一类二阶积分型发展方程反周期解问题

本文中,我们研究一类带有非单调扰动算子的二阶非线性发展方程的反周期问题,证明方程中的非单调扰动算子为极大单调的,并用极大单调算子的微单调扰动理论来证明此类方程的反周期解的存在性。     

Additive Maps Preserving Nilpotent Perturbation of Scalars

Let X be a Banach space over F(= R or C) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B_0(X) the set spanned by N(X). We give a structure result to the additive maps on FI + B_0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI + B_0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A~(-1)+ φ(T)I for all T ∈ FI + B_0(X) or Φ(T) = cAT*A~(-1)+ φ(T)I for all T ∈ FI + B_0(X), where c is a nonzero scalar,A is a τ-linear bijective transformation for some automorphism τ of F and φ is an additive functional.In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator.     

Coburn Type Operators and Compact Perturbations

A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T ? λ) = {0} or ker(T ? λ)^*= {0} for each λ ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property.Moreover, they study the stability of these properties under small compact perturbations.     

Multisplitting and Schwarz Methods for Solving Linear Complementarity Problems

In this paper we consider some synchronous and asynchronous multisplitting and Schwarz methods for solving the linear complementarity problems. We establish some convergence theorems of the methods by using the concept of M-splitting.     

Existence of a Nonstationary Poiseuille Solution

The nonstationary Poiseuille solution describing the flow of a viscous incompressible fluid in an infinite cylinder is defined as a solution of the inverse problem for the heat equation. The existence and uniqueness of such nonstationary Poiseuille solution with the prescribed flux F(t) of the velocity field is studied. It is proved that under some compatibility conditions on the initial data and flux F(t) the corresponding inverse problem has a unique solution in Holder spaces.Original Russian Text Copyright © 2005 Pileckas K. and Keblikas V.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 649–662, May–June, 2005.     

具有非线性扰动的中立型系统的时滞相关稳定性

本研究了具有非线性扰动的中立型系统鲁棒稳定的时滞相关准则。基于LMI方法，并利用S—过程获得了依赖于时滞的鲁棒稳定性准则，所得结果优于已有结论。最后给出一个实例说明本方法的有效性。     

Weak invariance of the multidimensional rank statistic for nonstationary absolutely regular processes

In this paper, we study the weak invariance of the multidimensional rank statistic when the underlying random variables are nonstationary absolutely regular.     

Nutation electron spin echo ofE-centers in quartz

Attenuation of the signals of the nutation echo of E’-centers in crystalline and glass quartz was experimentally investigated at room temperature. The nutation echo in EPR was excited in the single-photon regime and formed by two Zeeman-field pulses with duration t₁ and t₂ (t₁<t₂) and time interval between them τ. The echo signal was recorded during the second pulse at t≈2t₁+τ. It was established that this signal attenuation, measured as t₁ increased, follows an, exponential law, its rate Γ is much less than 1/T₂ (T₂ is the transverse relaxation time), and it linearly increases with an increase in the amplitude of the exciting SHF field B₁. The parameters of the dependence of Γ on B₁ correlate with the parameters of the analogous dependence revealed previously for attenuation of nutation of E’-centers in quartz in the two-photon regime at T=4.2 K. At the same time, the value of Γ measured with different values of τ is independent of B₁ and is equal to 1/T₁, where T₁ is the longitudinal relaxation time. A. N. Sevchenko Scientific Research Institute of Applied Physical Problems, 7, Kurchatov St., Minsk, 220064, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 405–411, May–June, 1998.     

Small random perturbations of one-dimensional diffusion processes

In the present paper we consider the small random perturbations of one-dimensional diffusion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistical estimates of the exit times as the perturbations tend to zero. Partially supported by the Young Teachers Foundation of Beijing Institute of Technology     

Sliding mode control of uncertain systems: a singular perturbation approach

In this paper we consider a nonlinear control system affectedby deterministic uncertainty and described by a system of ordinarydifferential equations. The uncertainty is modelled by a multivaluedmap whose t-measurable and x-Lipschitz selections representthe possible system dynamics of the uncertain system. We proposea dynamical feedback control design, based on the singular perturbationtheory, which allows all the possible system trajectories correspondingto the system dynamics to have the same prescribed behaviour.Specifically, given a manifold K of the state space, definedas the zeros of a smooth map, the proposed control steers andthen holds, during finite or infinite time intervals, any possiblesystem trajectory to any prescribed neighbourhood of K. A resultensuring the exact attainability of K is also provided. Someexamples illustrating the obtained results are presented.