Negative exterior curvature foliations on compact Riemannian manifolds

The topological structure of compact Riemannian manifolds that admit hyperbolic foliations is studied. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 673–676, November, 1997. Translated by S. S. Anisov     

The impact of 2-neighborhoods on graph structure

Connected regular graphs of diameter greater than 2 with 2-neighborhoods isomorphic to a certain graph Δ of diameter 2 are studied. Regular graphs of diameter 2 with 2-neighborhoods isomorphic to the distance-regular graph Δ of diameter 3 are also studied. It is prowed that 2-locally Schrikhande graphs do not exist. Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 892–897, December, 1997. Translated by S. S. Anisov     

Automatic recognition of interpolation in modal calculi

We deal with some issues on automatic recognition of interpolation properties in modal calculi extending the logics S5 and S4.3. Supported by RFBR grant No. 06-01-00358 and by INTAS grant No. 04-77-7080. __________ Translated from Algebra i Logika, Vol. 46, No. 1, pp. 103–119, January–February, 2007.     

Continuous projections, duality, and the diagonal mapping in weighted spaces of holomorphic functions with mixed norm

The content of this paper is reflected by its title. Bibliography: 16 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 268–275. Translated by S. V. Kislyakov.     

Sharp inequality for deviation of Rogozinski sums and the second continuity modulus in the space of periodic continuous functions

The sharp constant (uniformly in n) is found in a Jackson-type inequality involving the Rogozinski sums of order n and the second modulus of continuity with step π/(n+1). Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 26–45. Translated by S. Yu. Pilyugin.     

Variational problem of the two-phase medium elasticity theory for the zero surface tension coefficient

In this article, we give a proof of the existence theorem for an equilibrium state for the surface tension coefficient σ=0 and investigate the behavior of the equilibrium state for small σ. Bibliography: 4 titles. Dedicated to N. N. Uraltseva on her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1900, pp. 208–225. Translated by S. Yu. Pilyugin.     

Multiplicative factorizations of integral representations by quadratic forms

Multiplicative dependence of integral representations of integers by positive definite quadratic forms in an odd number of variables on square factors of the represented numbers is studied. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 15–55. Translated by A. S. Goloubeva.     

Two analogs of the Rudin-Carleson theorem

In this article, a new asymptotic estimate for embeddings of singular measures into H^1,∞ is proved and an application to multidimensional analogs of the theorem of Rudin-Carleson is given. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 200–209. Translated by S. V. Kislyakov.     

Four counterexamples to the Fubini theorem

In this paper we study signed measures. Our main results are as follows: the Fubini theorem is not true in the general case; the Jordan parts of a transition measure are not necessarily transition measures; the operation of taking the Jordan parts does not necessarily commute with multiplying by the initial measure; the product of σ-bounded measures need not be a σ-bounded measure. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 124–127, July, 1997. Translated by S. S. Anisov     

Null-quadrics of codimension 4 in ℂ7

In this paper we study the automorphisms of nondegenerate quadrics of type (4, 3). In particular, we classify the so-called null-quadrics (we prove that there are exactly two null-quadrics up to equivalence), and find their automorphism groups. Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 657–665, November, 1997. Translated by S. S. Anisov     

On orientable real algebraicM-surfaces

Here we study relations between homology classes determined by real points of a real algebraicM-surface. We prove new congruences involving the Euler characteristics of the connected components of the set of these real points. Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 510–526, October, 1997. Translated by S. S. Anisov     

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     

Inverse problem for jacobi systems with symmetry

A Jacobi homogeneous linear system of partial differential equations is recovered by its infinitesimal operator and a universal invariant of a one-parameter Lie group. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 86–89. Translated by S. Yu. Pilyugin.     

Minimal widths of metric spaces

The minimal width of an arbitrary metric space is defined as the greatest lower bound of its Kolmogorov widths under all isometric embeddings in all possible Banach spaces and is computed or estimated in a number of examples. Supported by RFBR grant No. 96-15-96249. Human Moscow State Technical University. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 33, No. 4, 49, October–December, 1999. Translated by R. S. Ismagilov     

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.     

Bernstein widths of embeddings of Lebesgue spaces

Let (K, μ) be a measurable space with μ(K)=1. Let Ip,q: L^p (K, μ)→L^q (K, μ) be the embedding operator. The Bernstein widths of I_{p, q} are considered. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 166–169. Translated by S. V. Kislyakov.     

On characteristic functions of multidimensional distributions

We consider the possibility of a multidimensional generalization of M. Krein’s theorem on extension of a positive-definite function from an interval to the real line with preservation of positive definiteness. Under some additional conditions, this problem is reduced to the lattice case. An extension criterion for the lattice case is given. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 143–149. Translated by S. Yu. Pilyugin.     

Compactness of distributions of cadlag random functions

LetT be equal to [0, 1], moreover, letE be a Polish space; we analyze the classical properties of theE-valued cadlag functions onT and their convergence to adapt them in the probabilistic analysis of the cadlag random functions and of the convergence of their laws. I.R.M.A., Université Louis Pasteur et C.N.R.S., 7, rue René Descartes, 67084 Strasbourg Cédex. Translated from Lietuvos Matematikos Rinkinys, Vol. 34, No. 3, pp. 288–307, July–September, 1994. Translated by V. Mackevičius     

Functional representations for correlators of spin chains

For a finite spin chain, a functional representation of the generating function of the XY-model at nonzero temperature is obtained. Bibliography: 16 titles. Dedicated to the memory of V. N. Popov Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 224, 1995, pp. 192–207. Translated by V. S. Kapitonov.