Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq-Burgersequation are presented in this letter.They are used to generate new solutions of the classical Boussinesq-Burgerseq...Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq-Burgersequation are presented in this letter.They are used to generate new solutions of the classical Boussinesq-Burgersequation.展开更多
A new grey forecasting model based on BP neural network and Markov chain was proposed. In order to combine the grey forecasting model with neural network, an important theorem that the grey differential equation is eq...A new grey forecasting model based on BP neural network and Markov chain was proposed. In order to combine the grey forecasting model with neural network, an important theorem that the grey differential equation is equivalent to the time response model, was proved by analyzing the features of grey forecasting model(GM(1,1)). Based on this, the differential equation parameters were included in the network when the BP neural network was constructed, and the neural network was trained by extracting samples from grey system's known data. When BP network was converged, the whitened grey differential equation parameters were extracted and then the grey neural network forecasting model (GNNM(1,1)) was built. In order to reduce stochastic phenomenon in GNNM(1,1), the state transition probability between two states was defined and the Markov transition matrix was established by building the residual sequences between grey forecasting and actual value. Thus, the new grey forecasting model(MNNGM(1,1)) was proposed by combining Markov chain with GNNM(1,1). Based on the above discussion, three different approaches were put forward for forecasting China electricity demands. By comparing GM(1, 1) and GNNM(1,1) with the proposed model, the results indicate that the absolute mean error of MNNGM(1,1) is about 0.4 times of GNNM(1,1) and 0.2 times of GM(I, 1), and the mean square error of MNNGM(1,1) is about 0.25 times of GNNM(1,1) and 0.1 times of GM(1,1).展开更多
A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation (ENSO) atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmo...A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation (ENSO) atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat- terns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.展开更多
In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transform...In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.展开更多
The analytical solutions to 1D Schrdinger equation (in depth direction) in double gate (DG) MOSFETs are derived to calculate electron density and threshold voltage.The non uniform potential in the channel is concern...The analytical solutions to 1D Schrdinger equation (in depth direction) in double gate (DG) MOSFETs are derived to calculate electron density and threshold voltage.The non uniform potential in the channel is concerned with an arbitrary depth so that the analytical solutions agree well with numerical ones.Then,an implicit expression for electron density and a closed form of threshold voltage are presented fully comprising quantum mechanical (QM) effects.This model predicts an increased electron density with an increasing channel depth in subthreshold region or mild inversion region.However,it becomes independent on channel depth in strong inversion region,which is in accordance with numerical analysis.It is also concluded that the QM model,which barely considers a box like potential in the channel,slightly over predicts threshold voltage and underestimates electron density,and the error increases with an increasing channel depth or a decreasing gate oxide thickness.展开更多
By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation (η|, which can arrange master equations of density operators p(t) in quant...By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation (η|, which can arrange master equations of density operators p(t) in quantum statistics as state-vector evolution equations due to the elegant properties of (η|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p(t) at time t in 〈η| representation is proportional to that of the initial po in the decayed entangled state (ηe^-kt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f(d^2η/π)(η|ρ〉D(η), which is different from all the previous known representations.展开更多
First. we use graph theory to further clarify information of nodes and topics. Next, our paper analyzes the factor which affects the nodes probability of being conspirators. According to requirement 1, each node is gi...First. we use graph theory to further clarify information of nodes and topics. Next, our paper analyzes the factor which affects the nodes probability of being conspirators. According to requirement 1, each node is given an initial probability in being a conspirator on the basis of the acquired information.Then we conduct calculations with the iterative equation produced by factor analysis to get the priority list of the 83 given nodes. In addition, according to requirement 2, we make some changes of the nodes information before solving the iterativc modcl above. Compared with former result, some changes of priority and probability of being conspirator emerges.Finally, based upon requirement 3, we pick out some infomaation from some certain topic by semantic analysis and text analysis. A new group of indexes are solved out with TOPSIS to finish the information-gathering period. The terminal indicator, containing the information of nodes and topics, is a weighted average value of the indexes obtained above and the indexes obtained in requirement 1 with the method of the variation coefficient.展开更多
Using the integral representation of the Jost solution,we deduce some conditions as the kernel functionN(x,y,t)if the Jost solution satisfies the two Lax equations.Then we verify the multi-soliton solution of NLS equa...Using the integral representation of the Jost solution,we deduce some conditions as the kernel functionN(x,y,t)if the Jost solution satisfies the two Lax equations.Then we verify the multi-soliton solution of NLS equationwith non-vanishing boundary conditions if we prove that these conditions can be demonstrated by the GLM equation,which determines the kernel function N(x,y,t)in according to the inverse scattering method.展开更多
The purpose of this paper is to pose a new question to speed-up mutual understanding among team members or/and group of experts when communicating over the Internet in forms of virtual collaboration, electronic brains...The purpose of this paper is to pose a new question to speed-up mutual understanding among team members or/and group of experts when communicating over the Internet in forms of virtual collaboration, electronic brainstorming, network strategic conversation, etc. We have previously proposed an approach that the convergent control mechanism based on the fundamental principles of thermodynamic and inverse problem solution method, as well as various artificial intelligence techniques, be incorporated into the communicative process. This paper shows a further development of the approach in terms of applying The Fuzzy Tychonoff Theorem along with quantum techniques provide to reach a high level of holistic discourse which is achieved not only through the application of fundamental principles of compactness of the topological space, but also utilizing quantum entanglement and complementarity principles for discourse structuring in a special way. The approach is implemented as the Responsibility Thinking System (RTS) tested in the course of finding the decisions of the real life issues.展开更多
In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the...In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.展开更多
In nonlinear physics, the modified Korteweg de-Vries (mKdV) as one of the important equation of nonfinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE...In nonlinear physics, the modified Korteweg de-Vries (mKdV) as one of the important equation of nonfinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE method is presented for constructing new exact solutions. In addition to the new solutions of the mKdV equation, the consistent Riccati expansion (CRE) method can unearth other equations.展开更多
In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis.Three predominant subspace algorithms,i.e.,Krylov-Schur method,implicit...In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis.Three predominant subspace algorithms,i.e.,Krylov-Schur method,implicitly restarted Arnoldi method and Jacobi-Davidson method,are modified with some complementary techniques to make them suitable for modal analysis.Detailed descriptions of the three algorithms are given.Based on these algorithms,a parallel solution procedure is established via the PANDA framework and its associated eigensolvers.Using the solution procedure on a machine equipped with up to 4800processors,the parallel performance of the three predominant methods is evaluated via numerical experiments with typical engineering structures,where the maximum testing scale attains twenty million degrees of freedom.The speedup curves for different cases are obtained and compared.The results show that the three methods are good for modal analysis in the scale of ten million degrees of freedom with a favorable parallel scalability.展开更多
文摘Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq-Burgersequation are presented in this letter.They are used to generate new solutions of the classical Boussinesq-Burgersequation.
基金Project(70572090) supported by the National Natural Science Foundation of China
文摘A new grey forecasting model based on BP neural network and Markov chain was proposed. In order to combine the grey forecasting model with neural network, an important theorem that the grey differential equation is equivalent to the time response model, was proved by analyzing the features of grey forecasting model(GM(1,1)). Based on this, the differential equation parameters were included in the network when the BP neural network was constructed, and the neural network was trained by extracting samples from grey system's known data. When BP network was converged, the whitened grey differential equation parameters were extracted and then the grey neural network forecasting model (GNNM(1,1)) was built. In order to reduce stochastic phenomenon in GNNM(1,1), the state transition probability between two states was defined and the Markov transition matrix was established by building the residual sequences between grey forecasting and actual value. Thus, the new grey forecasting model(MNNGM(1,1)) was proposed by combining Markov chain with GNNM(1,1). Based on the above discussion, three different approaches were put forward for forecasting China electricity demands. By comparing GM(1, 1) and GNNM(1,1) with the proposed model, the results indicate that the absolute mean error of MNNGM(1,1) is about 0.4 times of GNNM(1,1) and 0.2 times of GM(I, 1), and the mean square error of MNNGM(1,1) is about 0.25 times of GNNM(1,1) and 0.1 times of GM(1,1).
基金Under the auspices of National Natural Science Foundation of China (No.40876010)Key Direction in Knowledge Innovation Programs of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08)+2 种基金Research and Development Special Fund for Public Welfare Industry (Meteorology) (No. GYHY200806010)LASG State Key Laboratory Special Fund, Foundation of E-Institutes of Shanghai Municipal Education Commission (No.E03004)Natural Science Foundation of Education Department of Fujian Province (No.JA10288)
文摘A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation (ENSO) atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat- terns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.
基金the State Key Basic Research Program of China under Grant No.2004CB318000the Research Fund for the Doctoral Program of Higher Education of China under Grant No.20060269006
文摘In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.
文摘The analytical solutions to 1D Schrdinger equation (in depth direction) in double gate (DG) MOSFETs are derived to calculate electron density and threshold voltage.The non uniform potential in the channel is concerned with an arbitrary depth so that the analytical solutions agree well with numerical ones.Then,an implicit expression for electron density and a closed form of threshold voltage are presented fully comprising quantum mechanical (QM) effects.This model predicts an increased electron density with an increasing channel depth in subthreshold region or mild inversion region.However,it becomes independent on channel depth in strong inversion region,which is in accordance with numerical analysis.It is also concluded that the QM model,which barely considers a box like potential in the channel,slightly over predicts threshold voltage and underestimates electron density,and the error increases with an increasing channel depth or a decreasing gate oxide thickness.
基金supported by President Foundation of Chinese Academy of Sciences and National Natural Science Foundation of China under Grant Nos. 10775097 and 10874174
文摘By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation (η|, which can arrange master equations of density operators p(t) in quantum statistics as state-vector evolution equations due to the elegant properties of (η|. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p(t) at time t in 〈η| representation is proportional to that of the initial po in the decayed entangled state (ηe^-kt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f(d^2η/π)(η|ρ〉D(η), which is different from all the previous known representations.
文摘First. we use graph theory to further clarify information of nodes and topics. Next, our paper analyzes the factor which affects the nodes probability of being conspirators. According to requirement 1, each node is given an initial probability in being a conspirator on the basis of the acquired information.Then we conduct calculations with the iterative equation produced by factor analysis to get the priority list of the 83 given nodes. In addition, according to requirement 2, we make some changes of the nodes information before solving the iterativc modcl above. Compared with former result, some changes of priority and probability of being conspirator emerges.Finally, based upon requirement 3, we pick out some infomaation from some certain topic by semantic analysis and text analysis. A new group of indexes are solved out with TOPSIS to finish the information-gathering period. The terminal indicator, containing the information of nodes and topics, is a weighted average value of the indexes obtained above and the indexes obtained in requirement 1 with the method of the variation coefficient.
基金the Huazhong University of Science and Technology under Grant No.0101011110National Natural Science Foundation of China under Grant No.10375041
文摘Using the integral representation of the Jost solution,we deduce some conditions as the kernel functionN(x,y,t)if the Jost solution satisfies the two Lax equations.Then we verify the multi-soliton solution of NLS equationwith non-vanishing boundary conditions if we prove that these conditions can be demonstrated by the GLM equation,which determines the kernel function N(x,y,t)in according to the inverse scattering method.
文摘The purpose of this paper is to pose a new question to speed-up mutual understanding among team members or/and group of experts when communicating over the Internet in forms of virtual collaboration, electronic brainstorming, network strategic conversation, etc. We have previously proposed an approach that the convergent control mechanism based on the fundamental principles of thermodynamic and inverse problem solution method, as well as various artificial intelligence techniques, be incorporated into the communicative process. This paper shows a further development of the approach in terms of applying The Fuzzy Tychonoff Theorem along with quantum techniques provide to reach a high level of holistic discourse which is achieved not only through the application of fundamental principles of compactness of the topological space, but also utilizing quantum entanglement and complementarity principles for discourse structuring in a special way. The approach is implemented as the Responsibility Thinking System (RTS) tested in the course of finding the decisions of the real life issues.
文摘In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.
基金Supported by the National Natural Science Foundation of China under Grant No.11175092Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201017148K.C.Wong Magna Fund in Ningbo University
文摘In nonlinear physics, the modified Korteweg de-Vries (mKdV) as one of the important equation of nonfinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE method is presented for constructing new exact solutions. In addition to the new solutions of the mKdV equation, the consistent Riccati expansion (CRE) method can unearth other equations.
基金supported by the National Defence Basic Fundamental Research Program of China(Grant No.C1520110002)the Fundamental Development Foundation of China Academy Engineering Physics(Grant No.2012A0202008)
文摘In this paper we study the algorithms and their parallel implementation for solving large-scale generalized eigenvalue problems in modal analysis.Three predominant subspace algorithms,i.e.,Krylov-Schur method,implicitly restarted Arnoldi method and Jacobi-Davidson method,are modified with some complementary techniques to make them suitable for modal analysis.Detailed descriptions of the three algorithms are given.Based on these algorithms,a parallel solution procedure is established via the PANDA framework and its associated eigensolvers.Using the solution procedure on a machine equipped with up to 4800processors,the parallel performance of the three predominant methods is evaluated via numerical experiments with typical engineering structures,where the maximum testing scale attains twenty million degrees of freedom.The speedup curves for different cases are obtained and compared.The results show that the three methods are good for modal analysis in the scale of ten million degrees of freedom with a favorable parallel scalability.