Diffusion processes with identical bridges

It is shown that diffusions with identical bridges compose classes of stochastic processes for which the methods of calculation of distributions of functionals are identical as well. Some particular classes of such processes are considered. Bibliography: 8 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 29–42.This research was supported in part by the Russian Foundation for Basic Research, grants 02-01-00265, 00-15-96019, and 99-01-04027 (joint with DFG).Translated by V. N. Sudakov.     

Distribution of functionals of Brownian motion stopped at the moment inverse to a linear combination of local times

We consider linear combinations of coefficients of local times with different signs. A new version of the Feynman-Kac formula for Brownian motion stopped at the moment inverse to this linear combination is proved. Bibliography: 6 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 43–54.This research was supported in part by the Russian Foundation for Basic Research, grants 02-01-00265, 00-15-96019, and 99-01-04027 (joint with DFG)Translated by V. N. Sudakov.     

Distribution of the shape of Markovian random words

The distribution of the shape of the semi-standard tableau of a random word in k letters is asymptotically given by the distribution of the spectrum of a random traceless k×k Gaussian Unitary Ensemble (GUE) matrix provided that these letters are independent with uniform distribution. Kuperberg (2002) conjectured that this result by Johansson (2001) remains valid if the letters of the word are generated by an irreducible Markov chain on the alphabet with cyclic transition matrix. In this paper we give a proof of this conjecture for an alphabet with k=2 letters.Research supported by DFG GO-420/3-3 in Bielefeld.Research supported by INTAS 99-00317, RFBR–DFG 99-01-04027.Mathematics Subject Classification (2000): 82B41, 60C05, 60F05, 60F10     

One property of student’s distribution with two degrees of freedom

Characterizations of Students t₂-distribution and some related distributions based on regressional properties of order statistics are obtained. Bibliography: 8 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 148–157.This research was supported by the Russian Foundation for Basic Research, grants 00-15-96019, 01-01-00031, and 02-01-00779.Translated by A. V. Sudakov.     

Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields

The central limit theorem is proved for the integral-type functionals of nonlinear transformations of two-and three-dimensional uniform isotropic Gaussian random fields. A theorem on convergence of finite-dimensional distributions of these functionals to the corresponding distributions of the Wiener process is also established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 472–480, April, 1993.     

On distributions of random variables chosen at random

The existence of typical distributions for random variables chosen at random from a finite-dimensional random variable vector space of high dimension is established. Possible typical distributions are described, and conditions for the typical distribution to be standard Gaussian are given. Bibliography: 2 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 153–160. Translated by the author.     

Singularity and absolute continuity of measures associated with the rotation of a circle

The problem of whether the infinite convolution of certain discrete distributions naturally associated with the rotation of a circle through an irrational angle of α is singular or absolutely continuous for different values of α is studied. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 223, 1995, pp. 323–336. This paper is partially supported by the Russian Foundation for Basic Research, grant 94-01-00921. Translated by N. A. Sidorov.     

Basis ranks of solvable quasivarieties of groups andl-groups

We point out quasivarieties of torsion-free solvable groups (and varieties of solvable l-groups) which are not generated by their all n-generated groups (l-groups), i.e., basis ranks for such are infinite. Supported by RFFR grant No. 99-01-00156. Translated fromAlgebra i Logika, Vol. 39, No. 5, pp. 586–594, September–October, 2000.     

Completion of Linearly Ordered Groups

We give examples of linearly ordered groups that are not embeddable in divisible orderable. In the first example, the group does not embed in any divisible group with strictly isolated unity. In the second example, the group in question is an O*-group, and in the third, it is a group with a central system of convex subgroups. To my teacher A. I. Kokorin Supported by RFBR grant Nos. 96-01-00358, 99-01-00335, and 03-01-00320. __________ Translated from Algebra i Logika, Vol. 44, No. 6, pp. 664–681, November–December, 2005.     

Quasiconformal immersions of Riemannian manifolds and a picard type theorem

We study singularities of quasiconformal immersions of Riemannian manifolds and show that the phenomenon of compulsory continuation holds in dimensionn≥3. In particlar, this result in a stronger version of the Picard theorem—one without omitted values. Supported by RFBR grant No. 99-01-01179. Moscow State University, Department of mechanics and mathematics Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 34, No. 3, pp. 37–48, July–September, 2000. Translated by V. A. Zorich     

Universal Horn classes and antivarieties of algebraic systems

We define and study universal Horn classes dual to varieties in both the syntactic and the semantic sense. Such classes, which we call antivarieties, appear naturally, e.g., in graph theory and in formal language theory. The basic results are the characterization theorem for antivarieties, the theorem on cores in axiomatizable color-families, and the decidability theorem for universal theories of families of interpretations of formal languages. Supported by RFFR grants Nos. 99-01-000485 and 96-01-00097, and also by DFG grant No. 436113/2670. Translated fromAlgebra i Logika, Vol. 39, No. 1, pp. 3–22, January–February, 2000.     

A process of orthogonalization in the Gauss space

A group of orthogonal operators is considered which transforms a given family of Gaussian random variables into a family independent of another given Gaussian family. A way to study distributions of suprema for such families is proposed. Bibliography:5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 300–311     

Asymptotics of a multiple Cauchy integral with rapidly oscillating exponential

An asymptotic expansion uniform with respect to a parameter is obtained for a multiple Cauchy integral with a rapidly oscillating exponential in the integrand under the assumption that the singularity lines are in a general position.Translated fromMatematicheskie Zametki, Vol. 58, No. 2, pp. 231–242, August, 1995.The work was financially supported by the Russian Foundation for Basic Research under grant No. 94-01-00193-a.     

Two criteria of goodness-of-fit for Cauchy distributions based on characterizations

In this paper, we construct two criteria of goodness-of-fit for Cauchy distributions. These critiria are based on characterizations. The first characterization is due to Arnold, and the second one goes back to Ramachandran. The Bahadur efficiency for these criteria is found. Bibliography: 10 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 139–146.This research was supported by the Russian Foundation for Basic Research, grant 01-01-00245, and by the Program Leading Scientific Schools, grant 00-15-96019.Translated by V. N. Sudakov.     

The embedding problem with metabelian kernel

The relationship between the solvability conditions for the embedding problem with metabelian kernel over a p-extension of fields and the associated embedding problem of the first kind with a maximal p-group is studied. It is proved that these problems are equivalent. Bibliography: 1title. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 97–99.The present paper was supported by the Russian Foundation for Basic Research, grant No. 96-01-00854.     

Thorin classes of Lévy processes and their transforms

We define and characterize Thorin classes {ie294-01}, of infinitely divisible distributions on R ₊. We investigate Poisson, Karlin, and Bessel transforms of Thorin classes and also consider extended Thorin classes {ie294-02}. Canonical representation and self-decomposability properties of Thorin subordinated Gaussian Lévy processes are discussed. As an example, a subordinated Cauchy process is considered in detail.     

Some properties of autostable models

Established are (1) a nonuniform criterion for the stability of models in terms of enumeration reducibility of constructivizations; (2) a criterion for the autostability of certain particular classes of models close to algebraic number fields; (3) a uniform autostability of each 1-constructive model that is autostable. Supported by RFFR grant No. 096-01-01525 and by ISF grant NQ 6000. Translated fromAlgebra i Logika, Vol. 35, No. 6, pp. 685–698, November–December, 1996.     

Uniformn-analytic polynomial approximations of functions on rectifiable contours in ℂ

We study approximations of functions byn-analytic polynomials in the uniform norm on closed rectifiable Jordan curves in the complex plane. It is shown that, in contrast to the case of uniform approximations by complex polynomials, there are no topological criteria for the existence of such approximations. We obtain a criterion for the existence ofn-analytic polynomial approximations in terms of analytic properties of these curves. Translated fromMatematicheskie Zametki, Vol. 59, No. 4, pp. 603–609, April, 1996. The author is extremely grateful to A. G. Vitushkin and P. V. Paramonov for the statement of the problem and their attention to the work. The work was partially supported by the Russian Foundation for Basic Research under grant No. 93-01-00225.     

Lattices with unique irreducible decompositions

We define the concept of a minimal decomposition in a lattice, and prove that all the currently known lattices with unique irreducible decompositions are in fact lattices with minimal ones. Also, the characterization of a class of lattices with minimal decompositions is given. A new proof of the Crawley-Dilworth characterization theorem for the class of coalgebraic strongly coatomic lattices with unique irreducible decompositions obtains as a consequence. In memory of Victor A. Gorbunov Supported by the RF State Committee of Higher Education (1998 project), by RFFR grant No. 99-01-00485, and jointly by RFFR and DFG grants Nos. 96-01-00097 and 436113/2670 respectively. Translated fromAlgebra i Logika, Vol. 39, No. 1, pp. 93–103, January–February, 2000.     

Large nilpotent subgroups of finite simple groups

Orders and the structure of large nilpotent subgroups in all finite simple groups are determined. In particular, it is proved that if G is a finite simple non-Abelian group, and N is some of its nilpotent subgroups, then |N|²<|G|. Supported through FP “Integration” project No. 274, by RFFR grant No. 99-01-00550, by International Soros Education Program for Exact Sciences (ISEP) grant No. S99-56, and by a SO RAN grant for Young Scientists, Presidium Decree No. 83 of 03/10/2000. Translated fromAlgebra i Logika, Vol. 39, No. 5, pp. 526–546, September—October, 2000.