Factoring with Pell conics by Rasa Šleževičienė

“… In the paper the Pell conics method for factoring integers, based on observations of Lemmer­meyer [2, 3], is presented explicitly. …”
Get full text

On finitely equivalent continua by Janusz J. Charatonik

“…For positive integers m and n, relations between (hereditary) m- and n-equivalence are studied, mostly for arc-like continua. …”
Get full text

Exceptional Sets for Sums of Prime Cubes in Short Interval by Gongrui Chen

“…Let EN,X denote the number of even integers n, with N−X≤n≤N, such that n cannot be written as n=p13+⋯+p83. …”
Get full text

Units in families of totally complex algebraic number fields by L. Ya. Vulakh

“…Multidimensional continued fraction algorithms associated with GLn(ℤk), where ℤk is the ring of integers of an imaginary quadratic field K, are introduced and applied to find systems of fundamental units in families of totally complex algebraic number fields of degrees four, six, and eight.…”
Get full text

On (a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs by Martin Bača, Andrea Semaničová-Feňovčíková, Tao-Ming Wang, Guang-Hui Zhang

“…An (a,s)-vertex-antimagic edge labeling (or an (a,s)-VAE labeling, for short) of G is a bijective mapping from the edge set E(G) of a graph G to the set of integers 1,2,…,|E(G)| with the property that the vertex-weights form an arithmetic sequence starting from a and having common difference s, where a and s are two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. …”
Get full text

Study on the Variation Law of Static Transmission Error for Cylindrical Gear by Chang Lehao, Liu Geng, He Zhaoxia

“…Under the same loading condition,the transmission error will have local minimum fluctuations when the overlap（ or transverse） contact ratio is close to integers,while it will have local maximum fluctuations when the total contact ratio of a helical gear pair is close to integers. …”
Get full text

On the cardinality of subsequence sums II by Jiang, Xing-Wang, Li, Ya-Li

“…Let $A=(\underbrace{a_1,\ldots ,a_1}_{r_1},\underbrace{a_2,\ldots ,a_2}_{r_2},\ldots ,\underbrace{a_k,\ldots ,a_k}_{r_k})$ be a finite sequence of integers with $a_1…”
Get full text

Approximation Properties of Durrmeyer Type of (p,q)-Bleimann, Butzer, and Hahn Operators by Qing-Bo Cai, İsmet Yüksel, Ülkü Dinlemez Kantar, Bayram Çekim

“…In this study, we introduce a Durrmeyer type of Bleimann, Butzer, and Hahn operators (BBH) on (p,q)-integers. We derive the some approximation properties for these operators. …”
Get full text

Evaluations of a Weighted Average of Gauss Sums by Wen-Kai Shao, Yuan He

“…By making use of some properties of the cotangent function and the Bernoulli polynomials, we explicitly evaluate the weighted average of Gauss sums in terms of the special values of Dirichlet L-functions at positive integers.…”
Get full text

A commutativity theorem for left s-unital rings by Hamza A. S. Abujabal

“…If there exist nonnegative integers m>1, k≥0, and n≥0 such that for any x, y in R, [xky−xnym,x]=0, then R is commutative.…”
Get full text

Note on the Lower Bound of Least Common Multiple by Shea-Ming Oon

“…Consider a sequence of positive integers in arithmetic progression with . Denote the least common multiple of by . …”
Get full text

On the Diophantine equation x2+2k=yn by S. Akhtar Arif, Fadwa S. Abu Muriefah

“…By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various theorems regarding the solutions of this equation in rational integers are proved. A conjecture regarding the solutions of this equation has been put forward and proved to be true for a large class of values of k and n.…”
Get full text

On periodic rings by Xiankun Du, Qi Yi

“…It is proved that a ring is periodic if and only if, for any elements x and y, there exist positive integers k,l,m, and n with either k≠m or l≠n, depending on x and y, for which xkyl=xmyn. …”
Get full text

Normal Families of Zero-Free Meromorphic Functions by Yuntong Li

“…Let 𝑎(≠0),𝑏∈ℂ, and 𝑛 and 𝑘 be two positive integers such that 𝑛≥2. Let ℱ be a family of zero-free meromorphic functions defined in a domain 𝒟 such that for each 𝑓∈ℱ, 𝑓+𝑎(𝑓(𝑘))𝑛−𝑏 has at most 𝑛𝑘 zeros, ignoring multiplicity. …”
Get full text

On (p,q)-Analogue of Gamma Operators by Wen-Tao Cheng, Wen-Hui Zhang

“…In this paper, a kind of new analogue of Gamma type operators based on (p,q)-integers is introduced. The Voronovskaja type asymptotic formula of these operators is investigated. …”
Get full text

Global Attractivity of a Higher-Order Difference Equation by R. Abo-Zeid

“…The aim of this work is to investigate the global stability, periodic nature, oscillation, and the boundedness of all admissible solutions of the difference equation xn+1=Axn-2r-1/(B-C∏i=lkxn-2i), n=0,1,2,… where A,B,C are positive real numbers and l,r,k are nonnegative integers, such that l≤k.…”
Get full text

On the Dynamics of a Higher-Order Rational Difference Equation by A. M. Ahmed

“…The aim of this paper is to investigate the global asymptotic stability and the periodic character for the rational difference equation xn+1=αxn-1/(β+γΠi=lkxn-2ipi),  n=0,1,2,…, where the parameters α,β,γ,pl,pl+1,…,pk are nonnegative real numbers, and l,k are nonnegative integers such that l≤k.…”
Get full text

Identities of Symmetry for Higher-Order Generalized q-Euler Polynomials by D. V. Dolgy, D. S. Kim, T. G. Kim, J. J. Seo

“…We investigate the properties of symmetry in two variables related to multiple Euler q-l-function which interpolates higher-order q-Euler polynomials at negative integers. From our investigation, we can derive many interesting identities of symmetry in two variables related to generalized higher-order q-Euler polynomials and alternating generalized q-power sums.…”
Get full text

On structure of certain periodic rings and near-rings by Moharram A. Khan

“…The aim of this work is to study a decomposition theorem for rings satisfying either of the properties xy=xpf(xyx)xq or xy=xpf(yxy)xq, where p=p(x,y),q=q(x,y) are nonnegative integers and f(t)∈tℤ[t] vary with the pair of elements x,y, and further investigate the commutativity of such rings. …”
Get full text

On Generalized Periodic-Like Rings by Howard E. Bell, Adil Yaqub

“…Call R generalized periodic-like if for all x∈R∖(N∪J∪Z) there exist positive integers m, n of opposite parity for which xm−xn∈N∩Z. …”
Get full text