The Interpolation Problem on the Maximal Ideal Space of H~∞

ＴｈｅＩｎｔｅｒｐｏｌａｔｉｏｎＰｒｏｂｌｅｍｏｎｔｈｅＭａｘｉｍａｌＩｄｅａｌＳｐａｃｅｏｆＨ~∞￥ＧｕｏＫｕｎｇｕ（郭坤宇）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ，６１００６４）Ａｂｓ?..     

Characterizations of Strongly Regular Rings

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＳｔｒｏｎｇｌｙＲｅｇｕｌａｒＲｉｎｇｓＺｈａｎｇＪｕｌｅ（章聚乐）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈｕ２４１０００）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉ...     

Fuzzy拓扑学—层次结构和点式处理

建设在Ｆｕｚｚｙ集合基础上的Ｆｕｚｚｙ拓扑学，经过２０多年发展，现在已自具特色，日趋成熟，本文力图从点式处理和层次结构角度反映其基本思想、具体构造和主要结果。并且说明Ｆｕｚｚｙ拓扑学研究与经数学的关系。从这里可以看到，Ｆｕｚｚｙ拓扑研究无论是基本思想还是研究方法都有其独到之处。     

Secret sharing schemes on access structures with intersection number equal to one

The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, structures such that there is at most one participant in the intersection of any two different minimal qualified subsets. The main result in this work is the complete characterization of the ideal access structures with intersection number equal to one. In addition, bounds on the optimal information rate are provided for the non-ideal case.     

On the Hartshorne-Speiser-Lyubeznik theorem about Artinian modules with a Frobenius action

Let be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring (associated to and the Frobenius homomorphism , in the indeterminate ) that is both -torsion and Artinian over .

     

Ideal and non-ideal behaviour of {1-butyl-1-methylpyrrolydinium bis(trifluoromethylsulfonyl)imide + γ-butyrolactone} binary mixtures

Density, electrical conductivity and viscosity of binary liquid mixtures of 1-butyl-1-methylpyrrolydinium bis(trifluoromethylsulfonyl)imide, [bmpyrr][NTf₂], with γ-butyrolactone (GBL) were measured at temperatures from (293.15 to 323.15) K and at atmospheric pressure over the whole composition range. Excess molar volumes have been calculated from the experimental densities and fitted with the Redlich–Kister polynomial equation. These values are positive over the whole range of ionic liquid mole fraction and at all temperatures. In the range between 0.55 and 0.6 [bmpyrr][NTf₂] mole fraction, an ideal behaviour of the ionic liquid mixture with molecular solvent was observed for the first time. Other volumetric properties, such as isobaric thermal expansion coefficients, partial molar volumes and partial molar volumes at infinite dilution have been also calculated, in order to obtain information about interactions between GBL and selected ionic liquid. Positive values of these properties for both components also indicate weaker interactions between GBL and IL compared to the pure components. From the viscosity results, the Angell strength parameter was calculated and found to be 3.24 indicating that [bmpyrr][NTf₂] is a “fragile” liquid. From the volumetric and transport properties obtained, formation of the [bmpyrr]⁺ micellar structures was also discussed. All the results are compared to those obtained for imidazolium-based ionic liquid with GBL.     

Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators

This paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It shows that Alexandrov L-topologies can be induced by L-fuzzy relations without any preconditions. Second, the concept of similarity of L-fuzzy relations is introduced and variations of an L-fuzzy relation are investigated. Third, algebraic structures on similarity of L-fuzzy relations are obtained. Finally, we prove that the subset of the transitive L-fuzzy relations similar to a fixed L-fuzzy relation is a complete distributive lattice.     

Pointwise versus equal (quasi-normal) convergence via ideals

We prove a characterization showing when the ideal pointwise convergence does not imply the ideal equal (aka quasi-normal) convergence. The characterization is expressed in terms of a cardinal coefficient related to the bounding number b$\mathfrak{b}$. We also prove a characterization showing when the ideal equal limit is unique.     

Remarks on ideal boundedness, convergence and variation of sequences

We answer the questions asked by Faisant et al. (2005) [2]. The first main result states that for every admissible ideal I⊂P(N) the quotient space l^∞(I)/c₀(I) is complete. The second main result states that consistently there is an admissible ideal I⊂P(N) such that the sets W(I), of all real sequences with finite I-variation, and c^?(I), of all restrictively I-convergent sequences, are equal.