In the paper, we study the stability of Hilbert space generalized frames under perturbations. We get some results that are in spirit close to classical results for discrete frames, due to OLE Christensen.
The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient co...The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient conditions for the finite extensions of generalizedBessel sequences to generalized frames or tight generalized frames are provided, and everyresult is illustrated by the corresponding example.展开更多
Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acc...Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average π_(4) and geometric average Π_(4) is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter r goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter γ increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy S_(ABCDI), S_(ABCIDI), S_(ABICIDI) and S_(AIBICIDI) always decrease with the controllable angle θ, while the entropies S_(3-3 non), S_(3-2 non), S_(3-1 non) and S_(3-0 non) first increase with the angle θ and then decrease with it.展开更多
The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's th...The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.展开更多
Based on finite element method and finite strip method, a simplified approach was presented to analyze high rise frame tube structures. The generalized strip element is introduced and then the generalized stiffness ma...Based on finite element method and finite strip method, a simplified approach was presented to analyze high rise frame tube structures. The generalized strip element is introduced and then the generalized stiffness matrices for beam and column line are derived by using the displacement functions that describe the nodal displacements and displacement transforms. Furthermore, the formulas for the generalized stiffness matrix of generalized strip element and load arrays corresponding to the displacement parameters were developed. It is shown through a series of numerical computation that the nodal angular displacements at the same floor in a generalized strip element are approximately identical. A comparison of the finite element method and the finite strip method shows that the simplified approach not only is accurate, but also reduces the number of basic unknown quantities.展开更多
This paper deals with a problem of application generation together with their Graphic User Interface （GUI）. Particularly, the source code generator based on dynamic frames was improved for more effective specificati...This paper deals with a problem of application generation together with their Graphic User Interface （GUI）. Particularly, the source code generator based on dynamic frames was improved for more effective specification of GUI. It＇s too demanding for the developers to have specification of the application that contain all physical coordinates and other details of buttons and other GUI elements. The developed solution for this problem is based on post-processing of generated source code using iterators for specifying coordinates and other values of graphic elements. The paper includes two examples of generating web applications and their GUI.展开更多
The interesting phenomenon of frame dragging which is associated with the rotation of the source in the field of Kerr family is discussed, and the angular velocity of an uncharged test particle is obtained with a stra...The interesting phenomenon of frame dragging which is associated with the rotation of the source in the field of Kerr family is discussed, and the angular velocity of an uncharged test particle is obtained with a straightforward mathematical method.展开更多
This paper proposes the automatic generation of the middle frame and the middle frame automatic coloring method of two-dimensional animation process, users simply given starting key frames and end key frames, Accordin...This paper proposes the automatic generation of the middle frame and the middle frame automatic coloring method of two-dimensional animation process, users simply given starting key frames and end key frames, According to the algorithm proposed in this paper, the system can automatically generate all key frames that in the middle, and based on the starting key frame and termination of key frame color, the generated in the middle of the frame will been automatically chromatically. The experimental results show that, the automatic generation of intermediate frames and the middle frame automatic coloring method of two-dimensional animation is proposed in this paper production process can be successfully used in animation production, greatlyimproving the efficiency of animation.展开更多
Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized ...Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized frames.展开更多
In this paper, we introduce and study the generalized frame in a separableHilbert space H. Using operator-theoretic-methods, we give some conditions for a gen-eralized frame to be a tight frame, a dual frame, or an in...In this paper, we introduce and study the generalized frame in a separableHilbert space H. Using operator-theoretic-methods, we give some conditions for a gen-eralized frame to be a tight frame, a dual frame, or an independent frame in H. We alsoprove some results concerning generalized frame operators.展开更多
In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard gen...In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.展开更多
Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a t...Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？展开更多
In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA （GFMRA）. In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets, and show a gen...In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA （GFMRA）. In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets, and show a general approach to the constructions of non-MRA wavelets. Finally we present two examples to illustrate the theory.展开更多
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable coup...Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.展开更多
The two gate formula for a diffusion X_t in R^n is considered.The formula gives an expressionof the density function of X_t in terms of the path integral of the Brownian bridge starting from xand ending on y at time t.
Motivated by the applications to generalized Howell designs and multiply constant-weight codes, we establish an asymptotic existence theorem for(k, λ)-frames of type g^n with a pair of orthogonal frame resolutions vi...Motivated by the applications to generalized Howell designs and multiply constant-weight codes, we establish an asymptotic existence theorem for(k, λ)-frames of type g^n with a pair of orthogonal frame resolutions via decompositions of edge-colored complete digraphs into prescribed edge-colored subgraphs.展开更多
Motivated by K-frames and fusion frames, we study K-fusion frames in Hilbert spaces. By the means of operator K, frame operators and quotient operators, several necessary and sufficient conditions for a sequence of cl...Motivated by K-frames and fusion frames, we study K-fusion frames in Hilbert spaces. By the means of operator K, frame operators and quotient operators, several necessary and sufficient conditions for a sequence of closed subspaces and weights to be a K-fusion frame are obtained, and operators preserving K-fusion frames are discussed. In particular, we are interested in the K-fusion frames with the structure of unitary systems. Given a unitary system which has a complete wandering subspace, we give a necessary and sufficient condition for a closed subspace to be a K-fusion frame generator.展开更多
文摘In the paper, we study the stability of Hilbert space generalized frames under perturbations. We get some results that are in spirit close to classical results for discrete frames, due to OLE Christensen.
基金partially supported by the National Natural Science Foundation of China(61471410)
文摘The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient conditions for the finite extensions of generalizedBessel sequences to generalized frames or tight generalized frames are provided, and everyresult is illustrated by the corresponding example.
基金partially supported by the 20210414-SIPIPN, Mexico。
文摘Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average π_(4) and geometric average Π_(4) is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter r goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter γ increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy S_(ABCDI), S_(ABCIDI), S_(ABICIDI) and S_(AIBICIDI) always decrease with the controllable angle θ, while the entropies S_(3-3 non), S_(3-2 non), S_(3-1 non) and S_(3-0 non) first increase with the angle θ and then decrease with it.
文摘The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.
基金Fund of Science and Technology Develop-ment of Shanghai ( No.0 2 ZF14 0 5 6)
文摘Based on finite element method and finite strip method, a simplified approach was presented to analyze high rise frame tube structures. The generalized strip element is introduced and then the generalized stiffness matrices for beam and column line are derived by using the displacement functions that describe the nodal displacements and displacement transforms. Furthermore, the formulas for the generalized stiffness matrix of generalized strip element and load arrays corresponding to the displacement parameters were developed. It is shown through a series of numerical computation that the nodal angular displacements at the same floor in a generalized strip element are approximately identical. A comparison of the finite element method and the finite strip method shows that the simplified approach not only is accurate, but also reduces the number of basic unknown quantities.
文摘This paper deals with a problem of application generation together with their Graphic User Interface （GUI）. Particularly, the source code generator based on dynamic frames was improved for more effective specification of GUI. It＇s too demanding for the developers to have specification of the application that contain all physical coordinates and other details of buttons and other GUI elements. The developed solution for this problem is based on post-processing of generated source code using iterators for specifying coordinates and other values of graphic elements. The paper includes two examples of generating web applications and their GUI.
文摘The interesting phenomenon of frame dragging which is associated with the rotation of the source in the field of Kerr family is discussed, and the angular velocity of an uncharged test particle is obtained with a straightforward mathematical method.
文摘This paper proposes the automatic generation of the middle frame and the middle frame automatic coloring method of two-dimensional animation process, users simply given starting key frames and end key frames, According to the algorithm proposed in this paper, the system can automatically generate all key frames that in the middle, and based on the starting key frame and termination of key frame color, the generated in the middle of the frame will been automatically chromatically. The experimental results show that, the automatic generation of intermediate frames and the middle frame automatic coloring method of two-dimensional animation is proposed in this paper production process can be successfully used in animation production, greatlyimproving the efficiency of animation.
基金the National Natural Science Foundation of China (19771056)
文摘Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized frames.
基金Supported by National Natural Science Foundation of China (19971056)
文摘In this paper, we introduce and study the generalized frame in a separableHilbert space H. Using operator-theoretic-methods, we give some conditions for a gen-eralized frame to be a tight frame, a dual frame, or an independent frame in H. We alsoprove some results concerning generalized frame operators.
基金the National Natural Science Foundation of China （No. 10771101） and Chuangxin Funds of Nanjing University of Aeronautics and Astronautics （No. 987561）.
文摘In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.
文摘Generalized sampling in a shift invariant subspace V of L2（R） is considered. A function f in V is processed with different filters Lm and then one tries to reconstruct f from the samples L^mf（j＇k）. We develop a theory of how to do this in the case when V possesses a shift invariant frame. Special attention is paid to the question： How to obtain dual frames with compact support？
文摘In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA （GFMRA）. In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets, and show a general approach to the constructions of non-MRA wavelets. Finally we present two examples to illustrate the theory.
基金supported by the National Natural Science Foundation of China(1127100861072147+1 种基金11071159)the First-Class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project(A13-0101-12-004)
文摘Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.
文摘A new dispersive relation is found and a half-pow tormulas for the generalize Miodek equation under the deeaying conditions at infinity are obtained.
基金This project is supported by the National Natural Science Foundation of China
文摘The two gate formula for a diffusion X_t in R^n is considered.The formula gives an expressionof the density function of X_t in terms of the path integral of the Brownian bridge starting from xand ending on y at time t.
基金supported by National Natural Science Foundation of China(Grant Nos.11431003 and 11471032)Fundamental Research Funds for the Central Universities(Grant Nos.2016JBM071 and 2016JBZ012)
文摘Motivated by the applications to generalized Howell designs and multiply constant-weight codes, we establish an asymptotic existence theorem for(k, λ)-frames of type g^n with a pair of orthogonal frame resolutions via decompositions of edge-colored complete digraphs into prescribed edge-colored subgraphs.
基金Supported by National Natural Science Foundation of China(Grant Nos.11671201 and 11571247)
文摘Motivated by K-frames and fusion frames, we study K-fusion frames in Hilbert spaces. By the means of operator K, frame operators and quotient operators, several necessary and sufficient conditions for a sequence of closed subspaces and weights to be a K-fusion frame are obtained, and operators preserving K-fusion frames are discussed. In particular, we are interested in the K-fusion frames with the structure of unitary systems. Given a unitary system which has a complete wandering subspace, we give a necessary and sufficient condition for a closed subspace to be a K-fusion frame generator.
