Topological Simplicity of a Certain LF-Algebra

We show that the LF-algebra considered by Akkar and Nacir in [1] is topologically simple.     

Xor on one‐defect systems

We present a network experiment that investigates the computational power of cellular automata on the simplest irregular lattice. One cellular automaton whose apparent complexity increased is Rule 60, the left neighbor Xor operator. It went from being nested to complex. That makes Xor a candidate for universal computational power. We present the evidence in terms of the size of cycle lengths, transients, and size of boolean expressions. © 2006 Wiley Periodicals, Inc. Complexity 12: 13–29, 2006     

Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.     

Ti对铸造镍基高温合金中碳化物和拓扑密排相影响

采用光学显微镜、扫描电子显微镜和透射电子显微镜等测试技术,研究了经过标准热处理和时效处理后的不同Ti含量合金的微观组织。 研究发现,标准热处理后不同Ti含量合金的相组成相同,主要由γ、γ′、MC和M23C6型碳化物组成;随着Ti含量增加,合金组织中的碳化物数量逐渐增加。 不含Ti的合金中的MC碳化物的组成主要是TaC,而含Ti合金中MC型碳化物组成为(Ta,Ti)C,并且随着Ti含量增加,MC碳化物中M组成元素Ta和Ti的比值（Ta/Ti）逐渐减小。 通过研究900 ℃不同时间时效处理后合金微观组织发现,随着Ti含量增加,合金中拓扑密排相(TCP)析出趋势逐渐增加。 含质量分数2.7%Ti的合金经900 ℃/500 h时效处理后,组织中析出了针状富含Cr、W和Mo的σ相。 这表明要保证合金具有良好的组织稳定性,需要控制合金中Ti的加入量。     

集对Fuzzy格及其在格表示论中的应用

用幂集格构造了集对 Ｆｕｚｚｙ 格（这与用整数对构造有理数集有相似之处）,并用它证明了完整的软代数表示定理,即定义了到自身的映射且有最大元和最小元的格为软代数的充要条件是它与某个集对 Ｆｕｚｚｙ 格的子格同构．这样,与分配格在幂集 Ｂｏｏｌｅ 格中表示相对应,软代数在集对 Ｆｕｚｚｙ 格中有表示,在理论上是很完美的     

Properties of Standard n-Ideals of a Lattice

An n-ideal of a lattice L is a convex sublattice containing a fixed element n L and it is called standard if it is a standard element of the lattice of n-ideals I_n(L). In this paper we have shown that, for a neutral element n of a lattice L, the principal n-ideal a_n of a lattice L is a standard n-ideal if and only if a n is standard and a n is dual standard. We have also shown that if n is a neutral element and (n] and [n) are relatively complemented, then every homomorphism n-kernels of L is a standard n-ideal and every standard n-ideal is the n-kernel of precisely one congruence relation. Finally, we have shown that, for a relatively complemented lattice L with 0 and 1, C(L) is a Boolean algebra if and only if every standard n-ideal of L is a principal n-ideal.AMS Subject Classification (2000) 06B10 06B99 06C15     

RRF rings which are not LRF

Define a ringA to be RRF (respectively LRF) if every right (respectively left)A-module is residually finite. We determine the necessary and sufficient conditions for a formal triangular matrix ring to be RRF (respectively LRF). Using this we give examples of RRF rings which are not LRF.     

Characterization of Linear Structures

We study the notionof linear structure of a function defined from F ^mto F ⁿ, and in particular of a Boolean function.We characterize the existence of linear structures by means ofthe Fourier transform of the function. For Boolean functions,this characterization can be stated in a simpler way. Finally,we give some constructions of resilient Boolean functions whichhave no linear structure.