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991.
Solutions of the Fokker-Planck (Kramers) equation in position-velocity space for the double-well potentiald
2x2/2+d4x4/4 in terms of matrix continued fractions are derived. It is shown that the method is also applicable to a Boltzmann equation with a BGK collision operator. Results of eigenvalues and of the Fourier transform of correlation functions are presented explicitly. The lowest nonzero eigenvalue is compared with the escape rate in the weak noise limit for various damping constants and the susceptibility is compared with the zero-friction-limit result. 相似文献
992.
Regina C. Elandt-Johnson 《Journal of multivariate analysis》1978,8(2):244-254
We call a set of univariate distributions with the same mathematical form but different parameter values a family . Consider a bivariate Gumbel Type A survival distribution, S12(x1, x2), defined in (2.1), for which both marginal distributions, S1(x1), S2(x2), belong to the same family, of distributions. It is proved in this paper that subject to weak conditions, the crude hazard rates, h1(t) and h2(t), are proportional if and only if the marginal hazard rates, λ1(t) and λ2(t), are proportional (Theorem 1). It is also shown that the survival functions of W = min(X1, X2), and of the identified minimum, Wi = Xi, for Xi < Xj, j ≠ i, belong to the same family as do S1(x1), S2(x2) (Corollary 1). Counter-examples of distributions other than Gumbel Type A, for which these properties do not hold, are given. Some applications to the analysis of competing risks, using a family of Gompertz distributions, are discussed. 相似文献
993.
New integral and differential formulas for zonal polynomials are proved. As illustrations, zonal polynomials corresponding to partitions of two parts are computed. A method is presented, based on a certain partial differential operator, for expressing an orthogonally invariant polynomial as a linear combination of zonals. Zonal polynomials are expressed as linear combinations of well-known symmetric polynomials. 相似文献
994.
M. Schechter 《Journal of Optimization Theory and Applications》1977,23(3):389-400
A symmetric duality theory for programming problems with homogeneous objective functions was published in 1961 by Eisenberg and has been used by a number of authors since in establishing duality theorems for specific problems. In this paper, we study a generalization of Eisenberg's problem from the viewpoint of Rockafellar's very general perturbation theory of duality. The extension of Eisenberg's sufficient conditions appears as a special case of a much more general criterion for the existence of optimal vectors and lack of a duality gap. We give examples where Eisenberg's sufficient condition is not satisfied, yet optimal vectors exist, and primal and dual problems have the same value. 相似文献
995.
D. P. Bertsekas 《Journal of Optimization Theory and Applications》1982,36(2):221-252
In this paper, we consider Newton's method for solving the system of necessary optimality conditions of optimization problems with equality and inequality constraints. The principal drawbacks of the method are the need for a good starting point, the inability to distinguish between local maxima and local minima, and, when inequality constraints are present, the necessity to solve a quadratic programming problem at each iteration. We show that all these drawbacks can be overcome to a great extent without sacrificing the superlinear convergence rate by making use of exact differentiable penalty functions introduced by Di Pillo and Grippo (Ref. 1). We also show that there is a close relationship between the class of penalty functions of Di Pillo and Grippo and the class of Fletcher (Ref. 2), and that the region of convergence of a variation of Newton's method can be enlarged by making use of one of Fletcher's penalty functions.This work was supported by the National Science Foundation, Grant No. ENG-79-06332. 相似文献
996.
New results on a class of exact augmented Lagrangians 总被引:3,自引:0,他引:3
S. Lucidi 《Journal of Optimization Theory and Applications》1988,58(2):259-282
In this paper, a new continuously differentiable exact augmented Lagrangian is introduced for the solution of nonlinear programming problems with compact feasible set. The distinguishing features of this augmented Lagrangian are that it is radially unbounded with respect to the multiplier and that it goes to infinity on the boundary of a compact set containing the feasible region. This allows one to establish a complete equivalence between the unconstrained minimization of the augmented Lagrangian on the product space of problem variables and multipliers and the solution of the constrained problem.The author wishes to thank Dr. L. Grippo for having suggested the topic of this paper and for helpful discussions. 相似文献
997.
998.
Some methods of making fuzzy decisions include a comparison of fuzzy sets on the same space. Methods have been published which suffer from lack of discrimination between alternatives and occasional conflict with intuitive choice. These methods are reviewed in this paper and then a new approach is described which overcomes their drawbacks. Methods of evaluating the parameter used in decision-making are given which can be varied to incorporate different utility functions. 相似文献
999.
In this paper the Parseval theorem for Laplace and Stieltjestransforms which was proved by Yurekli (1989, IMA J. Appl. Math.,42, 241249) for conventional functions is proved forgeneralized functions. The theorem yields some corollaries similarto the corollaries in Yurekli (1989). 相似文献
1000.
李玉成 《数学物理学报(A辑)》2003,23(5):520-525
该文研究复Clifford分析中的超单演函数,即方程z_n Df(z)+(n-1)Qf′=0的解. 记f(z)=Pf(z)+Qf(z)e_n,f(z)∈C^2(Ω),f(z): Ω → C^{n+1},Ω C^{n+1},得出超单演函数的几个性质. 相似文献