In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are c...In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are consequences of Theorem 2 in this paper if‖B‖2<1.展开更多
In this paper,it is shown that the homoclinic orbits exist in iterated functional systems.so do the solitary wave structures.Moreover,Harr father wavelet,Mexican Cap wavelet,and other closed form wavelets have this so...In this paper,it is shown that the homoclinic orbits exist in iterated functional systems.so do the solitary wave structures.Moreover,Harr father wavelet,Mexican Cap wavelet,and other closed form wavelets have this solitary wave structure,too So wavelet is a certain kind of solitary wave.展开更多
In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-p...In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-parity state ｜ψσ〉. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state ｜ψe〉 and the odd-parity state ｜ψo〉 constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states ｜ψe〉 and ｜ψo〉 is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.展开更多
The law of conservation of energy is one of the most fundamental laws of nature.According to the law of the conservation of energy,the non-linear and non-conservative quasi-variational principle of flexible body dynam...The law of conservation of energy is one of the most fundamental laws of nature.According to the law of the conservation of energy,the non-linear and non-conservative quasi-variational principle of flexible body dynamics is established.The physical meaning of the quasi-stationary value conditions has been explained in non-linear and non-conservative flexible body dynamics.In the case study,the application in spacecraft dynamics is researched.展开更多
Derivatives of discontinuities being Dirac singularities, it is usually not possible to multiply them by discontinuous functions. However in the context of conservation laws we have shown in a recent paper that it can...Derivatives of discontinuities being Dirac singularities, it is usually not possible to multiply them by discontinuous functions. However in the context of conservation laws we have shown in a recent paper that it can be done. We shall make use of this new framework to revisit some upwind methods, mostly characteristic schemes, and show that they can be corrected to be conservative and to work on difficult problems such as Euler＇s equations for fluids. Numerous numerical results are given.展开更多
In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two ca...In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.展开更多
Reactive arthritis or Reiter＇s syndrome characteristically affects the joint of the lower limb in an asymmetrical pattern. Usually it does not affect the axial skeleton or upper limbs. Although cases of atraumatic at...Reactive arthritis or Reiter＇s syndrome characteristically affects the joint of the lower limb in an asymmetrical pattern. Usually it does not affect the axial skeleton or upper limbs. Although cases of atraumatic at- lantoaxial subluxations have been reported, no case of spon- taneous sternoclavicular dislocation in Reiter＇s syndrome has been reported. This paper describes a case of a 26 year old male patient who developed a spontaneous posterior sternoclavicular joint dislocation. No attempt of reduction was made and the patient was managed conservatively with good results.展开更多
文摘In this paper,we consider the following systems x″+ Bx′+ gradG(x,t) = 0.Weak sufficient condition for the existence of a unique 2π-periodic solution of the systems is given and the results in [1]~ [3],[7]~ [8]are consequences of Theorem 2 in this paper if‖B‖2<1.
基金The project supported by National Natural Science Foundation of China under Grant Nos.40045016 and No.40175016
文摘In this paper,it is shown that the homoclinic orbits exist in iterated functional systems.so do the solitary wave structures.Moreover,Harr father wavelet,Mexican Cap wavelet,and other closed form wavelets have this solitary wave structure,too So wavelet is a certain kind of solitary wave.
基金Supported by the Scientific Research Foundation of CUIT under Grant No.KYTZ201024the National Natural Science Foundation of China under Grant Nos.10775100,10974137 the Fund of Theoretical Nuclear Center of HIRFL of China
文摘In terms of reflection transformation of a matrix product state （MPS）, the parity of the MPS is defined. Based on the reflective parity non-conserved MPS pair we construct the even-parity state ｜ψe〉 and the odd-parity state ｜ψσ〉. It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations; instead the even-parity state ｜ψe〉 and the odd-parity state ｜ψo〉 constructed from them have the same long-range correlations for the parity non-conserved block operators. Moreover, the entanglement between a block of n contiguous spins and the rest of the spin chain for the states ｜ψe〉 and ｜ψo〉 is larger than that for the reflective MPS pair except for n = 1, and the difference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1. These characteristics indicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode, and that the parity conserved MPSs contain more correlation, coherence, and entanglement than the parity non-conserved ones.
基金supported by the National Natural Science Foundation of China(Grant No.10272034)the Fundamental Research Funds for the Central Universities of China(Grant No.HEUCF130205)
文摘The law of conservation of energy is one of the most fundamental laws of nature.According to the law of the conservation of energy,the non-linear and non-conservative quasi-variational principle of flexible body dynamics is established.The physical meaning of the quasi-stationary value conditions has been explained in non-linear and non-conservative flexible body dynamics.In the case study,the application in spacecraft dynamics is researched.
文摘Derivatives of discontinuities being Dirac singularities, it is usually not possible to multiply them by discontinuous functions. However in the context of conservation laws we have shown in a recent paper that it can be done. We shall make use of this new framework to revisit some upwind methods, mostly characteristic schemes, and show that they can be corrected to be conservative and to work on difficult problems such as Euler＇s equations for fluids. Numerous numerical results are given.
基金supported by the National Natural Science Foundations of China (Grant Nos.11072218 and 11272287)the Natural Science Foundations of Zhejiang Province of China (Grant No.Y6110314)
文摘In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.
文摘Reactive arthritis or Reiter＇s syndrome characteristically affects the joint of the lower limb in an asymmetrical pattern. Usually it does not affect the axial skeleton or upper limbs. Although cases of atraumatic at- lantoaxial subluxations have been reported, no case of spon- taneous sternoclavicular dislocation in Reiter＇s syndrome has been reported. This paper describes a case of a 26 year old male patient who developed a spontaneous posterior sternoclavicular joint dislocation. No attempt of reduction was made and the patient was managed conservatively with good results.
