关于随机动力系统的Fatou－Julia猜测

设Ｆ＝｛ｆ１，…，ｆＭ｝是一个次数大于１的多项式集合。我们证明了在一定条件下Ｆａｔｏｕ集Ｆ（Ｆ）没有游荡区域。更确切地说，对于Ｆ（Ｆ）的每一个分支Ω，存在整数ｍ≥０，ｎ≥０，ｍ≠ｎ和λ∈∑Ｍ使得Ｗｍα（Ω）和Ｗｎα（Ω）落入Ｆ（Ｆ）的同一分支     

Maximally Nonlinear Functions and Bent Functions

We give a construction of bent functions in 2n variables, here n is odd, by using maximally nonlinear functions on GF(2 ⁿ ).     

An Isotonic Regression Problem for Infinite-Dimensional Parameters

We consider an infinite-dimensional isotonic regression problem which is an extension of the suitably revised classical isotonic regression problem. Given p-summable data, for p finite and at least one, there exists an optimal estimator to our problem. For p greater than one, this estimator is unique and is the limit in the p-norm of the sequence of unique estimators in canonical finite-dimensional truncations of our problem. However, for p equal to one, our problem, as well as the finite-dimensional truncations, admit multiple optimal estimators in general. In this case, the sequence of optimal estimator sets to the truncations converges to the optimal estimator set of the infinite problem in the sense of Kuratowski. Moreover, the selection of natural best optimal estimators to the truncations converges in the 1-norm to an optimal estimator of the infinite problem.     

Analytical Linear Inequality Systems and Optimization

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.     

Connectedness of efficient solution sets for set-valued maps in normed spaces

In vector optimization, the topological properties of the set of efficient solutions are of interest. Several authors have studied this topic for point-valued functions. In this paper, we study the connectedness of the efficient solution sets in convex vector optimization for set-valued maps in normed spaces.The author would like to thank Professor W. T. Fu for helpful discussions concerning Theorem 3.1 and other valuable comments. Moreover, the author is grateful to Professor H. P. Benson and three referees for valuable remarks and suggestions concerning a previous draft of this paper.     

Borel stay-in-a-set games

Consider an n-person stochastic game with Borel state space S, compact metric action sets A ₁,A ₂,,A _n , and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state x and continuously on the actions (a ₁,a ₂,,a _n ) of the players. If the payoff to each player i is 1 or 0 according to whether or not the stochastic process of states stays forever in a given Borel set G _i , then there is an -equilibrium for every >0. AMS (1991) subject classification: 60G40, 91A60, 60E15, 46A55.     

Evolutionary insights on the willingness to communicate

While in previous models of pre-play communication players are forced to communicate, we investigate what happens if players can choose not to participate in this cheap talk. Outcomes are predicted by analyzing evolutionary stability in a population of a priori identical players. If the game following the communication rewards players who choose the same action then an efficient outcome is only guaranteed when participation in the pre-play communication is voluntary. If however players aim to coordinate on choosing different actions in the underlying game and there are sufficiently many messages then the highest payoff is selected when players are forced to talk to each other before playing the game. Received: September 2000/Revised: March 2003