The asymptotics of integral functionals of a multidimensional empirical process

Estimates of a rate of convergence of orderO(n ^–1) are obtained for integral functionals of an empirical process.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 10–16, 1987.     

Nonuniform estimates of the stability of the normal law under random perturbations of the scale parameter and some of their applications

Translated fromProblemy Ustoichivosti Stokhasticheskikh Modelei. Trudy Seminara, 1988, pp. 84–92.     

Numerical algorithm for the Mayer problem for nonlinear dynamic systems

An algorithm is proposed for numerical construction of optimal programmed controls in the Mayer problem for a nonlinear dynamic system. In each step of the optimization process, the algorithm uses the method of successive linearization with subsequent projection of the objective functional gradient on the constraints and recovery of violated boundary conditions and constraints. Solutions of some test problems are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 107–114, 1985.     

Synthesis of methyl ethers of methyl 2-acetamido-2-deoxy-α-D-glucopyranoside

A convenient method is proposed for the synthesis of all the individual methyl ethers of methyl 2-acetamido-2-deoxy-α-D-glucopyranoside based on the partial methylation of 2-acetamido-2-deoxy-α-D-glucopyranoside with dimethyl sulfate in an alkaline medium followed by preparative liquid column chromatography on silica gel of the resulting mixture of methyl ethers.     

Yb3+掺杂KY(WO4)2激光晶体生长、结构与光谱分析

采用顶部籽晶提拉法(TSSG)生长出Yb:KY(WO₄)₂(Yb:KYW)激光晶体.对预烧后的原料及晶体进行了XRD分析，结果表明，分别在920℃和600℃预烧8h后的熔质和助熔剂基本上形成一相，抑止了实验中的挥发问题；所生长的晶体为β-Yb:KYW，计算其晶格常数为a=1.063nm，b=1.034nm，c=0.755nm，β=130.75°.测得不同厚度样品的吸收光谱，结果表明样品在933nm和981nm有较强的吸收峰，计算出主峰981nm的吸收截面σ关键词： Yb:KYW TSSG法 晶体结构 光谱参数     

Van der Waerden continuity theorem for semisimple lie groups

As was proved by van der Waerden in 1933, every finite-dimensional locally bounded representation of a semisimple compact Lie group is continuous. This is the famous “van der Waerden continuity theorem,” and it motivated a vast literature. In particular, relationships between the assertion of the theorem (and of the inverse, in a sense, to this theorem) and some properties of the Bohr compactifications of topological groups were established, which led to the introduction and the study of certain classes of the so-called van der Waerden groups and algebras. Until now, after more than 70 years have passed, the van der Waerden theorem appears in monographs and surveys in diverse forms; new proofs were found and then simplified in important special cases. In this paper, we prove that the statement of the van der Waerden theorem remains valid for all (not necessarily compact) real semisimple Lie groups, i.e., any given finite-dimensional representation of a real semisimple Lie group is continuous if and only if this representation is locally bounded. More subtle results are also obtained. The main theorem contains several conditions equivalent to the continuity condition for a finite-dimensional representation. In particular, it is proved that every finite-dimensional representation of a real semisimple Lie group is continuous if and only if the restriction of this representation to the “compact” part, to the Abelian part, or to the nilpotent part of the Iwasawa decomposition is locally bounded, and the original van der Waerden theorem is also somewhat refined. For instance, the following assertion holds: every finite-dimensional representation of a compact semisimple Lie group is continuous if and only if the restriction of this representation to some maximal torus is locally bounded. Dedicated to the memory of George Mackey (1916–2006) Partially supported by the Russian Foundation for Basic Research under grant no. 02-01-00574, by the Program of Supporting the Leading Scientific Schools under grant no. NSh 619.203.1, and by the INTAS grant.     

Logarithmic L 2-Small Ball Asymptotics with Respect to a Self-Similar Measure for Some Gaussian Processes

We find logarithmic small ball asymptotics for the L₂-norm with respect to self-similar measures for a certain class of Gaussian processes including Brownian motion, Ornstein-Uhlenbeck process, and their integrated counterparts. Bibliography: 46 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 190–213.