Mostrando recursos 1 - 20 de 158

  1. Poisson Summation Formulae and the Wave Equation with a Finitely Supported Measure as Initial Velocity

    Diaz, Jesus Ildefonso; Meyer, Yves
    New Poisson summation formulae have been recently discovered by Nir Lev and Alexander Olevskii since 2013. But some other examples were concealed in an old paper by Andrew Guinand dating from 1959. This was observed by the second author in 2016. In the present contribution a third approach is proposed. Guinand's work follows from some simple observations on solutions of the wave equation on the three dimensional torus. If the initial velocity is a Dirac mass at the origin, the solution is Guinand's distribution. Using this new approach one can construct a large family of initial velocities which give rise to crystalline measures generalizing Guinand's solution.

  2. About the Degenerate Spectrum of the Tension Field for Mappings into a Symmetric Riemannian Manifold

    Kourouma, Moussa
    Let $(M,g)$ and $(N,h)$ be compact Riemannian manifolds, where $(N,h)$ is symmetric, $v\in W^{1,2}((M,g),(N,h))$, and $\tau $ is the tension field for mappings from $(M,g)$ into $(N,h)$. We consider the nonlinear eigenvalue problem $\tau (u)-\lambda \exp _{u}^{-1}v=0$, for $u$ $\in W^{1,2}(M,N)$ such that $u_{\left\vert \partial M\right. }=v_{\left\vert \partial M\right.}$, and $\lambda \in \mathbb{R}$. We prove, under some assumptions, that the set of all $\lambda $, such that there exists a solution $(u,\lambda )$ of this problem and a non trivial Jacobi field $V$ along $u$, is contained in $\mathbb{R}_{+}$, is countable, and has no accumulation point in $\mathbb{R}$. This result generalizes a well known one about the spectrum of...

  3. On Commutativity of Prime Γ-Rings with $θ$-Derivations

    Huang, Shuliang; Rehman, Nadeem ur
    Let $M$ be a prime $\Gamma-$ring, $I$ a nonzero ideal, $\theta$ an automorphism and $d$ a $\theta-$derivation of $M$. In this article we have proved the following result: (1) If $d([x,y]_{\alpha})=\pm([x,y]_{\alpha})$ or $d((x\circ y)_{\alpha})=\pm((x\circ y)_{\alpha})$ for $x, y\in I; \alpha\in \Gamma$, then $M$ is commutative. (2) Under the hypothesis $d\theta=\theta d$ and $Char M\neq2$, if $(d(x)\circ d(y))_{\alpha}=0$ or $[d(x),d(y)]_{\alpha}=0$ for all $x, y\in I;\alpha\in \Gamma$, then $M$ is commutative. (3) If $d$ acts as a homomorphism or an anti-homomorphism on $I$, then $d=0$ or $M$ is commutative. Moreover, an example is given to demonstrate that the primeness imposed on the hypothesis of the various results is essential.

  4. Existence of Solutions of Some Nonlinear $φ$-Laplacian Equations with Neumann-Steklov Nonlinear Boundary Conditions

    Goli, Charles Etienne; Adje, Assohoun
    We study the existence of solutions of the quasilinear equation $$(D(u(t))\phi(u'(t)))'=f(t,u(t),u'(t)),\qquad a.e. \;\;t\in [0,T],$$ subject to nonlinear Neumann-Steklov boundary conditions on $[0,T]$, where $\phi: (-a,a)\rightarrow \mathbb{R}$ (for $0 < a < \infty$) is an increasing homeomorphism such that $\phi(0)=0$, $f:[0,T]\times\mathbb{R}^{2} \rightarrow \mathbb{R}$ a $L^1$-Carathéodory function, $D$ : $\mathbb{R}\longrightarrow (0,\infty)$ is a continuous function. Using topological methods, we obtain existence and multiplicity results.

  5. Hammerstein Equations with Lipschitz and Strongly Monotone Mappings in Classical Banach spaces

    Diop, C.; Sow, T. M. M.; Djitte, N.; Chidume, C. E.
    Let $E$ be a Banach space either $l_p$ or $L_p$ or $W^{m,p}$, $1 < p < \infty$, with dual $E^*$, and let $F :E\mapsto E^*$, $K: E^*\mapsto E $ be Lipschitz and strongly monotone mappings with $D(K)=R(F)=E^*$. Assume that the Hammerstein equation $u+KFu=0$ has a unique solution $\bar u$. For given $u_1\in E$ and $v_1\in E^*$, let $\{u_n\}$ and $\{v_n\}$ be sequences generated iteratively by: $u_{n+1} = J^{-1}(Ju_n -\lambda(Fu_n-v_n)),\,\,\,n\geq 1$ and $v_{n+1} = J(J^{-1}v_n-\lambda(Kv_n+u_n)),\,\,\,n\geq 1$, where $J$ is the duality mapping from $E$ into $E^*$ and $\lambda$ is a positive real number in $(0,1)$ satisfying suitable conditions. Then it is proved that the sequence $\{u_n\}$ converges strongly to $\bar...

  6. Periodic Homogenization of Schrödinger Type Equations with Rapidly Oscillating Potential

    Signing, Lazarus
    This paper is devoted to the homogenization of Shrödinger type equations with periodically oscillating coefficients of the diffusion term, and a rapidly oscillating periodic potential. One convergence theorem is proved and we derive the macroscopic homogenized model. Our approach is the well known two-scale convergence method.

  7. Convergence Analysis on Quadrilateral Grids of a DDFV Method for Subsurface Flow Problems in Anisotropic Heterogeneous Porous Media with Full Neumann Boundary Conditions

    Kinfack Jeutsa, A.; Njifenjou, A.; Nganhou, J.
    Our purpose in this paper is to present a theoretical analysis of the Discrete Duality Finite Volume method (DDFV method) for 2D-flow problems in anisotropic heterogeneous porous media with full Neumann boundary conditions. We start with the derivation of the discrete problem, and then we give a result of existence and uniqueness of a solution for that problem. Their theoretical properties, namely stability and error estimates in discrete energy norms and $L^2$-norm are investigated. Numerical tests are provided.

  8. Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions of Class r Under the Light of Measure Theory

    Zabsonre, Issa; Toure, Hamidou
    The aim of this work is to present new approach to study weighted pseudo almost periodic and automorphic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions. We study the existence and uniqueness of $(\mu,\nu)$-pseudo almost periodic and automorphic solutions of class $r$ for some neutral partial functional differential equations in a Banach space when the delay is distributed using the spectral decomposition of the phase space developed in Adimy and co-authors. Here we...

  9. A Note on Relations Between Hom-Malcev Algebras and Hom-Lie-Yamaguti Algebras

    Gaparayi, Donatien; Issa, A. Nourou
    A Hom-Lie-Yamaguti algebra, whose ternary operation expresses through its binary one in a specific way, is a multiplicative Hom-Malcev algebra. Any multiplicative Hom-Malcev algebra over a field of characteristic zero has a natural Hom-Lie-Yamaguti structure.

  10. Leibniz Homology of the Affine Indefinite Orthogonal Lie Algebra

    Biyogmam, Guy Roger
    In this paper, we construct several indefinite orthogonal invariants in terms of balanced tensors and use Lodder's structure theorem to provide the Leibniz (co)homology of the indefinite orthogonal Lie algebra in terms of these invariants.

  11. Multidimensional BSDE with Poisson Jumps in Finite Time Horizon

    Sagna, Yaya; Sow, Ahmadou Bamba
    This paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under weak monotonicity condition on the generator and by means of suitable sequences, we prove existence and uniqueness of solution.

  12. A New Version of the Central Limit Theorem

    Villamor, Enrique; Olivares, Pablo
    In this short note, we present a new version of the Central Limit Theorem whose proof is based on Levy's characterization of Brownian motion. The method in the proof may allow to extend the result to a more general context, e.g. to averaged sums of properly compensated dependent random variables.

  13. Rational Pairing Rank of a Map

    Yamaguchi, Toshihiro
    We define a rational homotopy invariant, the rational pairing rank $v_0(f)$ of a map $f:X\to Y$, which is a natural generalization of the rational pairing rank $v_0(X)$ of a space $X$ [16]. It is upper-bounded by the rational LS-category $cat_0(f)$ and lower-bounded by an invariant $g_0(f)$ related to the rank of Gottlieb group. Also it has a good estimate for a fibration $X\overset{j}{\to} E\overset{p}{\to} Y$ such as $v_0(E)\leq v_0(j) +v_0(p)\leq v_0(X) +v_0(Y)$.

  14. Inequalities for the Growth and Derivatives of a Polynomial

    Mir, Abdullah; Mboup, Mamadou
    In this paper, we present some inequalities for the growth and derivatives of a polynomial with zeros outside a circle of arbitrary radius $k\gt 0$. Our results provide improvements and generalizations of some well known polynomial inequalities.

  15. Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature

    Mahaman, Bazanfaré; Mboup, Mamadou
    In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature. We show that a complete noncompact manifold $M$ with asymptotically nonnegative Ricci curvature and sectional curvature $K(x)\ge \frac{C}{d_{p}(x)^{\alpha}}$ is diffeomorphic to the Euclidean space $\mathbb{R}^n$ under some conditions on the density of rays starting from the base point $p$ or on the volume growth of geodesic balls in $M$.

  16. On Jacobi Fields Along Eigenmappings of the Tension Field for Mappings into a Symmetric Riemannian Manifold

    Kourouma, Moussa
    We prove that the mean value (for some measure $\mu =\chi dx$ with $\chi \geq 0,dx=$ Riemannian measure) of the squared norm of the gradient of the unitary direction of a Jacobi field along an eigenmapping $v$ (associated to an eigenvalue $\lambda \geq 0$) of the tension field, for mappings from a compact Riemannian manifold $(M,g)$ into a symmetric Riemannian manifold $(N,h)$ of positive sectional curvature, is smaller than $c\lambda $, where $c>0$ depends only on the diameter and upper and lower curvature bounds of $(N,h)$. For negative $\lambda $, we prove that there is no nonvanishing Jacobi field along the eigenmappings, under the same assumptions on $(M,g)$...

  17. On Quotient Hypermodules

    Ostadhadi-Dehkordi, S.; Davvaz, B.
    A hypermodule is a multivalued algebraic system satisfying the module like axioms. In this paper, we construct quotient hypermodule. Let $M$ be a hypermodule, $N$ be a subhypermodule of $M$ and $I$ be a hyperideal of $R$. Then, $[M:N^{\ast}]$ is $R$-hypermodule and $[R:I^{\ast}]$-hypermodule, and prove that when $N$ is normal subhypemodule, $[M:N^{\ast}]$ is a $[R:I^{\ast}]$-module. Hence, the quotient hypermodules considered by Anvarieh and Davvaz are modules.

  18. Some Inequalities for Power Series of Selfadjoint Operators in Hilbert Spaces Via Wielandt and Reverses of Schwarz Inequalities

    Dragomir, S. S.; Seo, Y.
    In this paper we obtain some operator inequalities for functions defined by power series with complex coefficients and, more specifically, with nonnegative coefficients. In order to obtain these inequalities the classical Wielandt and some reverses of the Schwarz inequality for vectors in inner product spaces are utilized. Natural applications for some elementary functions of interest are also provided.

  19. Schläfli-type Mixed Modular Equations of Degrees $1$, $3$, $n$, and $3n$

    Naika, M. S. Mahadeva; Suman, N. P.; Chandankumar, S.
    In this paper, we establish several new Schläfli-type mixed modular equations of composite degrees. These equations are analogous to those recorded by Ramanujan in his second notebook. As an application, we establish several new explicit values for the Ramanujan-Weber class invariant $G_{n}$ for $n=12, 48, 51, 57, 3/4, 3/16, 3/17$ and $3/19$.

  20. Existence of Solutions of IVPs for Differential Systems on Half Line with Sequential Fractional Derivative Operators

    Liu, Yuji
    In this article, we establish some existence results for solutions of a initial value problem of a nonlinear fractional differential system on half line involving the sequential Riemann-Liouville fractional derivatives. Our analysis relies on the Schauder fixed point theorem. An efficiency example is presented to illustrate the main theorem. As far as the author knows, the present work is perhaps the first one that deals with such kind of initial value problems for fractional differential systems on half line.

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