A module M is called closed weak supplemented if for any closed submodule N of M, there is a submodule K of M such that M=K+N and K∩N<<M. Any direct summand of closed weak supplemented module is also closed wea...A module M is called closed weak supplemented if for any closed submodule N of M, there is a submodule K of M such that M=K+N and K∩N<<M. Any direct summand of closed weak supplemented module is also closed weak supplemented. Any nonsingular image of closed weak supplemented module is closed weak supplemented. Nonsingular V-rings in which all nonsingular modules are closed weak supplemented are characterized in Section 4.展开更多
Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.
In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-...In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M C^n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S^(2n-1) M are great circles.展开更多
In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinea...In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinear operator from K into E* (i. e.,the dual space of E) and S is a nonlinear operator from K into E. Our results are the essential improvements and extension of the results obtained previously by several authors including Thera,Ding,and Zeng.展开更多
In this paper, a new Ky Fan matching theorem is established in noncompact L-convex spaces. As applications, a fixed point theorem and equilibrium existence theorems for systems of general quasiequilibrium problems and...In this paper, a new Ky Fan matching theorem is established in noncompact L-convex spaces. As applications, a fixed point theorem and equilibrium existence theorems for systems of general quasiequilibrium problems and systems of quasiequilibrium problems in noncompact L-convex spaces are obtained.展开更多
Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment,vehicles,aircraft,piping systems,fluid flow,and even external movement of the human body.A portion...Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment,vehicles,aircraft,piping systems,fluid flow,and even external movement of the human body.A portion of the vibrational energy can be recovered using piezoelectric transduction and stored for subsequent smart system utilization for applications including powering wireless sensor devices for health condition monitoring of rotating machines and defence communication technology.The vibration environment in the considered application areas is varied and often changes over time and can have components in three perpendicular directions,simultaneously or singularly.This paper presents the development of analytical methods for modeling of self-powered cantilevered piezoelectric bimorph beams with tip mass under simultaneous longitudinal and transverse input base motions utilizing the weak and strong forms of Hamiltonian’s principle and space-and time-dependent eigenfunction series which were further formulated using orthonormalization.The reduced constitutive electromechanical equations of the cantilevered piezoelectric bimorph were subsequently analyzed using Laplace transforms and frequency analysis to give multi-mode frequency response functions(FRFs).The validation between theoretical and experimental results at the single mode of eigenfunction solutions reduced from multi-mode FRFs is also given.展开更多
基金Project (No. 102028) supported by the Natural Science Foundation of Zhejiang Province, China
文摘A module M is called closed weak supplemented if for any closed submodule N of M, there is a submodule K of M such that M=K+N and K∩N<<M. Any direct summand of closed weak supplemented module is also closed weak supplemented. Any nonsingular image of closed weak supplemented module is closed weak supplemented. Nonsingular V-rings in which all nonsingular modules are closed weak supplemented are characterized in Section 4.
文摘Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.
基金supported by the National Natural Science Foundation of China(Nos.11271304,11171277)the Program for New Century Excellent Talents in University(No.NCET-13-0510)+1 种基金the Fujian Province Natural Science Funds for Distinguished Young Scholars(No.2013J06001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M C^n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S^(2n-1) M are great circles.
文摘In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinear operator from K into E* (i. e.,the dual space of E) and S is a nonlinear operator from K into E. Our results are the essential improvements and extension of the results obtained previously by several authors including Thera,Ding,and Zeng.
基金Supported by the Natural Science Foundation of Guizhou Province (Grant No.[2011]2093)the Natural Science Research Foundation of Guizhou Provincial Education Department (Grant No.2008072)
文摘In this paper, a new Ky Fan matching theorem is established in noncompact L-convex spaces. As applications, a fixed point theorem and equilibrium existence theorems for systems of general quasiequilibrium problems and systems of quasiequilibrium problems in noncompact L-convex spaces are obtained.
文摘Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment,vehicles,aircraft,piping systems,fluid flow,and even external movement of the human body.A portion of the vibrational energy can be recovered using piezoelectric transduction and stored for subsequent smart system utilization for applications including powering wireless sensor devices for health condition monitoring of rotating machines and defence communication technology.The vibration environment in the considered application areas is varied and often changes over time and can have components in three perpendicular directions,simultaneously or singularly.This paper presents the development of analytical methods for modeling of self-powered cantilevered piezoelectric bimorph beams with tip mass under simultaneous longitudinal and transverse input base motions utilizing the weak and strong forms of Hamiltonian’s principle and space-and time-dependent eigenfunction series which were further formulated using orthonormalization.The reduced constitutive electromechanical equations of the cantilevered piezoelectric bimorph were subsequently analyzed using Laplace transforms and frequency analysis to give multi-mode frequency response functions(FRFs).The validation between theoretical and experimental results at the single mode of eigenfunction solutions reduced from multi-mode FRFs is also given.
