SINGULAR BOUNDARY PROPERTIES OF HARMONIC FUNCTIONS AND FRACTAL ANALYSIS

ＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＰＲＯＰＥＲＴＩＥＳＯＦＨＡＲＭＯＮＩＣＦＵＮＣＴＩＯＮＳＡＮＤＦＲＡＣＴＡＬＡＮＡＬＹＳＩＳＷＥＮＺＨＩＹＩＮＧＺＨＡＮＧＹＩＰＩＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪａｎｕａｒｙ１１，１９９５．Ｒｅｖｉ...     

HOMOMORPHISMS BETWEEN CHEVALLEY GROUPS OF TYPES C_nAND G_2 OVER FINITE FIELDS

ＨＯＭＯＭＯＲＰＨＩＳＭＳＢＥＴＷＥＥＮＣＨＥＶＡＬＬＥＹＧＲＯＵＰＳＯＦＴＹＰＥＳＣｎＡＮＤＧ２ＯＶＥＲＦＩＮＩＴＥＦＩＥＬＤＳＺＨＡＪＩＡＮＧＵＯＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＮｏｖｅｍｂｅｒ２，１９９４．ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐ...     

ON A PROBLEM OF SUMS OF MIXED POWERS （II）

ＯＮＡＰＲＯＢＬＥＭＯＦＳＵＭＳＯＦＭＩＸＥＤＰＯＷＥＲＳ（Ｉ）ＬＵＭＩＮＧＧＡＯＹＵＧＡＮＧＡｂｓｔｒａｃｔＬｅｔＲｂ，ｃ（ｎ）ｄｅｎｏｔｅｔｈｅｎｕｍｂｅｒｏｆｒｅｐｒｅｓｅｎｔａｔｉｏｎｓｏｆｎａｓｔｈｅｓｕｍｏｆｏｎｅｓｑｕａｒｅ，ｆｏ...     

SPECTRAL SEQUENCES OF COHOMOLOGIES OF SINGULARITIES OF C∞ MAPPINGS

ＳＰＥＣＴＲＡＬＳＥＱＵＥＮＣＥＳＯＦＣＯＨＯＭＯＬＯＧＩＥＳＯＦＳＩＮＧＵＬＡＲＩＴＩＥＳＯＦＣ∞ＭＡＰＰＩＮＧＳＸＩＡＯＥＲＪＩＡＮＡｂｓｔｒａｃｔＴｗｏｓｐｅｃｔｒａｌｓｅｑｕｅｎｃｅｓａｒｅｄｅｆｉｎｅｄｒｅｓｐｅｃｔｉｖｅｌｙｆｏｒｃｏｈ...     

DUAL ASPECTS OF THE QUASITRIANGULAR BIALGEBRAS AND THE BRAIDED BIALGEBRAS

ＤＵＡＬＡＳＰＥＣＴＳＯＦＴＨＥＱＵＡＳＩＴＲＩＡＮＧＵＬＡＲＢＩＡＬＧＥＢＲＡＳＡＮＤＴＨＥＢＲＡＩＤＥＤＢＩＡＬＧＥＢＲＡＳＬＵＤＩＭＩＮＧＡｂｓｔｒａｃｔＩｔｉｓｓｈｏｗｎｔｈａｔｔｈｅｄｕａｌｂｉａｌｇｅｂｒａｏｆａｎｙｑｕａｓｉｔｒｉ...     

INITIAL VALUE PROBLEMS FOR SECOND ORDER IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

ＩＮＩＴＩＡＬＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＩＭＰＵＬＳＩＶＥＩＮＴＥＧＲＯ┐ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳ＊＊ＧＵＯＤＡＪＵＮ＊ＡｂｓｔｒａｃｔＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕ...     

A GLOBAL ALGORITHM IN THE NUMERICAL RESOLUTION OF THEVISCOUS／INVISCID COUPLED PROBLEM

ＡＧＬＯＢＡＬＡＬＧＯＲＩＴＨＭＩＮＴＨＥＮＵＭＥＲＩＣＡＬＲＥＳＯＬＵＴＩＯＮＯＦＴＨＥＶＩＳＣＯＵＳ／ＩＮＶＩＳＣＩＤＣＯＵＰＬＥＤＰＲＯＢＬＥＭＸＵＣＨＵＡＮＪＵＭＡＤＡＹ，Ｙ．ＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＯｃｔｏｂｅｒ１７，１９...     

EMBEDDING FLOWS AND SMOOTH CONJUGACY

ＥＭＢＥＤＤＩＮＧＦＬＯＷＳＡＮＤＳＭＯＯＴＨＣＯＮＪＵＧＡＣＹＺＨＡＮＧＭＥＩＲＯＮＧＬＩＷＥＩＧＵＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＭａｒｃｈ２３，１９９４．ＲｅｖｉｓｅｄＮｏｖｅｍｂｅｒ１，１９９５．ＤｅｐａｒｔｍｅｎｔｏｆＡｐ...     

ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE

ＯＮＡＰＡＩＲＯＦＮＯＮＩＳＯＭＥＴＲＩＣＩＳＯＳＰＥＣＴＲＡＬＤＯＭＡＩＮＳＷＩＴＨＦＲＡＣＴＡＬＢＯＵＮＤＡＲＩＥＳＡＮＤＴＨＥＷＥＹＬＢＥＲＲＹＣＯＮＪＥＣＴＵＲＥＳＬＥＥＭＡＮ，Ｂ．Ｄ．ＣＨＥＮＨＵＡＭａｎｕｓｃｒｉｐｔｒｅｃ...     

ON A MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATOR （I）

ＯＮＡＭＵＬＴＩＬＩＮＥＡＲＯＳＣＩＬＬＡＴＯＲＹＳＩＮＧＵＬＡＲＩＮＴＥＧＲＡＬＯＰＥＲＡＴＯＲ（Ｉ）ＣＨＥＮＷＥＮＧＵＨＵＧＵＯＥＮＬＵＳＨＡＮＺＨＥＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＯｃｔｏｂｅｒ１８，１９９４．ＲｅｖｉｓｅｄＤｅｃｅ...     

Asymptotically optimal idling in the GI/GI/N+GI queue

We formulate a control problem for a GI/GI/N+GI queue, whose objective is to trade off the long-run average operational costs with server utilization costs. To solve the control problem, we consider an asymptotic regime in which the arrival rate and the number of servers grow large. The solution to an associated fluid control problem motivates that non-idling service disciplines are not in general optimal, unless some arrivals are turned away. We propose an admission control policy designed to ensure that servers have sufficient idle time, which we show is asymptotically optimal.     

拟线性椭圆变分不等式的障碍最优控制问题

对拟线性椭圆变分不等式的障碍最优控制问题(即以障碍为控制变量)进行了研究．指标泛函为Lagrange型,其中含有控制变量二阶导数的p次幂,这使得最优性条件的推导颇为不易．对所考虑的问题给出了最优控制的存在性定理以及必要条件．     

The existence results for optimal control problems governed by a variational inequality

In this paper, we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings. Moreover, as an application, we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle.     

Necessary extremum conditions in the optimal control problem with state constraints

The optimal control problem with state constraints is examined. An alternative to the available approaches to the study of this problem is proposed. The maximum principle and second-order necessary conditions are proved.     

Optimal control of a signorini contact problem

We are interested in finding the coefficient of friction which leads us to a given displacement on the contact surface between an elastic solid body and a rigid foundation. The mathematical formulation of the problem is an optimal control problem governed by a quasivariational inequality. We obtain an approximative caracterization, by using two families of penalized and regularized problems, for a given optimal control.     

The Solution of a Free Boundary Problem Related to Environmental Management Systems

Abstract

Explicit solutions of free boundary problems are notoriously difficult to find. In this article, we consider two log-normal diffusions. One represents the level of pollution, or degradation, in some environmental area. The second models the social, political, or financial cost of the pollution. A single control parameter is considered that reduces the rate of pollution. The optimal time to implement the change in the parameter is found by explicitly solving a free boundary problem. The novelty is that the smooth pasting conditions, which are difficult to justify, are not used in the derivation.     

A variational method of optimal control problems for nonlinear Schrödinger equations

Calculating the control function that is in the coefficients of the nonlinear Schrodinger equation and minimizes the objective functional consisting of two integrals is main aim of this article. After proving the existence and uniqueness of the solution, we have constituted an algorithm using the method of gradient of projection. Results are tested on a quantum‐mechanical problem. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 82–89, 2004.     

Hilbert空间中具无界控制的无限时区线性二次最优控制问题

本文研究了Hilbert空间中一类由解析半群支配的具无界控制的无限时区线性二次最优控制问题,其中指标中的控制项加权算子要求强制而状态项加权算子可允许为不定号.在指数能稳条件下,证明了任意的最优控制及其最优轨线必定连续,建立了正实引理作为此问题唯一可解的充要条件,并用代数Riccati方程的解给出了最优控制的闭环综合。     

A perturbation method for optimizing matrix stability

We present the first practical perturbation method for optimizing matrix stability using spectral abscissa minimization. Using perturbation theory for a matrix with simple eigenvalues and coupling this with linear programming, we successively reduce the spectral abscissa of a matrix until it reaches a local minimum. Optimality conditions for a local minimizer of the spectral abscissa are provided and proved for both the affine matrix problem and the output feedback control problem. Experiments show that this novel perturbation method is efficient, especially for a matrix with the majority of whose eigenvalues are already located in the left half of the complex plane. Moreover, unlike most available methods, the method does not require the introduction of Lyapunov variables. The method is illustrated for a small size matrix from an affine matrix problem and is then applied to large matrices actually arising from more sophisticated control problems used in the design of the Boeing 767 jet and a nuclear powered turbo-generator.     

An inverse problem of identifying the diffusion coefficient in a coupled parabolic‐elliptic system

This work studies a nonlinear inverse problem of reconstructing the diffusion coefficient in a parabolic‐elliptic system using the final measurement data, which has important application in a large field of applied science. Being different from other works, which are governed by single partial differential equations, the underlying mathematical model in this paper is a coupled parabolic‐elliptic system, which makes theoretical analysis rather difficult. On the basis of the optimal control framework, the identification problem is transformed into an optimization problem. Then the existence of the minimizer is proved, and the necessary condition that must be satisfied by the minimizer is also given. Since the optimal control problem is nonconvex, one may not expect a unique solution universally. However, the local uniqueness and stability of the minimizer are deduced in this paper.