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1.
An algorithm is proposed for solving the Signorini problem /1/ in the formulation of a unilateral variational problem for the boundary functional in the zone of possible contact /2/. The algorithm is based on a dual formulation of Lagrange maximin problems for whose solution a decomposition approach is used in the following sense: a Ritz process in the basis functions that satisfy the linear constraint of the problem, the differential equation in the domain, is used in solving the minimum problem (with fixed Lagrange multipliers); the maximum problem is solved by the method of descent (a generalization of the Frank-Wolf method) under convexity constraints on the Lagrange multipliers. The algorithm constructed can be conisidered as a modification of the well-known algorithm to find the Udzawa-Arrow-Hurwitz saddle points /3, 4/. The convergence of the algorithm is investigated. A numerical analysis of the algorithm is performed in the example of a classical contact problem about the insertion of a stamp in an elastic half-plane under approximation of the contact boundary by isoparametric boundary elements. The comparative efficiency of the algorithm is associated with the reduction in the dimensionality of the boundary value problem being solved and the possibility of utilizing the calculation apparatus of the method of boundary elements to realize the solution.  相似文献   

2.
Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.  相似文献   

3.
The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model.  相似文献   

4.
The stability of the stationary solution of the thermistor problem 1s proved using a Liapunov functional for a class of physically relevant electrical conductivity.  相似文献   

5.
On the growth of the Betti sequence of the canonical module   总被引:1,自引:1,他引:0  
We study the growth of the Betti sequence of the canonical module of a Cohen–Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen–Macaulay ring possessing a canonical module to be Gorenstein. GJL was partly supported by a grant from the National Security Agency. An erratum to this article can be found at  相似文献   

6.
This paper presents a new approximate method of Abel differential equation. By using the shifted Chebyshev expansion of the unknown function, Abel differential equation is approximately transformed to a system of nonlinear equations for the unknown coefficients. A desired solution can be determined by solving the resulting nonlinear system. This method gives a simple and closed form of approximate solution of Abel differential equation. The solution is calculated in the form of a series with easily computable components. The numerical results show the effectiveness of the method for this type of equation. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.  相似文献   

7.
The limiting (Mordukhovich) coderivative of the metric projection onto the second-order cone $\mathbb{R}^{n}$ is computed. This result is used to obtain a sufficient condition for the Aubin property of the solution map of a parameterized second-order cone complementarity problem and to derive necessary optimality conditions for a mathematical program with a second-order cone complementarity problem among the constraints.  相似文献   

8.
We obtain new sufficient conditions under which a set on the plane has the Pompeiu property. This result allows us to construct first examples of domains with the Pompeiu property with non-Lipschitz (and even fractal) boundary. In addition, we study the problem of determining the least radius of the ball on the sphere in which a given set is a Pompeiu set. We obtain the solution of this problem in the case of a biangle and a spherical half-disk. We also consider some applications to questions of complex analysis.  相似文献   

9.
The solution of the Riemann–Hilbert problem for an analytic function in a canonical domain for the case in which the data of the problem is piecewise constant can be expressed as a Christoffel–Schwartz integral. In this paper, we present an explicit expression for the parameters of this integral obtained by using a Jacobi-type formula for the Lauricella generalized hypergeometric function F D (N). The results can be applied to a number of problems, including those in plasma physics and the mechanics of deformed solids.  相似文献   

10.
In this article we prove a generalization of Weyl’s criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over open manifolds and get new results for its essential spectrum.  相似文献   

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