In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator esti...In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.展开更多
In this paper, we introduce the definition of L-fuzzy vector subspace, define its dimension by an L-fuzzy natural number. For a finite-dimensional L-fuzzy vector subspace, we prove that the equality holds without any ...In this paper, we introduce the definition of L-fuzzy vector subspace, define its dimension by an L-fuzzy natural number. For a finite-dimensional L-fuzzy vector subspace, we prove that the equality holds without any restricted conditions. At the same time, we deduce that the formula holds.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
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
We identify the functions whose polynomial multiples are weak＊ dense in Qp spaces and prove that if ｜f（z）｜ ≥ ｜g（z）｜ and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operato...We identify the functions whose polynomial multiples are weak＊ dense in Qp spaces and prove that if ｜f（z）｜ ≥ ｜g（z）｜ and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mx on Qp spaces is cellular indecomposable.展开更多
This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from t...This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.展开更多
By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equi...By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.展开更多
With the rapid integration of renewable energy sources,modern power systems are increasingly challenged by heightened volatility and uncertainty.Doubly-fed variable-speed pumped storage units(DFVS-PSUs)have emerged as...With the rapid integration of renewable energy sources,modern power systems are increasingly challenged by heightened volatility and uncertainty.Doubly-fed variable-speed pumped storage units(DFVS-PSUs)have emerged as promising technologies for mitigating grid oscillations and enhancing system flexibility.However,the excitation converters in DFVS-PSUs are prone to significant issues such as elevated common-mode voltage(CMV)and neutral-point voltage(NPV)fluctuations,which can lead to electromagnetic interference and degrade transient performance.To address these challenges,an optimized virtual space vector pulse width modulation(OVSVPWM)strategy is proposed,aiming to suppress CMV and NPV simultaneously through coordinated multi-objective control.Specifically,a dynamic feedback mechanism is introduced to adjust the balancing factor of basic vectors in the synthesized virtual small vector in real-time,achieving autonomous balancing of the NPV.To address the excessive switching actions introduced by the OVSVPWM strategy,a phase duty ratio-based sequence reconstruction method is adopted,which reduces the total number of switching actions to half of the original.A zero-level buffering scheme is employed to reconstruct the single-phase voltage-level output sequence,achieving peak CMV suppression down to udc/6.Simulation results demonstrate that the proposed strategy significantly improves electromagnetic compatibility and operational stability while maintaining high power quality.展开更多
This paper analyzes the global competitive landscape of smartphone technological innovation capacity using the latent semantic indexing(LSI)and the vector space model(VSM).It integrates the theory of technological eco...This paper analyzes the global competitive landscape of smartphone technological innovation capacity using the latent semantic indexing(LSI)and the vector space model(VSM).It integrates the theory of technological ecological niches and evaluates four key dimensions:patent quality,energy efficiency engineering,technological modules,and intelligent computing power.The findings reveal that USA has established strong technological barriers through standard-essential patents(SEPs)in wireless communication and integrated circuits.In contrast,Chinese mainland firms rely heavily on fundamental technologies.Qualcomm Inc.in USA and Taiwan Semiconductor Manufacturing Company(TSMC)in Chineses Taiwan have built a comprehensive patent porfolio in energy efficiency engineering.While Chinese mainland faces challenges in advancing dynamic frequency modulation algorithms and high-end manufacturing processes.Huawei Inc.in Chinese mainland leads in 5G module technology but struggles with ecosystem collaboration.Semiconductor manufacturing and radio frequency(RF)components still rely on external suppliers.This highlights the urgent need for innovation in new materials and open'source architectures.To enhance intelligent computing power,Chinese mainland firms must address coordination challenges.They should adopt scenario-driven technological strategies and build a comprehensive ecosystem that includes hardware,operating systems,and developer networks.展开更多
Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector...Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.展开更多
In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-...In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.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
New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations a...New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.展开更多
The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we ...The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.展开更多
In this paper, our focus is to investigate the notion of irresolute topological vector spaces. Irresolute topological vector spaces are defined by using semi open sets and irresolute mappings. The notion of irresolute...In this paper, our focus is to investigate the notion of irresolute topological vector spaces. Irresolute topological vector spaces are defined by using semi open sets and irresolute mappings. The notion of irresolute topological vector spaces is analog to the notion of topological vector spaces, but mathematically it behaves differently. An example is given to show that an irresolute topological vector space is not a topological vector space. It is proved that: 1) Irresolute topological vector spaces possess open hereditary property;2) A homomorphism of irresolute topological vector spaces is irresolute if and only if it is irresolute at identity element;3) In irresolute topological vector spaces, the scalar multiple of semi compact set is semi compact;4) In irresolute topological vector spaces, every semi open set is translationally invariant.展开更多
In this paper, the concept of I-bornological vector spaces and two examples of the spaces are given. Two methods on constructing new I-bornological vector spaces are discussed,one is using a（crisp） bornological vect...In this paper, the concept of I-bornological vector spaces and two examples of the spaces are given. Two methods on constructing new I-bornological vector spaces are discussed,one is using a（crisp） bornological vector space to induce an I-bornological vector space, the other is utilizing I-bornological linear maps to generate an I-bornological vector space.展开更多
In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence t...In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].展开更多
In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector sp...In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki＇s method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.展开更多
The aim of the present paper is to investigate intrinsically the notion of a concircular π-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the c...The aim of the present paper is to investigate intrinsically the notion of a concircular π-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of concurrent vector field in Finsler geometry. Some properties of concircular π-vector fields are obtained. Different types of recurrence are discussed. The effect of the existence of a concircular π-vector field on some important special Finsler spaces is investigated. Almost all results obtained in this work are formulated in a coordinate-free form.展开更多
In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasico...In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.展开更多
文摘In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.
文摘In this paper, we introduce the definition of L-fuzzy vector subspace, define its dimension by an L-fuzzy natural number. For a finite-dimensional L-fuzzy vector subspace, we prove that the equality holds without any restricted conditions. At the same time, we deduce that the formula holds.
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.
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 NNSF of China (10771130)Specialized Research Fund for the Doctoral Program of High Education (2007056004)+1 种基金NSF of GuangdongProvince (10151503101000025)NSF of Fujian Province (2009J01004)
文摘We identify the functions whose polynomial multiples are weak＊ dense in Qp spaces and prove that if ｜f（z）｜ ≥ ｜g（z）｜ and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mx on Qp spaces is cellular indecomposable.
基金Research supported in part by he National Sience Foundation Grant # DMS93-15963
文摘This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.
基金This project was supported by the NSF of Sichuan Education of China(2003A081)and SZD0406
文摘By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.
文摘With the rapid integration of renewable energy sources,modern power systems are increasingly challenged by heightened volatility and uncertainty.Doubly-fed variable-speed pumped storage units(DFVS-PSUs)have emerged as promising technologies for mitigating grid oscillations and enhancing system flexibility.However,the excitation converters in DFVS-PSUs are prone to significant issues such as elevated common-mode voltage(CMV)and neutral-point voltage(NPV)fluctuations,which can lead to electromagnetic interference and degrade transient performance.To address these challenges,an optimized virtual space vector pulse width modulation(OVSVPWM)strategy is proposed,aiming to suppress CMV and NPV simultaneously through coordinated multi-objective control.Specifically,a dynamic feedback mechanism is introduced to adjust the balancing factor of basic vectors in the synthesized virtual small vector in real-time,achieving autonomous balancing of the NPV.To address the excessive switching actions introduced by the OVSVPWM strategy,a phase duty ratio-based sequence reconstruction method is adopted,which reduces the total number of switching actions to half of the original.A zero-level buffering scheme is employed to reconstruct the single-phase voltage-level output sequence,achieving peak CMV suppression down to udc/6.Simulation results demonstrate that the proposed strategy significantly improves electromagnetic compatibility and operational stability while maintaining high power quality.
基金supported in part by the National Social Science Foundation of China(No.20BGL203).
文摘This paper analyzes the global competitive landscape of smartphone technological innovation capacity using the latent semantic indexing(LSI)and the vector space model(VSM).It integrates the theory of technological ecological niches and evaluates four key dimensions:patent quality,energy efficiency engineering,technological modules,and intelligent computing power.The findings reveal that USA has established strong technological barriers through standard-essential patents(SEPs)in wireless communication and integrated circuits.In contrast,Chinese mainland firms rely heavily on fundamental technologies.Qualcomm Inc.in USA and Taiwan Semiconductor Manufacturing Company(TSMC)in Chineses Taiwan have built a comprehensive patent porfolio in energy efficiency engineering.While Chinese mainland faces challenges in advancing dynamic frequency modulation algorithms and high-end manufacturing processes.Huawei Inc.in Chinese mainland leads in 5G module technology but struggles with ecosystem collaboration.Semiconductor manufacturing and radio frequency(RF)components still rely on external suppliers.This highlights the urgent need for innovation in new materials and open'source architectures.To enhance intelligent computing power,Chinese mainland firms must address coordination challenges.They should adopt scenario-driven technological strategies and build a comprehensive ecosystem that includes hardware,operating systems,and developer networks.
文摘Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.
基金supported by the Natural Science Foundation of Sichuan Education Department of China(No. 07ZA092)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.
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New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.
文摘The purpose of this paper is to construct near-vector spaces using a result by Van der Walt, with Z<sub>p</sub> for p a prime, as the underlying near-field. There are two notions of near-vector spaces, we focus on those studied by André [1]. These near-vector spaces have recently proven to be very useful in finite linear games. We will discuss the construction and properties, give examples of these near-vector spaces and give its application in finite linear games.
文摘In this paper, our focus is to investigate the notion of irresolute topological vector spaces. Irresolute topological vector spaces are defined by using semi open sets and irresolute mappings. The notion of irresolute topological vector spaces is analog to the notion of topological vector spaces, but mathematically it behaves differently. An example is given to show that an irresolute topological vector space is not a topological vector space. It is proved that: 1) Irresolute topological vector spaces possess open hereditary property;2) A homomorphism of irresolute topological vector spaces is irresolute if and only if it is irresolute at identity element;3) In irresolute topological vector spaces, the scalar multiple of semi compact set is semi compact;4) In irresolute topological vector spaces, every semi open set is translationally invariant.
基金Supported by the National Natural Science Foundation of China(Grant No.11301281)the Natural Science Foundation of Anhui Higher Education Institution(Grant No.KJ2012A136)
文摘In this paper, the concept of I-bornological vector spaces and two examples of the spaces are given. Two methods on constructing new I-bornological vector spaces are discussed,one is using a（crisp） bornological vector space to induce an I-bornological vector space, the other is utilizing I-bornological linear maps to generate an I-bornological vector space.
文摘In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].
基金Supported by the National Natural Science Foundation of China(Grant No.11401262)
文摘In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169（3）： 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki＇s method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.
文摘The aim of the present paper is to investigate intrinsically the notion of a concircular π-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of concurrent vector field in Finsler geometry. Some properties of concircular π-vector fields are obtained. Different types of recurrence are discussed. The effect of the existence of a concircular π-vector field on some important special Finsler spaces is investigated. Almost all results obtained in this work are formulated in a coordinate-free form.
基金supported by the Scientific Research Fun of Sichuan Normal University (09ZDL04)the Sichuan Province Leading Academic Discipline Project (SZD0406)
文摘In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.
