FR^A模的Fuzzy同态的几个重要结果

证明了ＦＲ＾Ａ模的第一同构定理、第二同构定理、同构扩展定理以及其他一些重要性质。     

HX环的存在性

自李洪兴１９９１年提出了ＨＸ环这一问题以来,一直有这么一个问题没有解决,即是否存在非平凡的ＨＸ环的例子？但至今既没有找到非平凡的ＨＸ环,也没有证明任一环Ｒ上仅存在平凡的ＨＸ环,钟育彬１９９５年证明了一类环上仅存在平凡的ＨＸ环,那么,是否所有环仅存在平凡的ＨＸ环呢？针对这一点,本文作进上步研究,构造了一个非平凡的ＨＸ环,并建立了ＨＸ环上的同态与同构定理,为进上步研究ＨＸ环奠定了基础。     

L∞(A,μ)到L∞(B,ν)的最小内同构

证明如果T是L∞(Ω1,A,μ)到L∞(Ω2,B,ν)内的同构且满足‖T‖·‖T-1‖≤1+ε,ε∈(0,1-5)则在一定条件下(T-‖T‖)接近于一个等距,其误差小于6ε.     

关于Quotient Context of Morita Context的讨论

本文讨论了ＱｕｏｔｉｅｎｔＣｏｎｔｅｘｔｏｆ Ｍｏｒｉｔａ Ｃｏｎｔｅｘｔ的一些性质,并在此基础上证明：如果ＤＲ是一个完备Ｇａｂｒｉｅｌ拓扑,则一个（Ｐ,Ｑ）的商（Ｐ,Ｑ）作为Ｒ与Ｓ之间ＭＣ,它的商同构于（Ｐ,Ｑ）的一个商。     

效应代数的不分明化滤子

在连续格值逻辑的语义框架下,以Lukasiewicz蕴涵算子为工具定义了连续格值逻辑上的效应代数之不分明化滤子的概念,将用G.Cantor集合理论所刻画的效应代数的滤子概念在连续格值谓词演算下给予重新刻画,给出了不分明滤子的几个等价描述和性质.在两个经典效应代数的效应态射与效应同构意义下,讨论了这种不分明滤子的像和前像问题.     

套代数上Jordan同构的刻画

设AlgN和AlgM为复可分Hilbert空间H上的两个非平凡套代数,φ:AlgN→AlgM是一个保单位线性双射.本文证明了若对任意A,B∈AlgN且AB=0,有φ(AοB)=φ(A)οφ(B)成立,则φ是同构或反同构.     

Mutation on knots and Whitney’s 2-isomorphism theorem

Whitney’s 2-switching theorem states that any two embeddings of a 2-connected planar graph in S ² can be connected via a sequence of simple operations, named 2-switching. In this paper, we obtain two operations on planar graphs from the view point of knot theory, which we will term “twisting” and “2-switching” respectively. With the twisting operation, we give a pure geometrical proof of Whitney’s 2-switching theorem. As an application, we obtain some relationships between two knots which correspond to the same signed planar graph. Besides, we also give a necessary and sufficient condition to test whether a pair of reduced alternating diagrams are mutants of each other by their signed planar graphs.     

直觉模糊变换半群

首先定义了直觉模糊变换半群的概念,给出了一种特殊的直觉模糊变换半群.其次,引入了直觉模糊变换半群上的直觉容许关系,讨论了两个直觉模糊变换半群间的关系,为直觉模糊有限自动机进一步的理论研究提供了代数方法.     

Commutative rings whose zero-divisor graph is a proper refinement of a star graph

A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G _c ^* be the subgraph of G induced on the vertex set V (G)\ {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G = Γ(R), which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G _c ^* has at least two connected components. We prove that the diameter of the induced graph G _c ^* is two if Z(R)² ≠ {0}, Z(R)³ = {0} and G _c ^* is connected. We determine the structure of R which has two distinct nonadjacent vertices α, β ∈ Z(R)* \ {c} such that the ideal [N(α) ∩ N(β)]∪ {0} is generated by only one element of Z(R)*\{c}. We also completely determine the correspondence between commutative rings and finite complete graphs K _n with some end vertices adjacent to a single vertex of K _n .     

Von Neumann Algebras Associated with the Group SL2（R）

Let M\mathcal{M} and N\mathcal{N} be the von Neumann algebras induced by the rational action of the group SL ₂(ℝ) and its subgroup P on the upper half plane \mathbbH\mathbb{H}. We have shown that N\mathcal{N} is spatial isomorphic to the group von Neumann algebra L_P\mathcal{L}_P and characterized M\mathcal{M} and its commutant M￠\mathcal{M}' and gotten a generalization of the Mautner’s lemma. It is also shown that the Berezin operator commutates with the Laplacian operator.