This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0, 1, 2, 3, 4, μTn-spaces and μR0-spaces are obtained and some relation...This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0, 1, 2, 3, 4, μTn-spaces and μR0-spaces are obtained and some relations among these spaces are established.展开更多
Let G be aπ-separable group for a set of primes, let N be a normal subgroup of G, and letθbe an Iπ-character （i.e., irreducibleπ-partial character） of N . We obtain a necessary and sufficient condition for the n...Let G be aπ-separable group for a set of primes, let N be a normal subgroup of G, and letθbe an Iπ-character （i.e., irreducibleπ-partial character） of N . We obtain a necessary and sufficient condition for the number of Iπ-characters of G overθ to take the possible maximum ｜G：N｜π. Some applications are given.展开更多
This article aims to present new terms of single-valued neutrosophic notions in theˇSostak sense,known as singlevalued neutrosophic regularity spaces.Concepts such as r-single-valued neutrosophic semi￡-open,r-single...This article aims to present new terms of single-valued neutrosophic notions in theˇSostak sense,known as singlevalued neutrosophic regularity spaces.Concepts such as r-single-valued neutrosophic semi￡-open,r-single-valued neutrosophic pre-￡-open,r-single valued neutrosophic regular-￡-open and r-single valued neutrosophicα￡-open are defined and their properties are studied as well as the relationship between them.Moreover,we introduce the concept of r-single valued neutrosophicθ￡-cluster point and r-single-valued neutrosophicγ￡-cluster point,r-θ￡-closed,andθ￡-closure operators and study some of their properties.Also,we present and investigate the notions of r-single-valued neutrosophicθ￡-connectedness and r-single valued neutrosophicδ￡-connectedness and investigate relationship with single-valued neutrosophic almost￡-regular.We compare all these forms of connectedness and investigate their properties in single-valued neutrosophic semiregular and single-valued neutrosophic almost regular in neutrosophic ideal topological spaces inˇSostak sense.The usefulness of these concepts are incorporated to multiple attribute groups of comparison within the connectedness and separateness ofθ￡andδ￡.展开更多
Fuzzy soft topology considers only membership value.It has nothing to do with the non-membership value.So an extension was needed in this direction.Vague soft topology addresses bothmembership and non-membership value...Fuzzy soft topology considers only membership value.It has nothing to do with the non-membership value.So an extension was needed in this direction.Vague soft topology addresses bothmembership and non-membership values simultaneously.Sometimes vague soft topology(single structure)is unable to address some complex structures.So an extension to vague soft bi-topology(double structure)was needed in this direction.To make this situation more meaningful,a new concept of vague soft bi-topological space is introduced and its structural characteristics are attempted with a new definition.In this article,new concept of vague soft bi-topological space(VSBTS)is initiated and its structural behaviors are attempted.This approach is based on generalized vague soft open sets,known as vague softβopen sets.An ample of examples are given to understand the structures.For the non-validity of some results,counter examples are provided to pay the price.Pair-wise vague softβopen and pair-wise vague softβclose sets are alsoaddressedwith examples in(VSBTS).Vague soft separation axioms are initiatedin(VSBTS)concerning soft points of the space.Other separation axioms are also addressed relative to soft points of the space.Vague soft bi-topological properties are studied with the application of vague softβopen sets with respect to soft points of the spaces.The characterization of vague softβclose as well as vague softβopen sets,characteristics of Bolzano Weirstrass property,vague soft compactness and its marriage with sequences,interconnection between sequential compactness and countable compactness in(VSBTS)with respect to softβopen sets are addressed.展开更多
Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works o...Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to theπ-block theory of aπ-separable group, defines the nilpotency of aπ-block, and proves that there is a unique B_(π')-character in a nilpotentπ-block.展开更多
Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts f...Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.展开更多
Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theor...Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theorem for π-subpairs. Note that our π-subpairs are different from what Robinson and Staszewski gave.展开更多
This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w＊-separable dual. It also gives some prop...This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w＊-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in Hilbert spaces.展开更多
基金Supported by the National Natural Science Foundation of China(10971185)
文摘This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0, 1, 2, 3, 4, μTn-spaces and μR0-spaces are obtained and some relations among these spaces are established.
基金Supported by the NSF of Shanxi Province(2013011001-3)
文摘Let G be aπ-separable group for a set of primes, let N be a normal subgroup of G, and letθbe an Iπ-character （i.e., irreducibleπ-partial character） of N . We obtain a necessary and sufficient condition for the number of Iπ-characters of G overθ to take the possible maximum ｜G：N｜π. Some applications are given.
文摘This article aims to present new terms of single-valued neutrosophic notions in theˇSostak sense,known as singlevalued neutrosophic regularity spaces.Concepts such as r-single-valued neutrosophic semi￡-open,r-single-valued neutrosophic pre-￡-open,r-single valued neutrosophic regular-￡-open and r-single valued neutrosophicα￡-open are defined and their properties are studied as well as the relationship between them.Moreover,we introduce the concept of r-single valued neutrosophicθ￡-cluster point and r-single-valued neutrosophicγ￡-cluster point,r-θ￡-closed,andθ￡-closure operators and study some of their properties.Also,we present and investigate the notions of r-single-valued neutrosophicθ￡-connectedness and r-single valued neutrosophicδ￡-connectedness and investigate relationship with single-valued neutrosophic almost￡-regular.We compare all these forms of connectedness and investigate their properties in single-valued neutrosophic semiregular and single-valued neutrosophic almost regular in neutrosophic ideal topological spaces inˇSostak sense.The usefulness of these concepts are incorporated to multiple attribute groups of comparison within the connectedness and separateness ofθ￡andδ￡.
文摘Fuzzy soft topology considers only membership value.It has nothing to do with the non-membership value.So an extension was needed in this direction.Vague soft topology addresses bothmembership and non-membership values simultaneously.Sometimes vague soft topology(single structure)is unable to address some complex structures.So an extension to vague soft bi-topology(double structure)was needed in this direction.To make this situation more meaningful,a new concept of vague soft bi-topological space is introduced and its structural characteristics are attempted with a new definition.In this article,new concept of vague soft bi-topological space(VSBTS)is initiated and its structural behaviors are attempted.This approach is based on generalized vague soft open sets,known as vague softβopen sets.An ample of examples are given to understand the structures.For the non-validity of some results,counter examples are provided to pay the price.Pair-wise vague softβopen and pair-wise vague softβclose sets are alsoaddressedwith examples in(VSBTS).Vague soft separation axioms are initiatedin(VSBTS)concerning soft points of the space.Other separation axioms are also addressed relative to soft points of the space.Vague soft bi-topological properties are studied with the application of vague softβopen sets with respect to soft points of the spaces.The characterization of vague softβclose as well as vague softβopen sets,characteristics of Bolzano Weirstrass property,vague soft compactness and its marriage with sequences,interconnection between sequential compactness and countable compactness in(VSBTS)with respect to softβopen sets are addressed.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10771132)Beijing Educational Committee (Grant No. Km200510028002)
文摘Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to theπ-block theory of aπ-separable group, defines the nilpotency of aπ-block, and proves that there is a unique B_(π')-character in a nilpotentπ-block.
基金supported by the National Natural Science Foundation of China(Grant No.10471085)the BS Foundation of Shandong Province,China(Grant No.03bs006).
文摘Let π be a set of primes and G a π-separable group. Isaacs defines the Bπ characters, which can be viewed as the "π-modular" characters in G, such that the Bp′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs' work, Slattery has developed some Brauer's ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer's three main theorems to the π-blocks. In this paper, depending on Isaacs' and Slattery's work, we will extend the first main theorem for π-blocks.
基金Supported by NSF of China(10471085)by BSF of Shandong(03bs006)
文摘Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theorem for π-subpairs. Note that our π-subpairs are different from what Robinson and Staszewski gave.
基金Supported by National Natural Science Foundation of China(Grant Nos.10926173,11171066 and 10771034)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.2010350311001)Natural Science Foundation of Fujian Province of China(Grant No.2009J05002)
文摘This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w＊-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in Hilbert spaces.
