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We consider the class of fermion models with a momentum cutoff Λ and an interaction containing derivatives. For the quasilocal fermion model with two coupling constants near a tricritical point, we classify the solutions of mass-gap equations for different values of coupling constants. The mass spectrum of the scalar excitations in the vicinity of the tricritical point is derived and it is found that two scalar exitations always arise when at least one of the constants exceeds its critical value. The mass formation for scalar bound states induced by static gluon fields (gluon condensates) is investigated. Bibliography 5 titles. [ABSTRACT FROM AUTHOR]

On the basis of the gauge equivalence between an elliptic analog of the O(3) sigma-model and the sinh-Gordon equation proved by the author, connection formulas are obtained. Their interpretation in terms of differential geometry is given. Bibliography: 9 titles. [ABSTRACT FROM AUTHOR]

The quantum group of upper triangular matrices and the Hopf algebra associated with the reflection equation are constructed for the R-matrix corresponding to the quantum Heisenberg group. Bibliography: 12 titles. [ABSTRACT FROM AUTHOR]

Hölder estimates and the existence of Hölder continuous generalized solutions of the first boundary problem for doubly nonlinear studies of the turbulent filtration of a liquid or a gas through a porous medium are obtained. Bibliography: 47 titles. [ABSTRACT FROM AUTHOR]

By the isomonodromy deformation method, the asymptotics of the general solution for the second Painlevé equation yxx=2y3+xy−α as Reα→∞ are described for any x. The corresponding formulas are also presented. Bibliography: 23 titles. [ABSTRACT FROM AUTHOR]

The functional representation of the partition function for the Hubbard model with strong Coulomb repulsion is obtained in the form of an integral with respect to auxiliary Grassmann variables. The approximate study of the phase transitions shows: [ABSTRACT FROM AUTHOR]

A method of taking account of the strong Coulomb correlations for the Kondo-lattice model is suggested. The elementary excitations and phase transitions in this model for the CuO2 layers in the superconducting oxides are investigated by this method. Bibliography: 12 titles. [ABSTRACT FROM AUTHOR]

The tetrahedron equation arises as a generalization of the famous Yang-Baxter equation to the 2+1-dimensional quantum field theory and three-dimensional statistical mechanics. Not much is known about its solutions. In the present paper, a systematic method of constructing nontrivial solutions to the tetrahedron equation with spin-like variables on the links is described. The essence of this method is the use of the so-called tetrahedral Zamolodchikov algebras. Bibliography: 12 titles. [ABSTRACT FROM AUTHOR]

The inverse scattering transform method for the dimensionally reduced self-dual equations of the Yang-Mills fields (Zakharov-Manakov system) is developed. Reductions on the scattering data are obtained. The resolvent theory for the auxiliary linear problem is developed. Dispersion relations and trace identities are presented. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

A wide class of quantum universal enveloping algebras uniquely corresponding to Hopf algebras H with spectrum Q(H) in the category of groups is defined. Such quantum algebras are the quantum groups of the simply connected solvable Lie groups P(H). Bibliography: 7 titles. [ABSTRACT FROM AUTHOR]

This paper is devoted to the calculation of superfluid current in the A-phase of helium-3. This calculation is connected with the solution of a nonhomogeneous ordinary differential equation arising in the low-temperature limit from the Gor'kov equation for normal and anomalous Green functions. The new solution is obtained in the form of the expansion in the eigenfunctions of the problem of an electron in a uniform magnetic field. In the formal high-temperature limit the result obtained in the paper reproduces the known result. Bibliography: 18 titles. [ABSTRACT FROM AUTHOR]

The three-band two-dimensional repulsive Hubbard model in the formalism of the temperature Green function is investigated. The applicability of the weak coupling approach at the values of the dimensionless coupling constant U/t≈10–11 is justified. The normal state, the antiferromagnetic state with Neel magnetic ordering on the “copper” sublattice, and the superconducting state with nontrivial Cooper pairing in channels with odd angular momenta are studied. The possibility of other magnetic states in the model is discussed. Bibliography: 20 titles. [ABSTRACT FROM AUTHOR]

Collective excitations in the antiferromagnetic and ferromagnetic states of the two-dimensional repulsive Hubbard model are investigated both in the phase transition vicinity (Ginsburg-Landau region |T−Tc|≪Tc) and in the low-temperature region T≪Tc using the functional integration method. The spectrum of collective excitation consists of one branch at T>Tc, and another branch (Goldstone branch) arises at Tc. The Goldstone branch at T≪Tc in the antiferromagnetic state is calculated including the anisotropic correction term to the linear dispersion law. The value of the nonphonon branch at the zero momentum is equal to the double gap of the fermion energy 2Δ. All the spectrum branches in the ferromagnetic state vanish at zero momentum $$\left( {\mathop {\lim }\limits_{k \to 0} E\left( k \right) = 0} \right)$$ . Bibliography: 6 titles. [ABSTRACT FROM AUTHOR]

In accordance with the demands of the so-called local approach to inverse problems, the set of “waves” uf (·, T) is studied, where uf (x,t) is the solution of the initial boundary-value problem utt−Δu=0 in Ω×(0,T), u|t<0=0, u|∂Ω×(0,T)=f, and the (singular) control f runs over the class L2((0,T); H−m (∂Ω)) (m>0). The following result is established. Let ΩT={x ∈ Ω : dist(x, ∂Ω)n (diam Ω<∞) filled with waves by a final instant of time t=T, let T*=inf{T : ΩT=Ω} be the time of filling the whole domain Ω. We introduce the notation Dm=Dom((−Δ)m/2), where (−Δ) is the Laplace operator, Dom(−Δ)=H2(Ω)∩H(Ω);D−m=(Dm)′;D−m(ΩT)={y∈D−m:supp y ⋐ ΩT. If Tt(·, T): f ∈ L2((0,T), H−m (∂Ω))} (∀m>0), which is dense in D−m(ΩT), does not contain the class C(ΩT). Examples of a ∈ C, a ∈ R, are presented. [ABSTRACT FROM AUTHOR]

In this paper, a uniqueness theorem on the solution of the Cauchy problem for a system of Maxwell equations is proved in the case where the coefficients ε and μ are analytic functions of coordinates and the initial data are given on an “immovable” surface Σ=Γ×[0≤t≤2T], where Γ is an analytic surface in R3. [ABSTRACT FROM AUTHOR]

The following acoustic diffraction problem is considered. The upper half-space is filled by an acoustic medium. Two semi-infinite thin plates are situated on the boundary of the upper half-space. One of the plates is backed by a semi-infinite periodical set of ribbed stiffeners. The source of an acoustic field is positioned on the other plate. The problem is reduced to an infinite system of linear algebraic equations. Such a system can be solved in a shortwave approximation. An expression for the acoustic field at a large distance from the junction of the plates is obtained. [ABSTRACT FROM AUTHOR]

A theorem is proved about the nondegeneracy and bijective nature of the mapping where {Ei}, i=1, ..., 2g+1, are branching points of the hyperelliptic curve Γ that corresponds to finite-gap solutions of the KdV equation; V, W are frequency vectors; c is the average value of the potential ug(x,t):. [ABSTRACT FROM AUTHOR]

A classical problem of acoustics is considered by the Sommerfeld-Maliuzhinets method. All geometric waves are computed explicitly. For diffracted waves, a numerical procedure based on a uniquely solvable Fredholm integral equation is elaborated. [ABSTRACT FROM AUTHOR]

The Neumann boundary-value problem on a plane, corresponding to the scattering of an H-polarized electromagnetic field on an ideal conductive cylinder with a narrow lengthwise split of finite depth, is considered. Asymptotic expansions with respect to a small parameter (the width of a split) for the poles of the solutions that have a small imaginary part are constructed. The resonance nature of these poles is shown. [ABSTRACT FROM AUTHOR]

An algorithm for computing the second term of the series of the ray method in the case of elastic inhomogeneous isotropic media is proposed. The main idea of the approach to the problem can be formulated as follows. Let a central (or support) ray of a ray tube be known. If we inroduce the ray-centered coordinates s, q1, q2 in the vicinity of the central ray, then the rays of the ray tube can be described by functions qi=qi(s, γ1, γ2), i=1,2, where s is the are length of the central ray and γj, j=1, 2, are the ray parameters. On the one hand, we show that the integrand of the second term of the series of the ray method can be expressed via the derivatives of the functions qi with respect to γj of the first, second, and third orders. On the other hand, additional differential equations for the derivatives as functions of s can be obtained from Euler's equations for the rays. This paper also contains initial conditions for the derivatives in the case of a point source. Thus, we obtain an algorithm involving additional differential equations for the derivatives $$\frac{{\partial q_i }}{{\partial \gamma _j }},\frac{{\partial ^2 q_i }}{{\partial \gamma _j \gamma _k }},\frac{{\partial ^3 q_i }}{{\partial \gamma _j \gamma _k \gamma _1 }}$$ , and the initial conditions for them at the source. The algorithm for calculating the mixed components of a vector of displacement is elaborated in detail. Unfortunately, the Russian version of this paper contains some errors, which have been corrected in the English translation of the paper. [ABSTRACT FROM AUTHOR]

An algorithm for computing the second term of the series of the ray method suggested in this paper is specified for the case of the dimension two and a half. By this is meant that the elastic paramenters of a medium depend on x, z only and the source and observation points are placed in a plane orthogonal to the y axis. Thus, to compute the wave field we need to take into account the rays which are placed in the plane indicated. This enables us to simplify the algorithm. We discuss the algorithm in detail for the case of a point source. [ABSTRACT FROM AUTHOR]

In this paper, the existence “in the large” of time-periodic classical solutions (with period T) is proved for the following two dissipative ε-approximations for the Navier-Stokes equations modified in the sense of O. A. Ladyzhenskaya: and the following two dissipative ε-approximations for the equations of motion of the Kelvin-Voight fluids: satisfying the free surface conditions on the boundary ϖΩ of a domain Ω⊂R3:. The free term f(x, t) in systems (1)–(4) is assumed to be t-periodic with period T. It is shown that as ε→0, the classical t-periodic solutions (with period T) of Eqs. (1)–(4) satisfying the free surface conditions (5) converge to the classicat t-periodic solutions (with period T) of the Navier-Stokes equations modified in the sense of O. A. Ladyzhenskaya and to the equations of motion of the Kelvin-Voight fruids, respectively, satisfying the boundary condition (5). [ABSTRACT FROM AUTHOR]

The equation where μ(x, y)=α(x)β(y), ρ(x, y)=α(x)β(y)(g(x)+d(y)) (α, β, g, d are given step functions), is considered. The problem is solved in explicit form and the asymptotic expansion of the solutions as ω→+∞ is found. [ABSTRACT FROM AUTHOR]

It is shown that in a cracked layer sandwiched between two elastic half-spaces, a slow wave propagates. For low frequencies the velocity of this wave is much less than its velocity in an infinite fluid. The dispersion and amplitude characteristics of the slow wave are studied as a function of the porosity and frequency. [ABSTRACT FROM AUTHOR]

A procedure is suggested for recovering two unknown coefficients in an isotropic elliptic operator given in a bounded domain. The BC-method developed by M. I. Belishev is used for solving this problem. [ABSTRACT FROM AUTHOR]

The principal term of the asymptotics is obtained for the two-dimensional problem of diffraction of a plane wave by a smooth cylinder with discontinuous impedance. A key domain in the vicinity of the light-shadow boundary (Fock region) is considered. It is assumed that the point of a jump of the surface impedance is placed near the light-shadow boundary. This gives rise to an intersection of the transition regions near the lightshadow terminator and in the vicinity of a ray reflected from the inhomogeneity of the boundary. The leading terms contain Fock integrals of a new type in addition to the standard ones. The asymptotics is simplified in the penumbral, illuminated, and shadowed regions. Asymptotic estimates of the integrals lead to a description of waves of a new type, which are absent for continuous impedance. [ABSTRACT FROM AUTHOR]

For a periodic layered medium in which every period consists of an elastic anisotropic layer and a fluid homogeneous layer, an effective model is derived by averaging. This model describes wave propagation and has two phases. The equations of this model are deduced in the case of the general anisotropy and in some special cases. [ABSTRACT FROM AUTHOR]

Effective models are derived for layered periodic elastic media'with slide contacts on all interfaces. In the case where each period consists of n layers with different plate velocities, the effective model has n phases. These models are investigated for typical media. [ABSTRACT FROM AUTHOR]

A linear mechanism of sharp frequency selectivity in the inner ear is developed. The cochlea is assumed to be a slightly varying wave guide with inhomogeneous cross section. The tectorial membrane is considered as an additional mass loading the narrow strip of the basilar membrane that underlies the rows of outer hair cells. A high concentration of mass along the middle line of the cochlea partition provides the sharpening of the tuning curve without significantly altering the phase. The dissipation of energy is assumed to hold in fluid boundary layers near the cochlea partition. The responses of the model with one and the same set of input parameters are compared with different experimental data obtained during the last decade, in the basal and apical parts of the cochlea. This paper demonstrates that a system such as cochlea is capable of performing sharply tuned linear frequency analysis without adding any outside energy to the input waveform to be analyzed. [ABSTRACT FROM AUTHOR]

The existence “in the small” of a unique classical solution is proved for the following two dissipative ε-approximations for the equations of aqueous solutions of polymers: satisfying the free surface condition on the boundary ΔΩ. It is shown that if ε→0 and v(x) weakly converges to v0(x) in J(Ω), then the pairs (vε, −1/ε divvε) and (vε, −1/ε(v divvε+x divv)) converge to a unique classical solution (v, p) of the initial boundary-value problem with free surface condition ( 3) for the equations of aqueous solutions of polymers [ABSTRACT FROM AUTHOR]

A method for computing sum multiple wave fields is proposed, taking into account all kinds of exchanges on the interfaces. This method is based on a description of an elementary wave by certain codes and on verifying some conditions imposed on the coefficients of reflection and refraction. We assume that the positions of a source and a receiver in a medium are arbitrary. [ABSTRACT FROM AUTHOR]

In this paper, the propagation of Love waves in anisotropic elastic media is studied. These waves are a similar to the transverse surface SH waves in the isotropic case. Necessary conditions for the existence of Love waves of this polarization type near the surface Σ of an anisotropic elastic body are deduced. The algorithm developed here makes it possible to find the direction (s) of transverse surface wave propagation (at every point on the surface Σ). The algorithm employed is illustrated by some special anisotropic cases. The space-time method is used to construct the asymptotics of Love waves for those types of anisotropic media the eikonal equation of which is valid on the surface of an elastic body. [ABSTRACT FROM AUTHOR]

In this paper we describe an approach for the construction of the substitutional method of obtaining Bayesian estimators HB(f) for H(f). This method is used to obtain Bayesian estimators for the characteristic function, for moments of fixed orders and for the probability of linear inequalities in the case of a multivariate normal distribution. [ABSTRACT FROM AUTHOR]

It is possible to introduce the concept of a stopping time in an algebraic way, and define for each stopping time a natural sigma-field. This yields a simple theorem about sample path regularity for processes with a complete separable metric state space. [ABSTRACT FROM AUTHOR]

We consider a process X(A) indexed by some sets A∈A, where A is a collection of sets. We prove a functional form of the Erdös-Rényi laws. The result may be specialized to get back and sometimes improve previous versions of the classical Erdös-Rényi laws. [ABSTRACT FROM AUTHOR]

In this paper three methods of the construction of approximations to generalized Poisson distributions are considered: approximation by a normal law, approximation by asymptotic distributions, the so-called Robbins mixtures, and approximation with the help of asymptotic expansions. Uniform and (for the first two methods) nonuniform estimates of the accuracy of the corresponding approximations are given. Some estimates for the concentration functions of generalized Poisson distributions are also presented. [ABSTRACT FROM AUTHOR]

An estimate of the rate of strong convergence of convolutions of probability measures is given under the assumption that the components of each convolution converge weakly and in total variation, respectively. [ABSTRACT FROM AUTHOR]

The behavior of a Galton-Watson process with state-dependent immigration in a Markovian random environment is investigated. We obtain a limit theorem in the near-critical case. [ABSTRACT FROM AUTHOR]

This is the first of several papers in which we consider problems related to the asymptotic distribution of the least squares estimate of the parameter γ in the AR(1) model where εk are independent identically distributed (i.i.d.) random variables in the domain of attraction of a stable law. In §1 we give a summary in the case εk is in the domain of attraction of the normal distribution. In §2 we consider errors in the domain of attraction of a (nonnormal) stable distribution. In §3 we prove a result in the case of the completely asymmetric stable distribution with α=β=1. [ABSTRACT FROM AUTHOR]

Let X1, X2, ..., Xn be independent and identically distributed random variables subject to a continuous distribution function F. Let X1∶n, X2∶n, ..., Xn∶n denote the corresponding order statistics. Write where n, k are fixed integers. We apply a result of Marsaglia and Tubilla on the lack of memory of the exponential distribution finction assuming that certain distribution functions involving the above order statistics are equal in two incommensurable points τ1, τ2 > 0; this characterizes the exponential distribution. As a special case it turns out that the equality (*) assumed for s=1, 2 and x=τ1, τ2 implies that F is exponential. [ABSTRACT FROM AUTHOR]

We show that the consideration of algebraic properties of exponential shift families allows one to simplify and unify the procedures of determination of the distribution of a sufficient statistic. We also present a new method for the estimation of a density function based on the determination of the distribution of a sufficient statistic. [ABSTRACT FROM AUTHOR]

A random-medium model which is a correlated distribution of points (particles) randomly positioned in the 3-dimensional space is considered. The construction of the medium starts from a noncorrelated (Poisson) distribution of parent particles, each of them initiates a finite Markov chain of its descendants. The complete collection of correlation functions of all orders within the scope of the model have been obtained. The use of the 3-dimensional stable law (Lévy law) as a transition probability allows us to present the correlation function in an explicit form. [ABSTRACT FROM AUTHOR]

An estimate of the decomposition stability of the Poisson distribution is obtained under the condition that the components are identical. The estimate is much sharper than that in the general case. [ABSTRACT FROM AUTHOR]

The problem of reconstruction of a multivariate distribution by means of translated moments is considered. [ABSTRACT FROM AUTHOR]