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1.
According to the Charzynski-Tammi conjecture, the symmetrized Pick function is extremal in the problem on the estimate for the nth Taylor coefficient in the class of holomorphic univalent functions close to the identical one. In this paper we find the exact value of M 4 such that the symmetrized Pick function is locally extremal in the problem on the estimate for the 4th Taylor coefficient in the class of holomorphic normalized univalent functions, whose module is bounded byM 4. 相似文献
2.
Yong Chan Kim 《Journal of Mathematical Analysis and Applications》2007,325(1):608-611
We show that the Alexander transform of a β-spirallike function is univalent when cosβ?1/2, which settles the problem posed by Robertson. We also solved a problem considered by Y.J. Kim and Merkes. 相似文献
3.
A Dirichlet problem for polyharmonic functions 总被引:1,自引:0,他引:1
In this article, the Dirichlet problem of polyharmonic functions is considered. As well the explicit expression of the unique
solution to the simple Dirichlet problem for polyharmonic functions is obtained by using the decomposition of polyharmonic
functions and turning the problem into an equivalent Riemann boundary value problem for polyanalytic functions, as the approach
to find the kernel functions of the solution for the general Dirichlet problem is given.
Project supported by NNSF of China. 相似文献
4.
The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained. 相似文献
5.
K. Schiefermayr 《Integral Transforms and Special Functions》2015,26(2):118-133
Consider the Chebotarev problem of finding a continuum S in the complex plane including some given points such that the logarithmic capacity of S is minimal. In this paper, we give a complete solution of this problem for the case of three given points with the help of Zolotarev's conformal mapping using Jacobian elliptic and theta functions. Moreover, for four given points, some special cases can be treated. 相似文献
6.
We discuss the global shape of a Hele–Shaw flow which is produced by the injection of fluid into the narrow gap between two parallel planes. We translate the problem into a problem concerning the shape of a quadrature domain of a finite positive measure for subharmonic functions and give sharp estimates of the distance from a fixed point to the frontier of the flow. 相似文献
7.
Nonlinear programming using minimax techniques 总被引:3,自引:0,他引:3
A minimax approach to nonlinear programming is presented. The original nonlinear programming problem is formulated as an unconstrained minimax problem. Under reasonable restrictions, it is shown that a point satisfying the necessary conditions for a minimax optimum also satisfies the Kuhn-Tucker necessary conditions for the original problem. A leastpth type of objective function for minimization with extremely large values ofp is proposed to solve the problem. Several numerical examples compare the present approach with the well-known SUMT method of Fiacco and McCormick. In both cases, a recent minimization algorithm by Fletcher is used.This paper is based on work presented at the 5th Hawaii International Conference on System Sciences, Honolulu, Hawaii, 1972. The authors are greatly indebted to V. K. Jha for his programming assistance and J. H. K. Chen who obtained some of the numerical results. This work was supported in part by the National Research Council of Canada under Grant No. A7239, by a Frederick Gardner Cottrell Grant from the Research Corporation, and through facilities and support from the Communications Research Laboratory of McMaster University. 相似文献
8.
This paper aims to establish duality and exact penalization results for the primal problem of minimizing an extended real-valued
function in a reflexive Banach space in terms of a valley-at-0 augmented Lagrangian function. It is shown that every weak
limit point of a sequence of optimal solutions generated by the valley-at-0 augmented Lagrangian problems is a solution of
the original problem. A zero duality gap property and an exact penalization representation between the primal problem and
the valley-at-0 augmented Lagrangian dual problem are obtained. These results are then applied to an inequality and equality
constrained optimization problem in infinite-dimensional spaces and variational problems in Sobolev spaces, respectively.
The first author was supported by the Research Committee of Hong Kong Polytechnic University, by Grant 10571174 from the National
Natural Science Foundation of China and Grant 08KJB11009 from the Jiangsu Education Committee of China.
The second author was supported by Grant BQ771 from the Research Grants Council of Hong Kong.
We are grateful to the referees for useful suggestions which have contributed to the final presentation of the paper. 相似文献
9.
Shun-Chin Ho 《Numerical Functional Analysis & Optimization》2013,34(12):1560-1578
Considering a nonsmooth minimax fractional programming problem involving exponential (p, r)-invexity, we construct a mixed-type dual problem, which is performed by an incomplete Lagrangian dual model. This mixed-type dual model involves the Wolfe type dual and Mond-Weir type dual as the special cases under exponential (p, r)-invexity. We establish the mixed-type duality problem with conditions for exponential (p, r)-invexity and prove that the optimal values of the primary problem and the mixed-type duality problem have no duality gap under the framwork of exponential (p, r)-invexity. 相似文献
10.
传统的求解0-1规划问题方法大多属于直接离散的解法.现提出一个包含严格转换和近似逼近三个步骤的连续化解法:(1)借助阶跃函数把0-1离散变量转化为[0,1]区间上的连续变量;(2)对目标函数采用逼近折中阶跃函数近光滑打磨函数,约束条件采用线性打磨函数逼近折中阶跃函数,把0-1规划问题由离散问题转化为连续优化模型;(3)利用高阶光滑的解法求解优化模型.该方法打破了特定求解方法仅适用于特定类型0-1规划问题惯例,使求解0-1规划问题的方法更加一般化.在具体求解时,采用正弦型光滑打磨函数来逼近折中阶跃函数,计算效果很好. 相似文献
11.
We consider an extremal problem for even positive definite entire functions of exponential type with zero mean with power weight on the semiaxis. This problem is related to the multidimensional Jackson-Stechkin theorem in the space L 2(?n). 相似文献
12.
We reduce the problem of the zeros of an entire function related to the Painlevé I equation to the eigenvalue problem for
the Dirichlet problem for a fourth-order bilinear equation. In a simplified case, this problem reduces to the problem of the
position of the zeros of theta functions. We then apply the developed general method to the inverse scattering problem.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 175–187, November, 2008. 相似文献
13.
A Global Optimization Method for Solving Convex Quadratic Bilevel Programming Problems 总被引:4,自引:0,他引:4
We use the merit function technique to formulate a linearly constrained bilevel convex quadratic problem as a convex program with an additional convex-d.c. constraint. To solve the latter problem we approximate it by convex programs with an additional convex-concave constraint using an adaptive simplicial subdivision. This approximation leads to a branch-and-bound algorithm for finding a global optimal solution to the bilevel convex quadratic problem. We illustrate our approach with an optimization problem over the equilibrium points of an n-person parametric noncooperative game. 相似文献
14.
YuLiang Shen 《中国科学 数学(英文版)》2012,55(3):607-624
An open problem is to characterize the Fourier coefficients of Zygmund functions.This problem was also explicitly suggested by Nag and later by Teo and Takhtajan-Teo in the course of study of the universal Teichmu¨ller space.By a complex analysis approach,we give a characterization for the Fourier coefficients of a Zygmund function by a quadratic form.Some related topics are also discussed,including those analytic functions with quasiconformal deformation extensions. 相似文献
15.
Peter Somora 《Mathematica Slovaca》2008,58(4):439-454
A second order nonlinear differential equation with homogeneous Dirichlet boundary conditions is considered. An explicit expression
for the root functions for an autonomous nonlinear boundary value problem is obtained using the results of the paper [SOMORA,
P.: The lower bound of the number of solutions for the second order nonlinear boundary value problem via the root functions method, Math. Slovaca 57 (2007), 141–156]. Other assumptions are supposed to prove the monotonicity of root functions and to get the exact number
of solutions. The existence of infinitely many solutions of the boundary value problem with strong nonlinearity is obtained
by the root function method as well.
The paper was supported by the Grant VEGA No. 2/7140/27, Bratislava. 相似文献
16.
In this article, a new canonical function has been established to deal with Riemann boundary‐value problem of periodic analytic functions discussed in 16 . In comparison with the corresponding result in 16 , the expression of solution obtained here is much simpler. Then, we demonstrate the equivalence of solutions for the homogeneous Riemann problem. What's more, we obtain the precise rank of matrix of coefficients for the system of linear algebraic equations (4.35) in 16 . Those results can simplify the discussion of Riemann problem of single‐periodic polyanalytic functions in 16 . 相似文献
17.
We consider the problem of the time-dependent degenerate parametric amplifier. We obtain the quadratic invariant and use it to derive the wave function via its su(1, 1) algebraic basis and a unitary transformation to the time-dependent Schrödinger equation for the parametric amplifier. We obtain the real and the complex invariants, which we use to solve the time-dependent Cauchy problem. Using different integrability conditions, we find the most general solution, which we analyze extensively, providing details of the calculations. 相似文献
18.
S. S. Marchenkov 《Mathematical Notes》1999,66(5):577-584
For continuous functions specified on the Baire space, conditions for the representability of a function of several variables
as a superposition of functions of a smaller number of variables are considered. With the use of linear functions of the form
(1+α)t, a boundary value of the modulus of continuity separating the positive from the negative solution of the problem is found.
For the case in which the problem has a negative solution, a constructive method for obtaining (n+1)-variable continuous functions with modulus of continuity ϕ(t) that are not representable as superposition ofn-variable continuous functions with the same modulus of continuity ϕ(t) is suggested.
Translated fromMatermaticheskie Zametki, Vol. 66, No. 5, pp. 696–705, November, 1999. 相似文献
19.
Ronald K. Perline 《Numerical Functional Analysis & Optimization》2013,34(11-12):1139-1175
The continuity and differentiability for integral operator in Banach spaces are proved with respect to Lp–topology. The weak normal integrand is defined, so that a generalized measurable selection theorem is derived, and the conjugate functional for integral functional is formulated. The duality theorem of optimization problem for integral functional is established by using the conjugate functional. 相似文献
20.
Z. Wang 《BIT Numerical Mathematics》2008,48(4):799-819
We present a method for solving a class of box constrained variational inequality problems. The method makes use of a procedure
for identifying some components of the solution by bounding it with an interval vector. It is shown that the method computes
an approximate solution of the variational inequality problem by solving at most n reduced systems of equations, where n is the dimension of the problem. Among those systems, only the one of the smallest dimension has to be solved with high accuracy.
The others are solved merely to identify some components of the solution, and so the computation can be done under a very
mild requirement of accuracy. Numerical results are presented for the obstacle problem, to illustrate the efficiency of the
method.
AMS subject classification (2000) 90C33, 65G30, 65K10 相似文献