Surface instability in a finite thickness fluid saturated porous layer

The Rayleigh-Taylor (RT) instability at the interface between fluid and fluid saturated sparsely packed porous medium has been investigated making use of boundary layer approximation and Saffmann [8] boundary condition. An analytical solution for dispersion relation is obtained and is numerically evaluated for different values of the parameters. It is shown that RT instability can be controlled by a suitable choice of the thickness of porous layer, ratio of viscosities and the slip parameter.     

Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space

In the present paper, the dispersion equation which determines the velocity of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space has been obtained. The dispersion equation obtained is in agreement with the classical result of Love wave when the initial stresses and inhomogeneity parameters are neglected. Numerical results analyzing the dispersion equation are discussed and presented graphically. The result shows that the initial stresses have a pronounced influence on the propagation of torsional surface waves. It has also been shown that the effect of density, directional rigidities and non-homogeneity parameter on the propagation of torsional surface waves is prominent.     

Asymptotic behavior of the transition probability of a homogeneous Markov process with a finite number of states in a series model

The asymptotic behavior of the transition probabilities P_ij ⁽ⁿ⁾(t/_n) for a homogeneous stochastically continuous Markov process with a finite set of states E where E can be represented in the form E=E₀ U E₁ U ... U E_r, E₀ is the set of unessential states, E_k, k=1, ..., r are ergodic classes.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 574–576, April, 1992.     

Affine embeddings with a finite number of orbits

LetG be a reductive algebraic group and letH be a reductive subgroup ofG. We describe all pairs (G, H) such that, for any affineG-varietyX with a denseG-orbit isomorphic toG/H, the number ofG-orbits inX is finite.Work of both authors was supported by INTAS-OPEN-97-1570, by CRDF grant RM1-2088, and by RFBR grant 01-01-00756.     

On finite groups with a certain number of centralizers

LetG be a finite group and #Cent(G) denote the number of centralizers of its elements.G is calledn-centralizer if #Cent(G)=n, and primitiven-centralizer if #Cent(G)=#Cent(G/Z(G))=n. In this paper we investigate the structure of finite groups with at most 21 element centralizers. We prove that such a group is solvable and ifG is a finite group such thatG/Z(G)?A₅, then #Cent(G)=22 or 32. Moroever, we prove that A₅ is the only finite simple group with 22 centralizers. Therefore we obtain a characterization of A₅ in terms of the number of centralizers     

Homological identities for a finite homogeneous graph

An application of the Atiyah-Bott trace identity to the study of the spectral characteristics of a finite (q+1)-homogeneous factorgraph Y=Γ/X is given (X is an infinite (q+1)-homogeneous tree, Γ a free group of isometries of X). Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 205, 1993, pp. 110–121.     

Theories with only a finite number of existentially complete models

We construct, in particular, a countable universal theory with JEP which has exactly 2 non-isomorphic countable existentially complete models, and these two models can be either elementarily equivalent or inequivalent.     

Functions with a finite number of negative squares on semigroups

We consider indefinite functions on semigroups and their relation to representations in spaces with an indefinite metric. Special attention is given to functions of finite rank, where the space of representation is of finite dimension, and to functions for which the corresponding representation consists of bounded operators in Pontrjagin spaces.The authors wish to thankMarco Thill for useful remarks.     

Stable structures homogeneous for a finite binary language

LetL be a finite relational language andH(L) denote the class of all countable stableL-structuresM for which Th(M) admits elimination of quantifiers. ForM ∈H(L) define the rank ofM to be the maximum value of CR(p, 2), wherep is a complete 1-type over Ø and CR(p, 2) is Shelah’s complete rank. IfL has only unary and binary relation symbols there is a uniform finite bound for the rank ofM ∈H(L). This theorem confirms part of a conjecture of the first author. Intuitively it says that for eachL there is a finite bound on the complexity of the structures inH(L).     

On bounded functions with a finite number of negative squares

In the case of a locally compact abelian groupG we give a characterization of bounded continuous functions onG which have a finite number of negative squares. We show that these functions can be regarded in a certain sense as a special case of positive definite functions.     

On the number of homogeneous subgraphs of a graph

Let us defineG(n) to be the maximum numberm such that every graph onn vertices contains at leastm homogeneous (i.e. complete or independent) subgraphs. Our main result is exp (0.7214 log² n) ≧G(n) ≧ exp (0.2275 log² n), the main tool is a Ramsey—Turán type theorem. We formulate a conjecture what supports Thomason’s conjecture R(k, k)^1/k = 2.