On the measure of algebraic independence of values of derivatives of ap-adic modular function

The measure of the relative transcendence for the values of the derivatives of ap-adic Weyl-Lutz modular functionJ(q) at algebraic points is estimated. Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 431–440, March, 1997. Translated by O. V. Sipacheva     

A generalization of the denjoy integral

We prove that the IsekiM-integral is substantially more general than the Denjoy integral. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 766–772, November, 1997. Translated by I. P. Zvyagin     

On the definability of endomorphisms of a free group of the variety\mathfrak{A}\mathfrak{M} by a finite set of valuesby a finite set of values

In the paper we find out in what cases any endomorphism of a free metabelian group of rankn is uniquely determined by its values on finitely many elements of the group. Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 916–920, December, 1997 Translated by A. I. Shtern     

Structure of cohomology modules of linear bundles overG/B and weak ordering on the weyl group

We consider the cohomologyG-modules of linear bundles over the flag manifoldG/B over an algebraically closed field of prime characteristic. We study the structure of submodules of these modules and their homomorphisms. Translated fromMaternaticheskie Zametki, Vol. 62, No. 2, pp. 163–168, August, 1997. Translated by S. K. Lando     

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     

Structure of cohomology modules of linear bundles overG/B

We study the cohomologyG-modules of linear bundles over flag spacesG/B for algebraically closed fields of prime characteristic. Some series of submodules and quotient modules of these modules are described. Translated by S. K. Lando Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 10–17, July, 1997.     

Reconstruction of 3-submanifolds of large codimension in euclidean spaces from their gauss image

We present necessary and sufficient conditions for a regular three-dimensional manifold in the Grassmannian manifoldG(m, m+3) to be the Gauss image of a regular 3-submanifold in (m+3)-dimensional Euclidean space form>4. Translated fromMatemalicheskie Zametki, Vol. 62, No. 5, pp. 694–699, November, 1997. Translated by S. K. Lando     

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     

Problems of the theory of bitopological spaces. 2

This paper is the second part of a survey of recent results and new problems in the theory of bitopological spaces. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 208, 1993, pp. 5–67. Translated by A. A. Ivanov.     

Asymptotic analysis of the current-voltage characteristic of the Josephson junction

The current-voltage characteristic of the Josephson junction placed in a high-frequency electromagnetic field is obtained. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 101–106, 1990. Translated by A. Ya. Kazakov.     

Curvature identities for normal manifolds of killing type

We present two curvature identities and study the corresponding classesR ₁ andR ₂ of normal manifolds of Killing type. Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 351–362, September, 1997. Translated by S. S. Anisov     

An equivalence of two families of quantum integrable systems

An equivalence of two quantum integrable systems with complete set of quadratic integrals of motion is established. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 199, 1992, pp. 114–131. Translated by I. V. Komarov.     

On distribution of functionals of Brownian motion with linear drift

The paper deals with methods of calculation of the distributions of functionals of Brownian motion with linear drift. Various stopping time moments are considered. The cases where the moments take values equal to infinity are of special interest. Bibliography:5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 205–217. Translated by A. Sudakov.     

Finite groups with 2-nilpotent subgroups of even index

Finite groups with 2-nilpotent subgroups of even index are described. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 700–705, May, 1997. Translated by A. I. Shtern     

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     

Stability properties of cycles and tori of a simplest nonresonant wave-type equation

For a number of meaningful examples, nonresonant wave-type equations are shown to be characterized by periodic dynamics. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 744–750, November, 1997. Translated by O. V. Sipacheva     

Detection of gross errors by the chauvenet test for observations connected in a homogeneous markov chain

The Chauvenet rule for detection of gross errors is extended for the case of a stationary Gaussian Markov chain with unknown correlation. Bibliography:4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 207, pp. 137–142, 1993. Translated by L. Khalfin.     

Space-time gaussian beams of electromagnetic waves

Space-time Gaussian beams in a nonhomogeneous electromagnetic medium concentrated near space rays are constructed. Bibliography: 4 title. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 115–121, 1990. Translated by A. P. Kachalov.     

Pharpening of a feller theorem on the law of iterated logarithms

In the paper, a sharpened version of a theorem of W. Feller on the law of iterated logarithms is proved. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 117–123. Translated by the author.