Asymptotic Stability for a Class of Nonlinear Difference Equations by Chang-you Wang, Shu Wang, Zhi-wei Wang, Fei Gong, Rui-fang Wang

“…We study the global asymptotic stability of the equilibrium point for the fractional difference equation xn+1=(axn-lxn-k)/(α+bxn-s+cxn-t), n=0,1,…, where the initial conditions x-r,x-r+1,…,x1,x0 are arbitrary positive real numbers of the interval (0,α/2a),l,k,s,t are nonnegative integers, r=max⁡⁡{l,k,s,t} and α,a,b,c are positive constants. …”
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Schur Convexity and Inequalities for a Multivariate Symmetric Function by Ming-Bao Sun, Xin-Ping Li, Sheng-Fang Tang, Zai-Yun Zhang

“…In the article, we provide the Schur, Schur multiplicative, and Schur harmonic convexities properties for the symmetry function Fnx,r=Fnx1,x2,⋯,xn;r=∏1≤i1<i2<⋯<ir≤n ∑j=1r xij/1−xij1/r on 0,1n and find several new analytical inequalities by use of the majorization theory, where x=x1,⋯,xn∈0,1n, r=1,2,⋯,n and i1,i2,⋯,in are positive integers.…”
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Close-to-Convexity of Convolutions of Classes of Harmonic Functions by Raj Kumar Garg, Jay M. Jahangiri

“…For j=1,2 and for positive integers m and n, we consider classes of harmonic functions fj=hj+gj¯, where g1(z)=znh1(z) and g2′(z)=znh2′(z) or g1′(z)=znh1′(z) and g2′(z)=zmh2′(z), and we prove that their convolution f1⁎f2=h1⁎h2+g1⁎g2¯ is locally one-to-one, sense-preserving, and close-to-convex harmonic in z<1.…”
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Oscillation Criteria for a Class of Second-Order Neutral Delay Dynamic Equations of Emden-Fowler Type by Zhenlai Han, Tongxing Li, Shurong Sun, Chao Zhang, Bangxian Han

“…Here γ>0 is a quotient of odd positive integers with a and p being real-valued positive functions defined on &#x1D54B;. …”
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On the page-number of a circulant graph by Xiaoyuan Dong, Dengju Ma

“…The circulant graph C(m, n) is such a graph that its vertex set is [Formula: see text] and edge set is [Formula: see text], where m, n are positive integers satisfying [Formula: see text] and indices is read modulo m. …”
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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. …”
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Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales by Quanwen Lin, Baoguo Jia, Qiru Wang

“…As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ([x′(t)]α)′+csintxα(t)=cos⁡t, where α=p/q, p, q are odd positive integers.…”
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The Zeros of the Bergman Kernel for Some Reinhardt Domains by Jong-Do Park

“…This result is a complete characterization of the existence of zeros of the Bergman kernel for Dn for all positive integers n.…”
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On iterative solution of nonlinear functional equations in a metric space by Rabindranath Sen, Sulekha Mukherjee

“…Operator equations of the form Anu=Pmu, where u∈R, n and m positive integers, are also treated.…”
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Sign changes of the partial sums of a random multiplicative function II by Aymone, Marco

“…We study two models of random multiplicative functions: Rademacher random multiplicative functions supported on the squarefree integers $f$, and Rademacher random completely multiplicative functions $f^*$. …”
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Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques by M. Khalid Mahmood, Farooq Ahmad

“…For this purpose, root-finding iterative methods are employed for solving polynomial congruences of the form axn≡b(mod pk), k≥1, where a,b, and n>0 are integers which are not divisible by an odd prime p. …”
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Partition regularity of Pythagorean pairs by Nikos Frantzikinakis, Oleksiy Klurman, Joel Moreira

“…We address a core partition regularity problem in Ramsey theory by proving that every finite coloring of the positive integers contains monochromatic Pythagorean pairs (i.e., $x,y\in {\mathbb N}$ such that $x^2\pm y^2=z^2$ for some $z\in {\mathbb N}$ ). …”
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Uniqueness Theorems on Difference Monomials of Entire Functions by Gang Wang, Deng-li Han, Zhi-Tao Wen

“…It assumed that f and g are transcendental entire functions with finite order and Ek)(1,fnf(z+c))=Ek)(1,gng(z+c)), where c is a nonzero complex constant and n, k are integers. It is proved that if one of the following holds (i) n≥6 and k=3, (ii) n≥7 and k=2, and (iii) n≥10 and k=1, then fg=t1 or f=t2g for some constants t2 and t3 which satisfy t2n+1=1 and t3n+1=1. …”
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Direct sums of J-rings and radical rings by Xiuzhan Guo

“…We prove that if R satisfies (∗) given x, y in R there exist integers m=m(x,y)>1 and n=n(x,y)>1 such that xmy=xyn and if each x∈R is the sum of a potent element and a nilpotent element, then N and P are ideals and R=N⊕P. …”
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Cyclotomic equations and square properties in rings by Benjamin Fine

“…It is shown that this holds in an infinite class of rings which includes the integers, polynomial rings over many fields and Zpn where P is a prime such that −3 is not a square modp. …”
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Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs by Sumiya Nasir, Nazeran Idrees, Afshan Sadiq, Fozia Bashir Farooq, Salma Kanwal, Muhammad Imran

“…A finite, simple graph of order k is said to be a strongly multiplicative graph when all vertices of the graph are labeled by positive integers 1,2,3,…,k such that the induced edge labels of the graph, obtained by the product of labels of end vertices of edges, are distinct. …”
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Power of a determinant with two physical applications by James D. Louck

“…The generalization of this map to arbitrary square arrays of nonnegative integers, having given row and column sums, is also given.…”
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Novel and effective secret sharing scheme by Run-hua SHI, Liu-sheng HUANG, Wei YANG, Hong ZHONG

“…A novel secret sharing scheme was proposed.This scheme consisted of two layer protocols:in the first layer,a larger secret was split into t smaller integers (sub-secrets) based on the Stern-Brocot tree; in the lower layer,t sub-secrets obtained from the first layer were regarded as t initial states in one-dimensional cellular automaton model,and then from the t initial states it could dynamic create all participants’ shares according to the simple fixed rule.This scheme could dynamic add new member,adjust the threshold value and renew the secret and the shares.Besides,there were still other advantages that the costs of the computation were very low and the size of the shares was very small.The results of analysis show that it was secure and very efficient.…”
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Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral by Tim Johnson

“…Ulam’s spiral reveals patterns in the prime numbers by presenting positive integers in a right-angled whorl. The classic spatial prisoner’s dilemma (PD) reveals pathways to cooperation by presenting a model of agents interacting on a grid. …”
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Error Correction for Check Digit Systems over p-Groups and Applications to DNA Sequences by Louis Beaugris

“…Inspired by a check digit system constructed from the companion matrix of a primitive polynomial over the integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula> and that focused on error detection, this work develops error-correction formulas for single errors and transposition errors for that check digit scheme. …”
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