Authors:B. Miraftab; R. Nikandish Pages: 1 - 10 Abstract: Let R be a ring with unity. The co-maximal ideal graph of R, denoted by \(\Gamma (R)\) , is a graph whose vertices are all non-trivial left ideals of R, and two distinct vertices \(I_1\) and \(I_2\) are adjacent if and only if \(I_1 + I_2 = R\) . In this paper, some results on the co-maximal ideal graphs of matrix algebras are given. For instance, we determine the domination number, the clique number and a lower bound of the independence number of \(\Gamma (M_n(\mathbb {F}_q))\) , where \(M_n(\mathbb {F}_q)\) is the ring of \(n\times n\) matrices over the finite field \(\mathbb {F}_q\) . Furthermore, we characterize all rings (not necessarily commutative) whose domination numbers of their co-maximal ideal graphs are finite. Among other results, we show that if \(\Gamma (R)\cong \Gamma (M_n(\mathbb {F}_q))\) , where \(n\ge 2\) is a positive integer and R is a ring, then \(R\cong M_n(\mathbb {F}_q)\) . Also, it is proved that if R and \(R'\) are two finite reduced rings and \(\Gamma (M_m(R))\cong \Gamma (M_n(R'))\) , for some positive integers \(m,n\ge 2\) , then \(m=n\) and \(R\cong R'\) . PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0141-7 Issue No:Vol. 24, No. 1 (2018)

Authors:M. Hamidi; A. Broumand Saeid Pages: 11 - 35 Abstract: In this paper, we introduce a strongly regular relation on hyper EQ-algebra as a fundamental relation and study some of its properties. We construct the quotient of any hyper EQ-algebra via (regular relation) strongly regular relations. Finally, relationships between filter and EQ-filter are studied in detail. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0159-x Issue No:Vol. 24, No. 1 (2018)

Authors:M. S. Mahadeva Naika; C. Shivashankar Pages: 37 - 60 Abstract: In 2002 Andrews, Lewis and Lovejoy introduced partition function PD(n), the number of partitions of n with designated summands and using modular forms they obtained many congruences modulo 3 and powers of 2. For example, they proved \(PD(3n+2)\equiv 0 \pmod {3}\) . In this paper, we study various arithmetic properties of \(PD_2(n)\) modulo 3 and powers of 2, where \(PD_2(n)\) denotes the number of bipartitions of n with designated summands. We obtain congruences like \(PD_2(3^{\alpha +3}(3n+2))\equiv 0 \pmod {3}\) , \(PD_2(3^{\alpha +3}(6n+4))\equiv 0 \pmod {3}\) , \(PD_2(24n+15)\equiv 0\pmod {2^5}\) , \(PD_2(24n+23)\equiv 0\pmod {2^5}\) , \(PD_2(24n+12)\equiv 0\pmod {12}\) and \(PD_2(18n+15)\equiv 0\pmod {48}\) . PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0140-8 Issue No:Vol. 24, No. 1 (2018)

Authors:José Jaime Hernández Castillo Pages: 61 - 79 Abstract: We give conditions to determine if a cycle is indecomposable in the higher Chow group \(\text {CH}^{r}(X,m;\mathbb {Q})\) , for X a complex smooth projective variety. We show that the primitive part of topological invariant associated with an arithmetic normal function of a cycle is related to its decomposability. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0146-2 Issue No:Vol. 24, No. 1 (2018)

Authors:Zhanmin Zhu Pages: 81 - 94 Abstract: Let R be a ring and n be a positive integer. R is called left n-coherent, if every n-presented left R-module is \((n+1)\) -presented. A left R-module M is called (n, 0)-injective if Ext \(^1_R(V, M)=0\) for every n-presented module V, a right R-module F is called (n, 0)-flat if Tor \(^R_1(F, V)=0\) for every n-presented module V, a left R-module M is called (n, 0)-projective if \(\mathrm{Ext}^1_R(M, N)=0\) for any (n, 0)-injective module N, and a right R-module M is called (n, 0)-cotorsion if \(\mathrm{Ext}^1_R(F, M)=0\) for any (n, 0)-flat module F. We give some characterizations and properties of (n, 0)-projective modules and (n, 0)-cotorsion modules. n-coherent rings, n-hereditary rings and n-regular rings are characterized by (n, 0)-projective modules, (n, 0)-cotorsion modules, (n, 0)-injective modules and (n, 0)-flat modules. PubDate: 2018-04-01 DOI: 10.1007/s40590-017-0160-z Issue No:Vol. 24, No. 1 (2018)

Authors:Tugce Pekacar Calci; Abdullah Harmanci; Burcu Ungor Pages: 95 - 106 Abstract: In this paper, we deal with a new approach to quasipolarity notion for rings, namely an element a of a ring R is called weakly nil-quasipolar if there exists \(p^2 = p\in comm^2(a)\) such that \(a + p\) or \(a-p\) is nilpotent, and the ring R is called weakly nil-quasipolar if every element of R is weakly nil-quasipolar. The class of weakly nil-quasipolar rings lies properly between the classes of nil-quasipolar rings and quasipolar rings. Although it is an open problem whether strongly clean (even quasipolar) rings have stable range one, we show that there is an affirmative answer for weakly nil-quasipolar rings. It is also proved that if R is a weakly nil-quasipolar NI ring, then R / N(R) is commutative. Moreover, we consider the question of when certain \(2 \times 2\) matrices over a commutative local ring is weakly nil-quasipolar. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0145-3 Issue No:Vol. 24, No. 1 (2018)

Authors:S. Mirvakili; S. M. Anvariyeh; B. Davvaz Pages: 107 - 121 Abstract: This paper concerns a new relationship between hyperrings and rings. It is a continuation of ideas presented by Babaeia, Jafarpour, and Mousavi. We apply generalization of a complete part in a hyperring. We study the notion of strongly \(\mathcal {U}\) -regular relations on hyperrings and investigate some of their properties. In particular, we investigate the properties of rings derived from strongly \(\mathcal {U}\) -regular relations. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0157-z Issue No:Vol. 24, No. 1 (2018)

Authors:Runshi Zhang; Shitian Liu Pages: 123 - 131 Abstract: Let \(L_n(q)\) be the projective special linear group of degree n over a finite field of order q. In this paper, the projective special linear group \(L_3(q)\) , where \(q\in \{5,7,8,9\}\) is studied using degree graph and its order. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0152-4 Issue No:Vol. 24, No. 1 (2018)

Authors:M. Bracamonte; J. Ereú; J. Giménez; N. Merentes Pages: 133 - 153 Abstract: Using classical techniques related to the so-called Hardy–Vitali variation, we present the class of X-valued functions of bounded \(\Phi \) -variation in several variables, where \((X,d,+ )\) is a metric semigroup. We exhibit some of the main properties of this class; among them, we show that this class can be made into a normed space and present a counterpart of the renowned Riesz’s Lemma for the case in which \(X=\mathbb {R}\) with its usual metric. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0138-2 Issue No:Vol. 24, No. 1 (2018)

Authors:Abhijit Banerjee; Sujoy Majumder Pages: 155 - 180 Abstract: With the notion of weighted sharing of values we investigate the possible relation between two meromorphic functions when \(f^{n}P(f)f^{(k)}\) and \(g^{n}P(g)g^{(k)}\) share a non-zero polynomial. The results obtained in this paper improve, generalize and rectify a recent one of Cao and Zhang (J Inequal Appl 1:100, 2012). PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0156-0 Issue No:Vol. 24, No. 1 (2018)

Authors:Gerardo Hernández-del-Valle Pages: 203 - 217 Abstract: In this work we find a sequence of functions \(f_n\) at which the integral 1 $$\begin{aligned} v(t,x)=\int _{-\infty }^{\infty }e^{i\lambda x-\lambda ^2t/2-\lambda ^4/4}\mathrm{d}\lambda \end{aligned}$$ is identically zero for all \(t\ge 0\) , that is $$\begin{aligned} v(t,f_n(t))=0\qquad \forall t\ge 0. \end{aligned}$$ The function v, after proper change of variables and rotation of the path of integration, is known as the Pearcey integral or Pearcey function, indistinctly. We also show that each \(f_n\) is expressed in terms of a second order non-linear ODE, which turns out to be of the Rayleigh-type. Furthermore, the initial conditions which uniquely determine each \(f_n\) , depend on the zeros of an Lévy stable function of order 4 defined as $$\begin{aligned} \phi (x)=\int _{-\infty }^{\infty }e^{i\lambda x-\lambda ^4/4}\mathrm{d}\lambda . \end{aligned}$$ As a byproduct of these facts, we develop a methodology to find a class of functions which solve the moving boundary problem of the heat equation. To this end, we make use of generalized Airy functions, which in some particular cases fall within the category of functions with infinitely many real zeros, studied by Pólya. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0142-6 Issue No:Vol. 24, No. 1 (2018)

Authors:Gradimir V. Milovanović; Vijay Gupta; Neha Malik Pages: 219 - 237 Abstract: In the present paper, we consider (p, q)-analogue of the beta operators and using it, we propose the integral modification of the generalized Bernstein polynomials. We estimate some direct results on local and global approximation. Also, we illustrate some graphs for the convergence of (p, q)-Bernstein–Durrmeyer operators for different values of the parameters p and q using Mathematica package. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0139-1 Issue No:Vol. 24, No. 1 (2018)

Authors:Mouataz Billah Mesmouli; Abdelouaheb Ardjouni; Ahcene Djoudi Pages: 239 - 255 Abstract: In this paper, we study the existence of periodic solutions of the nonlinear neutral system of differential equations $$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}t}x\left( t\right) =A\left( t\right) x\left( t\right) +\frac{\mathrm{d}}{\mathrm{d}t} Q\left( t,x\left( t-g\left( t\right) \right) \right) +\int _{-\infty }^{t}D\left( t,s\right) F\left( x\left( s\right) \right) \mathrm{d}s. \end{aligned}$$ Using Krasnoselskii’s fixed point theorem, we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness of periodic solution and stability of the zero solution. Our results extend some earlier publications. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0155-1 Issue No:Vol. 24, No. 1 (2018)

Authors:M. R. Molaei Pages: 257 - 267 Abstract: In this essay we consider topological cocycles via semibornology and group structures. Global and local attractors via semibornological nonautonomous sets are studied. We show that global semibornological pullback attractors are compact and positively invariant. We introduce the concept of global \((g,\beta )\) pullback attractors and we show that they are also compact and positively invariant. We prove that semibornological pullback attractors are invariant objects under topological equivalencies. We present a method for finding absorbing sets when the state space of the dynamical system of a cocycle is a convex semibornological vector space. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0158-y Issue No:Vol. 24, No. 1 (2018)

Authors:Gennadiy Gubreev; Anna Tarasenko Pages: 269 - 278 Abstract: A quite general theorems on unconditional bases in separable Hilbert spaces, given in terms of values of entire operator valued vector-functions, were established in the papers [2–4]. In the present paper, we give a detailed analysis of the hypothesis of these theorems. We present examples of various classes of vector-functions that satisfy some of the hypothesis of the above theorems. On the other hand, we show that there exist natural classes of vector-functions that do not satisfy some of the hypothesis of Theorem A. PubDate: 2018-04-01 DOI: 10.1007/s40590-016-0153-3 Issue No:Vol. 24, No. 1 (2018)

Authors:David A. Dickey; Graciela González-Farías; Nelson Muriel Abstract: Cointegration tests are studied for seasonal time series with large periods. The study is performed asymptotically as the period tends to infinity, which is shown to allow a simple limit distribution to be established. These results offer a simple diagnostic tool for cointegration when the seasonal period is expected to be large, and its critical values do not depend on the form of the deterministic components present in the model. An application to climatic factors and outbreaks of dengue in Mexico illustrates the methods. PubDate: 2018-04-25 DOI: 10.1007/s40590-018-0201-2

Authors:José María Montesinos-Amilibia Abstract: Mennicke (Proc R Soc Edinb Sect A 67:309–352, 1963; Proc R Soc Edinb Sect A 88:151–157, 1981) investigated the number of conic points with isotropies of orders 3, 4 and 6 that can appear in the orientable twofold orbifold covering of the orbifold \(Q_{f}\) associated with an integral ternary quadratic form. Mennicke made essential use of a theorem of Jones (The Arithmetic Theory of Quadratic Forms. The Carus Mathematical Monographs, vol. 10. MAA, Baltimore, 1950, Theorem 86). In this paper we revisit Mennicke’s results and we extend them to \(Q_{f},\) that is, even when \(Q_{f}\) is non-orientable. Our method is new and independent of Jones’ Theorem. We also study the possible cusp points. PubDate: 2018-04-23 DOI: 10.1007/s40590-018-0199-5

Authors:Dionicio Pastor Dallos Santos Abstract: Using degree for \(\alpha \) -condensing maps, we obtain the existence of at least one solution for nonlinear boundary value problems $$\begin{aligned} \left\{ \begin{array}{lll} (\varphi (u' ))' = f(t,u,u') &{} &{} \\ u(0)=u(1)=u'(0), &{} &{} \quad \quad \end{array}\right. \end{aligned}$$ where \(\varphi : X\rightarrow X \) is a linear homeomorphism, \(f:\left[ 0, 1\right] \times X \times X \rightarrow X \) is a continuous function and X is a real Banach space. PubDate: 2018-04-20 DOI: 10.1007/s40590-018-0200-3

Authors:Muhammad Arif; Shahid Mahmood; Rafi Ullah Abstract: In this paper, we define two families of analytic functions using the concept of the starlikeness with respect to symmetrical points, Janowski functions and functions of bounded boundary rotation. We study here integral representation theorem, coefficient bounds, coefficient difference and arc-length problem of the newly defined class. PubDate: 2018-04-16 DOI: 10.1007/s40590-018-0198-6

Authors:A. Abouelaz; A. Achak; R. Daher; N. Safouane Abstract: The Weinstein transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. Donoho–Stark’s uncertainty principle is obtained for the Weinstein transform. PubDate: 2018-04-11 DOI: 10.1007/s40590-018-0197-7