In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets a...In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets are presented. The main results are:(1) A uniform complete poset L is meet uniform continuous iff ↑(U∩↓x) is a uniform Scott set for each x∈L and each uniform Scott set U;(2) A uniform complete poset L is meet uniform continuous iff for each x∈L and each uniform subset S, one has x∧∨ S =∨{x∧s|s∈S}. In particular, a complete lattice L is meet uniform continuous iff L is a complete Heyting algebra;(3) A uniform complete poset is meet uniform continuous iff every principal ideal is meet uniform continuous iff all closed intervals are meet uniform continuous iff all principal filters are meet uniform continuous;(4) A uniform complete poset L is meet uniform continuous if L1 obtained by adjoining a top element 1 to L is a complete Heyting algebra;(5) Finite products and images of uniform continuous projections of meet uniform continuous posets are still meet uniform continuous.展开更多
The plenum chamber of a heat setting machine is a key structure for distributing hot air to different air channels.Its outlet velocity uniformity directly determines the heating uniformity of textiles,significantly af...The plenum chamber of a heat setting machine is a key structure for distributing hot air to different air channels.Its outlet velocity uniformity directly determines the heating uniformity of textiles,significantly affecting the heat setting performance.In a traditional heat setting machine,the outlet airflow maldistribution of the plenum chamber still exists.In this study,a novel plenum chamber with an airfoil baffle was established to improve the uniformity of the velocity distribution at the outlet in a heat setting machine.The structural influence of the plenum chamber on the velocity distribution was investigated using a computational fluid dynamics program.It was found that a chamber with a smaller outlet partition thickness had a better outlet velocity uniformity.The structural optimization of the plenum chamber was conducted using the particle swarm optimization algorithm.The outlet partition thickness,the transverse distance and the longitudinal distance of the optimized plenum chamber were 20,686.2 and 274.6 mm,respectively.Experiments were carried out.The experimental and simulated results showed that the optimized plenum chamber with an airfoil baffle could improve the outlet velocity uniformity.The air outlet velocity uniformity index of the optimized plenum chamber with an airfoil baffle was 4.75%higher than that of the plenum chamber without an airfoil baffle and 5.98%higher than that of the conventional chamber with a square baffle in a commercial heat setting machine.展开更多
Image segmentation is a key and fundamental problem in image processing,computer graphics,and computer vision.Level set based method for image segmentation is used widely for its topology flexibility and proper mathem...Image segmentation is a key and fundamental problem in image processing,computer graphics,and computer vision.Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation.However,poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation.In this paper,we present a region consistency constraint term to measure the regional consistency on both sides of the boundary,this term defines the boundary of the image within a range,and hence increases the stability of the level set model.The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary.Furthermore,this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour.The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary.展开更多
In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A ...In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.展开更多
In this article sharper estimates on the radii of absorbing sets for the Kuramoto_Sivashinsky equation are given. It is proved that radii of absorbing sets will decay to zero as the coefficient of viscosity tends to a...In this article sharper estimates on the radii of absorbing sets for the Kuramoto_Sivashinsky equation are given. It is proved that radii of absorbing sets will decay to zero as the coefficient of viscosity tends to a certain critical value, which is more reasonable in the physical sence compared with classical results.展开更多
In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give i...In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give its fractal characterization. We find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from translating the vector （x,y） with its radix expansion.展开更多
In this paper,the definition of absolutely balanced and uniformly balanced for graphs are introduced,the difference between balance graphs are pointed out.Using（p,p＋1）-graph as an example,we explained the existence...In this paper,the definition of absolutely balanced and uniformly balanced for graphs are introduced,the difference between balance graphs are pointed out.Using（p,p＋1）-graph as an example,we explained the existence of this difference and obtained some new results.展开更多
First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of...First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.展开更多
This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a f...This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.展开更多
The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust fo...The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model.However,the analytical expressions of MSED and MD are currently only available in the hypercube,but both types of deviations in other studies are just approximations.Although it can obtain good approximations in the low-dimensional case,the calculation will be more complicated for an experiment with more variables.Therefore,in this paper,an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points.Furthermore,the design’s optimality is considered and illustrated by examples under the same uniformity.展开更多
Let K be a(bounded)closed uniformly convex subset of a Banach space X.We show that(i)the nearest point map is well-defined and always continuous from X onto K,(ii)there is a reflexive space Y with a uniform rotund in ...Let K be a(bounded)closed uniformly convex subset of a Banach space X.We show that(i)the nearest point map is well-defined and always continuous from X onto K,(ii)there is a reflexive space Y with a uniform rotund in every direction norm such that Y contains K as a subset and the nearest point map PK:Y→K is uniformly continuous from any bounded set containing K onto K.展开更多
云计算为大数据提供了展示和共享的平台.为了防止隐私泄露,这些数据中往往包含人为添加的不确定因素,如何挖掘这些不确定数据是大数据共享亟待解决的问题.在用于共享的大数据中,不确定数据通过对精确数据的泛化处理来实现,具有均匀分布...云计算为大数据提供了展示和共享的平台.为了防止隐私泄露,这些数据中往往包含人为添加的不确定因素,如何挖掘这些不确定数据是大数据共享亟待解决的问题.在用于共享的大数据中,不确定数据通过对精确数据的泛化处理来实现,具有均匀分布特性,这一特性不利于精确查询,但可为关联规则的挖掘提供便利条件.首先,依据泛化值之间可能的相交或包含关系,将泛化值进行分层聚类,为了保存与不确定数据集挖掘相关的重要信息,给出了构建不确定频繁模式树的算法,在此基础上,提出了频繁项集挖掘子算法(data mining algorithm for uncertain frequent item-sets,UFI-DM)和关联规则生成子算法(algorithm for generating association rules,GAR),分别用于挖掘频繁项集和生成关联规则,最后,通过理论分析和实验比对,论证了算法的可行性和有效性.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671008 11101212)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20170483)the Fund of University Speciality Construction of Jiangsu Province(Grant No.PPZY2015B109)
文摘In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets are presented. The main results are:(1) A uniform complete poset L is meet uniform continuous iff ↑(U∩↓x) is a uniform Scott set for each x∈L and each uniform Scott set U;(2) A uniform complete poset L is meet uniform continuous iff for each x∈L and each uniform subset S, one has x∧∨ S =∨{x∧s|s∈S}. In particular, a complete lattice L is meet uniform continuous iff L is a complete Heyting algebra;(3) A uniform complete poset is meet uniform continuous iff every principal ideal is meet uniform continuous iff all closed intervals are meet uniform continuous iff all principal filters are meet uniform continuous;(4) A uniform complete poset L is meet uniform continuous if L1 obtained by adjoining a top element 1 to L is a complete Heyting algebra;(5) Finite products and images of uniform continuous projections of meet uniform continuous posets are still meet uniform continuous.
基金National Natural Science Foundation of China(No.62173307)the Key R&D Projects of Science and Technology Department of Zhejiang Province,China(Nos.2023C01158,2022C01065 and 2022C01188)the Fundamental Research Funds of Zhejiang Sci-Tech University,China(No.22242298-Y)。
文摘The plenum chamber of a heat setting machine is a key structure for distributing hot air to different air channels.Its outlet velocity uniformity directly determines the heating uniformity of textiles,significantly affecting the heat setting performance.In a traditional heat setting machine,the outlet airflow maldistribution of the plenum chamber still exists.In this study,a novel plenum chamber with an airfoil baffle was established to improve the uniformity of the velocity distribution at the outlet in a heat setting machine.The structural influence of the plenum chamber on the velocity distribution was investigated using a computational fluid dynamics program.It was found that a chamber with a smaller outlet partition thickness had a better outlet velocity uniformity.The structural optimization of the plenum chamber was conducted using the particle swarm optimization algorithm.The outlet partition thickness,the transverse distance and the longitudinal distance of the optimized plenum chamber were 20,686.2 and 274.6 mm,respectively.Experiments were carried out.The experimental and simulated results showed that the optimized plenum chamber with an airfoil baffle could improve the outlet velocity uniformity.The air outlet velocity uniformity index of the optimized plenum chamber with an airfoil baffle was 4.75%higher than that of the plenum chamber without an airfoil baffle and 5.98%higher than that of the conventional chamber with a square baffle in a commercial heat setting machine.
基金supported in part by the NSFC-Zhejiang Joint Fund of the Integration of Informatization and Industrialization(U1609218)NSFC(61772312,61373078,61772253)+1 种基金the Key Research and Development Project of Shandong Province(2017GGX10110)NSF of Shandong Province(ZR2016FM21,ZR2016FM13)
文摘Image segmentation is a key and fundamental problem in image processing,computer graphics,and computer vision.Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation.However,poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation.In this paper,we present a region consistency constraint term to measure the regional consistency on both sides of the boundary,this term defines the boundary of the image within a range,and hence increases the stability of the level set model.The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary.Furthermore,this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour.The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary.
基金supported by the National Natural Science Foundation of China(11671252)supported by the National Natural Science Foundation of China(11771278)
文摘In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.
文摘In this article sharper estimates on the radii of absorbing sets for the Kuramoto_Sivashinsky equation are given. It is proved that radii of absorbing sets will decay to zero as the coefficient of viscosity tends to a certain critical value, which is more reasonable in the physical sence compared with classical results.
基金Supported by the National Science Foundation of China (10671180) and Jiangsu University (05JDG041)
文摘In this paper, we study the intersection of Mcmullen set with its rational translation. The main difficulty is that the generating structure of the intersection. By the radix expansion of translating vector, we give its fractal characterization. We find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from translating the vector （x,y） with its radix expansion.
基金Supported by the Natural Science Foundation of Shanxi Province（2008011010） Supported by the Scientific Research and Key Subject Foundation of University of Science and Technology of Suzhou
文摘In this paper,the definition of absolutely balanced and uniformly balanced for graphs are introduced,the difference between balance graphs are pointed out.Using（p,p＋1）-graph as an example,we explained the existence of this difference and obtained some new results.
基金the Natural Science Foundation of Sichuan Education Department of China (Nos.2003A081 and SZD0406)
文摘First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.
基金supported by the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NNSF of China(12371312)+1 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the project cooperation between Guangxi Normal University and Yulin Normal University.
文摘This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.
基金Supported by Science and Technology Fund for Basic Research of Guizhou Province([2020]1Y010)National Nature Sciences Foundation of China(11901260,12071096,12501342)Specialized Fund for the Doctoral Development of Kaili University(BS202502028)。
文摘The upper bound on the model error will be decreased when the mean square error and the maximum distance deviation are sufficiently small in the uniform designs for mixture experiments and the design is more robust for the model.However,the analytical expressions of MSED and MD are currently only available in the hypercube,but both types of deviations in other studies are just approximations.Although it can obtain good approximations in the low-dimensional case,the calculation will be more complicated for an experiment with more variables.Therefore,in this paper,an algorithm based on lattice point partitioning design is proposed to obtain the analytical expression of the MSED and MD in the region covered by the lattice points.Furthermore,the design’s optimality is considered and illustrated by examples under the same uniformity.
基金Supported by NSFC(Grant Nos.12071389,12471132)the Natural Science Foundation of Fujian Province(Grant No.2024J01028)+1 种基金Fujian Province Science Foundation for Youths(Grant No.2022J05279)Xiamen University of Technology high-level talents research launch project(Grant No.YKJ22012R)。
文摘Let K be a(bounded)closed uniformly convex subset of a Banach space X.We show that(i)the nearest point map is well-defined and always continuous from X onto K,(ii)there is a reflexive space Y with a uniform rotund in every direction norm such that Y contains K as a subset and the nearest point map PK:Y→K is uniformly continuous from any bounded set containing K onto K.
文摘云计算为大数据提供了展示和共享的平台.为了防止隐私泄露,这些数据中往往包含人为添加的不确定因素,如何挖掘这些不确定数据是大数据共享亟待解决的问题.在用于共享的大数据中,不确定数据通过对精确数据的泛化处理来实现,具有均匀分布特性,这一特性不利于精确查询,但可为关联规则的挖掘提供便利条件.首先,依据泛化值之间可能的相交或包含关系,将泛化值进行分层聚类,为了保存与不确定数据集挖掘相关的重要信息,给出了构建不确定频繁模式树的算法,在此基础上,提出了频繁项集挖掘子算法(data mining algorithm for uncertain frequent item-sets,UFI-DM)和关联规则生成子算法(algorithm for generating association rules,GAR),分别用于挖掘频繁项集和生成关联规则,最后,通过理论分析和实验比对,论证了算法的可行性和有效性.
