Delay dynamic equations with stability.
Delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays.
Diamond- Jensen's inequality on time scales.
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.
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...
Discrete differential operators in multidimensional Haar wavelet spaces.
Discrete fractional calculus with the nabla operator.
Discrete inequalities of Wirtinger's type for higher differences.
Discrete isothermic surfaces.
Discrete singular functionals
In the paper the discrete version of the Morse’s singularity condition is established. This condition ensures that the discrete functional over the unbounded interval is positive semidefinite on the class of the admissible functions. Two types of admissibility are considered.
Discretized representations of harmonic variables by bilateral Jacobi operators.
Do nonsingular globally bounded positon solutions exist?
Dynamics behaviors of a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls.