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??We study the linear quadratic optimal stochastic control problem which is jointly driven by Brownian motion and L\'{e}vy processes. We prove that the new affine stochastic differential adjoint equation exists an inverse process by applying the profound section theorem. Applying for the Bellman's principle of quasilinearization and a monotone iterative convergence method, we prove the existence and uniqueness of the solution of the backward Riccati differential equation. Finally, we prove that the optimal feedback control exists, and the value function is composed of the initial value of the solution of the related backward Riccati differential equation and the related adjoint equation.     

Invariant measures for equicontinuous semigroups of continuous transformations of a compact Hausdorff space

Equicontinuous semigroups of transformations of a compact Hausdorff space and their sets of all invariant (Borel, regular and probabilistic) measures are studied. Conditions equivalent to the existence of at least one invariant measure are given. The (algebraic and topological) structure of the set of invariant measures is researched.     

Group symmetry in tensor categories and duality for orbifolds

A duality for orbifolds is presented as an application of group extensions in tensor categories.     

瑞香狼毒防治仓储害虫活性物质的研究

瑞香狼毒 (ＳｔｅｌｌｅｒａｃｈａｍｅｊａｓｍｅＬ .)又名断肠草 ,为瑞香科狼毒属植物。瑞香狼毒在我国大部分地区均有分布 ,盛产于四川、河北、山西等地。其性苦、平、辛、有毒 ,有逐水、祛痰、破积、杀虫之功效。据文献报道 ,瑞香狼毒除了可作为中药外 ,还可以用来防治菜青虫、蚜虫、松毛虫 ,甚至可以用来杀蚊、驱蝇、灭蛆等。作者前期工作曾以瑞香狼毒根为材料 ,初步研究了根及根粉粗提物对米象、玉米象、谷蠹的防治效果。发现瑞香狼毒对米象、玉米象、谷蠹等仓储害虫均有较好的防治功效[1] 。本文以米象为试虫 ,以生物活性跟踪法对瑞…     

Noncommuting selfmaps and invariant approximations

Common fixed-point results are established for a new class of noncommuting selfmaps. We apply them to obtain several invariant approximation results which unify, extend, and complement well-known results.     

Asymptotic expansions in sequential estimation for the first-order random coefficient autoregressive model: Regenerative approach

Edgeworth expansions for the distribution of a sequential least squares estimator in the random coefficient autoregressive (RCA) model are derived. The regenerative approach to second-order asymptotic analysis of Markov-type statistical models is developed.     

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois.     

Properties of holomorphic Wiener functions —skeleton,contraction, and local Taylor expansion

Summary We show that each holomorphic Wiener function has a skeleton which is intrinsic from several viewpoints. In particular, we study the topological aspects of the skeletons by using the local Taylor expansion for holomorphic Wiener functions.Supported in part by the Grant-in-Aid for Science Research 03740120 Min. Education     

Finite-gap Solutions of the Fuchsian Equations

We find a new class of Fuchsian equations, with algebro-geometric solutions associated to a hyperelliptic curve. A method for calculating its arithmetic genus and branching points is suggested. Numerous examples are given.     

Polynomial decay rate for the dissipative wave equation

Using Fourier integral operators with special amplitude functions, we analyze the stabilization of the wave equation in a three-dimensional bounded domain on which exists a trapped ray bouncing up and down infinitely between two parallel parts of the boundary.