一类超过程的泛函及轨道连续性

对于DW-超过程我们首先推广了Dynkin的线性可加泛函的表示定理,然后应用该结果给出了超过程轨道连续的一个充分条件,从而在非常广泛的条件下用不同的方法推广了已有的结论。     

超布朗运动关于区域的首中方式

应用Ｌｅ Ｇａｌｌ的超布朗运动的轨道构造,研究超布朗运动关于区域的着中方式,证明了它在首中一个区域时,其支撑集与区域闭包的交集的点数不大于２,并提出了一个猜想。     

带迁入的分枝粒子系统的波动极限

本文研究了一个带迁入的对称稳定粒子系统，对此系统作时间和空间的重新标度，得到了重新标度过程的一个大数定律，证明了重新标度过程的波动极限是Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ超过程．     

超Ornstein-Uhlenbeck过程击中概率估计

本文首先通过布朗运动的时间和空间变换给出一类Ornstein-Uhlenbeck过程局部最大值分布的概率估计,然后研究相应的超Ornstein-Uhlenbeck过程的击中概率问题,并给出了它的一个上界估计.     

超--α对称稳定过程的局部灭绝性

考虑初始测度为Ｌｅｂｅｓｇｕｅ测度μ的超α－对称稳定（记为α－ＳＳ）过程,其分枝特征为ψ（ｘ,ｚ）＝－γ（ｘ）ｚ＾１＋β（０〈β≤１）。本文研究这类超过程的局部灭绝性。运用纯分析的方法我们首先得到了局部灭绝的一个充分条件,借助这一条件,对较特殊的γ（ｘ）＝（１＋│ｘ│）＾θ（θ〈βｄ）,证明了与之联系的超α－ＳＳ过程存在局部灭绝的临界值θ＾＊,同时给出它的一个上界βｄ－α。若γ（ｘ）≡１,这意味着     

S—调和函数与超过程的Dirichlet问题

本文定义了超Hunt过程的S-调和函数与Dirichlet问题．定义在Dc上的有界函数f可以扩张到Rd上的函数h使得F（P）=exp＜-h,μ＞为D内S-调和函数并且在D的规则边界点上满足Dirichlet边界条件     

分支机制依赖于种群总数的临界的超过程

该文研究分支机制依赖于种群总数的粒子系统的列的极限行为。在自然的假设下,该粒子系统列弱收敛于一个分支机制依赖于种群总数的超过程。在第三部分中给出该 超过程的鞅刻画,第四部分利用“随机化”的累积半群证明该鞅问题的唯一性。     

超空时调和函数与一类非线性抛物方程

本文对超扩散过程定义了超空时调和函数并讨论了它们的某些性质，在此基础上建立了一类非线性抛物方程的正解与超空时调和函数之间的对应关系．     

一类超一致椭圆扩散过程的极限定理

本文研究了分支特征为ψ（x,z）=γz^1+β（0<β≤1）形式的超一致椭圆扩散过程,当初始值X₀（dx）为底过程的某类不变测度时,给出了当空间维数d满足βd≤2时,超过程X_t依分布收敛于0测度,当βd>2时,X_t则依分布收敛于一个非退化的随机测度.     

两物种超过程分枝特征的刻画

本文运用调和分析的方法，通过对二元连续函数的积分表示问题的研究，得到了一类两物种超过程的分枝特征的一般刻画。     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Construction of normal bases of rings of integral elements of certain fields of algebraic functions

This article is devoted to the construction of normal bases of rings of integral elements of certain fields of algebraic functions. These fields are algebraic extensions of the initial fields, given by appropriate algebraic equations. The extensions are given only by the monodromy group. The device of the matrix Riemann boundary-value problem on a Riemann surface is used.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 1004–1007, July, 1990.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Variant of statistical interpretation of the formation of viscoelastic deformations of polymers

A variant of a statistical probability interpretation of elementary micromechanisms of formation of viscoelastic deformations of polymers is examined with the aid of the concept of dissymmetric media and the dissymmetry coefficient. A new rheological relationship is obtained, a particular case of which is the known equation of a typical linear viscoelastic body. A method is given for determining the relaxation spectrum for different intensity functions figuring in the rheological relationships. The results of the calculation are compared with the experimental data, exemplified by the creep of polyamide P-68.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 392–396, May–June, 1973.     

Invariant properties of systems of equations of the mechanics of inhomogeneous fluids

The invariant properties of the fundamental system of equations of the mechanics of inhomogeneous fluids and its widely used approximations are analysed by the methods of continuous group theory. Simplifying assumptions significantly alter the invariant properties of the systems of equations. Both extending and contracting the admissible symmetry group can occur and provide evidence of the violation of the conditions of equivalence between the original and derived systems. For example, the use of the incompressibility and Boussinesq approximations leads to extension of the concept of an inertial reference frame to all frames moving relative to one another with arbitrary linear acceleration.     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.     

Lengths of periods of continued fractions of square roots of integers

Empirical study of the period’s length T of the continued fractions of $\sqrt{Q}$ (for growing integers Q) shows several strange asymptotical results, for instance, $T\leq C\sqrt{Q}\ln{Q}$ . These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.