On the Rolewicz theorem for evolution operators

We give a short proof of a generalization of the Rolewicz theorem based on the uniform boundedness principle.

     

On the stability of some integer programming algorithms

In the present paper we develop our approach for studying the stability of integer programming problems. We prove that the L-class enumeration method is stable on integer linear programming problems in the case of bounded relaxation sets [9]. The stability of some cutting plane algorithms is discussed.     

Mode beating in spot-size converter lasers

An anomalous modulation in the wavelength spectrum has been observed in lasers with spot-size converters. This intensity modulation is shown to be caused by beating between the fundamental lasing mode and radiation modes in the taper. This results in a periodic modulation in the net gain spectrum, which causes wavelength jumps between adjacent net gain maxima, and a drive current dependent spectral width that is expected to affect system performance. The amplitude of this spectral modulation is reduced significantly by either using an angled rear-facet which reflects the beating radiation modes away from the laser axis, or by using a nonlinear, adiabatic taper.     

BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u＂ = ｜u｜^p

In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation.     

On existence and stability in the theory of swelling porous elastic soils

The aim of this paper is to introduce a new functional in thestudy of swelling porous elastic soils saturated by a fluid.This new functional is a useful tool; it allows us to provethe existence of solutions in the case of a compressible fluid.We also prove the stability of solutions and the exponentialdecay in the case of an incompressible fluid. We study as wellthe continuous dependence with respect to the initial time.     

A Stability Estimate for a Solution of the Problem of Determining the Dielectric Permittivity

We consider the problem of determining the dielectric permittivity for a nonconducting and nonmagnetic medium. As information we take the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindrical domain. These traces correspond to a solution to some direct problem for the Maxwell system. The impulse source of the current flux lies outside the domain in which the coefficient is sought. The main result of the article is a stability estimate for a solution to the inverse problem in question.     

森林发展系统的一个非线性半离散模型

本文建立了森林发展系统的一类非线性林龄面积结构的半离散模型 ,并讨论了半离散系统解的存在唯一性 ,给出了线性半离散系统稳定的一些充分条件     

Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter

In this work we study connections between various asymptotic properties of the nonlinear filter. It is assumed that the signal has a unique invariant probability measure. The key property of interest is expressed in terms of a relationship between the observation σ field and the tail σ field of the signal, in the stationary filtering problem. This property can be viewed as the permissibility of the interchange of the order of the operations of maximum and countable intersection for certain σ-fields. Under suitable conditions, it is shown that the above property is equivalent to various desirable properties of the filter such as

(a) uniqueness of invariant measure for the signal,

(b) uniqueness of invariant measure for the pair (signal, filter),

(c) a finite memory property of the filter,

(d) a property of finite time dependence between the signal and observation σ fields and

(e) asymptotic stability of the filter.

Previous works on the asymptotic stability of the filter for a variety of filtering models then identify a rich class of filtering problems for which the above equivalent properties hold.     

A Stability Estimate for a Solution to a Three-Dimensional Inverse Problem for the Maxwell Equations

We consider the problem of determining dielectric permittivity and conductivity in the Maxwell equations. As additional information we prescribe the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindric domain. We establish a stability estimate for a solution to the inverse problem and a uniqueness theorem.     

Convergence of Computational Methods and Stability of Self-Balanced Stresses under Shrinkage of Spherical Inclusions of a Damageable Material

Some iterative methods for calculating self-balanced stresses under shrinkage of a ball inclusion enclosed in a spherical matrix of a physically nonlinear damageable material. The stability of this system was studied using methods of catastrophe theory. It has been established that the beginning of divergence of the proposed iterative processes coincides with the moment of transition of the system to an unstable position of equilibrium.