031
Arxiv.org
by Saif Ullah; Latif Ahmad; Muhammad Farooq; Saleem Abdullah
texts

eye 7

favorite 0

comment 0

The solution of integro-differential equations have a major role in the fields of science and engineering. Different approaches both numerical and analytic are used to solve these type of equations. In this paper, the solution of fuzzy convolution Volterra integro-differential equation is investigated using fuzzy Laplace transform method under generalized Hukuhara differentiability. Finally, the method is illustrated with few examples to show the ability of the proposed method.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1403.7936
We consider skew ruled surfaces in the three-dimensional Euclidean space and some geometrically distinguished families of curves on them whose normal curvature has a concrete form. The aim of this paper is to find and classify all ruled surfaces with the mentioned property.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1512.00393
Arxiv.org
texts

eye 10

favorite 0

comment 0

This theorem is based on holomorphy of studied functions and the fact that nearby of a singularity point the imaginary part of the specific function can accept zero value.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1606.03950
Arxiv.org
by Johan Kok; Naduvath Sudev; Muhammad Kamran Jamil
texts

eye 7

favorite 0

comment 0

In this paper, we introduce the notion of the rainbow neighbourhood and a related graph parameter namely, the rainbow neighbourhood number of a graph $G$. We report on preliminary results thereof. We also establish a necessary and sufficient condition for the existence of a rainbow neighbourhood in the line graph of a graph $G$.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1703.01089
In 1898, Riemann had announced the following conjecture : the nontrivial roots (zeros) $s=\alpha+i\beta$ of the zeta function, defined by: $$\zeta(s) = \sum_{n=1}^{+\infty}\frac{1}{n^s},\,\mbox{for}\quad \Re(s)>1$$ have real part $\alpha= \frac{1}{2}$. We give a proof that $0
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1703.05319
Arxiv.org
by Manash Jyoti Borah; Bipan Hazarika
texts

eye 3

favorite 0

comment 0

The main aim of this paper is to introduced the operations "Union" and "Intersection," and four operators $O_1, O_2, O_3, O_4 $ on interval-valued hesitant fuzzy soft sets and discuss some of their properties.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1604.00902
Arxiv.org
by Huan Huang; Congxin Wu
texts

eye 15

favorite 0

comment 0

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite non-differentiable points. In the previous work, this convolution method only can be used to construct differentiable approximations for continuous fuzzy numbers whose possible...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1509.01456
Arxiv.org
by Octavian Cira; Florentin Smarandache
texts

eye 9

favorite 0

comment 0

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1603.08456
Arxiv.org
texts

eye 4

favorite 0

comment 0

We deal with an hypergroupoid endowed with a relation denoted by "$\le$", we call it $\le$--hypergroupoid. We prove that a nonempty subset $A$ of a $\le$--hypergroupoid $H$ is a prime (resp. semiprime) ideal of $H$ if and only if its characteristic function $f_A$ is a fuzzy prime (resp. fuzzy semiprime) ideal of $H$.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1603.09651
In an article, E. Grafarend and B. Schaffrin studied the geometry of non-linear adjustment of the planar trisection problem using the Gauss Markov model and the method of the least squares. This paper develops the same method working on an example of the determination of a point by trilateration in the three-dimensional geodetic option for determining the coordinates $(x, y, z)$ of an unknown point from measurements known distances to $n$ points.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1701.03158
Arxiv.org
texts

eye 6

favorite 0

comment 0

We give a Goldbach's pair for even numbers that are in a specific form. Consider the following two functions where $x$ and $m$ are odd integers greater than $1$. $g(x,m) = x+2m-(x-m)mod(2m),$ and $f(x)$ returns the smallest prime factor of $x$. Let $n$ be an odd integer greater than $1$. Set $p_{max}$ and $d$ such that $p_{max} = $ maximum of $f(g(n^2-2n+2, p))$ taken over the odd primes $p\leq n$, and $d=(n^2-2n+2-p_{max})mod(2p_{max})$. We observe that every even number of the form...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1703.08039
Arxiv.org
by Johan Kok; N. K. Sudev; K. P. Chithra; K. A. Germina; U. Mary
texts

eye 5

favorite 0

comment 0

The concepts of linear Jaco graphs and Jaco-type graphs have been introduced as certain types of directed graphs with specifically defined adjacency conditions. The distinct difference between a pure Jaco graph and a Jaco-type graph is that for a pure Jaco graph, the total vertex degree $d(v)$ is well-defined, while for a Jaco-type graph the vertex out-degree $d^+(v)$ is well-defined. Hence, in the case of pure Jaco graphs a challenge is to determine $d^-(v)$ and $d^+(v)$ respectively and for...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1608.00856
Arxiv.org
by İsmet Altıntaş; Kemal Taşköprü
texts

eye 4

favorite 0

comment 0

This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft cone metric spaces.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1610.01515
Arxiv.org
by E. Peyghan; B. Samadi; A. Tayebi
texts

eye 4

favorite 0

comment 0

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft separation axioms that have been studied by Min and Shabir-Naz. By constructing a special soft topological space, show that some classical results in general topology are not true about soft topological spaces, for instance every compact Housdorff spaces need not be...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1401.6933
In this paper, the Vitali-like convergence theorem is established. As its application we complete the proof of the Riemann Hypothesis.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1402.5952
Arxiv.org
by Latif Ahmad; Muhammad Farooq; Saif Ullah; Saleem Abdullah
texts

eye 3

favorite 0

comment 0

A natural way to model dynamic systems under uncertainty is to use fuzzy boundary value problems (FBVPs) and related uncertain systems. In this paper we use fuzzy Laplace transform to find the solution of two-point boundary value under generalized Hukuhara differentiability. We illustrate the method for the solution of the well known two-point boundary value problem Schrodinger equation, and homogeneous boundary value problem. Consequently, we investigate the solutions of FBVPs under as a new...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1403.0571
Arxiv.org
by Ricardo Almeida; Nuno R. O. Bastos
texts

eye 6

favorite 0

comment 0

The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on first-order derivatives, and thus we convert the fractional problem into a standard one. With some examples we show the accuracy of the method, and then we present the utility of the method by solving a fractional integral equation.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1512.03791
Arxiv.org
by Garret Sobczyk
texts

eye 15

favorite 0

comment 0

This article explores the geometric algebra of Minkowski spacetime, and its relationship to the geometric algebra of Euclidean 4-space. Both of these geometric algebras are algebraically isomorphic to the 2x2 matrix algebra over Hamilton's famous quaternions, and provide a rich geometric framework for various important topics in mathematics and physics, including stereographic projection and spinors, and both spherical and hyperbolic geometry. In addition, by identifying the time-like Minkowski...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1703.01244
Arxiv.org
by Johan Kok; Sudev Naduvath
texts

eye 4

favorite 0

comment 0

A vertex $v$ of a given graph is said to be in a rainbow neighbourhood of $G$ if every colour class of $G$ consists of at least one vertex from the closed neighbourhood $N[v]$. A maximal proper colouring of a graph $G$ is a Johan colouring if and only if every vertex of $G$ belongs to a rainbow neighbourhood of $G$. In general all graphs need not have a Johan colouring, even though they admit a chromatic colouring. In this paper, we characterise graphs which admit a Johan colouring. We also...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1704.02869
Arxiv.org
texts

eye 8

favorite 0

comment 0

In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for some finite series. We demonstrate a method for generation of variants of the identities based on the findings. The identities are useful for solving various infinite products.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1611.01375
Arxiv.org
texts

eye 10

favorite 0

comment 0

This paper develops a framework of algebra whereby every Diophantine equation is made quickly accessible by a study of the corresponding row entries in an array of numbers which we call the Newtonian triangles. We then apply this framework to the understandimg of the Fermat's Last Theorem and discuss some of its direct consequences.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1404.1472
Arxiv.org
texts

eye 10

favorite 0

comment 0

In this note we present solutions of arbitrary polynomial equations in nested periodic radicals.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1406.1948
Arxiv.org
by Nikos Bagis
texts

eye 5

favorite 0

comment 0

We analyze the double series of Bessel functions given by Ramanujan. Using a very simple lemma we establish the uniform convergence of these series. By this we address to the Gauss circle problem.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1410.5853
Arxiv.org
by Chelton D. Evans; William K. Pattinson
texts

eye 23

favorite 0

comment 0

Integration at a point is a new kind of integration derived from integration over an interval in infinitesimal and infinity domains which are spaces larger than the reals. Consider a continuous monotonic divergent function that is continually increasing. Apply the fundamental theorem of calculus. The integral is a difference of the function integrated at the end points. If one of these point integrals is much-greater-than the other in magnitude delete it by non-reversible arithmetic. We call...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1503.00817
Arxiv.org
by Brett Pansano
texts

eye 15

favorite 0

comment 0

This purpose of this paper is to note an interesting identity derived from an integral in Gradshteyn and Ryzhik using techniques from George Boros'(deceased) Ph.D thesis. The idenity equates a sum to a product by evaluating an integral in two different ways. A more general form of the idenity is left for further investigation.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1503.04678
Arxiv.org
by Melek Erdogdu; Mustafa Ozdemir
texts

eye 13

favorite 0

comment 0

In this paper, we investigate the surfaces generated by binormal motion of Bertrand curves, which is called Razzaboni surface, in Minkowski 3-space. We discussed the geometric properties of these surfaces in M^3 according to the character of Bertrand geodesics. Then, we define the Razzaboni transformation for a given Razzaboni surface. In other words, we prove that there exists a dual of Razzaboni surface for each case. Finally, we show that Razzaboni transformation maps the surface M, which...
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1503.06446
The Collatz variations pattern seems not to have any recurrence relation between numbers. But knowing that there is at least a natural number that converges after several iterations we construct a function $f_{X,Y}$ that is equal to the value of convergence for all convergent sequences. A canonical decomposition can be expressed for such numbers.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1702.04659
Arxiv.org
by I. Paniello
texts

eye 9

favorite 0

comment 0

We consider the set of ($n\times n\times n$) cubic stochastic matrices of type (1,2) together with different multiplication rules that not only retain their stochastic properties but also endow this set with an associative semigroup structure. Then we introduce different actions of the semigroup of nonnegative column stochastic $n\times n$ matrices on the set of cubic stochastic matrices of type (1,2) and study how these actions translate to the cubic matrix slices and marginal distributions....
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1704.06775
Arxiv.org
by Nicolas Le Bihan
texts

eye 20

favorite 0

comment 0

Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal processing (detection, filtering, estimation). Just like in the complex case, circularity for a quaternion-valued random variable is related to the symmetries of its probability density function. As a consequence, properness of quaternion random variables...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1505.06182
Project Gutenberg
by Basil Edward Hammond
texts

eye 46

favorite 0

comment 0

Book from Project Gutenberg: The Political Institutions of the Ancient Greeks
Topics: Political science, JC, Greece -- Politics and government
Source: https://www.gutenberg.org/ebooks/49368
Arxiv.org
by Fortuné Massamba; Salomon Joseph Mbatakou
texts

eye 5

favorite 0

comment 0

We study the geometry of Finsler submanifolds using the pulled-back approach. We define the Finsler normal pulled-back bundle and obtain the induced geometric objects, namely, induced pullback Finsler connection, normal pullback Finsler connection, second fundamental form and shape operator. Under a certain condition, we prove that induced and intrinsic Hashiguchi connections coincide on the pulled-back bundle of Finsler submanifold.
Topics: General Mathematics, Mathematics
Source: http://arxiv.org/abs/1703.08506
Arxiv.org
by Simone Farinelli
texts

eye 6

favorite 0

comment 0

A quantization procedure for the Yang-Mills equations for the Minkowski space $\mathbf{R}^{1,3}$ is carried out in such a way that field maps satisfying Wightman's axioms of Constructive Quantum Field Theory can be obtained. Moreover, the spectrum of the corresponding QCD Hamilton operator is proven to be positive and bounded away from zero except for the case of the vacuum state which has vanishing energy level. The particles corresponding to all solution fields are bosons. As expected from...
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1406.4177
Arxiv.org
by Debaroti Das; P. K. De
texts

eye 3

favorite 0

comment 0

Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on Lp metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their respective value and ambiguity indices. Finally, some comparative results are given in tabular form.
Topics: Mathematics, General Mathematics
Source: http://arxiv.org/abs/1410.7155