In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new...In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.展开更多
Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex: spaces. As applications, some new fixe...Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex: spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature.展开更多
Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the re...Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.展开更多
Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A o...Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.展开更多
Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are...In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.展开更多
In this article,we discuss the stability ofε-isometries for L∞,λ-spaces.Indeed,we first study the relationship among separably injectivity,injectivity,cardinality injectivity and universally left stability of L∞,...In this article,we discuss the stability ofε-isometries for L∞,λ-spaces.Indeed,we first study the relationship among separably injectivity,injectivity,cardinality injectivity and universally left stability of L∞,λ-spaces as well as we show that the second duals of universally left-stable spaces are injective,which gives a partial answer to a question of Bao-Cheng-Cheng-Dai,and then we prove a sharpen quantitative and generalized Sobczyk theorem which gives examples of nonseparable L∞-spaces X(but not injective)such that the couple(X,Y)is stable for every separable space Y.This gives a new positive answer to Qian's problem.展开更多
This paper formulates the category of L-fuzzy spaces and fuzzy functions.It shows that the category of topological spaces and continuous fuzzy functions is a direct generalization of TOP and LTOP Moreover,it defines t...This paper formulates the category of L-fuzzy spaces and fuzzy functions.It shows that the category of topological spaces and continuous fuzzy functions is a direct generalization of TOP and LTOP Moreover,it defines the concept of proximity space on L-fuzzy space and introduces its fundamental properties.A comparison between the classical case and the ordinary case has been outlined.展开更多
We extend the notion of a uniform space in a natural way by defining a uniform spaces in L-fuzzy spaces.Although these spaces seem quite similar to ordinary case,we show that the category of this uniform spaces is a g...We extend the notion of a uniform space in a natural way by defining a uniform spaces in L-fuzzy spaces.Although these spaces seem quite similar to ordinary case,we show that the category of this uniform spaces is a good extension of the category of ordinary uniform spaces and the category of L-uniform spaces.Moreover,we introduce the concept of uniform topological spaces in the framework of uniform spaces in L-fuzzy spaces.Furthermore,the relation between proximity and uniform spaces in L-fuzzy spaces will be established.展开更多
In this paper an evaluation of the influence of luminance L* at the L*a*b* color space during color segmentation is presented. A comparative study is made between the behavior of segmentation in color images using onl...In this paper an evaluation of the influence of luminance L* at the L*a*b* color space during color segmentation is presented. A comparative study is made between the behavior of segmentation in color images using only the Euclidean metric of a* and b* and an adaptive color similarity function defined as a product of Gaussian functions in a modified HSI color space. For the evaluation synthetic images were particularly designed to accurately assess the performance of the color segmentation. The testing system can be used either to explore the behavior of a similarity function (or metric) in different color spaces or to explore different metrics (or similarity functions) in the same color space. From the results is obtained that the color parameters a* and b* are not independent of the luminance parameter L* as one might initially assume.展开更多
We prove the existence of both final L-double gradation fuzzy topological spaces and final L-double fuzzy closure spaces. From this fact,we define and study the notions of the L-double quotient spaces and the sum of L...We prove the existence of both final L-double gradation fuzzy topological spaces and final L-double fuzzy closure spaces. From this fact,we define and study the notions of the L-double quotient spaces and the sum of L-double fuzzy closure spaces. Finally,we study the additivity of two kinds of L-double fuzzy closure spaces.展开更多
In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characte...In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.展开更多
In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.
文摘In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.
基金the NNSF of China(19871059)and the NSF of Education Department of Sichuan Province([2000]25)
文摘Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex: spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature.
文摘Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.
文摘Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.
基金Supported by the National Natural Science Foundation of China(1057115610871173)
文摘Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
文摘In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.
基金supported by the Natural Science Foundation of China(11601264)the Natural Science Foundation of Fujian Province of China(2019J05103)+1 种基金the Outstanding Youth Scientific Research Personnel Training Program of Fujian Provincethe High level Talents Innovation and Entrepreneurship Project of Quanzhou City(2017Z032)
文摘In this article,we discuss the stability ofε-isometries for L∞,λ-spaces.Indeed,we first study the relationship among separably injectivity,injectivity,cardinality injectivity and universally left stability of L∞,λ-spaces as well as we show that the second duals of universally left-stable spaces are injective,which gives a partial answer to a question of Bao-Cheng-Cheng-Dai,and then we prove a sharpen quantitative and generalized Sobczyk theorem which gives examples of nonseparable L∞-spaces X(but not injective)such that the couple(X,Y)is stable for every separable space Y.This gives a new positive answer to Qian's problem.
文摘This paper formulates the category of L-fuzzy spaces and fuzzy functions.It shows that the category of topological spaces and continuous fuzzy functions is a direct generalization of TOP and LTOP Moreover,it defines the concept of proximity space on L-fuzzy space and introduces its fundamental properties.A comparison between the classical case and the ordinary case has been outlined.
文摘We extend the notion of a uniform space in a natural way by defining a uniform spaces in L-fuzzy spaces.Although these spaces seem quite similar to ordinary case,we show that the category of this uniform spaces is a good extension of the category of ordinary uniform spaces and the category of L-uniform spaces.Moreover,we introduce the concept of uniform topological spaces in the framework of uniform spaces in L-fuzzy spaces.Furthermore,the relation between proximity and uniform spaces in L-fuzzy spaces will be established.
文摘In this paper an evaluation of the influence of luminance L* at the L*a*b* color space during color segmentation is presented. A comparative study is made between the behavior of segmentation in color images using only the Euclidean metric of a* and b* and an adaptive color similarity function defined as a product of Gaussian functions in a modified HSI color space. For the evaluation synthetic images were particularly designed to accurately assess the performance of the color segmentation. The testing system can be used either to explore the behavior of a similarity function (or metric) in different color spaces or to explore different metrics (or similarity functions) in the same color space. From the results is obtained that the color parameters a* and b* are not independent of the luminance parameter L* as one might initially assume.
文摘We prove the existence of both final L-double gradation fuzzy topological spaces and final L-double fuzzy closure spaces. From this fact,we define and study the notions of the L-double quotient spaces and the sum of L-double fuzzy closure spaces. Finally,we study the additivity of two kinds of L-double fuzzy closure spaces.
文摘In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.
文摘In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.
