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  • Articles  (71)
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  • Articles  (71)
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  • 1
    Publication Date: 2017-05-17
    Description: 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 \(\varphi \) .
    Print ISSN: 2193-5343
    Electronic ISSN: 2193-5351
    Topics: Mathematics
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  • 2
    Publication Date: 2017-05-17
    Description: 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.
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    Topics: Mathematics
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  • 3
    Publication Date: 2017-05-03
    Description: 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.
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    Topics: Mathematics
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  • 4
    Publication Date: 2017-04-19
    Description: 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.
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    Topics: Mathematics
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  • 5
    Publication Date: 2017-04-18
    Description: 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.
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    Topics: Mathematics
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  • 6
    Publication Date: 2017-04-18
    Description: 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.
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    Topics: Mathematics
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  • 7
    Publication Date: 2017-04-14
    Description: 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.
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    Topics: Mathematics
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  • 8
    Publication Date: 2017-04-12
    Description: 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.
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    Topics: Mathematics
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  • 9
    Publication Date: 2017-02-22
    Description: 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.
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    Topics: Mathematics
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  • 10
    Publication Date: 2017-02-17
    Description: 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.
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    Topics: Mathematics
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