Abstract: This paper gives the complete proof of the Conjecture given by Hazarika and this author jointly which deals with a necessary and sufficient condition for the hyponormality of Toeplitz operator, \(T_\varphi \) on the weighted Bergman space with certain polynomial symbols under some assumptions about the Fourier coefficients of the symbol \(\varphi \) . PubDate: 2017-05-16

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: 2017-05-16

Abstract: In this paper, we consider the problem of existence and multiplicity of conformal metrics on a Riemannian compact 4-dimensional manifold \((M^4,g_0)\) with positive scalar curvature. We prove a new existence criterium which provides existence results for a dense subset of positive functions and generalizes Bahri–Coron Euler–Poincaré type criterium. Our argument gives estimates of the Morse index of the founded solutions and has the advantage to extend known existence results. Moreover, it provides, for generic K Morse Inequalities at Infinity, which give a lower bound on the number of metrics with prescribed scalar curvature in terms of the topological contribution of its critical points at Infinity to the difference of topology between the level sets of the associated Euler–Lagrange functional. PubDate: 2017-05-02

Abstract: This paper is concerned with prescribing the fractional Q-curvature on the unit sphere \(\mathbb {S}^{n}\) endowed with its standard conformal structure \(g_0\) , \(n\ge 4\) . Since the associated variational problem is noncompact, we approach this issue with techniques passed by Abbas Bahri, as the well known theory of critical points at infinity, as well as some lesser known topological invariants that appear here as criteria for existence results. PubDate: 2017-04-18

Abstract: In the paper, the authors establish explicit formulas for asymptotic and power series expansions of the exponential and the logarithm of asymptotic and power series expansions. The explicit formulas for the power series expansions of the exponential and the logarithm of a power series expansion are applied to find explicit formulas for the Bell numbers and logarithmic polynomials in combinatorics and number theory. PubDate: 2017-04-17

Abstract: In this paper, we prove that every rank one cubic derivation on a unital integral domain is identically zero. From this conclusion, under certain conditions, we achieve that the image of a cubic derivation on a commutative algebra is contained in the Jacobson radical of algebra. As the main result of the current study, we prove that every cubic derivation on a finite dimensional algebra, under some circumstances, is identically zero. PubDate: 2017-04-17

Abstract: In this paper, we study the partial differential equation 1 $$\begin{aligned} \begin{aligned} \partial _tu&= k(t)\Delta _\alpha u - h(t)\varphi (u),\\ u(0)&= u_0. \end{aligned} \end{aligned}$$ Here \(\Delta _\alpha =-(-\Delta )^{\alpha /2}\) , \(0<\alpha <2\) , is the fractional Laplacian, \(k,h:[0,\infty )\rightarrow [0,\infty )\) are continuous functions and \(\varphi :\mathbb {R}\rightarrow [0,\infty )\) is a convex differentiable function. If \(0\le u_0\in C_b(\mathbb {R}^d)\cap L^1(\mathbb {R}^d)\) we prove that (1) has a non-negative classical global solution. Imposing some restrictions on the parameters we prove that the mass \(M(t)=\int _{\mathbb {R}^d}u(t,x)\mathrm{d}x\) , \(t>0\) , of the system u does not vanish in finite time, moreover we see that \(\lim _{t\rightarrow \infty }M(t)>0\) , under the restriction \(\int _0^\infty h(s)\mathrm{d}s<\infty \) . A comparison result is also obtained for non-negative solutions, and as an application we get a better condition when \(\varphi \) is a power function. PubDate: 2017-04-12

Abstract: In this article, we investigate the direct problem of approximation theory in the variable exponent Smirnov classes of analytic functions, defined on a doubly connected domain bounded by two Dini-smooth curves. PubDate: 2017-04-11

Abstract: In this paper we consider a class of fractional nonlinear neutral stochastic evolution inclusions with nonlocal initial conditions in Hilbert space. Using fractional calculus, stochastic analysis theory, operator semigroups and Bohnenblust–Karlin’s fixed point theorem, a new set of sufficient conditions are formulated and proved for the existence of solutions and the approximate controllability of fractional nonlinear stochastic differential inclusions under the assumption that the associated linear part of the system is approximately controllable. An example is provided to illustrate the theory. PubDate: 2017-02-21

Abstract: The purpose of this paper is to introduce Picard–Krasnoselskii hybrid iterative process which is a hybrid of Picard and Krasnoselskii iterative processes. In case of contractive nonlinear operators, our iterative scheme converges faster than all of Picard, Mann, Krasnoselskii and Ishikawa iterative processes in the sense of Berinde (Iterative approximation of fixed points, 2002). We support our analytic proofs with a numerical example. Using this iterative process, we also find the solution of delay differential equation. PubDate: 2017-02-16

Abstract: This paper presents an analysis of a Markovian feedback queueing system with reneging and retention of reneged customers, multiple working vacations and Bernoulli schedule vacation interruption, where customers’ impatience is due to the servers’ vacation. The reneging times are assumed to be exponentially distributed. After the completion of service, each customer may reenter the system as a feedback customer for receiving another regular service with some probability or leave the system. A reneged customer can be retained in many cases by employing certain convincing mechanisms to stay in queue for completion of service. Thus, a reneged customer can be retained in the queueing system with some probability or he may leave the queue without receiving service. We establish the stationary analysis of the system. The probability generating functions of the stationary state probabilities is obtained, we deduce the explicit expressions of the system sizes when the server is in a normal service period and in a Bernoulli schedule vacation interruption, respectively. Various performance measures of the system are derived. Finally, we present some numerical examples to demonstrate how the various parameters of the model influence the behavior of the system. PubDate: 2017-01-20

Abstract: We develop the Benkhettou–Hassani–Torres fractional (noninteger order) calculus on timescales by proving two chain rules for the \(\alpha \) -fractional derivative and five inequalities for the \(\alpha \) -fractional integral. The results coincide with well-known classical results when the operators are of (integer) order \(\alpha = 1\) and the timescale coincides with the set of real numbers. PubDate: 2016-12-27

Abstract: In this paper, we introduce some new concepts to the field of probability theory: \(\left( k,s\right) \) -Riemann–Liouville fractional expectation and variance functions. Some generalized integral inequalities are established for \(\left( k,s\right) \) -Riemann–Liouville expectation and variance functions. PubDate: 2016-12-26

Abstract: This paper is a survey on bubbling phenomena occurring in some geometric problems. We present here a few problems from conformal geometry, gauge theory and contact geometry and we give the main ideas of the proofs and important results. We focus in particular on the Yamabe type problems and the Weinstein conjecture, where A. Bahri made a huge contribution by introducing new methods in variational theory. PubDate: 2016-12-26

Abstract: We study the nonexistence of nontrivial solutions for the nonlinear elliptic system $$\begin{aligned} \left\{ \begin{array}{lll} (-\Delta _x)^{\alpha /2}u+ x ^{2\delta } (-\Delta _y)^{\beta /2}u+ x ^{2\eta } y ^{2\theta } (-\Delta _z)^{\gamma /2}u&{}=&{} v^p,\\ \\ (-\Delta _x)^{\mu /2}v+ x ^{2\delta } (-\Delta _y)^{\nu /2}v+ x ^{2\eta } y ^{2\theta } (-\Delta _z)^{\sigma /2}v&{}=&{} u^q, \\ \end{array} \right. \end{aligned}$$ where \((x,y,z)\in \mathbb {R}^{N_1}\times \mathbb {R}^{N_2}\times \mathbb {R}^{N_3}\) , \(0<\alpha ,\beta ,\gamma ,\mu , \nu , \sigma \le 2\) , \(\delta , \eta ,\theta \ge 0\) , and \(p,q>1\) . Here, \((-\Delta _x)^{\alpha /2}\) , \(0<\alpha <2\) , is the fractional Laplacian operator of order \(\alpha /2\) with respect to the variable \(x\in \mathbb {R}^{N_1}\) , \((-\Delta _y)^{\beta /2}\) , \(0<\beta <2\) , is the fractional Laplacian operator of order \(\beta /2\) with respect to the variable \(y\in \mathbb {R}^{N_2}\) , and \((-\Delta _z)^{\gamma /2}\) , \(0<\gamma <2\) , is the fractional Laplacian operator of order \(\gamma /2\) with respect to the variable \(z\in \mathbb {R}^{N_3}\) . Using a weak formulation approach, sufficient conditions are provided in terms of space dimension and system parameters. PubDate: 2016-12-19

Abstract: In this paper, we establish sufficient conditions for the existence of local solutions for a class of Cauchy type problems with arbitrary fractional order. The results are established by the application of the contraction mapping principle and Schaefer’s fixed point theorem. An example is provided to illustrate the applicability of the results. PubDate: 2016-12-01

Abstract: Let a simply-connected homogeneous space \({X}\) satisfy the condition of \({{\rm dim} \pi_{\rm even}(X)\otimes {\mathbb{Q}}=2}\) and \({{\rm dim} \pi_{\rm odd}(X)\otimes {\mathbb{Q}}=3}\) (then, we say it is of (2, 3) type), which is the smallest rank in non-formal pure spaces. Then, we compute the Sullivan minimal model of the Dold–Lashof classifying space \({{\rm Baut}_1 X}\) according to Nishinobu and Yamaguchi (Topol Appl 196:290–307, 2015) and observe whether or not its rational cohomology is a polynomial algebra, which is a necessary condition for the Serre spectral sequence of any fibration over a sphere with fibre \({X}\) to degenerate at term \({E_2}\) . PubDate: 2016-10-31

Abstract: Let M be a module over a commutative ring R. The annihilating-submodule graph of M, denoted by AG(M), is a simple graph in which a non-zero submodule N of M is a vertex if and only if there exists a non-zero proper submodule K of M such that N K = (0), where N K, the product of N and K, is denoted by (N : M)(K : M)M and two distinct vertices N and K are adjacent if and only if N K = (0). This graph is a submodule version of the annihilating-ideal graph. We prove that if AG(M) is a tree, then either AG(M) is a star graph or a path of order 4 and in the latter case \({M\cong F \times S}\) , where F is a simple module and S is a module with a unique non-trivial submodule. Moreover, we prove that if M is a cyclic module with at least three minimal prime submodules, then gr(AG(M)) = 3 and for every cyclic module M, \({cl({\rm AG}(M)) \geq {\rm Min}(M) }\) . PubDate: 2016-09-20

Abstract: A class of periodic boundary value problems for higher order fractional differential equations with impulse effects is considered. We first convert the problem to an equivalent integral equation. Then, using a fixed-point theorem in Banach space, we establish existence results of solutions for this kind of boundary value problem for impulsive singular higher order fractional differential equations. Two examples are presented to illustrate the efficiency of the results obtained. PubDate: 2016-08-02

Abstract: In this paper, we introduce (p, q)-Bernstein Durrmeyer operators. We define (p, q)-beta integral and use it to obtain the moments of the operators. We obtain uniform convergence of the operators by using Korovkin’s theorem. We estimate direct results of the operators by means of modulus of continuity and Peetre K-functional. Finally, we find Voronovskaya-type theorem for the operators. PubDate: 2016-08-02