Abstract: Abstract In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order. PubDate: 2018-03-01

Abstract: Abstract Let R be a prime ring with the extended centroid C and symmetric Martindale quotient ring \(Q_s(R)\) . In this paper we prove the following result. Let \(F: R \rightarrow R\) be a generalized derivation associated with a non-zero derivation d on R and let h be an additive map of R such that \(F(x)x=xh(x)\) for all \(x\in R\) . Then either R is commutative or \(F(x)=xp\) and \(h(x)=px\) where \(p\in Q_{s}(R)\) . PubDate: 2017-12-29

Abstract: Abstract The initial value problem for a coupled nonlinear Schrödinger system with unbounded potential is investigated. In the defocusing case, global well-posedness is obtained. In the focusing case, the existence and stability/instability of standing waves are established. Moreover, global well-posedness is discussed via the potential well method. PubDate: 2017-12-15

Abstract: Abstract In this paper, we study various arithmetic properties of the function \(\overline{p}_{2,\,\, k}(n)\) , which denotes the number of \((2,\,\, k)\) -regular overpartitions of n with odd \(k > 1\) . We prove several infinite families of congruences modulo 8 for \(\overline{p}_{2,\,\, k}(n)\) . For example, we find that for all non-negative integers \(\beta , n\) and \(k\equiv 1\pmod {8}\) , \(\overline{p}_{2,\,\, k}(2^{1+\beta }(16n+14))\equiv ~0\pmod {8}\) . PubDate: 2017-12-14

Abstract: Abstract In this paper, we use techniques and tools from time scale calculus to state and prove many refinements on the discrete Hermite–Hadamard inequality. PubDate: 2017-12-12

Abstract: Abstract We show that the characteristic polynomial of a symmetric pentadiagonal Toeplitz matrix is the product of two polynomials given explicitly in terms of the Chebyshev polynomials. PubDate: 2017-12-11

Abstract: Abstract We present three new sets of weighted partial sums of the Gaussian q-binomial coefficients. To prove the claimed results, we will use q-analysis, Rothe’s formula and a q-version of the celebrated algorithm of Zeilberger. Finally we give some applications of our results to generalized Fibonomial sums. PubDate: 2017-12-08

Abstract: Abstract In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting properties. We explore these relations and present some examples. Also, we present applications of these codes to secret sharing schemes. PubDate: 2017-12-01

Abstract: Abstract We construct a metrical framed \(f(3,-1)\) -structure on the (1, 1)-tensor bundle of a Riemannian manifold equipped with a Cheeger–Gromoll type metric and by restricting this structure to the (1, 1)-tensor sphere bundle, we obtain an almost metrical paracontact structure on the (1, 1)-tensor sphere bundle. Moreover, we show that the (1, 1)-tensor sphere bundles endowed with the induced metric are never space forms. PubDate: 2017-12-01

Abstract: Abstract The aim of this paper is to give an overview of results related to nonlinear wave equations during the last half century. In this regard, we present results concerning existence, decay and blow up for classical nonlinear equations. After that, we discuss briefly some important results of the variable-exponent Lebesgue and Sobolev spaces. Results related to nonexistence and blow up for wave equations with non-standard nonlinearities (nonlinearities involving variable exponents) are given in more detail. Finally, we present some recent decay and blow up results together with their proofs. PubDate: 2017-11-27

Abstract: Abstract New identities and inequalities are given for weighted majorization theorem for n-convex functions by using extension of the Montgomery identity and Green function. Various bounds for the reminders in new generalizations of weighted majorization formulae are provided using Čebyšev type inequalities. Mean value theorems are also discussed for functional related to new results. PubDate: 2017-11-17

Abstract: Abstract The aim of the article is to study the unsteady magnetohydrodynamic-free convection flow of an electrically conducting incompressible viscous fluid over an infinite vertical plate with ramped temperature and constant concentration. The motion of the plate is a rectilinear translation with an arbitrary time-dependent velocity. Closed-form solutions for the temperature, concentration and velocity fields of the fluid are obtained. The influence of transverse magnetic field that is fixed relative either to fluid or plate is studied. Furthermore, the effects of system parameters on the fluid velocity are analyzed through numerical simulations and graphical illustrations. PubDate: 2017-10-06

Abstract: Abstract Let G be a group and \(\omega (G)=\{o(g) g\in G\}\) be the set of element orders of G. Let \(k\in \omega (G)\) and \(s_k= \{g\in G o(g)=k\} \) . Let \(nse(G)=\{s_k k\in \omega (G) \}\) . In this paper, we prove that if G is a group and \(G_2 (4)\) is the Chevalley group such that \(nse(G)=nse(G_2 (4))\) , then \(G\cong G_2 (4)\) . PubDate: 2017-09-22

Abstract: Abstract A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem. PubDate: 2017-09-06

Abstract: Abstract For a sequence of positive numbers \(\beta =\{\beta _{n}\}_{n\in \mathbb {Z}}\) , the space \(L^2(\beta )\) consists of all \(f(z)=\sum _{-\infty }^\infty a_nz^n\) , \(a_n\in \mathbb {C}\) for which \(\sum _{-\infty }^\infty a_n ^2\beta _n^2<\infty \) . For a bounded function \(\varphi (z)=\sum _{-\infty }^\infty a_nz^n\) , the slant weighted Toeplitz operator \(A_\varphi ^{(\beta )}\) is an operator on \(L^2(\beta )\) defined as \(A_\varphi ^{(\beta )}=WM_\varphi ^{(\beta )}\) , where \(M_\varphi ^{(\beta )}\) is the weighted multiplication operator on \(L^2(\beta )\) and W is an operator on \(L^2(\beta )\) such that \(Wz^{2n}=z^n\) , \(Wz^{2n-1}=0\) for all \(n\in \mathbb {Z}\) . In this paper we show that for a trigonometric polynomial \(\varphi (z)=\sum _{n=-p}^q a_nz^n\) , \(A_\varphi ^{(\beta )}\) cannot be hyponormal unless \(\varphi \equiv 0\) . We also show that, for \(k \ge 2 \) the \(k^{th}\) order slant weighted Toeplitz operator \( U_{k,\varphi }^{(\beta )}\) cannot be hyponormal unless \(\phi \equiv 0 \) . Also the compression of \( U_{k,\varphi }^{(\beta )}\) to \(H^2(\beta )\) , denoted by \( V_{k,\varphi }^{(\beta )}\) , cannot be hyponormal unless \(\phi \equiv 0 \) . PubDate: 2017-09-05

Abstract: Abstract Let X be a simply connected CW-complex of finite type and \({\mathbb {K}}\) an arbitrary field. In this paper, we use the Eilenberg–Moore spectral sequence of \(C_*(\Omega (X), \mathbb K)\) to introduce a new homotopical invariant \(\textsc {r}(X, {\mathbb {K}})\) . If X is a Gorenstein space with nonzero evaluation map, then \(\textsc {r}(X, {\mathbb {K}})\) turns out to interpolate \(\mathrm {depth}(H_*(\Omega (X), {\mathbb {K}}))\) and \(\mathrm {e}_{{\mathbb {K}}}(X)\) . We also define for any minimal Sullivan algebra \((\Lambda V,d)\) a new spectral sequence and make use of it to associate to any 1-connected commutative differential graded algebra (A, d) a similar invariant \(\textsc {r}(A,d)\) . When \((\Lambda V,d)\) is a minimal Sullivan model of X, this invariant fulfills the relation \(\textsc {r}(X, {\mathbb {K}}) = \textsc {r}(\Lambda V,d)\) . PubDate: 2017-09-01

Abstract: Abstract In this paper, we characterize spaces such that their one-point compactification (resp., Herrlich compactification) is weakly submaximal. We also establish a necessary and sufficient condition on \(T_{0}\) -spaces in order to get their one-point compactification (resp., Herrlich compactification) \(T_{D}\) -spaces. PubDate: 2017-08-30

Abstract: Abstract In this paper, our aim is to deduce some sharp Turán type inequalities for the remainder q-exponential functions. Our results are shown to be generalizations of results which were obtained by Alzer (Arch Math 55, 462–464, 1990). PubDate: 2017-08-21

Abstract: Abstract In this paper, we prove the existence of at least one periodic solution for some nonlinear parabolic boundary value problems associated with Leray–Lions’s operators with variable exponents under the hypothesis of existence of well-ordered sub- and supersolutions. PubDate: 2017-08-19

Abstract: Abstract We obtain minimal dimension matrix representations for each of the Lie algebras of dimensions five, six, seven and eight obtained by Turkowski that have a non-trivial Levi decomposition. The key technique involves using the invariant subspaces associated to a particular representation of a semi-simple Lie algebra to help in the construction of the radical in the putative Levi decomposition. PubDate: 2017-08-17