On Approximations of First Integrals for Strongly Nonlinear Oscillators

In this paper strongly nonlinear oscillator equations will be studied.It will be shown that the recently developed perturbation method based onintegrating factors can be used to approximate first integrals. Not onlyapproximations of first integrals will be given, butit will also be shown how in a rather efficient way the existence and stability oftime-periodic solutions can be obtained from these approximations. In particularthe generalized Rayleigh oscillator equation will be studied in detail, and it will beshown that at least five limit cycles can occur.     

非自治系统渐近稳定的充分条件

本文对 Liapunov关于渐近稳定性的基本定理进行改进 ,在附加辅助函数前提下 ,同时放宽了 V正定 ,有无穷小上界 .V负定的条件 .改进了文 [1 ]～ [6]相应结果     

Local asymptotic normality of multivariate ARMA processes with a linear trend

The local asymptotic normality (LAN) property is established for multivariate ARMA models with a linear trend or, equivalently, for multivariate general linear models with ARMA error term. In contrast with earlier univariate results, the central sequence here is correlogram-based, i.e. expressed in terms of a generalized concept of residual cross-covariance function.     

二维Fredholm积分方程Nystrom方法的渐近展开及其外推

本文讨论了求解二维第二类Ｆｒｅｄｈｏｌｍ积分方程的Ｎｙｓｔｒｏｍ方法，得到了数值解的逐项渐近展开，从而可进行Ｒｉｃｈａｒｄｓｏｎ外推，提高数值解的精度。     

一类拟平稳序列极值的极限律

Ｋ．Ｆ．Ｔｕｒｋｍａｎ讨论了一类拟平稳序列最大值的渐近分布。本文利用点过程收全党一理得到水平超出点过程的收敛定理和第ｒ个最大值的渐近分布及前ｒ个最大值的联合渐近分布。     

Algebraic independence of the periods of abelian integrals

Abelian integrals of the first and the second kind are proved to have two algebraically independent periods. Some corollaries concerning the algebraic independence of the values of Euler's beta and gamma functions at rational points are derived.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 681–691, November, 1996.     

Randomly flashing diffusion: Asymptotic properties

The theory of abstract Markov operators and semigroups is applied for studying asymptotics of a randomly flashing diffusion process. The probability distribution of the process is determined by a set of two partial differential equations and sufficient conditions for the existence of a stationary solution of the equations are formulated, and convergence of solutions to the stationary solution is proved.     

BRS Cohomology and the Chern Character in Noncommutative Geometry

We briefly report on new results concerning a perturbation expansion structure within the framework of an analytic version of perturbative quantum chromodynamics (pQCD). This approach combines the RG symmetry with the Källén–Lehmann analyticity in the Q² variable. The procedure of analytization matches this analyticity with the RG invariance by adding to the analytized invariant coupling some nonperturbative contributions containing no adjustable parameters. In turn, the new perturbative expansion (the APT expansion) for an observable represents asymptotic expansion over a nonpower set of specific functions rather than in powers of . We analyze this set and show that it obeys different properties in various ranges of the Q² variable. In the UV, it is close to the power set used in the pQCD calculation. However, generally, this set is of a more complicated nature. In the low Q² region the behavior of is oscillating. Here, the APT expansion has a feature of asymptotic expansion à la Erdélyi. The issue of the consistency of an analytization procedure with the RG structure of observables is also discussed.     

Global qualitative analysis of coupled three-level food chains

A coupled model for three-level food chain is considered, the coupling rule is discretized Laplacian diffusion type. The focus of this paper is on the global behavior of solutions. We will show that the differences of the same level population density approach zero as t→∞, provided that the coupling strength is sufficiently large.     

Family of instantons of the Kraichnan model with a frozen velocity field

We find the family of instantons of the Kraichnan model with a frozen velocity field. Using these instantons, we investigate the asymptotic behavior of higher orders of the perturbation theory series constructed for the response function. We demonstrate that although the number of diagrams increases factorially with the degree of the perturbation series term, the perturbation series itself has a finite and sometimes even infinite convergence radius. We thus disprove the commonly accepted view that the type of series convergence can be determined by estimating the number of diagrams in higher orders of the perturbation theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 2, pp. 200–213, February, 2009.