Periodic Solutions of Some Polynomial Differential Systems in Dimension 3 via Averaging Theory by Amar Makhlouf, Lilia Bousbiat

“…=az+εR(x,y,z)+h3(t), where P, Q, and R are polynomials in the variables x, y, and z of degree n,  hi(t)=hi(t+2π) with i=1,2,3 being periodic functions, a is a real number, and ε is a small parameter.…”
Get full text

Nearly Derivations on Banach Algebras by M. Eshaghi Gordji, H. Khodaei, G. H. Kim

“…Let 𝑛 be a fixed integer greater than 3 and let 𝜆 be a real number with 𝜆≠(𝑛2−𝑛+4)/2. We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖∑1≤𝑖<𝑗≤𝑛1≤𝑘𝑙≠𝑖,𝑗≤𝑛𝑓((𝑥𝑖+𝑥𝑗∑)/2+𝑛−2𝑙=1𝑥𝑘𝑙∑)+𝑓(𝑛𝑖=2𝑥𝑖)+𝑓(𝑥1∑)‖≤‖𝜆𝑓(𝑛𝑖=1𝑥𝑖)‖.…”
Get full text

Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces by Chin-Tzong Pang, Eskandar Naraghirad

“…Our results are applicable in the function spaces Lp, where 1<p<∞ is a real number.…”
Get full text

MECHANICAL STATE ANALYSIS USING QUANTUM THEORY AND MATHEMATICAL MORPHOLOGICAL FILTER by SHI Ying

“…Aiming at the erosion operator for the mathematical morphological filter（ MMF）,the quantum-inspired weighting structuring element（ QWSE） is proposed based on the quantum theory to extract fault information of mechanical vibration signal.Firstly,after analyzing the system with multiple quantum bits,a method which is employed to map the quantum space to the real number space is presented and the calculation formula of the QWSE is obtained. …”
Get full text

Immune computing-based base station location planning in the TD-SCDMA network by ZHU Si-feng1, LIU Fang1, CHAI Zheng-yi1

“…To reduce the cost of TD-SCDMA network construction,a solution of base station location planning problem based on immune computing was proposed.The difficulties of TD-SCDMA base station construction and the principle of location planning were expound,clonal multiplication operator,clonal mutation and clonal selection operator with real-number encoding were designed,the framework of immune memory clonal algorithm for base station location plan-ning problem was given,and simulation experiments were done to validate the proposed algorithm.Experimental result shows that the proposed solution can obtain higher network coverage rate with lower cost of network construction rela-tively,and has the advantage of good application value.…”
Get full text

Transcendence of $L(1,\chi _s)/\Pi $ in positive characteristic. A simple automata-style proof by Liu, Si-Han, Yao, Jia-Yan

“…Carlitz defined $\Pi $, an analog of the real number $\pi $, and D. Goss defined $L(s,\chi )$, analogs of Dirichlet $L$-functions. …”
Get full text

On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices by Abeer M. Albalahi, Akbar Ali

“…For a graph G, its general sum-connectivity is usually denoted by χαG and is defined as the sum of the numbers dGu+dGvα over all edges uv of G, where dGu,dGv represent degrees of the vertices u,v, respectively, and α is a real number. This paper addresses the problem of finding graphs possessing the minimum χα value over the class of all trees with a fixed order n and fixed number of pendent vertices n1 for α>1. …”
Get full text

Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1 by Kaoutar Lamrini Uahabi, Mohammed Zaoui

“…We deal with the family B(n,k,r) of trinomial arcs defined as the set of roots of the trinomial equation zn=αzk+(1−α), where z=ρeiθ is a complex number, n and k are two integers such that 0<k<n, and α is a real number between 0 and 1. These arcs B(n,k,r) are continuous arcs inside the unit disk, expressed in polar coordinates (ρ,θ). …”
Get full text

The Second and Fourth Moments of Discrete Gaussian Distributions over Lattices by Wei Zhao, Guoyou Qian

“…For any n-dimensional vector c and positive real number s, let Ds,c and DΛ,s,c denote the continuous Gaussian distribution and the discrete Gaussian distribution over Λ, respectively. …”
Get full text

Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework by Porfirio Toledo

“…The purpose of this paper is to study the existence of solutions of a Hamilton-Jacobi equation in a minimax discrete-time case and to show different characterizations for a real number called the critical value, which plays a central role in this work. …”
Get full text

Vertex-Edge-Degree-Based Topological Properties for Hex-Derived Networks by Ali Ahmad, Muhammad Imran

“…A topological index can be focused on uprising of a chemical structure into a real number. The degree-based topological indices have an active place among all topological indices. …”
Get full text

Some Upper Bounds on the First General Zagreb Index by Muhammad Kamran Jamil, Aisha Javed, Ebenezer Bonyah, Iqra Zaman

“…The first general Zagreb index MγG or zeroth-order general Randić index of a graph G is defined as MγG=∑v∈Vdvγ where γ is any nonzero real number, dv is the degree of the vertex v and γ=2 gives the classical first Zagreb index. …”
Get full text

Generalized dissipativeness in a Banach space by David R. Gurney

“…Suppose X is a real or complex Banach space with dual X* and a semiscalar product [,]. For k a real number, a subset B of X×X will be called k-dissipative if for each pair of elements (x1,y1), (x2,y2) in B, there existsh∈{f∈X*:[x,f]=|x|2=|f|2}such thatRe[y1−y2,h]≤k|x1−x2|2.This definition extends a notion of dissipativeness which is equivalent to having k equal zero here. …”
Get full text

Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation by Jun-Rui Yue, Jian-Ping Sun, Shuqin Zhang

“…We consider the following boundary value problem of nonlinear fractional differential equation: (CD0+αu)(t)=f(t,u(t)),  t∈[0,1],  u(0)=0,   u′(0)+u′′(0)=0,  u′(1)+u′′(1)=0, where α∈(2,3] is a real number,  CD0+α denotes the standard Caputo fractional derivative, and f:[0,1]×[0,+∞)→[0,+∞) is continuous. …”
Get full text

Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping by Hassan Azadi Kenary, Themistocles M. Rassias, H. Rezaei, S. Talebzadeh, Won-Gil Park

“…Using fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 𝑟2𝑓((𝑥+𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥−𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥+𝑦−𝑧)/𝑟)+𝑟2𝑓((−𝑥+𝑦+𝑧)/𝑟)=4𝑓(𝑥)+4𝑓(𝑦)+4𝑓(𝑧), where 𝑟 is a positive real number, in non-Archimedean normed spaces.…”
Get full text

Multiple Solutions to Fractional Difference Boundary Value Problems by Huiqin Chen, Yaqiong Cui, Xianglan Zhao

“…The following fractional difference boundary value problems ▵νyt=-ft+ν-1,yt+ν-1, y(ν-2)=y(ν+b+1)=0 are considered, where 1<ν≤2 is a real number and ▵νy(t) is the standard Riemann-Liouville fractional difference. …”
Get full text

On the First Three Extremum Values of Variable Sum Exdeg Index of Trees by Shu-Bo Chen, Syed Sheraz Asghar, Muhammad Ahsan Binyamin, Zahid Iqbal, Tayyeb Mahmood, Adnan Aslam

“…For a graph G, its variable sum exdeg index is defined as SEIaG=∑xy∈EGadx+ady, where a is a real number other than 1 and dx is the degree of a vertex x. …”
Get full text

Complex-Valued Migrativity of Complex Fuzzy Operations by Yingying Xu, Haifeng Song, Lei Du, Songsong Dai

“…In addition, α−migrativity for various fuzzy operations on [0, 1] has been well discussed, where α is a real number and α∈0,1. Thus, this paper studies α−migrativity for binary functions on the unit circle of the complex plane O, where α is a complex number and α∈O. …”
Get full text