On stationary equilibria of a single-controller stochastic game

We consider a two-person, general-sum, rational-data, undiscounted stochastic game in which one player (player II) controls the transition probabilities. We show that the set of stationary equilibrium points is the union of a finite number of sets such that, every element of each of these sets can be constructed from a finite number of extreme equilibrium strategies for player I and from a finite number of pseudo-extreme equilibrium strategies for player II. These extreme and pseudo-extreme strategies can themselves be constructed by finite (but inefficient) algorithms. Analogous results can also be established in the more straightforward case of discounted single-controller games.     

非自伴算子代数间的等距代数同构

设Ｇｉ是满足第二可数性公理的、Ｈａｕｓｄｏｒｆｆ的、顺从的、ｒ－离散的、主的局部紧群胚，并且有一个紧开Ｇ－集覆盖；设Ｐｉ是Ｇｉ中含Ｇ＿ｉ￣０的开闭集，且满足及相应的模是具有性质ＤＣ的Ｃ（Ｇｉ）的子代数（ｉ＝１，２）．本文证明从Ａ（Ｐ１）到Ａ（Ｐ２）上的每一个等距代数同构可以扩张成从Ｃ（Ｇ１）到Ｃ（Ｇ２）上的Ｃ－同构，进一步，可以对Ｃ（Ｇ２）重新坐标化，使得这个Ｃ－同构可由一个群胚同构生成．     

对-二甲氨基苯甲醛苯甲酰腙及其锌(Ⅱ)、镉(Ⅱ)配合物的合成与光学性质

合成了对-二甲氨基苯甲醛苯甲酰腙(配体)及其锌(Ⅱ)、镉(Ⅱ)配合物,通过元素分析、IR、MS对结构进行表征,研究了配体及锌(Ⅱ)、镉(Ⅱ)配合物的紫外光谱和荧光光谱。这些物质都有较强的荧光,适合掺入涂料中做成荧光涂料。     

Variations on Weyl's theorem

In this note we study the property (w), a variant of Weyl's theorem introduced by Rako?evi?, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T^*) coincide whenever T^* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w).     

Chemoinformatics: a new field with a long tradition

Chemoinformatics is the application of informatics methods to solve chemical problems. Although this term was introduced only a few years ago, this field has a long history with its roots going back more than 40 years. Work on chemical structure representation and searching, quantitative structure–activity relationships, chemometrics, molecular modeling as well as computer-assisted structure elucidation and synthesis design was initiated in the 1960s. These different origins have now merged into a discipline of its own that is in full bloom. All areas of chemistry from analytical chemistry to drug design can benefit from chemoinformatics methods. And there are still many challenging chemical problems waiting for solutions through the further development of chemoinformatics.     

The Domínguez–Lorenzo condition and multivalued nonexpansive mappings

Let E be a nonempty bounded closed convex separable subset of a reflexive Banach space X   which satisfies the Domínguez–Lorenzo condition, i.e., an inequality concerning the asymptotic radius of a sequence and the Chebyshev radius of its asymptotic center. We prove that a multivalued nonexpansive mapping T:E→2^X$T:E\to 2^X$ which is compact convex valued and such that T(E)$T(E)$ is bounded and satisfies an inwardness condition has a fixed point. As a consequence, we obtain a fixed-point theorem for multivalued nonexpansive mappings in uniformly nonsquare Banach spaces which satisfy the property WORTH, extending a known result for the case of nonexpansive single-valued mappings. We also prove a common fixed point theorem for two nonexpansive commuting mappings t:E→E$t:E\to E$ and T:E→KC(E)$T:E\to \mathit{KC}(E)$ (where KC(E)$\mathit{KC}(E)$ denotes the class of all compact convex subsets of E) when X is a uniformly convex Banach space.     

On Banach spaces with Kasparov and Yu's Property (H)

A new geometric property of Banach spaces recently introduced by G. Kasparov and G. Yu, called Property (H), has important applications to the strong Novikov conjecture and the coarse Novikov conjecture, yet is far from being well understood. In this paper, we investigate various uniformly continuous maps on unit spheres of Banach spaces and prove that all separable Banach lattices with nontrivial cotype have Property (H).     

A note about proving non-Γ under a finite non-microstates free Fisher information assumption

We prove that if X₁,…,Xn (n>1) are self-adjoints in a W^∗-probability space with finite non-microstates free Fisher information, then the von Neumann algebra W^∗(X₁,…,Xn) they generate doesn't have property Γ (especially is not amenable). This is an analog of a well-known result of Voiculescu for microstates free entropy. We also prove factoriality under finite non-microstates entropy.     

Rearrangement of conditionally convergent series on a small set

We consider ideals I of subsets of the set of natural numbers such that for every conditionally convergent series _∑n∈ωan and every there is a permutation such that _∑n∈ωaπr(n)=r and

     

Star-Configurations in ℙ2 Having Generic Hilbert Function and the Weak Lefschetz Property

We prove that a star-configuration 𝕏 in ?² is defined by general forms of degrees ≤2 if and only if 𝕏 has generic Hilbert function. We also show that if 𝕏 and 𝕐 are star-configurations in ?² defined by general forms of degrees ≤2 and σ(𝕏) ≠ σ(𝕐), then the ring R/(I _𝕏 + I _𝕐) has the Weak Lefschetz property. These two results generalize results of Ahn and Shin [3 Ahn , J. , Shin , Y. S. ( 2012 ). The minimal free resolution of a star-configuration in ? ⁿ and the weak lefschetz property . J. Korean Math. Soc. 49 ( 2 ): 405 – 417 . [Google Scholar]]. Furthermore, we find the Lefschetz element of the graded Artinian ring R/(I _𝕏 + I _?) precisely when 𝕏 and ? are two star-configurations in ?² defined by general forms F ₁,…, F _s , and G ₁,…, G _s , L, respectively, with deg F _i  = deg G _i  = 2 for every i ≥ 1, and deg L = 1 with s ≥ 3.