Definitionen der Bernoulli-Polynome mit Hilfe ihrer Multiplikationstheoreme.
Delay dynamic equations with stability.
Delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays.
Développements asymptotiques -Gevrey et séries -sommables
Nous donnons une version -analogue de l’asymptotique Gevrey et de la sommabilité de Borel, dues respectivement à G. Watson et E. Borel et systématiquement développées depuis une quinzaine d’années par J.-P. Ramis, Y. Sibuya, etc. Le but de ces auteurs était l’étude des équations différentielles dans le champ complexe. De même notre but est l’étude des équations aux -différences dans le champ complexe, dans la ligne de G.D. Birkhoff et W.J. Trjitzinsky.Plus précisément, nous introduisons une nouvelle...
Diamond- Jensen's inequality on time scales.
Difference equations for functions analytic beyond several squares.
Difference equations of Volterra type and extension of Lyapunov's method.
Difference equations on discrete polynomial hypergroups.
Difference functions of periodic measurable functions
We investigate some problems of the following type: For which sets H is it true that if f is in a given class ℱ of periodic functions and the difference functions are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by ℌ(ℱ,G), that is, , we try to characterize ℌ(ℱ,G) for some interesting classes of functions ℱ ⊃ G. We study classes of measurable functions on the circle group that are invariant for changes on null-sets (e.g. measurable...
Difference independence of the Riemann zeta function
Difference of Function on Vector Space over F
In [11], the definitions of forward difference, backward difference, and central difference as difference operations for functions on R were formalized. However, the definitions of forward difference, backward difference, and central difference for functions on vector spaces over F have not been formalized. In cryptology, these definitions are very important in evaluating the security of cryptographic systems [3], [10]. Differential cryptanalysis [4] that undertakes a general purpose attack against...
Difference operators from interpolating moving least squares and their deviation from optimality
We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp. 37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.
Difference operators from interpolating moving least squares and their deviation from optimality
We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.
Difference properties of higher orders for continuity and Riemann integrability
Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices
2000 Mathematics Subject Classification: 42C05.We give an easy procedure for solving of the direct and the inverse spectral problems for the equation. Guseynov used a procedure of the Gelfand-Levitan type for the case N = 1. We use another procedure and this procedure is more easy and transparent.
Dirichlet boundary value problems of nonlinear functional difference equations with Jacobi operators.
Discrete analogues of singular and maximal Radon transforms.
Discrete Analogues of the Heisenberg-Weyl Algebra.
Discrete analogues of Wirtinger's inequality for a two-dimensional array
Discrete complex analysis – the medial graph approach
We discuss a new formulation of the linear theory of discrete complex analysis on planar quad-graphs based on their medial graphs. It generalizes the theory on rhombic quad-graphs developed by Duffin, Mercat, Kenyon, Chelkak and Smirnov and follows the approach on general quad-graphs proposed by Mercat. We provide discrete counterparts of the most fundamental objects in complex analysis such as holomorphic functions, differential forms, derivatives, and the Laplacian. Also, we discuss discrete versions...