On the Solutions of a System of Third-Order Rational Difference Equations by A. M. Alotaibi, M. S. M. Noorani, M. A. El-Moneam

“…The structure of the solutions for the system nonlinear difference equations xn+1=ynyn-2/(xn-1+yn-2), yn+1=xnxn-2/(±yn-1±xn-2), n=0,1,…, is clarified in which the initial conditions x-2, x-1, x0, y-2, y-1, y0 are considered as arbitrary positive real numbers. …”
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On the Periodicity of a Difference Equation with Maximum by Ali Gelisken, Cengiz Cinar, Ibrahim Yalcinkaya

“…We investigate the periodic nature of solutions of the max difference equation xn+1=max⁡{xn,A}/(xnxn−1), n=0,1,…, where A is a positive real parameter, and the initial conditions x−1=Ar−1 and x0=Ar0 such that r−1 and r0 are positive rational numbers. …”
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N-Laplacian equations in ℝN with critical growth by João Marcos B. do Ó

“…., a(x)→∞ as |x|→∞ and the nonlinearity f behaves like exp(α|u|N/(N−1)) when |u|→∞.…”
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Diffeomorphism groups of connected sum of a product of spheres and classification of manifolds by Samuel Omoloye Ajala

“…In [1] and [2] a classification of a manifold M of the type (n,p,1) was given where Hp(M)=Hn−p(M)=ℤ is the only non-trivial homology groups. …”
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Dynamical Behavior of a System of Third-Order Rational Difference Equation by Qianhong Zhang, Jingzhong Liu, Zhenguo Luo

“…This paper deals with the boundedness, persistence, and global asymptotic stability of positive solution for a system of third-order rational difference equations xn+1=A+xn/yn-1yn-2, yn+1=A+yn/xn-1xn-2, n=0,1,…, where A∈(0,∞), x-i∈(0,∞); y-i∈(0,∞), i=0,1,2. …”
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Evaluation of the Response of Sorghum to Tillage Systems and Nitrogen Fertilization by Marwan Ramadhan, Sadiq Muhsin

“…Whereas Cavire 2 under CT showed best performance with 120 kg N ha−1 in the QL location in terms of biomass yield character.…”
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The Frobenius number associated with the number of representations for sequences of repunits by Komatsu, Takao

“…In this paper, we give the generalized Frobenius number when $a_j=(b^{n+j-1}-1)/ (b-1)$ ($b\ge 2$) as a generalization of the result of $p=0$ in [16].…”
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Global Behavior of the Max-Type Difference Equation xn+1=max⁡{1/xn,An/xn−1} by Taixiang Sun, Bin Qin, Hongjian Xi, Caihong Han

“…We study global behavior of the following max-type difference equation xn+1=max⁡{1/xn,An/xn−1}, n=0,1,…, where {An}n=0∞ is a sequence of positive real numbers with 0≤inf⁡An≤sup⁡An<1. …”
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Study on the Existence and Uniqueness of Solution of Generalized Capillarity Problem by Li Wei, Liling Duan, Haiyun Zhou

“…By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta (1978), the abstract result on the existence and uniqueness of the solution in Lp(Ω) of the generalized Capillarity equation with nonlinear Neumann boundary value conditions, where 2N/(N+1)<p<+∞ and N≥1 denotes the dimension of RN, is studied. …”
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Subclasses of α-spirallike functions associated with Ruscheweyh derivatives by Neng Xu, Dinggong Yang

“…Making use of the Ruscheweyh derivatives, we introduce the subclasses T(n,α,λ)(n∈{0,1,2,3,…},−π/2<α<π/2,and0≤λ≤cos2α) of functions f(z)=z+∑k=2∞akzk which are analytic in |z|<1. …”
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Metal-Free Synthesis of α-H Chlorine Alkylaromatic Hydrocarbons Driven by Visible Light by Lidia De Luca, Luca Ledda, Andrea Porcheddu, Massimo Carraro, Luisa Pisano, Silvia Gaspa

“…Here, we report the synthesis of benzyl chlorides and α-chloro alkyl arenes, mediated by visible light, starting from variously substituted toluenes and <i>N,N</i>-dichloroacetamide as a chlorinating reagent. …”
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Rings and groups with commuting powers by Hazar Abu-Khuzam, Adil Yaqub

“…Let R be a ring with identity which satisfies (i) xnyn=ynxn for all x,y in R, and (ii) for x,y in R, there exists a positive integer k=k(x,y) depending on x and y such that xkyk=ykxkand (n,k)=1. Then R is commutative. This result also holds for a group G. …”
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Weight Distribution of Periodic Errors and Optimal/Anti-Optimal Linear Codes by Pankaj Kumar Das

“…The paper discusses weight distribution of periodic errors and then the optimal case on bounds of parity check digits for (n=n1+n2, k) linear codes over GF(q) that corrects all periodic errors of order r in the first block of length n1 and all periodic errors of order s in the second block of length n2 and no others. …”
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Deposition of Atmospheric Nitrogen Compounds in Humid Tropical Cuba by Osvaldo Cuesta-Santos, Arnaldo Collazo, Antonio Wallo, Roberto Labrador, Maria Gonzalez, Paulo Ortiz

“…In Cuba, main atmospheric deposition of nitrogen compounds varies from approximately 12.0 to 65.0 kg N ha�1 year�1 in rural areas. Ammonia and ammonium are the most important elements in Cuba�s tropical conditions.…”
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Dynamics and Solutions of a Fifth-Order Nonlinear Difference Equation by M. M. El-Dessoky, E. M. Elabbasy, Asim Asiri

“…The main objective of this paper is to study the behavior of the rational difference equation of the fifth-order yn+1=αyn+βynyn-3/(Ayn-4+Byn-3), n=0,1,…, where α,β,A, and B are real numbers and the initial conditions y-4,y-3,y-2,y-1 and y0 are positive real numbers such that Ay-4+By-3≠0. …”
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The Structure of Isomorphic Digraph from Powers Modulo pe by Jinxing Zhao, Guixin Deng, Tiejun Liu

“…In this paper, we obtain necessary and sufficient conditions for G(n,k1)≃G(n,k2) when n=pe.…”
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Global Stability of a Rational Difference Equation by Guo-Mei Tang, Lin-Xia Hu, Gang Ma

“…We consider the higher-order nonlinear difference equation 𝑥𝑛+1=(𝑝+𝑞𝑥𝑛−𝑘)/(1+𝑥𝑛+𝑟𝑥𝑛−𝑘),𝑛=0,1,… with the parameters, and the initial conditions 𝑥−𝑘,…,𝑥0 are nonnegative real numbers. …”
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Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements by Kuo-Liang Su

“…It will be shown and induced that the d-dimensional indices in the Banach spaces version conditions ∑n(E‖Xn‖p/|nα|p)<∞ are sufficient to yield limmin1≤j≤d(nj)→∞(1/|nα|)∑k≤n∏j=1d(1−(kj−1)/nj)Xk=0 a.s. for arrays of James-type orthogonal random elements. …”
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A Double Inequality for the Trigamma Function and Its Applications by Zhen-Hang Yang, Yu-Ming Chu, Xiao-Jing Tao

“…As applications, some new approximation algorithms for the circumference ratio π and Catalan constant G=∑n=0∞-1n/(2n+1)2 are given. Here, ψ′ is the trigamma function.…”
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A New Multivariable Grey Convolution Model Based on Simpson’s Rule and Its Applications by Song Ding, Ruojin Li

“…Three empirical studies are carried out for verifying the above advantages of the optimized model, compared with the conventional GMC (1, n), GMCG (1, n), GM (1, n), and DGM (1, n) models. Results show that the new background values can effectively be calculated based on Simpson’s rule, and the optimized models significantly outperform other competing models in most cases.…”
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