Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they ...Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they occur,the body parts that are involved,and the frequency at which they present.For example,tremors can be mild to severe,are stress sensitive,and can affect arms,legs,or the head (Dirkx and Bologna,2022).展开更多
This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate v...This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate values of the energy spectrum of the whole class.展开更多
The O( N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions.The problem is directly related to that of a quantum double well anharmonic o...The O( N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions.The problem is directly related to that of a quantum double well anharmonic oscillator in an external field.A finite dimensional matrix equation for the problem is constructed explicitly,along with analytical expressions for some excited states in the system.The corresponding Niven equations for determining the polynomial solutions for the problem are given.展开更多
With the （ k, n ）-threshold scheme of secret sharing in the field of information security technology as an application background, the concept of set （ k, n ）-exact cover is presented in this paper. It is a modifi...With the （ k, n ）-threshold scheme of secret sharing in the field of information security technology as an application background, the concept of set （ k, n ）-exact cover is presented in this paper. It is a modification of the original concept of set covering problem. It is also different from the concept of exact cover defined by J.E. Hopcmft. Some properties of （k, n ） -exact cover are investigated; a sufficient condition for a set to be （ k, n ） -exactly coverable is given. It follows that a feasible assignment scheme of a set for the （ k, n） -exact eover is obtained if this set satisfies the sufficient condition.展开更多
We study a mixed spin-（3/2,1） ladder system with antiferromagnetic rung coupling and next-nearest-neighbor interaction.The exactly solved Ising-chain model is employed to investigate the ground-state properties and ...We study a mixed spin-（3/2,1） ladder system with antiferromagnetic rung coupling and next-nearest-neighbor interaction.The exactly solved Ising-chain model is employed to investigate the ground-state properties and thermodynamics of the low-dimensional ladder system.Our results show that the competition between different exchange couplings brings in a large variety of ground states characterized by various values of normalized magnetization equal to 0,1/5,2/5,3/5,1.Moreover,an interesting double-peak structure is also detected in the thermal dependence of magnetic susceptibility and specific heat when the frustration comes into play.It is shown that the double-peak phenomenon at zero-field for the case of AF2 ground-state arises from the very strong antiferromagnetic rung coupling,while other cases are attributed to the excitations induced by temperature and external field around the phase boundary.展开更多
[问][380]在《大学英语》(修订本)精读第三册(1998年8月第2次印刷)p.213上Cloze练习中有一个句子:It was April 30,1945,exactly 12years and 3 months to the day Hitler had initiated theenormous power of the Third Reich.请问句中...[问][380]在《大学英语》(修订本)精读第三册(1998年8月第2次印刷)p.213上Cloze练习中有一个句子:It was April 30,1945,exactly 12years and 3 months to the day Hitler had initiated theenormous power of the Third Reich.请问句中exactly与to the day能连用吗? [答]句中的exactly与to the day不能连用。展开更多
We propose an algebraic model, presenting individual contributions separately in the system of interest, for the exact solutions of one-dimensional Poisson-Schr?dinger equations used generally in semiconductor device ...We propose an algebraic model, presenting individual contributions separately in the system of interest, for the exact solutions of one-dimensional Poisson-Schr?dinger equations used generally in semiconductor device simulations. The model presented here reveals an interesting relation between the corresponding Poisson and Schr?dinger equation for the physical structure considered, which leads to closed solutions without solving the required electrostatic equation.展开更多
A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, th...A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.展开更多
A two-fold Cayley tree with fully q-coordinated sites is constructed and the spin-1 Blume-Capel model in the presence of an external magnetic field is solved exactly. The relevant properties such as magnetization m an...A two-fold Cayley tree with fully q-coordinated sites is constructed and the spin-1 Blume-Capel model in the presence of an external magnetic field is solved exactly. The relevant properties such as magnetization m and square magnetic moment q are investigated as functions of temperature and external magnetic fieId both for ferromagnetic and antiferromagnetic couplings. In the study, we propose a possible mechanism of the plateau based on the exchange couplings.展开更多
Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordi...Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.展开更多
A solvable Anderson lattice model is formulated.The exact eigenstates of model Hamiltonian are constructed by using the Bethe ansatz.The Be the ansatz equations are obtained from the periodic boundary conditions.
Finding exact solutions for Riemann–Liouville(RL)fractional equations is very difficult.We propose a general method of separation of variables to study the problem.We obtain several general results and,as application...Finding exact solutions for Riemann–Liouville(RL)fractional equations is very difficult.We propose a general method of separation of variables to study the problem.We obtain several general results and,as applications,we give nontrivial exact solutions for some typical RL fractional equations such as the fractional Kadomtsev–Petviashvili equation and the fractional Langmuir chain equation.In particular,we obtain non-power functions solutions for a kind of RL time-fractional reaction–diffusion equation.In addition,we find that the separation of variables method is more suited to deal with high-dimensional nonlinear RL fractional equations because we have more freedom to choose undetermined functions.展开更多
The non PT-symmetric exactly solvable Hamiltonian describing a system of a fermion in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction is considered. We poin...The non PT-symmetric exactly solvable Hamiltonian describing a system of a fermion in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction is considered. We point out all properties of both of the original Mandal and the original Jaynes-Cummings Hamitonians. It is shown that these Hamiltonians are respectively pseudo-hermitian and hermitian REF _Ref536606452 \r \h \* MERGEFORMAT [1] REF _Ref536606454 \r \h [2]. Like the direct approach to invariant vector spaces used in Refs. REF _Ref536606456 \r \h [3] REF _Ref536606457 \r \h [4], we reveal the exact solvability of both the Mandal and Jaynes-Cummings Hamiltonians after expressing them in the position operator and the impulsion operator.展开更多
In this paper,we present a Runge-Kutta Discontinuous Galerkin(RKDG)method for solving the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations under the Lagrangian framework.The fluid part of the idea...In this paper,we present a Runge-Kutta Discontinuous Galerkin(RKDG)method for solving the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations under the Lagrangian framework.The fluid part of the ideal MHD equations along with z-component of the magnetic induction equation are discretized using a DG method based on linear Taylor expansions.By using the magnetic fluxfreezing principle which is the integral form of the magnetic induction equation of the ideal MHD,an exactly divergence-free numerical magnetic field can be obtained.The nodal velocities and the corresponding numerical fluxes are explicitly calculated by solving multidirectional approximate Riemann problems.Two kinds of limiter are proposed to inhibit the non-physical oscillation around the shock wave,and the second limiter can eliminate the phenomenon of mesh tangling in the simulations of the rotor problems.This Lagrangian RKDG method conserves mass,momentum,and total energy.Several numerical tests are presented to demonstrate the accuracy and robustness of the proposed scheme.展开更多
By discussing the zeros of periodic.solutions we give in this paper a criterion for the existence of exactly n+1 simple 4-periodic solutions of the differential delay equation x(T)= -f(x(t-1)).
An n-tournament T_n is called k-reducible if auy of its (n--k+1)-subtourna-ments is reducible. An n-tournament T_n is called exactly k-reducible if it is k-reducible but not (k+1)-reducible. The numbers of all isomorp...An n-tournament T_n is called k-reducible if auy of its (n--k+1)-subtourna-ments is reducible. An n-tournament T_n is called exactly k-reducible if it is k-reducible but not (k+1)-reducible. The numbers of all isomorphic classes of ntournaments and strong n-tournaments arc denoted by t(n) and s(n) respectively.展开更多
The phenomenon Anderson localization explains the metalinsulator transition in a material with the increase of disorder and its electrons’transport change from diffusive into localized.The study of the Anderson local...The phenomenon Anderson localization explains the metalinsulator transition in a material with the increase of disorder and its electrons’transport change from diffusive into localized.The study of the Anderson localization has been extended to many fields of physics,including the quasiperiodic or incommensurate systems.展开更多
A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydr...A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations written in semi-Lagrangian formulation on moving quadrilateral meshes.In this method,the fluid part of the ideal MHD equations along with zcomponent of the magnetic induction equation is discretized by the RKDG method as our previous paper[47].The numerical magnetic field in the remaining two directions(i.e.,x and y)are constructed by using the magnetic flux-freezing principle which is the integral form of the magnetic induction equation of the ideal MHD.Since the divergence of the magnetic field in 2D is independent of its z-direction component,an exactly divergence-free numerical magnetic field can be obtained by this treatment.We propose a new nodal solver to improve the calculation accuracy of velocities of the moving meshes.A limiter is presented for the numerical solution of the fluid part of the MHD equations and it can avoid calculating the complex eigen-system of the MHD equations.Some numerical examples are presented to demonstrate the accuracy,non-oscillatory property and preservation of the exactly divergence-free property of our method.展开更多
In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regiona...In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.展开更多
基金supported by the German Research Foundation (SFB-TR 295)(to MM)。
文摘Pathological tremor is one of the cardinal symptoms in Parkinson's disease (PD).Tremor is comprised of involuntary,rhythmic,a nd oscillating movements that can vary according to the circumstances under which they occur,the body parts that are involved,and the frequency at which they present.For example,tremors can be mild to severe,are stress sensitive,and can affect arms,legs,or the head (Dirkx and Bologna,2022).
文摘This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate values of the energy spectrum of the whole class.
基金Support by the U.S.National Science Foundation(PHY-0500291&OCI-0904874)the Southeastern Universities Research Association,the Natural Science Foundation of China(11175078)+1 种基金the Doctoral Program Foundation of State Education Ministry of China(20102136110002)the LSU-LNNU joint research program(9961).
文摘The O( N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions.The problem is directly related to that of a quantum double well anharmonic oscillator in an external field.A finite dimensional matrix equation for the problem is constructed explicitly,along with analytical expressions for some excited states in the system.The corresponding Niven equations for determining the polynomial solutions for the problem are given.
基金Supported by the National Natural Science Foundation of China (No. 60673053 90718011 )
文摘With the （ k, n ）-threshold scheme of secret sharing in the field of information security technology as an application background, the concept of set （ k, n ）-exact cover is presented in this paper. It is a modification of the original concept of set covering problem. It is also different from the concept of exact cover defined by J.E. Hopcmft. Some properties of （k, n ） -exact cover are investigated; a sufficient condition for a set to be （ k, n ） -exactly coverable is given. It follows that a feasible assignment scheme of a set for the （ k, n） -exact eover is obtained if this set satisfies the sufficient condition.
基金Project supported by the National Natural Science Foundation of China(Grant No.11547236)the General Project of the Education Department of Liaoning Province,China(Grant No.L2015130)+1 种基金the Fundamental Research Funds for the Central Universities,China(Grant Nos.DC201501065 and DCPY2016014)the Doctoral Starting-up Foundation of Dalian Nationalities University,China
文摘We study a mixed spin-（3/2,1） ladder system with antiferromagnetic rung coupling and next-nearest-neighbor interaction.The exactly solved Ising-chain model is employed to investigate the ground-state properties and thermodynamics of the low-dimensional ladder system.Our results show that the competition between different exchange couplings brings in a large variety of ground states characterized by various values of normalized magnetization equal to 0,1/5,2/5,3/5,1.Moreover,an interesting double-peak structure is also detected in the thermal dependence of magnetic susceptibility and specific heat when the frustration comes into play.It is shown that the double-peak phenomenon at zero-field for the case of AF2 ground-state arises from the very strong antiferromagnetic rung coupling,while other cases are attributed to the excitations induced by temperature and external field around the phase boundary.
文摘[问][380]在《大学英语》(修订本)精读第三册(1998年8月第2次印刷)p.213上Cloze练习中有一个句子:It was April 30,1945,exactly 12years and 3 months to the day Hitler had initiated theenormous power of the Third Reich.请问句中exactly与to the day能连用吗? [答]句中的exactly与to the day不能连用。
文摘We propose an algebraic model, presenting individual contributions separately in the system of interest, for the exact solutions of one-dimensional Poisson-Schr?dinger equations used generally in semiconductor device simulations. The model presented here reveals an interesting relation between the corresponding Poisson and Schr?dinger equation for the physical structure considered, which leads to closed solutions without solving the required electrostatic equation.
文摘A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
文摘A two-fold Cayley tree with fully q-coordinated sites is constructed and the spin-1 Blume-Capel model in the presence of an external magnetic field is solved exactly. The relevant properties such as magnetization m and square magnetic moment q are investigated as functions of temperature and external magnetic fieId both for ferromagnetic and antiferromagnetic couplings. In the study, we propose a possible mechanism of the plateau based on the exchange couplings.
文摘Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.
基金Supported by the National Natural Science Foundation of China。
文摘A solvable Anderson lattice model is formulated.The exact eigenstates of model Hamiltonian are constructed by using the Bethe ansatz.The Be the ansatz equations are obtained from the periodic boundary conditions.
文摘Finding exact solutions for Riemann–Liouville(RL)fractional equations is very difficult.We propose a general method of separation of variables to study the problem.We obtain several general results and,as applications,we give nontrivial exact solutions for some typical RL fractional equations such as the fractional Kadomtsev–Petviashvili equation and the fractional Langmuir chain equation.In particular,we obtain non-power functions solutions for a kind of RL time-fractional reaction–diffusion equation.In addition,we find that the separation of variables method is more suited to deal with high-dimensional nonlinear RL fractional equations because we have more freedom to choose undetermined functions.
文摘The non PT-symmetric exactly solvable Hamiltonian describing a system of a fermion in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction is considered. We point out all properties of both of the original Mandal and the original Jaynes-Cummings Hamitonians. It is shown that these Hamiltonians are respectively pseudo-hermitian and hermitian REF _Ref536606452 \r \h \* MERGEFORMAT [1] REF _Ref536606454 \r \h [2]. Like the direct approach to invariant vector spaces used in Refs. REF _Ref536606456 \r \h [3] REF _Ref536606457 \r \h [4], we reveal the exact solvability of both the Mandal and Jaynes-Cummings Hamiltonians after expressing them in the position operator and the impulsion operator.
基金supported by National Natural Science Foundation of China(12071046,11671049,91330107,11571002 and 11702028)China Postdoctoral Science Foundation(2020TQ0013).
文摘In this paper,we present a Runge-Kutta Discontinuous Galerkin(RKDG)method for solving the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations under the Lagrangian framework.The fluid part of the ideal MHD equations along with z-component of the magnetic induction equation are discretized using a DG method based on linear Taylor expansions.By using the magnetic fluxfreezing principle which is the integral form of the magnetic induction equation of the ideal MHD,an exactly divergence-free numerical magnetic field can be obtained.The nodal velocities and the corresponding numerical fluxes are explicitly calculated by solving multidirectional approximate Riemann problems.Two kinds of limiter are proposed to inhibit the non-physical oscillation around the shock wave,and the second limiter can eliminate the phenomenon of mesh tangling in the simulations of the rotor problems.This Lagrangian RKDG method conserves mass,momentum,and total energy.Several numerical tests are presented to demonstrate the accuracy and robustness of the proposed scheme.
基金Chinese National Foundation for Natural Sciences.
文摘By discussing the zeros of periodic.solutions we give in this paper a criterion for the existence of exactly n+1 simple 4-periodic solutions of the differential delay equation x(T)= -f(x(t-1)).
文摘An n-tournament T_n is called k-reducible if auy of its (n--k+1)-subtourna-ments is reducible. An n-tournament T_n is called exactly k-reducible if it is k-reducible but not (k+1)-reducible. The numbers of all isomorphic classes of ntournaments and strong n-tournaments arc denoted by t(n) and s(n) respectively.
文摘The phenomenon Anderson localization explains the metalinsulator transition in a material with the increase of disorder and its electrons’transport change from diffusive into localized.The study of the Anderson localization has been extended to many fields of physics,including the quasiperiodic or incommensurate systems.
基金supported by National Natural Science Foundation of China(Nos.12071046,11671049,91330107,11571002 and 11702028)China Postdoctoral Science Foundation(No.2020TQ0013).
文摘A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations written in semi-Lagrangian formulation on moving quadrilateral meshes.In this method,the fluid part of the ideal MHD equations along with zcomponent of the magnetic induction equation is discretized by the RKDG method as our previous paper[47].The numerical magnetic field in the remaining two directions(i.e.,x and y)are constructed by using the magnetic flux-freezing principle which is the integral form of the magnetic induction equation of the ideal MHD.Since the divergence of the magnetic field in 2D is independent of its z-direction component,an exactly divergence-free numerical magnetic field can be obtained by this treatment.We propose a new nodal solver to improve the calculation accuracy of velocities of the moving meshes.A limiter is presented for the numerical solution of the fluid part of the MHD equations and it can avoid calculating the complex eigen-system of the MHD equations.Some numerical examples are presented to demonstrate the accuracy,non-oscillatory property and preservation of the exactly divergence-free property of our method.
文摘In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.
