In this paper, we investigate the new agegraphic dark energy model in the framework of Brans-Dicke theory, which is a natural extension of the Einstein＇s general relativity. In this framework the form of the new ageg...In this paper, we investigate the new agegraphic dark energy model in the framework of Brans-Dicke theory, which is a natural extension of the Einstein＇s general relativity. In this framework the form of the new agegraphic dark energy density takes as pq = 3n^2Ф（t）η^-2, where η is the conformal age of the universe and Ф（t） is the Brans-Dicke scalar field representing the inverse of the time-variable Newton＇s constant. We derive the equation of state of the new agegraphic dark energy and the deceleration parameter of the universe in the Brans-Dicke theory. It is very interesting to find that in the Brans-Dicke theory the agegraphic dark energy realizes quintom-like behavior, i.e., its equation of state crosses the phantom divide ω= -1 during the evolution. We also compare the situation of the agegraphic dark energy model in the Brans-Dicke theory with that in the Einstein＇s theory. In addition, we discuss the new agegraphic dark energy model with interaction in the framework of the Brans-Dicke theory.展开更多
In the 5-year WMAP data analysis, a new parametrization form for dark energy equation-of-state was used, and it has been shown that the equation-of-state, w（z）, crosses the cosmological-constant boundary w = -1. Bas...In the 5-year WMAP data analysis, a new parametrization form for dark energy equation-of-state was used, and it has been shown that the equation-of-state, w（z）, crosses the cosmological-constant boundary w = -1. Based on this observation, in this paper, we investigate the reconstruction of quintom dark energy model. As a single-real-sealarfield model of dark energy, the generalized ghost condensate model provides us with a successful mechanism for realizing the quintom-like behavior. Therefore, we reconstruct this scalar-field quintom dark energy model from the WMAP 5-year observational results. As a comparison, we also discuss the quintom reconstruction based on other specific dark energy ansatzs, such as the CPL parametrization and the holographic dark energy scenarios.展开更多
A semi-direct sum of two Lie algebras of four-by-four matrices is presented,and a discrete four-by-fourmatrix spectral problem is introduced.A hierarchy of discrete integrable coupling systems is derived.The obtainedi...A semi-direct sum of two Lie algebras of four-by-four matrices is presented,and a discrete four-by-fourmatrix spectral problem is introduced.A hierarchy of discrete integrable coupling systems is derived.The obtainedintegrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity.Finally,we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discreteHamiltonian systems.展开更多
The time-convolutionless （TCL） quantum master equation provides a powerful tool to simulate reduced dynanfics of a quantum system coupled to a bath. The key quantity ill the TCL master equation is the so-called kern...The time-convolutionless （TCL） quantum master equation provides a powerful tool to simulate reduced dynanfics of a quantum system coupled to a bath. The key quantity ill the TCL master equation is the so-called kernel or generator, which describes eflhcts of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion （HEOM） and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with diflhrent sets of parameters, to investigate the convergence of the high order expansiolls of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.展开更多
A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation...A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given. Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period(frequency) of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.展开更多
In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we...In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator（or GREG）.展开更多
This study is connected with new Generalized Maximum Fuzzy Entropy Methods （GMax（F）EntM） in the form of MinMax（F）EntM and MaxMax（F）EntM belonging to us. These methods are based on primary maximizing Max（F）En...This study is connected with new Generalized Maximum Fuzzy Entropy Methods （GMax（F）EntM） in the form of MinMax（F）EntM and MaxMax（F）EntM belonging to us. These methods are based on primary maximizing Max（F）Ent measure for fixed moment vector function in order to obtain the special functional with maximum values of Max（F）Ent measure and secondary optimization of mentioned functional with respect to moment vector functions. Distributions, in other words sets of successive values of estimated membership function closest to （furthest from） the given membership function in the sense of Max（F）Ent measure, obtained by mentioned methods are defined as （MinMax（F）Ent）m which is closest to a given membership function and （MaxMax（F）Ent）m which is furthest from a given membership function. The aim of this study consists of applying MinMax（F）EntM and MaxMax（F）EntM on given wind speed data. Obtained results are realized by using MATLAB programme. The performances of distributions （MinMax（F）En0m and （MaxMax（F）Ent）m generated by using Generalized Maximum Fuzzy Entropy Methods are established by Chi-Square, Root Mean Square Error criterias and Max（F）Ent measure.展开更多
This paper is the spectator of the arrangement of an efficient transformation and exfunction technique to build up generalized exact solutions of the biological population model equation. Computational work and subseq...This paper is the spectator of the arrangement of an efficient transformation and exfunction technique to build up generalized exact solutions of the biological population model equation. Computational work and subsequent numerical results re-identify the effectiveness of proposed algorithm. It is pragmatic that recommended plan is greatly consistent and may be comprehensive to other nonlinear differential equations of fractional order.展开更多
The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic com...The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic compatibility and mechanical ana- logue have not yet been properly considered. In the present study, by discussing both these issues, we find that the two orders of fractional derivatives in the constitutive equation of the generalized Jeffreys fluid must be the same in order to ensure that the equation is physically correct. Based on this generalized Jeffreys fluid, a thermodynamically compatible generalized Oldryd-B fluid is also proposed by the convected coordinates approach.展开更多
A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a "small deformation" setting, a suite of simplified and interesting mode...A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a "small deformation" setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived.In the finite deformation setting, it is shown that an additive decomposition of the total velocity gradient into elastic and plastic parts emerges naturally from a micromechanical starting point that involves no notion of plastic deformation but only the elastic distortion,material velocity, dislocation density and the dislocation velocity. Moreover, a plastic spin tensor emerges naturally as well.展开更多
We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a...We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.展开更多
We investigate generalized chaplygin gas for warm inflationary scenario in the context of locally rotationally symmetric Bianchi type I universe model.We assume two different cases of dissipative coefficient,i.e.,cons...We investigate generalized chaplygin gas for warm inflationary scenario in the context of locally rotationally symmetric Bianchi type I universe model.We assume two different cases of dissipative coefficient,i.e.,constant as well as function of scalar field.We construct dynamical equations as well as a relationship between scalar and radiation energy densities under slow-roll approximation.We also derive slow-roll parameters,scalar and tensor power spectra,scalar spectral index,tensor to scalar ratio for analyzing inflationary background during high dissipative regime.We also use the WMAP7 data for the discussion of our parameters.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10705041
文摘In this paper, we investigate the new agegraphic dark energy model in the framework of Brans-Dicke theory, which is a natural extension of the Einstein＇s general relativity. In this framework the form of the new agegraphic dark energy density takes as pq = 3n^2Ф（t）η^-2, where η is the conformal age of the universe and Ф（t） is the Brans-Dicke scalar field representing the inverse of the time-variable Newton＇s constant. We derive the equation of state of the new agegraphic dark energy and the deceleration parameter of the universe in the Brans-Dicke theory. It is very interesting to find that in the Brans-Dicke theory the agegraphic dark energy realizes quintom-like behavior, i.e., its equation of state crosses the phantom divide ω= -1 during the evolution. We also compare the situation of the agegraphic dark energy model in the Brans-Dicke theory with that in the Einstein＇s theory. In addition, we discuss the new agegraphic dark energy model with interaction in the framework of the Brans-Dicke theory.
基金Supported by the Natural Science Foundation of China under Grant Nos.10705041 and 10975032
文摘In the 5-year WMAP data analysis, a new parametrization form for dark energy equation-of-state was used, and it has been shown that the equation-of-state, w（z）, crosses the cosmological-constant boundary w = -1. Based on this observation, in this paper, we investigate the reconstruction of quintom dark energy model. As a single-real-sealarfield model of dark energy, the generalized ghost condensate model provides us with a successful mechanism for realizing the quintom-like behavior. Therefore, we reconstruct this scalar-field quintom dark energy model from the WMAP 5-year observational results. As a comparison, we also discuss the quintom reconstruction based on other specific dark energy ansatzs, such as the CPL parametrization and the holographic dark energy scenarios.
基金the Natural Science Foundation of Shandong Province under Grant No.Q2006A04
文摘A semi-direct sum of two Lie algebras of four-by-four matrices is presented,and a discrete four-by-fourmatrix spectral problem is introduced.A hierarchy of discrete integrable coupling systems is derived.The obtainedintegrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity.Finally,we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discreteHamiltonian systems.
基金supported by the National Natural Science Foundation of China(No.21673246)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB12020300)
文摘The time-convolutionless （TCL） quantum master equation provides a powerful tool to simulate reduced dynanfics of a quantum system coupled to a bath. The key quantity ill the TCL master equation is the so-called kernel or generator, which describes eflhcts of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion （HEOM） and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with diflhrent sets of parameters, to investigate the convergence of the high order expansiolls of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.
基金Funded by the National Natural Science Foundation of China (No. 50375113).
文摘A physical model of sinusoidal function was established. It is generalized that the force is directly proportional to a power function of the distance in a classical spring-oscillator system. The differential equation of the generalized model was given. Simulations were conducted with different power values. The results show that the solution of the generalized equation is a periodic function. The expressions of the amplitude and the period(frequency) of the generalized equation were derived by the physical method. All the simulation results coincide with the calculation results of the derived expressions. A special function also was deduced and proven to be convergent in the theoretical analysis. The limit value of the special function also was derived. The generalized model can be used in solving a type of differential equation and to generate periodic waveforms.
基金Supported by the National Natural Science Foundation of China(10571093)
文摘In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator（or GREG）.
文摘This study is connected with new Generalized Maximum Fuzzy Entropy Methods （GMax（F）EntM） in the form of MinMax（F）EntM and MaxMax（F）EntM belonging to us. These methods are based on primary maximizing Max（F）Ent measure for fixed moment vector function in order to obtain the special functional with maximum values of Max（F）Ent measure and secondary optimization of mentioned functional with respect to moment vector functions. Distributions, in other words sets of successive values of estimated membership function closest to （furthest from） the given membership function in the sense of Max（F）Ent measure, obtained by mentioned methods are defined as （MinMax（F）Ent）m which is closest to a given membership function and （MaxMax（F）Ent）m which is furthest from a given membership function. The aim of this study consists of applying MinMax（F）EntM and MaxMax（F）EntM on given wind speed data. Obtained results are realized by using MATLAB programme. The performances of distributions （MinMax（F）En0m and （MaxMax（F）Ent）m generated by using Generalized Maximum Fuzzy Entropy Methods are established by Chi-Square, Root Mean Square Error criterias and Max（F）Ent measure.
文摘This paper is the spectator of the arrangement of an efficient transformation and exfunction technique to build up generalized exact solutions of the biological population model equation. Computational work and subsequent numerical results re-identify the effectiveness of proposed algorithm. It is pragmatic that recommended plan is greatly consistent and may be comprehensive to other nonlinear differential equations of fractional order.
基金supported by the National Natural Science Foundation of China(Grant No. 10972117)
文摘The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in theology. However, their thermodynamic compatibility and mechanical ana- logue have not yet been properly considered. In the present study, by discussing both these issues, we find that the two orders of fractional derivatives in the constitutive equation of the generalized Jeffreys fluid must be the same in order to ensure that the equation is physically correct. Based on this generalized Jeffreys fluid, a thermodynamically compatible generalized Oldryd-B fluid is also proposed by the convected coordinates approach.
文摘A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a "small deformation" setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived.In the finite deformation setting, it is shown that an additive decomposition of the total velocity gradient into elastic and plastic parts emerges naturally from a micromechanical starting point that involves no notion of plastic deformation but only the elastic distortion,material velocity, dislocation density and the dislocation velocity. Moreover, a plastic spin tensor emerges naturally as well.
基金supported by National Natural Science Foundation of China(Grant Nos.11371125,11171307 and 61374086)Natural Science Foundation of Zhejiang Province(Grant No.LY13A010004)+1 种基金Natural Science Foundation of Hunan Province(Grant No.12C0577)PhD Students Innovation Foundation of Hunan Province(Grant No.CX2012B153)
文摘We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.
文摘We investigate generalized chaplygin gas for warm inflationary scenario in the context of locally rotationally symmetric Bianchi type I universe model.We assume two different cases of dissipative coefficient,i.e.,constant as well as function of scalar field.We construct dynamical equations as well as a relationship between scalar and radiation energy densities under slow-roll approximation.We also derive slow-roll parameters,scalar and tensor power spectra,scalar spectral index,tensor to scalar ratio for analyzing inflationary background during high dissipative regime.We also use the WMAP7 data for the discussion of our parameters.
