Ground States for a Stationary Mean-Field Model for a Nucleon

In this paper we consider a variational problem related to a model for a nucleon interacting with the ω and σ mesons in the atomic nucleus. The model is relativistic, and we study it in a nuclear physics nonrelativistic limit, which is of a very different nature than the nonrelativistic limit in the atomic physics. Ground states are shown to exist for a large class of values for the parameters of the problem, which are determined by the values of some physical constants.     

Estimation of a Finite Population Total for a Censored Regression Model for a Study Variable

A model-based estimator of a finite population total using a tobit model for a study variable is proposed. Formulas for its approximate bias, approximate variance and an estimator of the variance are given. Simulation results show situations of possible effective applications of the model. The study is supported by the Nordplus Neighbour program of the Nordic Council of Ministers.     

Invariant Integrals for the Equilibrium Problem for a Plate with a Crack

We consider the equilibrium problem for a plate with a crack. The equilibrium of a plate is described by the biharmonic equation. Stress free boundary conditions are given on the crack faces. We introduce a perturbation of the domain in order to obtain an invariant Cherepanov–Rice-type integral which gives the energy release rate upon the quasistatic growth of a crack. We obtain a formula for the derivative of the energy functional with respect to the perturbation parameter which is useful in forecasting the development of a crack (for example, in study of local stability of a crack). The derivative of the energy functional is representable as an invariant integral along a sufficiently smooth closed contour. We construct some invariant integrals for the particular perturbations of a domain: translation of the whole cut and local translation along the cut.     

Symmetric excited states for a mean-field model for a nucleon

In this paper, we consider a stationary model for a nucleon interacting with the ω and σ mesons in the atomic nucleus. The model is relativistic, and we study it in a nuclear physics nonrelativistic limit. By a shooting method, we prove the existence of infinitely many solutions with a given angular momentum. These solutions are ordered by the number of nodes of each component.     

A method for solving a boundary problem for a nonlinear controlled system

An algorithm is proposed for constructing a control function that transfers a wide class of nonlinear systems of ordinary differential equations from an initial state to an arbitrarily small neighborhood of a given terminal state. The algorithm is convenient for numerical implementation. Taking into account the restrictions on the control and phase coordinates, a constructive criterion is obtained for choosing terminal states for which this transfer is possible. The problem of an interorbital flight is considered and modeled numerically.     

An error estimate for a finite-element scheme for a phase field model

In this paper we propose a fully discrete finite-element schemeto solve a non-linear system of parabolic equations for a phasefield model and demonstrate an error estimate of optimal orderin L² for this scheme. This error estimate conforms with thenumerical results presented at the end of this paper.     

On a sufficient condition for the existence of a common stabilizer for a family of dynamical systems

We consider the problem on the existence of a common stabilizing controller for a finite family of linear vector dynamical systems. A sufficient condition, obtained on the basis of topological methods, is presented for the existence of a common stabilizer. Constructive approaches to the development of an algorithm for verifying this condition are indicated.     

Necessary conditions for optimality for a diffusion with a non-smooth drift

The purpose of this paper is to establish the necessary conditions for optimality of a controlled stochastic differential system without differentiability assumptions on the drift. We use an approximation argument in order to obtain a sequence of smooth control problems, and we apply Ekeland's variational principle to derive the associated adjoint processes. Passing at the Limit with respect to the stable convergence, we obtain a weak adjoint process and the inequality between Hamiltonians. This result is a generalisation of Kushner's maximum principle     

Error estimates for a projection-difference method for a linear differential-operator equation

We study a projection-difference method for approximately solving the Cauchy problem u′(t) + A(t)u(t) + K(t)u(t) = h(t), u(0) = 0 for a linear differential-operator equation in a Hilbert space, where A(t) is a self-adjoint operator and K(t) is an operator subordinate to A(t). Time discretization is based on a three-level difference scheme, and space discretization is carried out by the Galerkin method. Under certain smoothness conditions on the function h(t), we obtain estimates for the convergence rate of the approximate solutions to the exact solution.     

Method for solving a boundary problem for a nonlinear control system with incomplete information

An easy-to-implement numerical method is proposed for synthesizing a feedback control function that transfers a wide class of nonlinear stationary systems from an initial state to a given terminal state with allowance for measured data. A constructive criterion is obtained for choosing terminal states for which this transfer is guaranteed. The problem of an interorbital flight is considered and numerically simulated.     

On a nonlocal problem for a parabolic equation

We study a nonlocal boundary-value problem for a parabolic equation in a two-dimensional domain, establish ana priori estimate in the energy norm, prove the existence and uniqueness of a generalized solution from the classW ₂ ^1,0 (Q _T ), and construct a difference scheme for the second-order approximation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 790–800, June, 1995.     

On a certain finite difference scheme for a model for diffusion of biological populations

In this note, we present a numerical scheme for finding an approximate solution of an equation which can be viewed as a model for spatial diffusion of age-dependent biological populations. Discretization of the model yields a linear system with a block tridiagonal matrix. Our main concern will be discussion of stability for this scheme by examining the eigenvalues of the block tridiagonal matrix. Numerical results are presented.     

Inequalities for a kinematic dynamo

A lower bound is determined for a functional occurring in dynamo theory. The significance of this bound for the critical Rayleigh number and heat source for a magnetohydrodynamic dynamo is then deduced from work of Proctor [4].     

Asymptotics for a Curve with a Given Distribution Density of the First Exit Position for a Wiener Process

The following inverse first exit problem for a Wiener process is considered: to find an upper class with a given distribution of the first exit point from the domain bounded by this curve. Some estimates are obtained for a curve with a given density at zero. Bibliography: 2 titles.     

On a posteriori estimates for a linearized Oldroyd's problem

We study and give some a posteriori estimates for finite element approximation of a linearized Oldroyd's problem for the approximation of viscoelastic fluid flows. The major difficulty lies in the coupling between two different kinds of equations: a hyperbolic equation associated to the constitutive equation and Stokes problem. These estimates are then obtained combining two different techniques used for each kind of equation: the first technique is given in (First ICIAM, Paris, 1987) for Stokes's equations and the second in (C.R. Acad. Sci. Paris. Ser. I. 322 (1996) 493) for Friedrichs's system.     

On a spectral problem for a classical biorthogonal system

We consider a mixed problem for a fourth-order equation and the corresponding spectral problem, which describes the system biorthogonal to the classical system of root functions for the loaded string problem.     

Method for Constructing Piecewise Quadratic Value Functions in a Control Problem for a Switched System

The problem of constructing internal approximations to solvability sets and the control synthesis problem for a piecewise linear system with control parameters and disturbances (uncertainties) are solved. The solution is based on the comparison principle and piecewise quadratic value functions of a special form. Relations defining such functions and, in particular, “continuous binding conditions” for the functions and their first derivatives are obtained. The results are used to construct numerical methods for solving the control synthesis problem for the class of switched systems under study. An example of approximate solution of the control synthesis problem in a target control problem for a nonlinear mathematical model of a pendulum with a flywheel is considered.     

On a recurrence method for solving a singularly perturbed Cauchy problem for a second order equation

In the present article, the method of deviating argument is applied to solving a singularly perturbed Cauchy problem for an ordinary differential equation of the second order with variable coefficients.     

Planning for a Single Specialty in a Health District

This paper discusses planning in the National Health Service. An outline of a general method for planning at the district level is illustrated with a case study in which a strategic plan was produced for the maternity services in Cambridge Health District. Some of the problems of ensuring implementation of proposals are then discussed.     

Constructing a 3-tree for a 3-connected matroid

In an earlier paper with Whittle, we showed that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid M. The purpose of this paper is to give a polynomial-time algorithm for constructing such a tree for M.