Pth moment input-to-state stability of stochastic impulsive switched delayed systems

This paper investigates the pth moment input-to-state stability (ISS) and the pth moment integral input-to-state stability (iISS) of stochastic impulsive switched delayed system with delayed impulses. By employing the method of multiple Lyapunov-Krasovskii functionals and the uniformly exponentially stable function, some relaxed Krasovskii-type sufficient conditions ensuring the pISS/piISS of the addressed systems are developed. These conditions imply the relationship among the impulsive frequency, the time delay existing in impulses, and the coefficients of the estimated upper bound for the derivative of a Lyapunov function. It is shown that if the continuous stochastic delayed dynamics is ISS, and the impulsive effects are destabilizing, then the stochastic impulsive switched delayed system is ISS with respect to the relationship. Compared with the existing results, the conditions obtained results have three relaxations, that is, the derivative of Lyapunov functions of subsystems are allowed to be sign-changing time-varying function rather than a negative definite constant, all subsystems are allowed to be unstable, and the effect of delayed impulses are considered. Finally, an example is provided to illustrate the effectiveness of the results.

FAST COMPUTATION OF GEOMETRIC MOMENTS AND INVARIANTS USING SCHLICK'S APPROXIMATION

Geometric moments have been used in several applications in the field of Computer Vision. Many techniques for fast computation of geometric moments have therefore been proposed in the recent past, but these algorithms mainly rely on properties of the moment integral such as piecewise differentiability and separability. This paper explores an alternative approach to approximating the moment kernel itself in order to get a notable improvement in computational speed. Using Schlick's approximation for the normalized kernel of geometric moments, the computational overhead could be significantly reduced and numerical stability increased. The paper also analyses the properties of the modified moment functions, and shows that the proposed method could be effectively used in all applications where normalized Cartesian moment kernels are used. Several experimental results showing the invariant characteristics of the modified moments are also presented.

An Improved Reversed-Flow Formulation of the Galerkin-Kantorovich-Dorodnitsyn Multi-Moment Integral Method

SummaryAn improved reversed-flow formulation of the Galerkin-Kantorovich-Dorodnitsyn multi-moment integral method is presented in this paper. Convergence and accuracy properties of the approximate solutions of the Stewartson lower branch similar flows are given. The approximate solutions obtained with the new formulation for the lower branch similar flows are, in general, more accurate than those obtained with the classical Pohlhausen method or either of the previous formulations used with the GKD method.

A General Formulation for the Evaluation of Two-center Moment Integral-An Extension

In two recent studies 1,2 we presented a general formulation for the evaluation of two-center moment integrals as well as the rotational properties of s, p, and d atomic orbitals needed in the quantum mechanical calculations of one-electron properties. In the present investigation, we extend the scope of our previous formulation by presenting a series of tabulations useful both to inorganic and organic chemists.

The Quantum-mechanical Calculation of One-electron Properties

Two-center moment integrals for SLATER-type atomic orbitals are explicitly expressed in terms of a general formula involving the three quantum numbers and the effective nuclear charge of each of the two orbitals, the internuclear distance, and the usual A and B functions. A corresponding expression for one-center moment integrals is also given. The use of the one- and two-center moment integral formulae in digital computer calculations is discussed.