Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance

We study the asymptotic behavior at large time of a solution to a system of nonlinear integro-differential equations which arises in mathematical modeling of diffusion of a magnetic field into a substance. We establish the corresponding stabilization rate.     

Motion of a container as a nonholonomous system in a curved section of a horizontal pipeline

The problem of the motion of a container in a curved section of a horizontal pipeline is solved using second-order Lagrange equations in the presence of nonholonous couplings. The special case of the motion of a container in a circular curve is examined.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 90–95, 1987.     

Construction of a Formula from a Syntactic Graph of a Sentence

The paper considers the construction of formulas describing relations between entities from a Russian sentence. We describe rules which help constructing such formulas from a syntax graph.     

On a mapping of a projective space into a sphere

We obtain an exact estimate for the minimum multiplicity of a continuous finite-to-one mapping of a projective space into a sphere for all dimensions. For finite-to-one mappings of a projective space into a Euclidean space, we obtain an exact estimate for this multiplicity for n = 2, 3. For n ≥ 4, we prove that this estimate does not exceed 4. Several open questions are formulated.     

An Asymptotic Expansion of a Solution of a Nonlinear Equation for a Steady Flow of a Stratified Fluid

We consider the problem of the two-dimensional motion of a nonviscous incompressible fluid in the field of gravity. To calculate the flow field, we use the method of the asymptotic expansion of the solution with respect to a small parameter. The constructed algorithm allows one to obtain a picture of the flow functions for the exact (nonlinear) problem of a perturbed flow of a stratified fluid. The main limitations of the algorithm are the absence of backflow zones (rotors) and a large typical horizontal size of the solution as compared with the depth of the flow. We give results of the calculations.     

Spectral properties of a Hamiltonian of a four-particle system on a lattice

We consider the Hamiltonian of a system of four arbitrary quantum particles with two-particle contact (noncompact) interaction potentials on a three-dimensional lattice perturbed by three-particle contact potentials. We describe the location of the essential spectrum of the Schrödinger operator corresponding to a four-particle system.     

Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution

We investigate the behavior of a diserete dynamical system in a neighborhood of a quasiperiodic trajeetory for the case of an infinite-dimensional Banach space We find conditions sufficient for the system considered to reduce, in such a neighborhood, to a system with quasiperiodic coefficients. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1661–1676, December, 1997.     

Symmetry-based solution of a model for a combination of a risky investment and a riskless investment

Benth and Karlsen [F.E. Benth, K.H. Karlsen, A note on Merton's portfolio selection problem for the Schwartz mean-reversion model, Stoch. Anal. Appl. 23 (2005) 687-704] treated a problem of the optimisation of the selection of a portfolio based upon the Schwartz mean-reversion model. The resulting Hamilton-Jacobi-Bellman equation in 1+2 dimensions is quite nonlinear. The solution obtained by Benth and Karlsen was very ingenious. We provide a solution of the problem based on the application of the Lie theory of continuous groups to the partial differential equation and its associated boundary and terminal conditions.     

On continuation of a topology from a system of generators of a group to a topology on the group

In this paper we establish conditions under which a topology is continued from a subset of a group to a topology on the group coordinated with the group operation.     

Dependence of the Green's function of a linear extension of a dynamical system on a torus upon a parameter

We study the dependence of the Green's function of a linear extension of a dynamical system on a torus upon a parameter.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 419–421, March, 1995.     

Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

Study of a discrete dynamic system in a neighborhood of a quasi-periodic trajectory

We study a discrete system in a neighborhood of a quasi-periodic trajectory. We obtain conditions for reducing a system in this neighborhood to a system with quasi-periodic coefficients. We determine the behavior of this system under the action of small perturbations.This work was prepared with the financial support of the Ukrainian State Committee on Science and Technology.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 12, pp. 1702–1711, December, 1992.     

Evolution of a regular precession of a solid body carrying a visco-elastic disk

The motion of inertia is studied of a system consisting of an axisymmetric solid body with fixed point and a homogeneous visco-elastic disk lying in the equatorial plane of the ellipsoid of inertia of the solid body (the center of disk coincides with the fixed point). In the case of a solid disk immobilized relative to the solid body the system accomplishes a regular precession (the case of Euler motion of a symmetric solid body with a fixed point /1/). The deformation of the disk is taking place in the plane of the disk, and is accompanied by energy dissipation is the cause of the regular precession finishing by steady rotation about the vector of the moment of momentum of the system /2/.     

Composition of a pseudodifferential operator and of a restriction to a submanifold

The results of Seeley on admissible Cauchy data for the solutions of a homogeneous elliptic equation on a manifold with boundary are extended to equations with a pseudodifferential operator.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 110, pp. 217–224, 1981.     

Shadowing in a neighborhood of a separatrix

We consider a model example of a diffeomorphism of a two-dimensional manifold with two hyperbolic fixed points joined by a separatrix. We show that, in a tubular neighborhood of the separatrix, every pseudotrajectory satisfying an additional error smallness condition is shadowed by an exact trajectory.     

Optimal construction of a selection of a subpopulation

Summary The problem of selecting a subpopulation from a given populationII is to be, on the basis of measurements of members ofII, achieved by choosing those members ofII who satisfy the standards determined by a given selection cirterion and rejecting those who do not. Since the optimum selection depends on the unknown parameter of the probability distribution ofII, it is here considered how to construct a decision function from the space of subsidiary sample having infor-mation on θ to the space of selections. Thus the existence of Bayes and minimax decision functions under the constraint defined by the selection criterion is proved. A necessary and sufficient condition for a decision function satisfying the constraint to be a Bayes decision function is also obtained. The Institute of Statistical Mathematics     

On a generalization of a theorem of Lyapunov

A constructive and simple proof is given of a generalization of a result of Lyapunov on the convexity of the range of vector measure.     

Refinement of a criterion for superfluidity of a classical liquid in a nanotube

The problem has a large parameter, the number N of particles (outside the condensate), and a small parameter, Planck’s constant ħ (more precisely, a dimensionless parameter containing ħ in the numerator). They turn out to be interrelated for Bose particles. Using the exact solution of the variational equation for a bosonic system in a capillary, we can obtain precise criteria restricting the superfluidity of a classical liquid in the capillary. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 524–528, June, 2008.     

关于一个素数和一个素数的k次方和问题

设k≥2,且Hk表示一个正整数n的集合,使得该集合中的元素满足a+bk≡n(modq)对任意的q,在模q的既约剩余系中有解,令Dk(N)表示所有的n≤N,且n∈Hk且不能表成p1+p2k=n形式的整数.那么在GRH下, Dk(N)相似文献