General Mathematics
A method is suggested for treating the well-known deficiency in the use of Pade approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of…
Conics and Cartesian ovals are very important curves in various fields of science. Also aspheric curves based on conics are useful in optics. Superconic curves recently suggested by A. Greynolds are extensions of both conics and Cartesian…
The idea of generating prime numbers through sequence of sets of co-primes was the starting point of this paper that ends up by proving two conjectures, the existence of infinitely many twin primes and the Goldbach conjecture. The main idea…
In the proposed matrix primes, through which one can readily generate a sequence of primes. The paper also proposes a number of theorems proved by which an infinite number of prime numbers twins
Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.
In this paper we introduce the quadratic Jaco graph. The characteristics, properties and some graph invariants of quadratic Jaco graphs are discussed. The observation that quadratic Jaco graphs are well-defined in respect of complete graphs…
The first study related to this paper was on the notion of primitive holes. This paper reports on research in respect of clique parameters and related properties thereof within Jaco-type graphs.
The main aim of the present book is to suggest some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and some inventory models related to capacity constraints.…
The behaviour of real zeroes of the Hurwitz zeta function $$\zeta (s,a)=\sum_{r=0}^{\infty}(a+r)^{-s}\qquad\qquad a > 0$$ is investigated. It is shown that $\zeta (s,a)$ has no real zeroes $(s=\sigma,a)$ in the region $a…
We give a popular account of the Banach-Tarski paradox and its connections with the axiom of choice.
In this paper we present a set transformation of points in a line of the Desargues affine plane in a additive group. For this, the first stop on the meaning of the Desargues affine plane, formulating first axiom of his that show proposition…
The aim of writing this paper is given in the title. The results on semigroups can be easily transferred to hyper-semigroups in the way indicated in the present paper.
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…
In this paper, we introduce special Smarandache curves according to Sabban frame on and we give some characterization of Smarandache curves. Besides, we illustrate examples of our results.
Let $X$ denotes a set of non-negative integers and $\mathscr{P}(X)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\to \mathscr{P}(X)-\{\emptyset\}$ such that the induced…
In this paper analyzes \textit{The Erd\H{o}s-Straus conjecture} asserts that $f$$(n)$ $>$ 0 for every $n$ $\geq$ 2, where $f(n)$ indicates the number of solutions to the Diophantine Equation…
Based on M. Grossman in \cite{Grossman83} and Grossman an Katz \cite{GrossmanKatz}, in this paper we discuss about the applications of bigeometric calculus in different branches of mathematics and economics.
We make an analytical proof for Lehmer's totient conjecture. Lehmer conjectured that there is no solution for the congruence equation $n-1\equiv 0~(mod~\phi(n))$ with composite integers,$n$, where $\phi(n)$ denotes Euler's totient function.…
A method is given for estimating clamped plane elastica. Arguments are made, and evidence is provided by way of illustrative examples, suggesting that the new method is quicker and more robust than standard discretisation, and more likely…
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…