Thousands of years ago,the concept of Jiu Zuo Shang Rou(久坐伤肉long-time sitting damages muscles)was introduced in traditional Chinese medicine(TCM).It was clearly recorded in ancient books,that prolonged sitting dis...Thousands of years ago,the concept of Jiu Zuo Shang Rou(久坐伤肉long-time sitting damages muscles)was introduced in traditional Chinese medicine(TCM).It was clearly recorded in ancient books,that prolonged sitting disrupts the circulation of qi and blood,damages muscles,impairs spleen function,and ultimately leads to diseases.Modern biomedical evidence shows that sedentary behavior,including prolonged sitting,affects endocrine,metabolic,and physiological functions,increasing the risk of chronic diseases.This article systematically reviews TCM records of the health impacts of long-time sitting and biomedical findings,to explore the pathophysiological mechanisms underlying the health risks of prolonged sitting.By integrating TCM's preventative philosophy,namely Zhi Wei Bing(治未病preventing a disease before it arises),with modern preventive medicine,this study offers insights into strategies for mitigating the health risks associated with sedentary behavior.展开更多
The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we disc...The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we discretize in time using the linearly backward differentiation formula,and by employing both the discrete Gronwall lemma and the discrete uniform Gronwall lemma,we establish that each numerical scheme is uniformly bounded in the H^(1)-norm.展开更多
In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a gen...In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal m KdV equation. In contrast with the classical mKdV equation,we find some new and different results on long-time asymptotics for the nonlocal mKdV equation and some additional assumptions about the scattering data are made in our main results.展开更多
Long-time coherent integration(LTCI)can remarkably improve the detection ability of radar for moving target.To increase the processing efficiency,this paper proposes a novel LTCI method based on segment time reversing...Long-time coherent integration(LTCI)can remarkably improve the detection ability of radar for moving target.To increase the processing efficiency,this paper proposes a novel LTCI method based on segment time reversing transform(STRT)and chirp z-transform(CZT).In this method,STRT operation is first presented to estimate the Doppler ambiguity factor,and keystone transform(KT)is used to correct the whole range migration(RM).Then,CZT and non-uniform fast Fourier transform(NUFFT)are used to estimate the parameters as well as correct the second and third order Doppler frequency migration(DFM).Compared with the existing methods,the proposed method can achieve RM correction and DFM correction without repetitive operation.The effectiveness of the proposed method is validated by both simulated and real data.展开更多
Long-time coherent integration(LTCI)is an effective way for radar maneuvering target detection,but it faces the problem of a large number of search parameters and large amount of calculation.Realizing the simultaneous...Long-time coherent integration(LTCI)is an effective way for radar maneuvering target detection,but it faces the problem of a large number of search parameters and large amount of calculation.Realizing the simultaneous compensation of the range and Doppler migrations in complex clutter back-ground,and at the same time improving the calculation efficiency has become an urgent problem to be solved.The sparse transformation theory is introduced to LTCI in this paper,and a non-parametric searching sparse LTCI(SLTCI)based maneuvering target detection method is proposed.This method performs time reversal(TR)and second-order Keystone transform(SKT)in the range frequency&slow-time data to complete high-order range walk compensation,and achieves the coherent integra-tion of maneuvering target across range and Doppler units via the robust sparse fractional Fourier transform(RSFRFT).It can compensate for the nonlinear range migration caused by high-order motion.S-band and X-band radar data measured in sea clutter background are used to verify the detection performance of the proposed method,which can achieve better detection performance of maneuvering targets with less computational burden compared with several popular integration methods.展开更多
In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler ti...In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler time-stepping. Then we apply the abstract framework of to prove its long-time convergence. Finally, a numerical example for solving driven cavity flows is given.展开更多
We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantu...We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.展开更多
By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in g...By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.展开更多
Evolution of the charged grains in a two-dimensional dusty plasma under a spatially harmonic external force,in particular,their long-time behaviors after the force has been withdrawn,is studied by using molecular dyna...Evolution of the charged grains in a two-dimensional dusty plasma under a spatially harmonic external force,in particular,their long-time behaviors after the force has been withdrawn,is studied by using molecular dynamics simulation.Under an external force and a grain–grain interaction force,initially homogeneously distributed grains can reach a quasistationary state in the form of a disk crystal.After the external force is withdrawn,the disk moves initially with its size and shape nearly unchanged until it rapidly stops moving,and eventually the disk grain rotates like a vortex.The time needed to reach the final state increases with the strength of the initial external force increasing.展开更多
This paper presents the results of a study of long-time relaxation (LR) and residual conductivity in n-type gallium phosphide (GaP) crystals irradiated by 50 MeV electrons. A manifold increase in photosensitivity and ...This paper presents the results of a study of long-time relaxation (LR) and residual conductivity in n-type gallium phosphide (GaP) crystals irradiated by 50 MeV electrons. A manifold increase in photosensitivity and quenching of residual conductivity was found as a result of irradiation. It is shown that LR in GaP is due to disordered regions (generated by electron irradiation) which have conductivity close to self one. The Fermi level in the disordered regions is determined by which is located deep in the forbidden band (Ее - 1.0 eV). LR effect is mainly explained by a spatial separation of electrons and holes, recombination of which is prevented by potential barriers. The observed increase in conductivity is associated with the increase in the concentration of minority carriers as well as with increase of the Hall mobility at the sample illumination.展开更多
In this article we extend ours framework of long time convergence for numeracal approximations of semilinear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J., 16(1)(2000), 1—28”, to t...In this article we extend ours framework of long time convergence for numeracal approximations of semilinear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J., 16(1)(2000), 1—28”, to the Gauss Ledendre full discretization. When apply the result to the Crank Nicholson finiteelement full discretization of the Navier Stokes equations, we can remore the grid ratio restriction of “Heywood, J. G. and Rannacher, R., SIAM J. Numer. Anal., 27(1990), 353—384”, and weaken the stability condition on the continuous solution.展开更多
In this work,we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector.Start from the Lax pair,we first construct the ba...In this work,we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector.Start from the Lax pair,we first construct the basis Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation.Furthermore,using the approach of Deift-Zhou nonlinear steepest descent,the explicit long-time asymptotics for the reverse space-time nonlocal Hirota is derived.For the reverse space-time nonlocal Hirota equation,since the symmetries of its scattering matrix are different with the local Hirota equation,the v(λ_(i))(i=0,1)would like to be imaginary,which results in theδ_(λi)^(0)contains an increasing t(±Imv(λ_(i)))/2,and then the asymptotic behavior for nonlocal Hirota equation becomes differently.展开更多
The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,th...The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.展开更多
Background The long-time exercise test （ET） is used to diagnose the primary periodic paralyses （PPs）.However the reference values of ET are many and various.This study aimed to investigate the reference value of l...Background The long-time exercise test （ET） is used to diagnose the primary periodic paralyses （PPs）.However the reference values of ET are many and various.This study aimed to investigate the reference value of long-time ET in the diagnosis of PPs.Methods We recruited 108 healthy subjects,68 patients with PPs,and 72 patients with other diseases for the study.The procedure of ET was made on the basis of the McManis＆#39; method.Electrical responses were recorded from right abductor digiti minimi （ADM） muscle when stimulation of the ulnar nerve at the wrist.After the compound muscle action potential （CMAP） was monitored,subjects were then asked to contract the muscle as strongly as possible for 5 minutes.CMAPs were recorded for 2 seconds immediately after cessation of exercise,then every 5 minutes for 10 minutes,and finally every 10 minutes for 50 minutes.In general,the CMAP amplitudes will fall below the pre-exercise levels in an hour.The largest decrease was calculated and used as results of ET.Results The CMAP amplitude decreases had no significant differences between groups when the healthy adults were grouped according to age,gender,height,weight and test time.Decreases in PPs patients （57.76%） were significantly more than in healthy subjects （15.21%） and other disease patients （18.10%,P 〈0.001）.Receiver operating characteristic （ROC） curve analysis showed that the best threshold is 35.50%.Conclusions In the long-time exercise test,threshold of 35.50% for the CMAP amplitude decrease was identified for abnormal.The result is not influenced by age,gender,height,weight,and test time.About 7.4% of healthy subjects were abnormal in ET.展开更多
In this paper,the authors apply■steepest descent method to study the Cauchy problem for the derivative nonlinear Schrödinger equation with finite density type initial data iqt+qxx+1(lq|^(2)q)_(x)=0,q(x,0)=q0(x),...In this paper,the authors apply■steepest descent method to study the Cauchy problem for the derivative nonlinear Schrödinger equation with finite density type initial data iqt+qxx+1(lq|^(2)q)_(x)=0,q(x,0)=q0(x),where lim x→±∞ qo(x)=g0(x)=q±and|q±|=1.Based on the spectral analysis of the Lax pair,they express the solution of the derivative Schrödinger equation in terms of solutions of a Riemann-Hilbert problem.They compute the long time asymptotic expansion of the solution in differeit space-time regions.For the regionζ=x/t with|ζ+2|<1,the long time asymptotic is given by q(x,t)=T(∞)^(-2)q^(r)Λ(x,t)+O(t^(-3/4)),in which the leading term is N(I)solitons,the second term is a residual error from a■equation.For the regionζ+2|>1,the long time asymptotic is given by q(x,t)=t(∞)^(-2)q^(r)Λ(x,t)-t^(-1/2)if11+O(t^(-3/4)) in which the leading term is N(I)solitons,the second t^(-1/2)order term is soliton-radiation interactions and the third term is a residual error from a■equation.These results are verification of the soliton resolution conjectuore for the derivative Schrödinger equation.In their case of finite density type initial data,the phase functionθ(z)is more complicated that in finite mass initial data.Moreover,two triangular decompositions of the jump matrix are used to open jump lines on the whole real axis and imaginary axis,respectively.展开更多
For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillator...For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.展开更多
In this paper,a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena.In the derivation of the present approach,the second order time derivative of the p...In this paper,a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena.In the derivation of the present approach,the second order time derivative of the physical quantity in the wave equation is treated as a substitution variable.Based on the temporal discretization with the Krylov deferred correction(KDC)technique,the original wave problem is then converted into the modified Helmholtz equation.The transformed boundary value problem(BVP)in space is efficiently simulated by using the meshless generalized finite difference method(GFDM)with Taylor series after truncating the second and fourth order approximations.The developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source function.Numerical results match with the analytical solutions and results by the COMSOL software,which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in longtime intervals.展开更多
In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is ...In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.展开更多
The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation u(t) - Au - f(u) = g(t) on Banach space V, and to prove the long-time error e...The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation u(t) - Au - f(u) = g(t) on Banach space V, and to prove the long-time error estimates for the approximation solutions. At first, we give the definition of long-time stability, and then prove the fact that stability and compatibility imply the uniform convergence on the infinite time region. Thus, we establish a general frame in order to prove the long-time convergence. This frame includes finite element methods and finite difference methods of the evolution equations, especially the semilinear parabolic and hyperbolic partial differential equations. As applications of these results we prove the estimates obtained by Larsson [5] and Sanz-serna and Stuart [6].展开更多
On the basis of the spectral analysis of the 4×4 matrix Lax pair,the initial value problem of the coherently-coupled nonlinear Schrödinger system is transformed into a 4×4 matrix Riemann–Hilbert proble...On the basis of the spectral analysis of the 4×4 matrix Lax pair,the initial value problem of the coherently-coupled nonlinear Schrödinger system is transformed into a 4×4 matrix Riemann–Hilbert problem.By using the nonlinear steepest decent method,the long-time asymptotics of the solution of the initial value problem for the coherently-coupled nonlinear Schrödinger system is obtained through deforming the Riemann–Hilbert problem into a solvable model one.展开更多
基金financed by the grants from the Zhejiang Province Higher Education Research Fund Program(NO.JG20220766)National Natural Science Foundation of China(No.71774147)Innovation and Entrepreneurship Training Program for College Students in Zhejiang Province(No.S202010344012)。
文摘Thousands of years ago,the concept of Jiu Zuo Shang Rou(久坐伤肉long-time sitting damages muscles)was introduced in traditional Chinese medicine(TCM).It was clearly recorded in ancient books,that prolonged sitting disrupts the circulation of qi and blood,damages muscles,impairs spleen function,and ultimately leads to diseases.Modern biomedical evidence shows that sedentary behavior,including prolonged sitting,affects endocrine,metabolic,and physiological functions,increasing the risk of chronic diseases.This article systematically reviews TCM records of the health impacts of long-time sitting and biomedical findings,to explore the pathophysiological mechanisms underlying the health risks of prolonged sitting.By integrating TCM's preventative philosophy,namely Zhi Wei Bing(治未病preventing a disease before it arises),with modern preventive medicine,this study offers insights into strategies for mitigating the health risks associated with sedentary behavior.
文摘The purpose of the current article is to study the H^(1)-stability for all positive time of the linearly extrapolated BDF2 timestepping scheme for the magnetohydrodynamics and Boussinesq equations.Specifically,we discretize in time using the linearly backward differentiation formula,and by employing both the discrete Gronwall lemma and the discrete uniform Gronwall lemma,we establish that each numerical scheme is uniformly bounded in the H^(1)-norm.
基金Supported by National Science Foundation of China under Grant Nos.11671095,51879045National Science Foundation of China under Grant No.11501365+1 种基金Shanghai Sailing Program supported by Science and Technology Commission of Shanghai Municipality under Grant No.15YF1408100Shanghai Youth Teacher Assistance Program No.ZZslg15056
文摘In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation(nonlocal mKdV) qt(x, t)+qxxx(x, t)-6 q(x, t)q(-x,-t)qx(x, t) = 0, which can be viewed as a generalization of the local classical mKdV equation. We first formulate the Riemann-Hilbert problem associated with the Cauchy problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear steepest-descent method to analyze the long-time asymptotics for the solution of the nonlocal m KdV equation. In contrast with the classical mKdV equation,we find some new and different results on long-time asymptotics for the nonlocal mKdV equation and some additional assumptions about the scattering data are made in our main results.
基金the National Natural Foundation of China(Nos.61771046,61731023 and 62171029).
文摘Long-time coherent integration(LTCI)can remarkably improve the detection ability of radar for moving target.To increase the processing efficiency,this paper proposes a novel LTCI method based on segment time reversing transform(STRT)and chirp z-transform(CZT).In this method,STRT operation is first presented to estimate the Doppler ambiguity factor,and keystone transform(KT)is used to correct the whole range migration(RM).Then,CZT and non-uniform fast Fourier transform(NUFFT)are used to estimate the parameters as well as correct the second and third order Doppler frequency migration(DFM).Compared with the existing methods,the proposed method can achieve RM correction and DFM correction without repetitive operation.The effectiveness of the proposed method is validated by both simulated and real data.
基金supported by the National Natural Science Foundation of China(62222120,61871391,U1933135)Shandong Provincial Natural Science Foundation(ZR2021YQ43).
文摘Long-time coherent integration(LTCI)is an effective way for radar maneuvering target detection,but it faces the problem of a large number of search parameters and large amount of calculation.Realizing the simultaneous compensation of the range and Doppler migrations in complex clutter back-ground,and at the same time improving the calculation efficiency has become an urgent problem to be solved.The sparse transformation theory is introduced to LTCI in this paper,and a non-parametric searching sparse LTCI(SLTCI)based maneuvering target detection method is proposed.This method performs time reversal(TR)and second-order Keystone transform(SKT)in the range frequency&slow-time data to complete high-order range walk compensation,and achieves the coherent integra-tion of maneuvering target across range and Doppler units via the robust sparse fractional Fourier transform(RSFRFT).It can compensate for the nonlinear range migration caused by high-order motion.S-band and X-band radar data measured in sea clutter background are used to verify the detection performance of the proposed method,which can achieve better detection performance of maneuvering targets with less computational burden compared with several popular integration methods.
基金The project supported by Laboratory of Computational Physics,Institute of Applied Physics & Computational Mathematics,T.O.Box 80 0 9,Beijing 1 0 0 0 88
文摘In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler time-stepping. Then we apply the abstract framework of to prove its long-time convergence. Finally, a numerical example for solving driven cavity flows is given.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11105133)
文摘We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.
文摘By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.
基金supported by the National Natural Science Foundation of China(Grant Nos.11975088 and 11705041)the Natural Science Foundation of Zhejiang Province,China(Grant No.LY15A050001)。
文摘Evolution of the charged grains in a two-dimensional dusty plasma under a spatially harmonic external force,in particular,their long-time behaviors after the force has been withdrawn,is studied by using molecular dynamics simulation.Under an external force and a grain–grain interaction force,initially homogeneously distributed grains can reach a quasistationary state in the form of a disk crystal.After the external force is withdrawn,the disk moves initially with its size and shape nearly unchanged until it rapidly stops moving,and eventually the disk grain rotates like a vortex.The time needed to reach the final state increases with the strength of the initial external force increasing.
文摘This paper presents the results of a study of long-time relaxation (LR) and residual conductivity in n-type gallium phosphide (GaP) crystals irradiated by 50 MeV electrons. A manifold increase in photosensitivity and quenching of residual conductivity was found as a result of irradiation. It is shown that LR in GaP is due to disordered regions (generated by electron irradiation) which have conductivity close to self one. The Fermi level in the disordered regions is determined by which is located deep in the forbidden band (Ее - 1.0 eV). LR effect is mainly explained by a spatial separation of electrons and holes, recombination of which is prevented by potential barriers. The observed increase in conductivity is associated with the increase in the concentration of minority carriers as well as with increase of the Hall mobility at the sample illumination.
文摘In this article we extend ours framework of long time convergence for numeracal approximations of semilinear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J., 16(1)(2000), 1—28”, to the Gauss Ledendre full discretization. When apply the result to the Crank Nicholson finiteelement full discretization of the Navier Stokes equations, we can remore the grid ratio restriction of “Heywood, J. G. and Rannacher, R., SIAM J. Numer. Anal., 27(1990), 353—384”, and weaken the stability condition on the continuous solution.
基金supported by the National Natural Science Foundation of China(No.12175069 and No.12235007)Science and Technology Commission of Shanghai Municipality(No.21JC1402500 and No.22DZ2229014)Natural Science Foundation of Shanghai(No.23ZR1418100)。
文摘In this work,we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector.Start from the Lax pair,we first construct the basis Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation.Furthermore,using the approach of Deift-Zhou nonlinear steepest descent,the explicit long-time asymptotics for the reverse space-time nonlocal Hirota is derived.For the reverse space-time nonlocal Hirota equation,since the symmetries of its scattering matrix are different with the local Hirota equation,the v(λ_(i))(i=0,1)would like to be imaginary,which results in theδ_(λi)^(0)contains an increasing t(±Imv(λ_(i)))/2,and then the asymptotic behavior for nonlocal Hirota equation becomes differently.
基金Project supported by the National Natural Science Foundation of China(Nos.10631020,10401019)the Basic Research Grant of Tsinghua University.
文摘The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.
文摘Background The long-time exercise test （ET） is used to diagnose the primary periodic paralyses （PPs）.However the reference values of ET are many and various.This study aimed to investigate the reference value of long-time ET in the diagnosis of PPs.Methods We recruited 108 healthy subjects,68 patients with PPs,and 72 patients with other diseases for the study.The procedure of ET was made on the basis of the McManis＆#39; method.Electrical responses were recorded from right abductor digiti minimi （ADM） muscle when stimulation of the ulnar nerve at the wrist.After the compound muscle action potential （CMAP） was monitored,subjects were then asked to contract the muscle as strongly as possible for 5 minutes.CMAPs were recorded for 2 seconds immediately after cessation of exercise,then every 5 minutes for 10 minutes,and finally every 10 minutes for 50 minutes.In general,the CMAP amplitudes will fall below the pre-exercise levels in an hour.The largest decrease was calculated and used as results of ET.Results The CMAP amplitude decreases had no significant differences between groups when the healthy adults were grouped according to age,gender,height,weight and test time.Decreases in PPs patients （57.76%） were significantly more than in healthy subjects （15.21%） and other disease patients （18.10%,P 〈0.001）.Receiver operating characteristic （ROC） curve analysis showed that the best threshold is 35.50%.Conclusions In the long-time exercise test,threshold of 35.50% for the CMAP amplitude decrease was identified for abnormal.The result is not influenced by age,gender,height,weight,and test time.About 7.4% of healthy subjects were abnormal in ET.
基金supported by the National Natural Science Foundation of China(Nos.51879045,1202624,118013233,11671095)。
文摘In this paper,the authors apply■steepest descent method to study the Cauchy problem for the derivative nonlinear Schrödinger equation with finite density type initial data iqt+qxx+1(lq|^(2)q)_(x)=0,q(x,0)=q0(x),where lim x→±∞ qo(x)=g0(x)=q±and|q±|=1.Based on the spectral analysis of the Lax pair,they express the solution of the derivative Schrödinger equation in terms of solutions of a Riemann-Hilbert problem.They compute the long time asymptotic expansion of the solution in differeit space-time regions.For the regionζ=x/t with|ζ+2|<1,the long time asymptotic is given by q(x,t)=T(∞)^(-2)q^(r)Λ(x,t)+O(t^(-3/4)),in which the leading term is N(I)solitons,the second term is a residual error from a■equation.For the regionζ+2|>1,the long time asymptotic is given by q(x,t)=t(∞)^(-2)q^(r)Λ(x,t)-t^(-1/2)if11+O(t^(-3/4)) in which the leading term is N(I)solitons,the second t^(-1/2)order term is soliton-radiation interactions and the third term is a residual error from a■equation.These results are verification of the soliton resolution conjectuore for the derivative Schrödinger equation.In their case of finite density type initial data,the phase functionθ(z)is more complicated that in finite mass initial data.Moreover,two triangular decompositions of the jump matrix are used to open jump lines on the whole real axis and imaginary axis,respectively.
基金supported by the Alexander von Humboldt Foundation。
文摘For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.
基金supported by the National Natural Science Foundation of China(Grant No.11802165)the Natural Science Foundation of Shandong Province of China(Grant No.ZR2017BA003)the China Postdoctoral Science Foundation(Grant No.2019M650158).
文摘In this paper,a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena.In the derivation of the present approach,the second order time derivative of the physical quantity in the wave equation is treated as a substitution variable.Based on the temporal discretization with the Krylov deferred correction(KDC)technique,the original wave problem is then converted into the modified Helmholtz equation.The transformed boundary value problem(BVP)in space is efficiently simulated by using the meshless generalized finite difference method(GFDM)with Taylor series after truncating the second and fourth order approximations.The developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source function.Numerical results match with the analytical solutions and results by the COMSOL software,which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in longtime intervals.
文摘In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in threedimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial data are close to the constant equilibrium state in H2-framework. If the initial datas in Ll-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.
文摘The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation u(t) - Au - f(u) = g(t) on Banach space V, and to prove the long-time error estimates for the approximation solutions. At first, we give the definition of long-time stability, and then prove the fact that stability and compatibility imply the uniform convergence on the infinite time region. Thus, we establish a general frame in order to prove the long-time convergence. This frame includes finite element methods and finite difference methods of the evolution equations, especially the semilinear parabolic and hyperbolic partial differential equations. As applications of these results we prove the estimates obtained by Larsson [5] and Sanz-serna and Stuart [6].
基金the National Natural Science Foundation of China(Grant Nos.11871440 and 11931017)。
文摘On the basis of the spectral analysis of the 4×4 matrix Lax pair,the initial value problem of the coherently-coupled nonlinear Schrödinger system is transformed into a 4×4 matrix Riemann–Hilbert problem.By using the nonlinear steepest decent method,the long-time asymptotics of the solution of the initial value problem for the coherently-coupled nonlinear Schrödinger system is obtained through deforming the Riemann–Hilbert problem into a solvable model one.
