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     

Looking for Difference Sets in Groups with Dihedral Images

We prove four theorems about groups with a dihedral (or cyclic) image containing a difference set. For the first two, suppose G, a group of order 2p with p an odd prime, contains a nontrivial (v, k, ) difference set D with order n = k – prime to p and self-conjugate modulo p. If G has an image of order p, then 0 2a + 2 for a unique choice of = ±1, and for a = (k – )/2p. If G has an image of order 2p, then and ( – 1)/( – 1). There are further constraints on n, a and . We give examples in which these theorems imply no difference set can exist in a group of a specified order, including filling in some entries in Smith's extension to nonabelian groups of Lander's tables. A similar theorem covers the case when p|n. Finally, we show that if G contains a nontrivial (v, k, ) difference set D and has a dihedral image D _2m with either (n, m) = 1 or m = p ^t for p an odd prime dividing n, then one of the C ₂ intersection numbers of D is divisible by m. Again, this gives some non-existence results.     

About the Notion of Semiring of Sets

We introduce a generalized notion of semiring and prove that all known properties that semirings have according to the old definition are preserved.     

Fuzzy集的基数

关于Fuzzy集的基数，[1]中曾对有限支集的Fuzzy集以及极苛刻条件下的无限Fuzzy集给出过一种定义。但是，正如本文将要指出的那样，该定义是不合理的。本文将从研究Fuzzy映射入手，给出Fuzzy集基数的一般性定义。基于这一定义，不但得到有关基数的大部分结论，而且有其自身的特殊性。     

Connecting orbits among Denjoy minimal sets for monotone twist map

In a Birkhoff region of instability for an exact area-preserving twist map, we construct some orbits connecting distinct Denjoy minimal sets. These sets correspond to the local, instead of global minimum of the Lagrangian action. In the earlier work, Mather constructed connecting orbits among Aubry-Mather sets and the global minimizer of the Lagrangian action.     

Minimal rambling sets with codimension one dominated splittings

In this paper,we study the dynamics of minimal rambling sets with codimension one dominatedsplittings     

Invariant Mean—Value Property and M—Harmonicity in the Unit Ball of R^n

In 1993,Ahern,Flores and Rudin showed that,if f is integrable over the unit ball BC^n of C^n and satisfies∫BC^nfoφdv=f（φ（0)) for every φ∈Aut(BC^n),then f is M-harmonic if and only if n≤11.The present paper is about an analogous question in the context of the unit ball Bn of R^n as well as in the weighted setting.     

Small Transitive Families of Subspaces

A family of subspaces of a complex separable Hilbert space is transitive if every bounded operator which leaves each of its members invariant is scalar. This article surveys some results concerning transitive families of small cardinality, and adds some new ones. The minimum cardinality of a transitive family in finite dimensions (greater than 2) is 4. In infinite dimensions a transitive pair of linear manifolds exists but the minimum cardinality of a transitive family of dense operator ranges or norm-closed subspaces is not known. However, a transitive family of dense operator ranges with 5 elements can be found, and so can a transitive family of norm-closed subspaces with 4 elements. In finite dimensions (> 1) three nest algebras (corresponding to maximal nests) can intersect in the scalar operators, but two cannot. It is not known if this is the case in infinite dimensions for maximal nests of type ω + 1. Four such nest algebras can intersect in the scalar operators. Received June 15, 2002, Accepted November 27, 2002