On an identity for dual fields

A new identity for dual fields is proved. Bibliography: 4 titles. Translated from,Zapiski Nauchnykh Seminarov POMI, Vol. 245, 1997, pp. 270–281. Translated by N. A. Slavnov.     

On a question of A. Woods and P. Bambah concerning codes of decomposable cubic forms

A commentary is given to the proof of a statement from an earlier paper by the author. Bibliography: 2 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 90–92. Translated by B. M. Bekker.     

Geometry of distributions of flags on Grassmann manifolds of a projective space. I

We consider intrinsic normalizations of distributions of flags of type (m, m+1) on the Grassmann manifold ofm-planes of a (2m+2)-dimensional projective space. Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 2, pp. 214–227, April–June, 2000. Translated by V. Mackevičius     

Estimates of the number of zeros of some functions with algebraic Taylor coefficients

We prove two theorems about the number of zeros of analytic functions from certain classes that include the SiegelE-andG-functions. By using these theorems, we arrive at a new proof of the Gel'fond-Schneider theorem and improve the result that the numerical determinant does not vanish in the proof of the Shidlovskii theorem. Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 817–824, June, 1997. Translated by M. A. Shishkova     

On the intrinsic normalizations of the seminonholonomic complexesSN Gr(m, n, (m+1)(n−m)−ϱ). I

Some intrinsic normalizations of seminonholonomic complexes of then-dimensional projective space are considered. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 517–538, October–December, 1999. Translated by R. Lapinskas     

Geometry of distributions of flags on Grassmann manifolds of a projective space. II

We consider intrinsic normalizations of distributions of flags of type (m, m+1) on the Grassmann manifold ofm-planes of a (2m+2)-dimensional projective space. Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 335–349, July–September, 2000. Translated by V. Mackevičius     

Intrinsic normalizations of a hyperplane distribution on the Grassmann manifold. I

We consider intrinsic normalizations of a hyperplane distribution on the Grassmann manifold of ann-dimensional projective space. Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp. 257–273, April–June, 1999. Translated by V. Mackevičius     

Local estimates of normal second derivatives for solutions of the Dirichlet problem for the prescribed quotient curvature equations

Local estimates from above for second normal derivatives of a solution of the Dirichlet problem for the prescribed quotient curvature equations are established. Bibliography: 11 titles. Dedicated to N. N. Uraltseva on her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 114–126. Translated by N. M. Ivochkina.     

On a multidimensional version of the tomographic problem

The main result: If the dimension of a Euclidean space with measure is high enough, only the first observation from a long series of observations with random independent choice of projection gives essential information on the measure. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 295–301. Translated by V. Sudakov.     

On reconstruction of density from a finite set of values of the radon transformation

In this paper, we give estimates of approximate (with respect to various metrics) reconstruction of smoothed density from a finite set of values of the Radon transformations for various smoothing kernels. Bibligraphy: 3 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 181–185. Translated by S. Yu. Pilyugin.     

One-dimensional perturbations of singular unitary operators

Under some natural restrictions, we prove that any one-dimensional perturbation of a singular unitary operator on a Hilbert space is unitarily equivalent to a model operator on a space determined (in a certain way) by two functions from the Hardy space H². Bibliography: 3 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 118–122. Translated by V. V. Kapustin.     

Quadrangles inscribed in an ellipse

Necessary and sufficient conditions are given under which a quadrangle similar to a given one can be inscribed in a given ellipse. The class of quadrangles for which this problem is solvable is described. Bibliography: 2 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 246, 1997, pp. 130–140. Translated by S. Yu. Pilyugin.     

Commuting algebraic correspondences and groups

In this paper, the naturalness of the appearance of the group approach in the study of problems of algebraic commutation is considered. New, previously unknown solutions are obtained. Special attention is paid to an example of commutation obtained from the icosahedral equation. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 662–670, May, 1997. Translated by A. I. Shtern     

On acyclicity of the set of solutions to the Cauchy problem for differential equations

The acyclicity of sets of solutions to the Cauchy problem is considered from the viewpoint of the axiomatic theory of solutions spaces of ordinary differential equations. We prove that the class of acyclic solution spaces is closed with respect to passing to the limit space. Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 836–842, December, 1997 Translated by M. A. Shishkova     

Semigroups presented by one relation and satisfying the Church-Rosser property

This paper is devoted to the study of semigroups presented by a single defining relationA=B and satisfying the Church-Rosser property. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 114–118, January, 1997. Translated by A. I. Shtern     

Characterization of elliptic distributions

We characterize elliptic distributions in ^d by an extremal property for a class of probability distances. A generalization to the case of Hilbert spaces is given. Bibliography: 2 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 294, 2002, pp. 19–28.Translated by Ya. I. Belopolskaya, L. B. Klebanov, and V. E. Volkovich.     

The subgroups of the group gl(2,k) that contain a nonsplit maximal torus

In the group GL(2,k), the lattice of the intermediate subgroups that contain the maximal nonsplit torus is studied for a field k of characteristic different from 2. In a number of cases, when formulating the results some additional restrictions are imposed. Bibliography: 3 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 136–146. Translated by A. I. Skopin.     

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.     

Some problems concerning universality in families ofn-Dimensional rational spaces

In this paper some problems concerning universality in families of n-dimensional rational spaces are given. Bibliography:17 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 208, 1993, pp. 98–102. Translated by S. D. Iliadis.