On commutativity of one-sided s-unital rings by H. A. S. Abujabal, M. A. Khan

“…The following theorem is proved: Let r=r(y)>1, s, and t be non-negative integers. If R is a left s-unital ring satisfies the polynomial identity [xy−xsyrxt,x]=0 for every x,y∈R, then R is commutative. …”
Get full text

Iterative Algorithm for Solving a System of Nonlinear Matrix Equations by Asmaa M. Al-Dubiban

“…We discuss the positive definite solutions for the system of nonlinear matrix equations and , where , are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive definite solutions are given. …”
Get full text

Properties of the function f(x)=x/π(x) by Panayiotis Vlamos

“…We study the expression 2f(x+y)−f(x)−f(y) for integers x,y≥2 and as an application we make several remarks in connection with the conjecture of Hardy and Littlewood.…”
Get full text

Infinite-Dimensional Modular Lie Superalgebra Ω by Xiaoning Xu, Bing Mu

“…Then an intrinsic property is obtained by the invariance of the filtration; that is, the integers in the definition of Ω are intrinsic. Therefore, we classify the infinite-dimensional modular Lie superalgebra Ω in the sense of isomorphism.…”
Get full text

p-Adic discrete dynamical systems and collective behaviour of information states in cognitive models by Andrie Khrennikov

“…We develop a model of functioning of complex information systems (in particular, cognitive systems) in that information states are coded by p-adic integers. An information state evolves by iterations of a discrete p-adic dynamical system. …”
Get full text

Mean number of real zeros of a random hyperbolic polynomial by J. Ernest Wilkins

“…Consider the random hyperbolic polynomial, f(x)=1pa1coshx+⋯+np×ancoshnx, in which n and p are integers such that n≥2,   p≥0, and the coefficients ak(k=1,2,…,n) are independent, standard normally distributed random variables. …”
Get full text

Prime divisors of some shifted products by Eric Levieil, Florian Luca, Igor E. Shparlinski

“…We study prime divisors of various sequences of positive integers A(n)+1, n=1,…,N, such that the ratios a(n)=A(n)/A(n−1) have some number-theoretic or combinatorial meaning. …”
Get full text

$q$-Rationals and Finite Schubert Varieties by Ovenhouse, Nicholas

“…The classical $q$-analogue of the integers was recently generalized by Morier-Genoud and Ovsienko to give $q$-analogues of rational numbers. …”
Get full text

On Erdős sums of almost primes by Gorodetsky, Ofir, Lichtman, Jared Duker, Wong, Mo Dick

“…In this article, we show that the sums restricted to odd integers are indeed monotonically decreasing in $k$, sufficiently large. …”
Get full text

Theoretical approaches of interval-valued fuzzy code and fuzzy soft code by Masresha Woldie, Jejaw Mebrat, Mihret Taye

“…Through this paper, we use the set of integers modulo 2, that is = {0, 1}.…”
Get full text

A new class of infinite products, and Euler's totient by Geoffrey B. Campbell

“…We introduce some new infinite products, the simplest being(1−y)∏k=2∞∏j∈ϕk(1−ykqj)1/k=(1−y1−qy)1/(1−q),where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q≠1. …”
Get full text

Commutativity theorems for rings and groups with constraints on commutators by Evagelos Psomopoulos

“…Let n>1, m, t, s be any positive integers, and let R be an associative ring with identity. …”
Get full text

Some fixed point theorems on nonlinear contractive mappings in Hilbert space by Namana Seshagiri Rao, Karusala Kalyani

“…Further this result is extended and generalized for some positive integers powers of a pair of continuous self mappings and then is devolved for a sequence of continuous self mappings in the Hilbert space. …”
Get full text

Wijsman Orlicz Asymptotically Ideal -Statistical Equivalent Sequences by Bipan Hazarika

“…An ideal is a family of subsets of positive integers which is closed under taking finite unions and subsets of its elements. …”
Get full text

Oscillation for Higher Order Dynamic Equations on Time Scales by Taixiang Sun, Qiuli He, Hongjian Xi, Weiyong Yu

“…We investigate the oscillation of the following higher order dynamic equation: {an(t)[(an-1(t)(⋯(a1(t)xΔ(t))Δ⋯)Δ)Δ]α}Δ+p(t)xβ(t)=0, on some time scale T, where n≥2, ak(t)   (1≤k≤n) and p(t) are positive rd-continuous functions on T and α,β are the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.…”
Get full text

The Structure of Isomorphic Digraph from Powers Modulo pe by Jinxing Zhao, Guixin Deng, Tiejun Liu

“…For positive integers n and k, let G(n,k) denote the digraph whose set of vertices is {0,1,2,…,n-1} and there is a directed edge from a to b if ak≡b  (mod n). …”
Get full text

Extended supersingular isogeny Diffie–Hellman key exchange protocol: Revenge of the SIDH by Daniel Cervantes‐Vázquez, Eduardo Ochoa‐Jiménez, Francisco Rodríguez‐Henríquez

“…SIDH operates on supersingular elliptic curves defined over Fp2, where p is a large prime number of the form p=4eA3eB−1 and eA and eB are positive integers such that 4eA≈3eB. A variant of the SIDH protocol, dubbed extended SIDH (eSIDH), is presented. …”
Get full text

Combinatorial and Multinomial Coefficients and its Computing Techniques for Machine Learning and Cybersecurity by Chinnaraji Annamalai

“… Mathematical and combinatorial techniques with nonnegative integers are used as computing algorithms for the programs development to apply in artificial intelligence and cybersecurity. …”
Get full text

A continuous version of multiple zeta functions and multiple zeta values by Li, Jiangtao

“…The evaluations of these functions at positive integers (continuous multiple zeta values) satisfy the shuffle product. …”
Get full text

On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces by Awad A. Bakery, Mustafa M. Mohammed

“…An ideal I is a hereditary and additive family of subsets of positive integers ℕ. In this paper, we will introduce the concept of generalized random n-normed space as an extension of random n-normed space. …”
Get full text