超格

引入了超格、子超格等概念,并研究了超格的直积以及超格的同态和同构.     

关于超格

首先给出了超格的最小元、最大元及有界超格的定义,并举例说明了这种定义的合理性.其次,进一步研究了超格的理想.     

超格的商结构

通过引入超格的强闭集、上半补超格、数量上界单位元等概念,引出超格上的等价关系.构造数量上界单位集,在此基础上进一步研究超格的一些性质.商代数结构定理的建立对于完善超格的商结构具有实际意义.     

超格的模糊超理想

利用模糊化方法,引入了超格的模糊超理想,给出了它的等价刻画;其次,在超格同态意义下,讨论了模糊超理想和生成模糊超理想的像与原像;最后,引入了素模糊超理想,研究了它们的拓扑结构。     

关于序超半群的左超理想的研究

本文在序超半群中引入了极小左超理想和极大左超理想的概念, 并讨论了它们的一些相关性质. 进一步地, 引入了序超半群的弱素左超理想、拟素左超理想、拟半素左超理想及弱拟素左超理想的概念, 并讨论这四种素超理想之间的关系. 而且通过左超理想和弱~$m$-系刻画了序超半群的弱拟素左超理想. 同时, 借助于$m$-系对序超半群的拟素左超理想给出刻画. 尤其证明了序超半群$S$是强半单的当且仅当$S$的每个左超理想是$S$的包含它的所有拟素左超理想的交.     

关于序超半群的模糊拟超理想

首先将超半群上拟超理想的概念推广到序超半群理论中,即在序超半群中定义并讨论了拟超理想的性质。进一步地,定义并研究了序超半群的模糊拟超理想,尤其刻画了由一个模糊集所生成的模糊拟超理想的结构。     

幂超格的性质

对幂超格的性质进行了研究.给出了幂超格直积、分配幂超格的概念并讨论了他们的性质.     

关于序*-半超群的超理想（英）

本文在序*-半超群上引入了素超理想、弱素超理想、半素超理想、弱半素超理想和不可约超理想的概念,同时建立了这五类超理想之间的关系,最后利用这些超理想刻画了半单序*-半超群和内禀正则序*-半超群的结构.     

M-超格的模糊度

通过研究超格与模糊集之间的关系,定义了超格的模糊度,给出了小于等于4阶M-超格的模糊度,并且研究了它的相关性质。     

Quantale中的素理想及弱素理想

本文把Quantale中的序结构与代数运算＆结合在一起给出了Quantale中素理想和弱素理想的概念。讨论了它们之间的关系,得到了Quantale中理想是(弱)素理想的充要条件。证明了与序半群中的一些经典结论相一致的命题。     

有界超格上的微分

在有界超格上引入微分,研究了有界超格上微分的一些性质.定义并研究了微分超格的微分超理想和微分超同余,并证明了如果$(L,d)$是一个有界强单微分超格并且$R$是$(L,d)$的一个强微分同余,则$(L/R,g)$仍是一个强单微分超格,其中$g$是由$d$诱导的商超格上的单强微分.     

Lattices Derived from Hyperlattices

In this article, by considering the notion of a hyperlattice and a superlattice, we give some examples of them, and we study their structures and their quotient structure with a regular relation. We introduce the relation ν on a hyperlattice L, and we let ν* be the transitive closure of ν. We show that ν* is a fundamental relation on a hyperlattice. The quotient L/ν* is called the fundamental lattice. Notice that the most important relations in hyperstructure theory are the fundamental ones. Finally, we give some interesting results about the fundamental lattices.     

Construction and Spectral Topology on Hyperlattices

In this paper by considering the notion of hyperlattice, we introduce good and s-good hyperlattices, homomorphism of hyperlattices and s-reflexives. We give some examples of them and we study their structures. We show that there exists a hyperlattice L such that ${x \vee x = \{x\}}In this paper by considering the notion of hyperlattice, we introduce good and s-good hyperlattices, homomorphism of hyperlattices and s-reflexives. We give some examples of them and we study their structures. We show that there exists a hyperlattice L such that x úx = {x}{x \vee x = \{x\}} for all x ? L{x \in L} and there exist x, y ? L{x, y \in L} which card(x úy) 1 1{card(x \vee y) \ne 1}. Also, we define a topology on the set of prime ideals of a distributive hyperlattice L and we will call it S(L){{{\mathcal S}(L)}}, then we show that S(L){{{\mathcal S}(L)}} is a T ₀-space. At the end, we obtain that each complemented distributive hyperlattice is a T ₁-space.     

The coherent potential method in the diffusion problem on a random substitution lattice

Based on the balance equation, we consider the diffusion problem on a hyperlattice with randomly distributed inaccessible sites. Using diagram methods, we find a self-consistent expression for the configurationally averaged Green’s function in the coherent potential approximation. We show that this approach is applicable in a broad range of concentrations of accessible sites. Using this approximation, we find the exact asymptotic form of the static diffusion coefficient for a low concentration of blocked sites. This allows making good estimates of the percolation threshold in the random-site diffusion problem on an arbitrary hyperlattice. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 2, pp. 252–261, November, 2006.     

On the hyperinvariant subspace problem III

In two recent papers (Foias and Pearcy, J. Funct. Anal., in press, Hamid et al., Indiana Univ. Math. J., to appear), the authors reduced the hyperinvariant subspace problem for operators on Hilbert space to the question whether every C₀₀-(BCP)-operator that is quasidiagonal and has spectrum the unit disc has a nontrivial hyperinvariant subspace (n.h.s.). In this note, we continue this study by showing, with the help of a new equivalence relation, that every operator whose spectrum is uncountable, as well as every nonalgebraic operator with finite spectrum, has a hyperlattice (i.e., lattice of hyperinvariant subspaces) that is isomorphic to the hyperlattice of a C₀₀, quasidiagonal, (BCP)-operator whose spectrum is the closed unit disc.     

Some Results Related to a Question of Hinkkanen

In this paper, we prove several results concerning meromorphic functions f and g of hyperorder less than one such that f^（j） and g^（j） have the same zeros and poles for j=0, 1, 2. We provide some examples to show that our results are sharp.     

幂格的理想与素理想

研究了幂格的理想和素理想,建立了格的理想与格上幂格的理想的一种联系,获得了格的理想(素理想)与它的商格的理想(素理想)之间的关系。