In this paper, we discuss the nonemptyness and boundedness of the solution set for P*-semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the c...In this paper, we discuss the nonemptyness and boundedness of the solution set for P*-semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the cone of semidefinite matrices, and obtain a main result that if the corresponding problem has a strict feasible point, then its solution set is nonemptyness and boundedness.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
In this paper,finite p-groups G with G/HGbeing cyclic for every minimal nonnormal subgroup H are classified up to isomorphism,where HGdenotes the normal closure of H.
Browder[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder's results in several aspects. Recently, H.M. Ko and K.K. Tan[2,3] generalized Browder's theorems to...Browder[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder's results in several aspects. Recently, H.M. Ko and K.K. Tan[2,3] generalized Browder's theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems oj set-valued mappings. They improve and generalize the important results in [1,2,3].展开更多
By applying the technique of continuous partition of unity and Tychonoff's fixed point theorem,. some new collectively fixed point theorems for a family of set-valued, mappings defined on the product space of nonc...By applying the technique of continuous partition of unity and Tychonoff's fixed point theorem,. some new collectively fixed point theorems for a family of set-valued, mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence of abstract economies are also obtained in G convex spaces. Our theorems theorems of improve, unify and generalized many important known results in recent literature.展开更多
1 Introduction and Main Results LetΩ■Rd(with d≥1)be a bounded domain with a C^2 boundary■Ω.LetωΩbe an open and nonempty subset with its characteristic functionχω.Let A■(aij)1≤i,j≤n∈R^n×n ...1 Introduction and Main Results LetΩ■Rd(with d≥1)be a bounded domain with a C^2 boundary■Ω.LetωΩbe an open and nonempty subset with its characteristic functionχω.Let A■(aij)1≤i,j≤n∈R^n×n and B■(bij)1≤i≤n,1≤j≤m∈ R^n×m be two constant matrices,where n≥2 and m≥1.展开更多
The topologioal degree are constructed for generalized pseudo-monotone mappings and for the sum of a maximal monotone mapwith a generalized pseudomnotone from a refelxive Banach space toits dual space.This generalizes...The topologioal degree are constructed for generalized pseudo-monotone mappings and for the sum of a maximal monotone mapwith a generalized pseudomnotone from a refelxive Banach space toits dual space.This generalizes topological degree for pseudomon-otone mappings and for the sum of a maximal monotone map witha bounded pseudomonotone mop from a reflexive Banach space to itsdual space which have been studied earlier by Browder and展开更多
Let N denote the set of all nonnegative integers and A be a subset of N.Let W be a nonempty subset of N.Denote by F~＊（W） the set of all finite,nonempty subsets of W.Fix integer g≥2,let Ag（W） be the set of all nu...Let N denote the set of all nonnegative integers and A be a subset of N.Let W be a nonempty subset of N.Denote by F~＊（W） the set of all finite,nonempty subsets of W.Fix integer g≥2,let Ag（W） be the set of all numbers of the form sum f∈Fafgf where F∈F＊（W）and 1≤af≤g-1.For i=0,1,2,3,let Wi = {n∈N｜n≡ i（mod 4）}.In this paper,we show that the set A = Ui3=0 Ag（Wi） is a minimal asymptotic basis of order four.展开更多
Let f be a homeomorphism of a compact tvs-cone metric space. In this paper,we show that f is tvs-cone expansive if and only if f has a generator. Further, it is proved that if f is tvs-cone expansive, then the set of ...Let f be a homeomorphism of a compact tvs-cone metric space. In this paper,we show that f is tvs-cone expansive if and only if f has a generator. Further, it is proved that if f is tvs-cone expansive, then the set of points having converging semiorbits under f is a countable set. Results of this paper improve some expansive homeomorphisms theorems in topological dynamics, which will help to research dynamical properties for homeomorphisms of tvs-cone metric spaces.展开更多
Let (X, d) be a complete metric space, (?) (X) be the collection of all fuzzy sets on X, then ω_α(A)={x∈X:A(x)≥α), A_α={x∈X:A (x)=α}, where A∈(?)(X), α∈(0, 1]. GB(X) denotes a family of all nonempty bounded...Let (X, d) be a complete metric space, (?) (X) be the collection of all fuzzy sets on X, then ω_α(A)={x∈X:A(x)≥α), A_α={x∈X:A (x)=α}, where A∈(?)(X), α∈(0, 1]. GB(X) denotes a family of all nonempty bounded closed sets (nonfuzzy) in X. If A, B∈(?)(X) and ω_α(A), ω_α(B)∈ CB(X), we can define ρ_α(A, B) = inf{d(x,y):x∈ω_α(A),y∈ω_α(B) } , D_α(A,B)= H(ω_α(A),ω_α(B)),where H is Hausdorff distance induced by d. Definition. Let F be a fuzzy mapping over X, i.e. a mapping from X to (?)(X). Write F (x) =F_x. To the point x_*∈X, if F_x_*(x_*)= α, then we say that the fixed degree of x_*展开更多
Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal wit...Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal with the ess. inf case, the transplantation of results to the ess. sup case being trivial.展开更多
<正> Let (T, μ)be a bounded Lebesgue measure space, X a separable Banach space. Integral is referred to Bochner integral. Let 2~x be the set of all subsets of X. For a set A(?)X, coA and clA denote the convex h...<正> Let (T, μ)be a bounded Lebesgue measure space, X a separable Banach space. Integral is referred to Bochner integral. Let 2~x be the set of all subsets of X. For a set A(?)X, coA and clA denote the convex hull and closure of A respectively. Set-valued map F:T→2~x is called nonempty and closed if for every t∈T, F(t) is nonempty展开更多
A new pivot method for oriented matroid progiamming is given out. This mathod is deterministic by nature and is general in the sense that its flexible pivot selection rule allows a family of possible algorithms to be ...A new pivot method for oriented matroid progiamming is given out. This mathod is deterministic by nature and is general in the sense that its flexible pivot selection rule allows a family of possible algorithms to be its special cases, including the so called criss-cross algorithm and the Edmonds-Fukuda algorithm as well. As an example of a special implementation of our general method, an extended version of the Edmonds-Fukuda algorithm is presented.展开更多
In this report, a new algorithm to construct a dual family of the Boolean function is presented. By double dual, all the prime implicate terms of the Boolean function or noncoherent fault tree can be obtained. To iden...In this report, a new algorithm to construct a dual family of the Boolean function is presented. By double dual, all the prime implicate terms of the Boolean function or noncoherent fault tree can be obtained. To identify all the system failure modes in the field of fault tree analysis on the noncoherent system, the important concept of the prime implicate set (PIS) must展开更多
Let X be a finite set. A free monoid generated by X is denoted by X~*. Every element of X~* is called a word over X and every subset of X~* is called a language over X. The identity of X~*, so called empty word, is de...Let X be a finite set. A free monoid generated by X is denoted by X~*. Every element of X~* is called a word over X and every subset of X~* is called a language over X. The identity of X~*, so called empty word, is denoted by λ. We set X^+=X~*—{λ}.展开更多
Ⅰ. INTRODUCTION It is well known that the Liouville number sum from k=1 to ∞ (g-k1（g≥2, ∈N） is transcendental. Cijsouw and Tijdeman proved the following general proposition: Suppose that the power
In the area of fuzzy topology, researches have been carried out in China and abroad in recent years. But the theory of the fuzzy function space, which is apparently important in fuzzy topology, has not been establishe...In the area of fuzzy topology, researches have been carried out in China and abroad in recent years. But the theory of the fuzzy function space, which is apparently important in fuzzy topology, has not been established yet. The important theories of compactness, separation and uniformities on a fuzzy topological space, related closely to the discussion of topological structure of the fuzzy function space, are so complicated that the research on the subject is rather difficult.展开更多
Klement first gave an axiomatic definition of a fuzzy σ-algebra which is a generalization of the family of fuzzy events considered by Zadeh. Following the method adopted by Lowen in studying fuzzy topology, Klement d...Klement first gave an axiomatic definition of a fuzzy σ-algebra which is a generalization of the family of fuzzy events considered by Zadeh. Following the method adopted by Lowen in studying fuzzy topology, Klement defined two important mappings ζ and κ, and proved some of their corresponding properties in the research of the relationship between classical and fuzzy σ-algebra. This note attempts: (ⅰ)展开更多
Let m≥（?）0, and a topological space X is said to be initial m-compact as long as every open cover of which the cardinal number not exceed the m has finite subcover. In this letter, suppose that X is a regular space...Let m≥（?）0, and a topological space X is said to be initial m-compact as long as every open cover of which the cardinal number not exceed the m has finite subcover. In this letter, suppose that X is a regular space, 2x denotes all nonempty closed subset with finite topology in X.展开更多
In [1] and [2], the late modal logician E. J. Lemmon investigated the connexion between the algebraic and Kripke’s semantics for two series of modal propositional systems;he also pronounced in [1] that a third paper ...In [1] and [2], the late modal logician E. J. Lemmon investigated the connexion between the algebraic and Kripke’s semantics for two series of modal propositional systems;he also pronounced in [1] that a third paper would be prepared to discuss the same connexion for quantifications of all the modal systems considered therein. Unfortunately, owing to his untimely death, this Paper did not come out. In this note we discuss the展开更多
文摘In this paper, we discuss the nonemptyness and boundedness of the solution set for P*-semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the cone of semidefinite matrices, and obtain a main result that if the corresponding problem has a strict feasible point, then its solution set is nonemptyness and boundedness.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1137123211226048+1 种基金11401355)the Natural Science Foundation of Shanxi Province(Grant No.2013011001-1)
文摘In this paper,finite p-groups G with G/HGbeing cyclic for every minimal nonnormal subgroup H are classified up to isomorphism,where HGdenotes the normal closure of H.
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences
文摘Browder[1] obtained the sharpened forms of the Schauder fixed point theorem. Many authors generalized Browder's results in several aspects. Recently, H.M. Ko and K.K. Tan[2,3] generalized Browder's theorems to the coincidence theorems of set-valued mappings. In this paper, we also show some coincidence theorems oj set-valued mappings. They improve and generalize the important results in [1,2,3].
文摘By applying the technique of continuous partition of unity and Tychonoff's fixed point theorem,. some new collectively fixed point theorems for a family of set-valued, mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence of abstract economies are also obtained in G convex spaces. Our theorems theorems of improve, unify and generalized many important known results in recent literature.
基金supported by National Natural Science Foundation of China(11771344 and 11701138).
文摘1 Introduction and Main Results LetΩ■Rd(with d≥1)be a bounded domain with a C^2 boundary■Ω.LetωΩbe an open and nonempty subset with its characteristic functionχω.Let A■(aij)1≤i,j≤n∈R^n×n and B■(bij)1≤i≤n,1≤j≤m∈ R^n×m be two constant matrices,where n≥2 and m≥1.
文摘The topologioal degree are constructed for generalized pseudo-monotone mappings and for the sum of a maximal monotone mapwith a generalized pseudomnotone from a refelxive Banach space toits dual space.This generalizes topological degree for pseudomon-otone mappings and for the sum of a maximal monotone map witha bounded pseudomonotone mop from a reflexive Banach space to itsdual space which have been studied earlier by Browder and
基金Supported by the National Natural Science Foundation of China(Grant No.11471017)
文摘Let N denote the set of all nonnegative integers and A be a subset of N.Let W be a nonempty subset of N.Denote by F~＊（W） the set of all finite,nonempty subsets of W.Fix integer g≥2,let Ag（W） be the set of all numbers of the form sum f∈Fafgf where F∈F＊（W）and 1≤af≤g-1.For i=0,1,2,3,let Wi = {n∈N｜n≡ i（mod 4）}.In this paper,we show that the set A = Ui3=0 Ag（Wi） is a minimal asymptotic basis of order four.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130136761472469+1 种基金11461005)the Doctoral Fund of Ministry of Education of China(Grant No.20123201120001)
文摘Let f be a homeomorphism of a compact tvs-cone metric space. In this paper,we show that f is tvs-cone expansive if and only if f has a generator. Further, it is proved that if f is tvs-cone expansive, then the set of points having converging semiorbits under f is a countable set. Results of this paper improve some expansive homeomorphisms theorems in topological dynamics, which will help to research dynamical properties for homeomorphisms of tvs-cone metric spaces.
文摘Let (X, d) be a complete metric space, (?) (X) be the collection of all fuzzy sets on X, then ω_α(A)={x∈X:A(x)≥α), A_α={x∈X:A (x)=α}, where A∈(?)(X), α∈(0, 1]. GB(X) denotes a family of all nonempty bounded closed sets (nonfuzzy) in X. If A, B∈(?)(X) and ω_α(A), ω_α(B)∈ CB(X), we can define ρ_α(A, B) = inf{d(x,y):x∈ω_α(A),y∈ω_α(B) } , D_α(A,B)= H(ω_α(A),ω_α(B)),where H is Hausdorff distance induced by d. Definition. Let F be a fuzzy mapping over X, i.e. a mapping from X to (?)(X). Write F (x) =F_x. To the point x_*∈X, if F_x_*(x_*)= α, then we say that the fixed degree of x_*
文摘Ⅰ. MAIN RESULT Let (Ω,P) be a probability space, and H a nonempty family of random variables. We denote by ess. inf H or ess. inf ξ∈ H the essential infimum of H, which always exists. In this note we only deal with the ess. inf case, the transplantation of results to the ess. sup case being trivial.
文摘<正> Let (T, μ)be a bounded Lebesgue measure space, X a separable Banach space. Integral is referred to Bochner integral. Let 2~x be the set of all subsets of X. For a set A(?)X, coA and clA denote the convex hull and closure of A respectively. Set-valued map F:T→2~x is called nonempty and closed if for every t∈T, F(t) is nonempty
基金Projects supported by the Natural Science Foundation of Fudan University.
文摘A new pivot method for oriented matroid progiamming is given out. This mathod is deterministic by nature and is general in the sense that its flexible pivot selection rule allows a family of possible algorithms to be its special cases, including the so called criss-cross algorithm and the Edmonds-Fukuda algorithm as well. As an example of a special implementation of our general method, an extended version of the Edmonds-Fukuda algorithm is presented.
文摘In this report, a new algorithm to construct a dual family of the Boolean function is presented. By double dual, all the prime implicate terms of the Boolean function or noncoherent fault tree can be obtained. To identify all the system failure modes in the field of fault tree analysis on the noncoherent system, the important concept of the prime implicate set (PIS) must
基金Project supported by the Science Fund of Academia Sinica
文摘Let X be a finite set. A free monoid generated by X is denoted by X~*. Every element of X~* is called a word over X and every subset of X~* is called a language over X. The identity of X~*, so called empty word, is denoted by λ. We set X^+=X~*—{λ}.
文摘Ⅰ. INTRODUCTION It is well known that the Liouville number sum from k=1 to ∞ (g-k1（g≥2, ∈N） is transcendental. Cijsouw and Tijdeman proved the following general proposition: Suppose that the power
文摘In the area of fuzzy topology, researches have been carried out in China and abroad in recent years. But the theory of the fuzzy function space, which is apparently important in fuzzy topology, has not been established yet. The important theories of compactness, separation and uniformities on a fuzzy topological space, related closely to the discussion of topological structure of the fuzzy function space, are so complicated that the research on the subject is rather difficult.
文摘Klement first gave an axiomatic definition of a fuzzy σ-algebra which is a generalization of the family of fuzzy events considered by Zadeh. Following the method adopted by Lowen in studying fuzzy topology, Klement defined two important mappings ζ and κ, and proved some of their corresponding properties in the research of the relationship between classical and fuzzy σ-algebra. This note attempts: (ⅰ)
文摘Let m≥（?）0, and a topological space X is said to be initial m-compact as long as every open cover of which the cardinal number not exceed the m has finite subcover. In this letter, suppose that X is a regular space, 2x denotes all nonempty closed subset with finite topology in X.
文摘In [1] and [2], the late modal logician E. J. Lemmon investigated the connexion between the algebraic and Kripke’s semantics for two series of modal propositional systems;he also pronounced in [1] that a third paper would be prepared to discuss the same connexion for quantifications of all the modal systems considered therein. Unfortunately, owing to his untimely death, this Paper did not come out. In this note we discuss the
