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.     

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.     

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.     

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     

Matheuristics for solving a multi-attribute collection problem for a charity organisation

This paper studies a real-life multi-attribute profit collecting vehicle routing problem, arising in the collection operations of a charity organisation in the United Kingdom. The problem involves a heterogeneous fleet of vehicles of different capacities, mandatory visits to a subset of vertices, time windows, rest requirements associated with maximum driving and working times, and partial collection. A mixed integer programming formulation of the problem is described, along with three matheuristics based on Tabu Search and Large Neighbourhood Search. Computational results on instances derived from the case study are presented, and insights are given from a practical implementation.     

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.     

Error estimates for a Galerkin method for a class of model equations for long waves

The Galerkin method, together with a second order time discretization, is applied to the periodic initial value problem for $$\frac{\partial }{{\partial t}}(u - (a(x)u_x )_x ) + (f(x,u))_x = 0$$ . Heref(x, ·) may be highly nonlinear, but a certain cancellation effect is assumed for∫f(x, u) _x u. Optimal order error estimates inL ₂,H ₁, andL _∞ are derived for a general class of piecewise polynomial spaces.     

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.     

An approximation scheme for a problem of search for a vector subset

We consider the following clustering problem: Given a vector set, find a subset of cardinality k and minimum square deviation from its mean. The distance between the vectors is defined by the Euclideanmetric. We present an approximation scheme (PTAS) that allows us to solve this problem with an arbitrary relative error ? in time O(n ^2/?+1(9/?)^3/? d), where n is the number of vectors of the input set and d denotes the dimension of the space.     

Existence of a solution for a Signorini contact problem for Maxwell-Norton materials

The aim of this article is to study the quasistatic evolutionof a Maxwell–Norton three-dimensional viscoelastic solidwith contact constraints. After introducing the appropiate functionalframework, we will discretize the problem in time using an implicitscheme whose resultant variational inequality is well posed.By using monotonicity arguments together with compensated compactnesstechniques, we will prove that the corresponding discrete solutionconverges to a solution of the continuous problem.     

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.     

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.     

Pointwise error estimates for a streamline diffusion scheme on a Shishkin mesh for a convection-diffusion problem

We analyze a streamline diffusion scheme on a special piecewiseunform mesh for a model time-dependent convection–diffusionproblem. The method with piecewise linear elements is shownto be convergent, independently of the diffusion parameter,with a pointwise accuracy of almost order 5/4 outside the boundarylayer and almost order 3/4 inside the boundary layer. Numericalresults are also given. stynes{at}bureau.ucc.ie     

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.     

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.