关于限制李超代数的分解

代数$A$ 称为不可分解的,如果 $A$ 不能分解成理想的直和.文中将证明满足$C(L_{\bar{0}})=C(L)=\{0\}$的限制李超代数能够分解成不可分解限制理想的直和,这种分解在不计理想次序的前提下是唯一的.而且还证明了限制李超代数的一些结果.     

Asymptotic conditions for the electromagnetic form factors of hadrons represented by the VMD model

A system of linear homogeneous algebraic equations for the coupling constant ratios of vector mesons to hadrons is derived by imposing the assumed asymptotic behavior upon the VMD pole parameterization of an hadron electromagnetic form factor. A similar system of equations with a simpler structure of the coefficients, taken as even powers of the vector-meson masses, is derived by means of integral superconvergent sum rules for the imaginary part of the considered form factor using its appropriate -function approximation. Although both systems have been derived starting from different properties of the electromagnetic form factor and they each have their own appearances, it is shown explicitly that they are fully equivalent. Received: 20 March 2002 / Revised version: 3 December 2002 / Published online: 7 March 2003     

On some periodic solutions of singularly perturbed parabolic equations

We present results from the theory of singular perturbations and, in particular, from a new branch of this theory (contrast alternating-type structures). __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 3, pp. 359–369, March, 2007.     

New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop.     

A second order numerical scheme for the solution of the one-dimensional Boussinesq equation

A predictor–corrector (P-C) scheme is applied successfully to a nonlinear method arising from the use of rational approximants to the matrix-exponential term in a three-time level recurrence relation. The resulting nonlinear finite-difference scheme, which is analyzed for local truncation error and stability, is solved using a P-C scheme, in which the predictor and the corrector are explicit schemes of order 2. This scheme is accelerated by using a modification (MPC) in which the already evaluated values are used for the corrector. The behaviour of the P-C/MPC schemes is tested numerically on the Boussinesq equation already known from the bibliography free of boundary conditions. The numerical results are derived for both the bad and the good Boussinesq equation and conclusions from the relevant known results are derived.      

Smooth Frame-Path Termination for Higher Order Sigma-Delta Quantization

We study the performance of finite frames for the encoding of vectors by applying standard higher-order sigma-delta quantization to the frame coefficients. Our results are valid for any quantizer with accuracy ε > 0 operating in the no-overload regime. The frames under consideration are obtained from regular sampling of a path in a Hilbert space. In order to achieve error bounds that are comparable to results on higher-order sigma-delta for the quantization of oversampled bandlimited functions, we construct frame paths that terminate smoothly in the zero vector, that is, with an appropriate number of vanishing derivatives at the endpoint.     

Embedding and wavelet decomposition of spaces of minimal splines

On a sequence of embedded nonuniform grids, chains of embedded spaces of minimal splines (not necessarily polynomial) are constructed. The wavelet decomposition is given. The basis wavelets are compactly supported and admit simple analytic representation. The corresponding decomposition and reconstruction formulas are derived. The variety of spaces under consideration is identified with the variety of complete sequences of points of the direct product of an interval and a projective plane. Bibliography: 20 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 35, 2007, pp. 15–31     

Oscillation of certain partial difference equations

In this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients, which may change sign. We obtain oscillation criteria for these equations. There are no results for the oscillation of these equations up to now.