Mathematics

In the article, we review and critique the Corollary and Theorem of Wiener index of a fuzzy graph and application to illegal immigration networks, and in addition to providing examples of violations.

The recent technique for estimating lower bounds of the prime counting function $\pi(x)=#\{p \leq x: p\text{ prime}\}$ by means of the irrationality measures μ(ζ(s))≥2 of special values of the zeta function claims that π(x)≫loglogx/logloglogx . This note improves the lower bound to π(x)≫logx , and extends the analysis to the irrationality measures μ(ζ(s))≥1 for rational ratios of zeta functions.

A vertex subset W⊆V of the graph G=(V,E) is an independent dominating set if every vertex in V∖W is adjacent to at least one vertex in W and the vertices of W are pairwise non-adjacent. We enumerate independent dominating sets in several classes of graphs made by a linear or cyclic concatenation of basic building blocks. Explicit recurrences are derived for the number of independent dominating sets of these kind of graphs. Generating functions for the number of independent dominating sets of triangular and squares cacti chain are also computed.

The novelty of this paper is to construct the explicit combinatorial formula for the number of all distinct fuzzy matrices of finite order, which leads us to invent a new sequence. In order to achieve this new sequence, we analyze the behavioral study of equivalence classes on the set of all fuzzy matrices of a given order under a suitable natural equivalence relation. In addition this paper characterizes the properties of non-equivalent classes of fuzzy matrices of order n with elements having degrees of membership values anywhere in the closed unit interval [0,1]. Further, this paper also derives some important relevant results by enumerating the number of all distinct fuzzy matrices of a given order in general. And also, we achieve these results by incorporating the notion of k-level fuzzy matrices, chains, and flags (maximal chains). Keywords: Fuzzy matrices; k-level fuzzy matrices; Chains; Flags; Binomial numbers

In this paper we investigate the combinatorical structure of the Kleene type truth tables of all bracketed formulae with n distinct variables connected by the binary connective of implication.

Philosophically, a repertoire of signifying practices as constitutive of a cultural endowment was said to be ambiguous or unworthy of pursuit. Currently, a unique capacity of the mind is considered to be its ability to produce a digital infinity. The infinity produced, here an operation expressing subjectivity, follows a simple principle according to which a limited set of means, here functions, are utilized to produce an infinite range of potentially meaningful expressions. It is from this concept that I propose a theory of subjectivity and the endowment from which it expresses a self in the world(s) it participates. In particular, I make a case for the subjectivity of blackness. I treat subjectivity as an operation in order to address problems with Identity theory, Afro-Pessimism, and to formalize an analysis of blackness despite the onto-epistemological commitments of racialized systems of categorization. In sum, subjectivity will be characterized as poetic computation.

The present paper deals with a study of curves on a smooth surface whose position vector always lies in the tangent plane of the surface and it is proved that such curves remain invariant under isometry of surfaces. It is also shown that length of the position vector, tangential component of the position vector and geodesic curvature of a curve on a surface whose position vector always lies in the tangent plane are invariant under isometry of surfaces.

We describe recurring patterns of numbers that survive each wave of the Sieve of Eratosthenes, including symmetries, uniform subdivisions, and quantifiable, predictive cycles that characterize their distribution across the number line. We generalize these results to numbers that are relatively prime to arbitrary sets of prime numbers and derive additional insights about the distribution of integers counted by Euler's phi-function.

The concept of the cyclic averages are introduced for a regular polygon P n and a Platonic solid T n . It is shown that cyclic averages of equal powers are the same for various P n ( T n ) , but their number is characteristic of P n ( T n ) . Given the definition of a circle (sphere) by the vertices of P n ( T n ) and on the base of the cyclic averages are established the common metrical relations of P n ( T n ) .

In this paper, we define a graph-theoretic analog for the Riemann tensor and analyze properties of the cyclic symmetry. We have developed a fuzzy graph-theoretic analog of the Riemann tensor and have analyzed its properties. We have also shown how the fuzzy analog satisfies the properties of the 6X6 matrix of the Riemann tensor by expressing it as a union of the fuzzy complete graph formed by the permuting vertex set and a Levi-Civita graph analog. We have concluded the paper with a brief discussion on the similarities between the properties of the fuzzy graphical analog and the Riemann tensor and how it can be a plausible analogous model for the Petrov-Penrose classification.