Volume 26, Issue 3

Let R be a prime ring with involution ⋆{\star}, and let σ, τ be endomorphisms on R . For any x,y∈R{x,y\in R}, let (x,y)σ,τ=x⁢σ⁢(y)+τ⁢(y)⁢x{(x,y)_{\sigma,\tau}=x\sigma(y)+\tau(y)x} and Cσ,τ⁢(R)={x∈R∣x⁢σ⁢(y)=τ⁢(y)⁢x}{C_{\sigma,\tau}(R)=\{x\in R\mid x\sigma(y)=\tau(y)x\}}. An additive subgroup U of R is said to be a (σ,τ){(\sigma,\tau)}-right Jordan ideal (resp. (σ,τ){(\sigma,\tau)}-left Jordan ideal) of R if (U,R)σ,τ⊆U{(U,R)_{\sigma,\tau}\subseteq U} (resp. (R,U)σ,τ⊆U{(R,U)_{\sigma,\tau}\subseteq U}), and U is called a (σ,τ){(\sigma,\tau)}-Jordan ideal if U is both a (σ,τ){(\sigma,\tau)}-right Jordan ideal and a (σ,τ){(\sigma,\tau)}-left Jordan ideal of R . A (σ,τ){(\sigma,\tau)}-Jordan ideal U of R is said to be a (σ,τ){(\sigma,\tau)}-⋆{\star}-Jordan ideal if U⋆=U{U^{\star}=U}. In the present paper, it is shown that if U is commutative, then R is commutative. The commutativity of R is also obtained if (U,U)σ,τ⊆Cσ,τ⁢(R){(U,U)_{\sigma,\tau}\subseteq C_{\sigma,\tau}(R)}. Some more results are obtained on the ⋆{\star}-prime ring with a characteristic different from 2.

In this paper we study the ruled surfaces generated by elliptic cylindrical curves in the isotropic 3-space 𝕀3{\mathbb{I}^{3}}. We classify such surfaces in 𝕀3{\mathbb{I}^{3}} with constant curvature and satisfying an equation in terms of the components of the position vector field and the Laplacian operator. Several examples are given and illustrated by figures.

A three-level finite difference scheme is studied for the initial-boundary value problem of the generalized Benjamin–Bona–Mahony–Burgers equation. The obtained algebraic equations are linear with respect to the values of the desired function for each new level. The unique solvability and absolute stability of the difference scheme are shown. It is proved that the scheme is convergent with the rate of order k-1{k-1} when the exact solution belongs to the Sobolev space W2k⁢(Q){W_{2}^{k}(Q)}, 1<k≤3{1<k\leq 3}.

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space Hp{H_{p}} to the Lebesgue space Lp{L_{p}} for all 0<p≤1{0<p\leq 1}. We also prove that the result is sharp in a particular sense.

In this paper, some known results on the absolute Riesz summability factors of infinite series and trigonometric Fourier series have been generalized for the |N¯,pn;θn|k{\lvert\bar{N},p_{n};\theta_{n}\rvert_{k}} summability method. Some new and known results are also obtained.

In a recent paper, we have introduced new sets of Sheffer and Brenke polynomial sequences based on higher order Bell numbers. In this paper, by using a more compact notation, we show another family of exponential polynomials belonging to the Sheffer class, called, for shortness, Sheffer–Bell polynomials. Furthermore, we introduce a set of logarithmic numbers, which are the counterpart of Bell numbers and their extensions.

In this paper, we introduce FS-coalgebras, which provide solutions of FS-equations and also solution of braid equations considered by Caenepeel, Militaru and Zhu. FS-coalgebras are constructed by using FS-equations and Harrison cocycles. As applications, we prove that every bialgebra H is an FS-bialgebra if and only if there is a two-sided integral α in H∗{H^{\ast}} such that ε⁢(α)=1{\varepsilon(\alpha)=1}, and we show that the crossed coproduct HR{H^{R}} introduced by the Harrison cocycle R is an FS-coalgebra when (H,R){(H,R)} is a finite-dimensional quasitriangular Hopf algebra or a Long copaired bialgebra.

The purpose of this paper is to study a nondifferentiable multiobjective fractional programming problem (MFP) in which each component of objective functions contains the support function of a compact convex set. For a differentiable function, we introduce the class of second-order (C,α,ρ,d)-V{(C,\alpha,\rho,d)-V}-type-I convex functions. Further, Mond–Weir- and Wolfe-type duals are formulated for this problem and appropriate duality results are proved under the aforesaid assumptions.

We generalize the Hardy inequality to Hardy–Morrey spaces.

In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with a polylogarithmic function and a p -adic invariant integral on ℤp{\mathbb{Z}_{p}}. By using umbral calculus, we derive some identities of those numbers and polynomials.

We consider multivalued stochastic integral equations driven by semimartingales. Such equations are formulated in two different forms, i.e., using multivalued stochastic up-trajectory and trajectory integrals, which are not equivalent. By the successive approximations method, we show the existence of a unique solution to each equation under a condition much weaker than the Lipschitz one. We indicate that the solutions are stable under small changes of the equation data. The results have immediate implications for solutions to single-valued stochastic integral equations driven by semimartingales.

The aim of this paper is to define the notion of lifting via a group morphism for a crossed module and give some properties of this type of liftings. Further, we obtain a criterion for a crossed module to have a lifting crossed module. We also prove that the category of the lifting crossed modules of a certain crossed module is equivalent to the category of group-groupoid actions on groups, where the group-groupoid corresponds to the crossed module.

In the present paper we introduce a new convolution operator on the class of all normalized analytic functions in |z|<1{|z|<1}, by using the hypergeometric function and the Owa–Srivastava operator Ωα{\Omega^{\alpha}} defined in [S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 1987, 5, 1057–1077]. This operator is a generalization of the operators defined in [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365] and [K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 2006, 2, 1872–1881]. Also we introduce some new subclasses of analytic functions using this operator and we discuss some interesting results, such as inclusion results and convolution properties. Our results generalize the results of [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365].

We introduce the notions of center, singularity and nilpotency (class) of a group with action on itself. Also, we describe a new package GwA for GAP4, including functions checking some properties of groups with action on itself with finite underlying group. As applications of the implemented functions, we give examples of groups with action satisfying Condition 1 stated in [3]. In other words, we get concrete examples of “coquecigrue” in the terminology of Loday [8, 9].

Using the Nevanlinna theory of the value distribution of meromorphic functions, the value distribution of complex partial q -difference polynomials of meromorphic functions of zero order is investigated. The existence of meromorphic solutions of some types of systems of complex partial q -difference equations in ℂn{\mathbb{C}^{n}} is also investigated. Improvements and extensions of some results in the literature are presented. Some examples show that our results are, in a certain sense, the best possible.