We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable...We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential.展开更多
By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-inter...By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-interference relation theorems,the F-interference discernibility theorem,the dependent separation theorem by interfereence,and the dependent separation principle by interference were presented; finally the application was given. By employing F-interference dependence and separation of S-rough laws,the changes of characteristic of dynamic systemic regularities could be recognized.展开更多
We study the effect of strain on band structure and valley-dependent transport properties of graphene heterojunctions.It is found that valley-dependent separation of electrons can be achieved by utilizing strain and o...We study the effect of strain on band structure and valley-dependent transport properties of graphene heterojunctions.It is found that valley-dependent separation of electrons can be achieved by utilizing strain and on-site energies.In the presence of strain,the values of transmission can be effectively adjusted by changing the strengths of the strain,while the transport angle basically keeps unchanged.When an extra on-site energy is simultaneously applied to the central scattering region,not only are the electrons of valleys K and K'separated into two distinct transmission lobes in opposite transverse directions,but the transport angles of two valleys can be significantly changed.Therefore,one can realize an effective modulation of valley-dependent transport by changing the strength and stretch angle of the strain and on-site energies,which can be exploited for graphene-based valleytronics devices.展开更多
In this paper, we introduce and study analytically a vectorial Cahn-Hilliard reaction model coupled with rate-dependent damage processes. The recently proposed Cahn-Hilliard reaction model can e.g. be used to describe...In this paper, we introduce and study analytically a vectorial Cahn-Hilliard reaction model coupled with rate-dependent damage processes. The recently proposed Cahn-Hilliard reaction model can e.g. be used to describe the behavior of electrodes of lithium-ion batteries as it includes both the intercalation reactions at the surfaces and the separation into different phases. The coupling with the damage process allows considering simultaneously the evolution of a damage field, a second important physical effect occurring during the charging or discharging of batteries. Mathematically, this is realized by a Cahn-Larch system with a non-linear Newton boundary condition for the chemical potential and a doubly non-linear differential inclusion for the damage evolution. We show that this system possesses an underlying generalized gradient structure which incorporates the non-linear Newton boundary condition. Using this gradient structure and techniques from the field of convex analysis we are able to prove constructively the existence of weak solutions.展开更多
The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult t...The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis （SCA） has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski＇s natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski＇s gradient.展开更多
This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which adm...This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.展开更多
Based on the generalization of the central limit theorem(CLT) to special dependent variables, this paper shows that maximization of the nonGaussianity(NG) measure can separate the statistically dependent source signal...Based on the generalization of the central limit theorem(CLT) to special dependent variables, this paper shows that maximization of the nonGaussianity(NG) measure can separate the statistically dependent source signals, and the novel NG measure is given by Cook's Euclidean distance using the Chebyshev-Hermite series expansion. Then, a novel blind source separation (BSS) algorithm for linear mixed signals is proposed using Cook's NG measure, which makes it possible to separate statistically dependent source signals. Moreover, the proposed separation algorithm can result in the famous FastICA algorithm. Simulation results show that the proposed separation algorithm is able to separate the dependent signals and yield ideal展开更多
文摘We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthén potential.
基金Science and Technology Foundations of the Education Committee of Fujian Province of China (No.JA09232, No.JA08236)Science and Technology Projects of Sanming University, China (No. HX201007/Z)
文摘By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-interference relation theorems,the F-interference discernibility theorem,the dependent separation theorem by interfereence,and the dependent separation principle by interference were presented; finally the application was given. By employing F-interference dependence and separation of S-rough laws,the changes of characteristic of dynamic systemic regularities could be recognized.
基金National Natural Science Foundation of China(Grant No.11574067)。
文摘We study the effect of strain on band structure and valley-dependent transport properties of graphene heterojunctions.It is found that valley-dependent separation of electrons can be achieved by utilizing strain and on-site energies.In the presence of strain,the values of transmission can be effectively adjusted by changing the strengths of the strain,while the transport angle basically keeps unchanged.When an extra on-site energy is simultaneously applied to the central scattering region,not only are the electrons of valleys K and K'separated into two distinct transmission lobes in opposite transverse directions,but the transport angles of two valleys can be significantly changed.Therefore,one can realize an effective modulation of valley-dependent transport by changing the strength and stretch angle of the strain and on-site energies,which can be exploited for graphene-based valleytronics devices.
文摘In this paper, we introduce and study analytically a vectorial Cahn-Hilliard reaction model coupled with rate-dependent damage processes. The recently proposed Cahn-Hilliard reaction model can e.g. be used to describe the behavior of electrodes of lithium-ion batteries as it includes both the intercalation reactions at the surfaces and the separation into different phases. The coupling with the damage process allows considering simultaneously the evolution of a damage field, a second important physical effect occurring during the charging or discharging of batteries. Mathematically, this is realized by a Cahn-Larch system with a non-linear Newton boundary condition for the chemical potential and a doubly non-linear differential inclusion for the damage evolution. We show that this system possesses an underlying generalized gradient structure which incorporates the non-linear Newton boundary condition. Using this gradient structure and techniques from the field of convex analysis we are able to prove constructively the existence of weak solutions.
基金the National Natural Science Foundation of China (Grant Nos. 60505005, 60674033, 60774094 and U0635001)Natural Science Fund of Guangdong Province, China (Grant Nos. 05103553 and 05006508)+1 种基金Postdoctoral Science Foundation for Innovation from South China University of TechnologyChina Postdoctoral Science Foundation (Grant No. 20070410237)
文摘The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis （SCA） has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski＇s natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski＇s gradient.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10371098, 10447007 and 10475055）, the Natural Science Foundation of Shaanxi Province of China （Grant No 2005A13）.
文摘This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.
基金The National Natural Science Foundation of China (No.60672049)the Science Foundation of Henan University of Technolo-gy(No.06XJC032)
文摘Based on the generalization of the central limit theorem(CLT) to special dependent variables, this paper shows that maximization of the nonGaussianity(NG) measure can separate the statistically dependent source signals, and the novel NG measure is given by Cook's Euclidean distance using the Chebyshev-Hermite series expansion. Then, a novel blind source separation (BSS) algorithm for linear mixed signals is proposed using Cook's NG measure, which makes it possible to separate statistically dependent source signals. Moreover, the proposed separation algorithm can result in the famous FastICA algorithm. Simulation results show that the proposed separation algorithm is able to separate the dependent signals and yield ideal
