Souslin树在特殊的力迫扩张中是保持的

如果M是ZFC的一个模型,在M中T是一个Souslin树,而P是一个满足Knaster条件的偏序,那么在P的力迫扩张M|G|中T仍是一个Souslin树.因此在random扩张中一个Souslin树保持不变.我们还讨论一些相关问题.     

关于紧序数空间可数次箱积的仿紧性

本文证明了如果对每个可数序数α,紧序数α+1的可数次箱积的商空间▽~ω(α+1)是特殊仿紧的,则对任意一个序数λ,▽~ω(λ+1)也是特殊仿紧的.     

不动点集为αP(2r+1)■的对合的流形

设r≥0为整数。当α表示R、C、H时,αP(2r+1)分别表示实数、复数、四元数射影2r+1空间。本文确定了不动点集为一个射影2r+1空间与若干球面不交并的闭流形M上所有对合(M,T)的流形。     

冯·诺依曼代数交叉积的一点注记

设α是可数离散群G和H的半直积G■_σH在冯·诺依曼代数M上的作用,则β_h=α_((e,h))AdU_h定义了群H在冯·诺依曼代数交叉积M■_αG上的作用β.本文证明了交叉积冯·诺依曼代数M■_α(G■_σH)与(M■_αG)■_βH是*-同构的,因此在一定条件下,冯·诺依曼代数的交叉积满足结合律.     

关于结合环类的下根构造在有限步终止的问题

1966年,Sulinski Anderson和Divineki在[1]中讨论了结合环类和交错环类的下根构造问题,并留下了有趣的问题:对每一个n=4,5,…,找一个环类(?),使n为使的最小整数,该问题作为第十一个公开问题出现在Szasz《Radicals of Rings》一书中。 本文解决了这一问题,并举例说明对每一个序数α,1<α≤w_o,w_o,w_o是第一个无穷序数,存在环类,使α为使的最小序数,文中还给出了的一些充分条件。     

3×3上三角算子矩阵的Weyl型定理

设A∈B(H1),B∈B(H2),C∈B(H3)为给定的三个算子,用M(D,E,F)= 表示一个作用在H1(?)H2(?)H3上的3×3算子矩阵．本文首先给出存在算子D∈B(H2,H1),E∈B(H3,H1),F∈B(H3,H2),使得M(D,E,F)为上半Fredholm算子(下半Fredholm算子)的充要条件．同时研究了3×3算子矩阵 M(D,E,F)的Weyl定理,α-Weyl定理,Browder定理和α-Browder定理．     

黎曼流形上混合边值问题的第一特征值估计

设M为一带边界M的紧致Riemann流形,本文考虑M上的下述混合边值条件的特征值问题 (△u+v_1u=0, u/n+αu|M=0,)其中n为M的外法向单位向量,α为一正常数。     

关于序数方程

§1.根据序数正常表示的唯一性,M.Sierpiński证明了方程ξ~2=η~3+1没有超限的序数解.本文目的在于拓广这一结果,而从事更广一类序数方程求解问题的研究.     

带有指定平均曲率函数的S~(n 1)内嵌入超曲面

设ψ是S~(n 1)上北极到平面P~*:x~(n 2)=O的球极投影,给定C~(k,α)(P~*\{O})内函数H(Y),如果H(Y)满足下述条件:有两个常数r_1,r_2;r_2≥1≥r_1>0,当|Y|>r_2时,当O<|Y|相似文献   

新题征展(63)

A　题组新编1 .( 1 )动点 M( x,y)满足( x - sinα) 2 + ( y - cosα) 2 =| xsinα+ ycosα- 1 | ,判断动点 M的轨迹类型 ;( 2 )动点 M( x,y)满足( x - sinα) 2 + ( y - cosα) 2 =| xsinα+ ycosα- 2 | ,判断动点 M的轨迹类型 ;( 3)动点 M( x,y)满足( x - sinα) 2 + ( y - cosα) 2 =2 | xsinα+ ycosα- 2 | ,判断动点 M的轨迹类型 ;( 4 )动点 M( x,y)满足2 ( x - sinα) 2 + ( y - cosα) 2 =| xsinα+ ycosα- 2 | ,判断动点 M的轨迹类型 .2 .( 1 )过点 P( 1 ,2 )的直线与 x、y轴的正半轴分别交于点 A、B,试求 S△ AOB 的最小…     

On universal spaces and absorbing sets related to a transfinite extension of covering dimension

R. Pol has shown that for every countable ordinal number α there exists a universal space for separable metrizable spaces X with trindX?α. W. Olszewski has shown that for every countable limit ordinal number λ there is no universal space for separable metrizable space with trIndX?λ. T. Radul and M. Zarichnyi have proved that for every countable limit ordinal number there is no universal space for separable metrizable spaces with dimWX?α where dimW is a transfinite extension of covering dimension introduced by P. Borst. We prove the same result for another transfinite extension dimC of the covering dimension.As an application, we show that there is no absorbing sets (in the sense of Bestvina and Mogilski) for the classes of spaces X with dimCX?α belonging to some absolute Borel class.     

Orders of accumulation of entropy on manifolds

For a continuous self-map T of a compact metrizable space with finite topological entropy, the order of accumulation of entropy of T is a countable ordinal that arises in the theory of entropy structure and symbolic extensions. Given any compact manifold M and any countable ordinal α, we construct a continuous, surjective self-map ofM having order of accumulation of entropy α. If the dimension of M is at least 2, then the map can be chosen to be a homeomorphism.     

N-Person stochastic games with upper semi-continuous payoffs

Every n-person stochastic game with a countable state space, finite action sets for the players and bounded, upper semi-continuous payoffs has an ε-equilibrium for every ε>0.     

Shortest paths with ordinal weights

We investigate the single-source-single-destination “shortest” path problem in directed, acyclic graphs with ordinal weighted arc costs. We define the concepts of ordinal dominance and efficiency for paths and their associated ordinal levels, respectively. Further, we show that the number of ordinally non-dominated path vectors from the source node to every other node in the graph is polynomially bounded and we propose a polynomial time labeling algorithm for solving the problem of finding the set of ordinally non-dominated path vectors from source to sink.     

报酬函数及转移速率族均非一致有界的连续时间折扣马氏决策规划

本文首次在报酬函数及转移速率族均非一致有界的条件下，对可数状态空间，可地动集的连续时间折扣马氏决策规划进行研究，文中引入一类新的无界报酬函数，在一类新的马氏策略中，讨论了最优策略的存在性及春结构，除证明了在有界报酬和一致有界转移速率族下成立的主要结果外，本文还得到一些重要结论。     

Limiting distributions of the number of pure strategy Nash equilibria in n-person games

We study the number of pure strategy Nash equilibria in a “random” n-person non-cooperative game in which all players have a countable number of strategies. We consider both the cases where all players have strictly and weakly ordinal preferences over their outcomes. For both cases, we show that the distribution of the number of pure strategy Nash equilibria approaches the Poisson distribution with mean 1 as the numbers of strategies of two or more players go to infinity. We also find, for each case, the distribution of the number of pure strategy Nash equilibria when the number of strategies of one player goes to infinity, while those of the other players remain finite.     

On the spectrum of Euler–Lagrange operator in the stability analysis of Bénard problem

In studying the stability of Bénard problem, we usually have to solve a variational problem to determine the critical Rayleigh number for linear or nonlinear stability. To solve the variational problem, one usually transforms it to an eigenvalue problem which is called Euler–Lagrange equations. An operator related to the Euler–Lagrange equations is usually referred to as Euler–Lagrange operator whose spectrum is investigated in this paper. We have shown that the operator possesses only the point spectrum consisting of real number, which forms a countable set. Moreover, it is found that the spectrum of the Euler–Lagrange operator depends on the thickness of the fluid layer.     

A periodic flow with infinite Epstein hierarchy

In 1975 D. Sullivan gave an example of a periodic flow on a compact 5-manifold with Epstein hierarchy of length one, and he asked whether the Epstein hierarchy of a compact foliation could have infinite length. We show that the answer is yes by constructing a periodic flow with this property on a compact 8-manifold. By modifying the example one can see that any countable ordinal can occur as the length of the Epstein hierarchy. It is known that only countable ordinals can occur [1].     

A note on termination of the Baer construction of the prime radical

The well known Baer construction of the prime radical shows that the prime radical of an arbitrary ring is the union of the chain of ideals of the ring, constructed by transfinite induction, which starts with 0 and repeats the procedure of taking the sum of ideals that are nilpotent modulo ideals in the chain already constructed. Amitsur showed that for every ordinal number α there is a ring for which the construction stops precisely at α. In this paper we construct such examples with some extra properties. This allows us to construct, for every countable non-limit ordinal number α, an affine algebra for which the construction terminates precisely at α. Such an example was known due to Bergman for α = 2.     

On the erugin and floquet-lyapunov theorems for countable systems of difference equations

For linear difference equations in the space of bounded number sequences, we prove an analog of the Erugin theorem on reducibility and present sufficient conditions for the reducibility of countable linear systems of difference equations with periodic coefficients.