In this contribution, my main attention is paid to the study of the geometric phase ora two-level system.Asymptotic expansion of the eigenvalue and analytic information are obtained. The results are illustrated with a...In this contribution, my main attention is paid to the study of the geometric phase ora two-level system.Asymptotic expansion of the eigenvalue and analytic information are obtained. The results are illustrated with an application to a specific atomic system.展开更多
This paper focuses on the robust H-infinity reliable control for a class of nonlinear neutral delay systems with uncertainties and actuator failures. We design a state feedback controller in terms of linear matrix ine...This paper focuses on the robust H-infinity reliable control for a class of nonlinear neutral delay systems with uncertainties and actuator failures. We design a state feedback controller in terms of linear matrix inequality(LMI)such that the plant satisfies robust H-infinity performance for all admissible uncertainties, and actuator failures among a prespecified subset of actuators. An example is also given to illustrate the effectiveness of the proposed approach.展开更多
We investigate the entropy squeezing of the nonlinear k-quantum JC model.A definition of squeezing is presented for this system based on the quantum information theory.The utility of the Definition is Illustrated by...We investigate the entropy squeezing of the nonlinear k-quantum JC model.A definition of squeezing is presented for this system based on the quantum information theory.The utility of the Definition is Illustrated by examining squeezing in the information entropy of a nonlinear k-quantum two-level atom.The influence of the atomic coherence and the detuning parameter on the properties of the information entropy and squeezing of the atomic variables is examined.展开更多
In this communication, two-mode nonlinear coherent states are reviewed and special cases are given.Starting from a three-level atom coupled to two modes of radiation with any form of nonlinearities of the two-modefiel...In this communication, two-mode nonlinear coherent states are reviewed and special cases are given.Starting from a three-level atom coupled to two modes of radiation with any form of nonlinearities of the two-modefields, we derive a Raman-coupled effective Hamiltonian by a unitary transformation, evaluated perturbatively in couplingconstants. We use the quantum entropy to measure the degree of entanglement in the time development of an effectivetwo-level atom interacting with two-mode nonlinear-coherent states. The results show that the nonlinearity effect yieldsthe superstructure of atomic Rabi oscillations and the effect of the Stark shift changes the quasiperiod of the field entropyevolution and entanglement between the particle and the field. A possible experimental test of a new effect is proposed.展开更多
A Svec^[1] obtained some results on surfaces in E^3 by the method of quasi-analytic function.This paper gives several global properties on closed surfaces with qenus zero by the similar method, obtains the main resul...A Svec^[1] obtained some results on surfaces in E^3 by the method of quasi-analytic function.This paper gives several global properties on closed surfaces with qenus zero by the similar method, obtains the main result that a closed special Weingartan surface with qeus zero in E^3 is a sphere,gives wo conditions for two surfaces with congrence property,and proves that there is not closed Bonnet surface with qenus zero.展开更多
The direct impact excitations of ground-state hydrogen atoms by protons and antiprotons are investigated by using an impact parameter treatment. The calculations are performed within the solution of the coupled differ...The direct impact excitations of ground-state hydrogen atoms by protons and antiprotons are investigated by using an impact parameter treatment. The calculations are performed within the solution of the coupled differential equations arising from the one-center atomic-orbital close-coupling approach as well as the impact parameter version of the first and second Born approximations. We have considered calculations that allow couplings to the n=1-5 states （up to g sub-levels） of the target atom as well as others, which neglect the effect of all states other than the initial and final states of the target atom. The sensitivity of the cross sections to the charge of the projectile is studied. The calculated cross sections are compared with those obtained by previous theoretical and experimental results.展开更多
Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on ...Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on these subspaces is square integrable. In this paper the characterization of admissible condition in terms of the Fourier transform is given. The wavelet transform is defined, and the orthogonal direct sum decomposition of function space L 2(P,dμ l) ) is obtained.展开更多
A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degen...A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.展开更多
A graph property is a set of graphs such that if the set contains some graph G then it also contains each isomorphic copy of G (with the same vertex set). A graph property P on n ventices is said to be elusive, if eve...A graph property is a set of graphs such that if the set contains some graph G then it also contains each isomorphic copy of G (with the same vertex set). A graph property P on n ventices is said to be elusive, if every decision tree algorithm recognizing P must examine all n(n - 1)/2 pairs of ventices in the worst case. Karp conjectured that every nontrivial monotone graph property is elusive. In this paper, this conjecture is proved for some cases. Especially,it is shown that if the abstract simplicial complex of a nontrivial monotone graph property P has dimension not exceeding 5, then P is elusive.展开更多
The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in L^P-norm) for a given function. The classic Delaunay triangula...The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in L^P-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function ‖x‖^2 among all the triangulations with a given set of vertices. For a more general function, a functiondependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure. The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function-depend entoptimal Delaunay triangulation is proved to exist for any given convex continuous function.On an optimal Delaunay triangulation associated with f, it is proved that △↓f at the interior vertices can be exactly recovered by the function values on its neighboring vertices.Since the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.展开更多
We discuss a sequence solutions uE for the E-L equations of the penalized energy defined by Chen-Struwe,We show that the blow-up set of uE is a H^m-2-rectifiable set and its weak limit satisfies a blow-up formula,Cons...We discuss a sequence solutions uE for the E-L equations of the penalized energy defined by Chen-Struwe,We show that the blow-up set of uE is a H^m-2-rectifiable set and its weak limit satisfies a blow-up formula,Consequently,the weak limit will be a stationary harmonic map if and only if the blow-up set is stationary.展开更多
A new type of intelligent CAI system for chemistry is developed inthis paPer based on automated reaJsoning with chemistry knowledge. The systemhas shown its ability to solve chemistry problems, to assist students and ...A new type of intelligent CAI system for chemistry is developed inthis paPer based on automated reaJsoning with chemistry knowledge. The systemhas shown its ability to solve chemistry problems, to assist students and teachersin studies and instruction with the automated reasoning functions. Its open modeof the knowledge base and its unique style of the illterface between the system andhuman provide more opportunities for the users to acquire living knowledge throughactive participation. The automated reasoning based on basic chemistry knowledgealso opened a new approach to the information storage and management of the ICAIsystem for sciences.展开更多
Peristaltic flow of a conducting Jeffrey fluid in an inclined asymmetric channel is investigated. The channel asymmetry is produced by considering a peristaltic wave train on the flexible walls of the channel with dif...Peristaltic flow of a conducting Jeffrey fluid in an inclined asymmetric channel is investigated. The channel asymmetry is produced by considering a peristaltic wave train on the flexible walls of the channel with different amplitudes and phases. The nonlinear governing equations are solved analytically by a perturbation technique. The expressions for the stream function, axial velocity and the pressure rise per wavelength are determined in terms of the Jeffrey number λ1, the Froude number Fr, the perturbation parameter 5, the angle of inclination θ and the phase difference Ф. Effects of the physical parameters on the velocity field and the pumping characteristics are discussed. It is observed that the size of the trapping bolus increase with an increase in the magnetic parameter and the volume flow rate. That is, the magnetic parameter and the volume flow rate have strong influence on the trapping bolus phenomenon.展开更多
This paper aims to explore RLC equivalent circuit synthesis method forreduced-order models of interconnect circuits obtained by Krylov subspace basedmodel order reduction (MOR) methods. To guarantee pure RLC equivalen...This paper aims to explore RLC equivalent circuit synthesis method forreduced-order models of interconnect circuits obtained by Krylov subspace basedmodel order reduction (MOR) methods. To guarantee pure RLC equivalent circuitscan be synthesized, both the structures of input and output incidence matrices and theblock structure of the circuit matrices should be preserved in the reduced-order models.Block structure preserving MOR methods have been well established. In this paper,we propose an embeddable Input-Output structure Preserving Order Reduction(IOPOR) technique to further preserve the structures of input and output incidencematrices. By combining block structure preserving MOR methods and IOPOR technique,we develop an RLC equivalent circuit synthesis method RLCSYN (RLC SYNthesis).Inline diagonalization and regularization techniques are specifically proposedto enhance the robustness of inductance synthesis. The pure RLC model, high modelingaccuracy, passivity guaranteed property and SPICE simulation robustness makeRLCSYN more applicable in interconnect analysis, either for digital IC design ormixedsignal IC simulation.展开更多
文摘In this contribution, my main attention is paid to the study of the geometric phase ora two-level system.Asymptotic expansion of the eigenvalue and analytic information are obtained. The results are illustrated with an application to a specific atomic system.
基金This work was supported by the National Natural Science Foundation of China (No. 60274009)the SRFDP (No. 20020145007)the Natural Science Foundation of Liaoning Province (No.20032020).
文摘This paper focuses on the robust H-infinity reliable control for a class of nonlinear neutral delay systems with uncertainties and actuator failures. We design a state feedback controller in terms of linear matrix inequality(LMI)such that the plant satisfies robust H-infinity performance for all admissible uncertainties, and actuator failures among a prespecified subset of actuators. An example is also given to illustrate the effectiveness of the proposed approach.
文摘We investigate the entropy squeezing of the nonlinear k-quantum JC model.A definition of squeezing is presented for this system based on the quantum information theory.The utility of the Definition is Illustrated by examining squeezing in the information entropy of a nonlinear k-quantum two-level atom.The influence of the atomic coherence and the detuning parameter on the properties of the information entropy and squeezing of the atomic variables is examined.
文摘In this communication, two-mode nonlinear coherent states are reviewed and special cases are given.Starting from a three-level atom coupled to two modes of radiation with any form of nonlinearities of the two-modefields, we derive a Raman-coupled effective Hamiltonian by a unitary transformation, evaluated perturbatively in couplingconstants. We use the quantum entropy to measure the degree of entanglement in the time development of an effectivetwo-level atom interacting with two-mode nonlinear-coherent states. The results show that the nonlinearity effect yieldsthe superstructure of atomic Rabi oscillations and the effect of the Stark shift changes the quasiperiod of the field entropyevolution and entanglement between the particle and the field. A possible experimental test of a new effect is proposed.
文摘A Svec^[1] obtained some results on surfaces in E^3 by the method of quasi-analytic function.This paper gives several global properties on closed surfaces with qenus zero by the similar method, obtains the main result that a closed special Weingartan surface with qeus zero in E^3 is a sphere,gives wo conditions for two surfaces with congrence property,and proves that there is not closed Bonnet surface with qenus zero.
文摘The direct impact excitations of ground-state hydrogen atoms by protons and antiprotons are investigated by using an impact parameter treatment. The calculations are performed within the solution of the coupled differential equations arising from the one-center atomic-orbital close-coupling approach as well as the impact parameter version of the first and second Born approximations. We have considered calculations that allow couplings to the n=1-5 states （up to g sub-levels） of the target atom as well as others, which neglect the effect of all states other than the initial and final states of the target atom. The sensitivity of the cross sections to the charge of the projectile is studied. The calculated cross sections are compared with those obtained by previous theoretical and experimental results.
文摘Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on these subspaces is square integrable. In this paper the characterization of admissible condition in terms of the Fourier transform is given. The wavelet transform is defined, and the orthogonal direct sum decomposition of function space L 2(P,dμ l) ) is obtained.
文摘A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.
文摘A graph property is a set of graphs such that if the set contains some graph G then it also contains each isomorphic copy of G (with the same vertex set). A graph property P on n ventices is said to be elusive, if every decision tree algorithm recognizing P must examine all n(n - 1)/2 pairs of ventices in the worst case. Karp conjectured that every nontrivial monotone graph property is elusive. In this paper, this conjecture is proved for some cases. Especially,it is shown that if the abstract simplicial complex of a nontrivial monotone graph property P has dimension not exceeding 5, then P is elusive.
文摘The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in L^P-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function ‖x‖^2 among all the triangulations with a given set of vertices. For a more general function, a functiondependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure. The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function-depend entoptimal Delaunay triangulation is proved to exist for any given convex continuous function.On an optimal Delaunay triangulation associated with f, it is proved that △↓f at the interior vertices can be exactly recovered by the function values on its neighboring vertices.Since the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.
文摘We discuss a sequence solutions uE for the E-L equations of the penalized energy defined by Chen-Struwe,We show that the blow-up set of uE is a H^m-2-rectifiable set and its weak limit satisfies a blow-up formula,Consequently,the weak limit will be a stationary harmonic map if and only if the blow-up set is stationary.
文摘A new type of intelligent CAI system for chemistry is developed inthis paPer based on automated reaJsoning with chemistry knowledge. The systemhas shown its ability to solve chemistry problems, to assist students and teachersin studies and instruction with the automated reasoning functions. Its open modeof the knowledge base and its unique style of the illterface between the system andhuman provide more opportunities for the users to acquire living knowledge throughactive participation. The automated reasoning based on basic chemistry knowledgealso opened a new approach to the information storage and management of the ICAIsystem for sciences.
文摘Peristaltic flow of a conducting Jeffrey fluid in an inclined asymmetric channel is investigated. The channel asymmetry is produced by considering a peristaltic wave train on the flexible walls of the channel with different amplitudes and phases. The nonlinear governing equations are solved analytically by a perturbation technique. The expressions for the stream function, axial velocity and the pressure rise per wavelength are determined in terms of the Jeffrey number λ1, the Froude number Fr, the perturbation parameter 5, the angle of inclination θ and the phase difference Ф. Effects of the physical parameters on the velocity field and the pumping characteristics are discussed. It is observed that the size of the trapping bolus increase with an increase in the magnetic parameter and the volume flow rate. That is, the magnetic parameter and the volume flow rate have strong influence on the trapping bolus phenomenon.
基金NSFC research project 90307017 and 60676018partly by the National Basic Research Program of China under the grant 2005CB321701+2 种基金partly by Cross-Century Outstanding Scholar’s fund of Ministry of Education of China,partly by the doctoral program foundation of Ministry of Education of China 20050246082partly by Shanghai Dawn Project 200601partly by the National Science Foundation(NSF)under Grant CCR-0306298.
文摘This paper aims to explore RLC equivalent circuit synthesis method forreduced-order models of interconnect circuits obtained by Krylov subspace basedmodel order reduction (MOR) methods. To guarantee pure RLC equivalent circuitscan be synthesized, both the structures of input and output incidence matrices and theblock structure of the circuit matrices should be preserved in the reduced-order models.Block structure preserving MOR methods have been well established. In this paper,we propose an embeddable Input-Output structure Preserving Order Reduction(IOPOR) technique to further preserve the structures of input and output incidencematrices. By combining block structure preserving MOR methods and IOPOR technique,we develop an RLC equivalent circuit synthesis method RLCSYN (RLC SYNthesis).Inline diagonalization and regularization techniques are specifically proposedto enhance the robustness of inductance synthesis. The pure RLC model, high modelingaccuracy, passivity guaranteed property and SPICE simulation robustness makeRLCSYN more applicable in interconnect analysis, either for digital IC design ormixedsignal IC simulation.
