In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of C...The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of China(Legislation Law) has led to two divergent views. One holds that "the local laws of cities with subordinate districts should take precedence over the regulations of provincial governments," while the other supports the exact opposite. This is a value judgment issue in legislation. To reach a solution, we need to clarify the premises based on the characteristics of the laws in question so that a basic common ground can be established for discussion. The first premise for traditional legislation is that a law should be based on experience as well as logic; the second is that the experience of authority subjects, plus the three aspects of logic should outweigh the experience of social subjects, plus the three aspects of logic. With respect to postmodern legislation, the first premise is that experience should override logic, and the second is that the experience of the authority subject should take precedence over that of social subject, with no requirements for logical consistency. Since Legislation Law fal s into the category of postmodern legislation, according to the premises, the argument that the local laws of cities with subordinate districts should take precedence enjoys wider acceptance, but the view is logically challenged in terms of conceptual consistency, system consistency and principle consistency. More studies must be conducted to facilitate the discussion.展开更多
Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system...Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.展开更多
Municipal solid waste generation is strongly linked to rising human population and expanding urban areas, with significant implications on urban metabolism as well as space and place values redefinition. Effective man...Municipal solid waste generation is strongly linked to rising human population and expanding urban areas, with significant implications on urban metabolism as well as space and place values redefinition. Effective management performance of municipal solid waste management underscores the interdisciplinarity strategies. Such knowledge and skills are paramount to uncover the sources of waste generation as well as means of waste storage, collection, recycling, transportation, handling/treatment, disposal, and monitoring. This study was conducted in Dar es Salaam city. Driven by the curiosity model of the solid waste minimization performance at source, study data was collected using focus group discussion techniques to ward-level local government officers, which was triangulated with literature and documentary review. The main themes of the FGD were situational factors (SFA) and local government by-laws (LGBY). In the FGD session, sub-themes of SFA tricked to understand how MSW minimization is related to the presence and effect of services such as land use planning, availability of landfills, solid waste transfer stations, material recovery facilities, incinerators, solid waste collection bins, solid waste trucks, solid waste management budget and solid waste collection agents. Similarly, FGD on LGBY was extended by sub-themes such as contents of the by-law, community awareness of the by-law, and by-law enforcement mechanisms. While data preparation applied an analytical hierarchy process, data analysis applied an ordinary least square (OLS) regression model for sub-criteria that explain SFA and LGBY;and OLS standard residues as variables into geographically weighted regression with a resolution of 241 × 241 meter in ArcMap v10.5. Results showed that situational factors and local government by-laws have a strong relationship with the rate of minimizing solid waste dumping in water bodies (local R square = 0.94).展开更多
With the help of large deviation of Brownian motion in the Hölder norm,local Strassen’s law of the iterated logarithm for increments of a Brownian motion in the Hölder norm is investigated.This paper promot...With the help of large deviation of Brownian motion in the Hölder norm,local Strassen’s law of the iterated logarithm for increments of a Brownian motion in the Hölder norm is investigated.This paper promotes the corresponding results by Gantert and Wei.展开更多
In this paper,we obtain the quasi sure local Chung’s functional law of the iterated logarithm for increments of a Brownian motion.As an application,a quasi sure Chung’s type functional modulus of continuity for a Br...In this paper,we obtain the quasi sure local Chung’s functional law of the iterated logarithm for increments of a Brownian motion.As an application,a quasi sure Chung’s type functional modulus of continuity for a Brownian motion is also derived.展开更多
In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from ...In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.展开更多
In this paper, using the concatenating method, a series of local structure-preserving algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multisymplectic algorithms, four local energy-preser...In this paper, using the concatenating method, a series of local structure-preserving algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multisymplectic algorithms, four local energy-preserving algorithms, four local momentumpreserving algorithms;of these, local energy-preserving and momentum-preserving algorithms have not been studied before. The local structure-preserving algorithms mentioned above are more widely used than the global structure-preserving algorithms, since local preservation algorithms can be preserved in any time and space domains, which overcomes the defect that global preservation algorithms are limited to boundary conditions. In particular, under appropriate boundary conditions, local preservation laws are global preservation laws.Numerical experiments conducted can support the theoretical analysis well.展开更多
The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certai...The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is exemplified by the multisymplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme.展开更多
In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure are constru...In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure are constructed for the equation, and the conservation laws of the continuous equation are presented. The multisymplectic discretization of each formulation is exemplified by the multi-symplectic Fourier pseudospectral scheme. The numerical experiments are given, and the results verify the efficiency of the Fourier pseudospectral method.展开更多
Going beyond the analytical model of the holistic state in rule of law discussion, we can classify the rule of law into national and local levels based on the stages and increments of its execution. The phenomenon of ...Going beyond the analytical model of the holistic state in rule of law discussion, we can classify the rule of law into national and local levels based on the stages and increments of its execution. The phenomenon of the local rule of law reflects the stages and incremental progress of building a rule of law China. It has a realistic foundation in society and a profound basis in legal theory. Comprehensively advancing the rule of law in China necessitates giving encouragement and support to construction of the rule of law at the local level. The attempts and experiments of local government enable us to explore and innovate the developmental model of the socialist rule of law with Chinese characteristics. The rule of law at the local level is embodied in three dimensions： ＂text--action---concept.＂ Assessment mechanisms and indicators for the local construction of the rule of law should also be established in accordance with this framework. The building of the rule of law at the local level should be synchronized with assessment of the rule of law. We need to optimize top-level design, conduct evaluations of local legislation, improve local rule of law work performance assessment and use a nile of law index to assess the local rule of law in an overall manner.展开更多
In this paper, we discuss the concept of local structure-preserving algorithms (SPAs) for partial differential equations, which are the natural generalization of the corresponding global SPAs. Local SPAs for the probl...In this paper, we discuss the concept of local structure-preserving algorithms (SPAs) for partial differential equations, which are the natural generalization of the corresponding global SPAs. Local SPAs for the problems with proper boundary conditions are global SPAs, but the inverse is not necessarily valid. The concept of the local SPAs can explain the difference between different SPAs and provide a basic theory for analyzing and constructing high performance SPAs. Furthermore, it enlarges the applicable scopes of SPAs. We also discuss the application and the construction of local SPAs and derive several new SPAs for the nonlinear Klein-Gordon equation.展开更多
In this paper, the multisymplectic Fourier pseudospectral scheme for initial-boundary value problems of nonlinear SchrSdinger equations with wave operator is considered. We investigate the local and global conservatio...In this paper, the multisymplectic Fourier pseudospectral scheme for initial-boundary value problems of nonlinear SchrSdinger equations with wave operator is considered. We investigate the local and global conservation properties of the multisymplectic discretization based on Fourier pseudospectral approximations. The local and global spatial conservation of energy is proved. The error estimates of local energy conservation law are also derived. Numerical experiments are presented to verify the theoretical predications.展开更多
The higher order wave equation of KdV type, which describes many important physical phenomena, has been investigated widely in last several decades. In this work, multi- symplectic formulations for the higher order wa...The higher order wave equation of KdV type, which describes many important physical phenomena, has been investigated widely in last several decades. In this work, multi- symplectic formulations for the higher order wave equation of KdV type are presented, and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is calculated by the multi-symplectic Fourier pseudospectral scheme. Numerical experiments are carried out, which verify the efficiency of the Fourier pseudospectral method.展开更多
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
基金part of the results(presented in stages)of"Research on the Legislative System of Cities with Subordinate Districts"(16XFX004)-a program of National Social Sciences Fund in Western China"Empirical Research on Local Legislation"(16XW16)-a research focus of Sichuan Academy of Social Sciences under a key program launched by the Publicity Department of the CPC Sichuan Provincial Committee
文摘The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of China(Legislation Law) has led to two divergent views. One holds that "the local laws of cities with subordinate districts should take precedence over the regulations of provincial governments," while the other supports the exact opposite. This is a value judgment issue in legislation. To reach a solution, we need to clarify the premises based on the characteristics of the laws in question so that a basic common ground can be established for discussion. The first premise for traditional legislation is that a law should be based on experience as well as logic; the second is that the experience of authority subjects, plus the three aspects of logic should outweigh the experience of social subjects, plus the three aspects of logic. With respect to postmodern legislation, the first premise is that experience should override logic, and the second is that the experience of the authority subject should take precedence over that of social subject, with no requirements for logical consistency. Since Legislation Law fal s into the category of postmodern legislation, according to the premises, the argument that the local laws of cities with subordinate districts should take precedence enjoys wider acceptance, but the view is logically challenged in terms of conceptual consistency, system consistency and principle consistency. More studies must be conducted to facilitate the discussion.
基金supported by the Chinese Scholarship Council(CSC)(No.201806340074)Shenzhen Clean Energy Research Institute and National Natural Science Foundation of China(No.12005141)+3 种基金supported by the US Department of Energy(No.DE-AC02-09CH11466)supported by the National MC Energy R&D Program(No.2018YFE0304100)National Key Research and Development Program(Nos.2016YFA0400600,2016YFA0400601 and 2016YFA0400602)the National Natural Science Foundation of China(Nos.11905220 and 11805273)。
文摘Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.
文摘Municipal solid waste generation is strongly linked to rising human population and expanding urban areas, with significant implications on urban metabolism as well as space and place values redefinition. Effective management performance of municipal solid waste management underscores the interdisciplinarity strategies. Such knowledge and skills are paramount to uncover the sources of waste generation as well as means of waste storage, collection, recycling, transportation, handling/treatment, disposal, and monitoring. This study was conducted in Dar es Salaam city. Driven by the curiosity model of the solid waste minimization performance at source, study data was collected using focus group discussion techniques to ward-level local government officers, which was triangulated with literature and documentary review. The main themes of the FGD were situational factors (SFA) and local government by-laws (LGBY). In the FGD session, sub-themes of SFA tricked to understand how MSW minimization is related to the presence and effect of services such as land use planning, availability of landfills, solid waste transfer stations, material recovery facilities, incinerators, solid waste collection bins, solid waste trucks, solid waste management budget and solid waste collection agents. Similarly, FGD on LGBY was extended by sub-themes such as contents of the by-law, community awareness of the by-law, and by-law enforcement mechanisms. While data preparation applied an analytical hierarchy process, data analysis applied an ordinary least square (OLS) regression model for sub-criteria that explain SFA and LGBY;and OLS standard residues as variables into geographically weighted regression with a resolution of 241 × 241 meter in ArcMap v10.5. Results showed that situational factors and local government by-laws have a strong relationship with the rate of minimizing solid waste dumping in water bodies (local R square = 0.94).
文摘With the help of large deviation of Brownian motion in the Hölder norm,local Strassen’s law of the iterated logarithm for increments of a Brownian motion in the Hölder norm is investigated.This paper promotes the corresponding results by Gantert and Wei.
基金Supported by National Natural Science Foundation of China(11661025)Science Research Foundation of Guangxi Education Department(YB2014117)+1 种基金Guangxi Natural Science Foundation(2018GXNSFBA281076,2017GXNSFBA198179)Guangxi Programme for Promoting Young Teachers’s Ability(2018KY0214).
文摘In this paper,we obtain the quasi sure local Chung’s functional law of the iterated logarithm for increments of a Brownian motion.As an application,a quasi sure Chung’s type functional modulus of continuity for a Brownian motion is also derived.
基金Supported by National Nature Science Foundation of China under Grant No. 10701081
文摘In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.
基金supported by the National Natural Science Foundation of China(11801277,11771213,12171245)。
文摘In this paper, using the concatenating method, a series of local structure-preserving algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multisymplectic algorithms, four local energy-preserving algorithms, four local momentumpreserving algorithms;of these, local energy-preserving and momentum-preserving algorithms have not been studied before. The local structure-preserving algorithms mentioned above are more widely used than the global structure-preserving algorithms, since local preservation algorithms can be preserved in any time and space domains, which overcomes the defect that global preservation algorithms are limited to boundary conditions. In particular, under appropriate boundary conditions, local preservation laws are global preservation laws.Numerical experiments conducted can support the theoretical analysis well.
基金Supported by the Differential Equation Innovation Team(CXTD003,2013XYZ19)
文摘The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is exemplified by the multisymplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme.
文摘In this paper, we consider multi-symplectic Fourier pseudospectral method for a high order integrable equation of KdV type, which describes many important physical phenomena. The multi-symplectic structure are constructed for the equation, and the conservation laws of the continuous equation are presented. The multisymplectic discretization of each formulation is exemplified by the multi-symplectic Fourier pseudospectral scheme. The numerical experiments are given, and the results verify the efficiency of the Fourier pseudospectral method.
基金the research results of"Research on the Sinification,Modernization and Populrization of Marxist Jurisprudential Theory,"a key project of the National Social Science Foundation(10AFX001)
文摘Going beyond the analytical model of the holistic state in rule of law discussion, we can classify the rule of law into national and local levels based on the stages and increments of its execution. The phenomenon of the local rule of law reflects the stages and incremental progress of building a rule of law China. It has a realistic foundation in society and a profound basis in legal theory. Comprehensively advancing the rule of law in China necessitates giving encouragement and support to construction of the rule of law at the local level. The attempts and experiments of local government enable us to explore and innovate the developmental model of the socialist rule of law with Chinese characteristics. The rule of law at the local level is embodied in three dimensions： ＂text--action---concept.＂ Assessment mechanisms and indicators for the local construction of the rule of law should also be established in accordance with this framework. The building of the rule of law at the local level should be synchronized with assessment of the rule of law. We need to optimize top-level design, conduct evaluations of local legislation, improve local rule of law work performance assessment and use a nile of law index to assess the local rule of law in an overall manner.
文摘In this paper, we discuss the concept of local structure-preserving algorithms (SPAs) for partial differential equations, which are the natural generalization of the corresponding global SPAs. Local SPAs for the problems with proper boundary conditions are global SPAs, but the inverse is not necessarily valid. The concept of the local SPAs can explain the difference between different SPAs and provide a basic theory for analyzing and constructing high performance SPAs. Furthermore, it enlarges the applicable scopes of SPAs. We also discuss the application and the construction of local SPAs and derive several new SPAs for the nonlinear Klein-Gordon equation.
基金This work was supported by E-Institutes of Shanghai Municlpal Education Commission N.E03004.
文摘In this paper, the multisymplectic Fourier pseudospectral scheme for initial-boundary value problems of nonlinear SchrSdinger equations with wave operator is considered. We investigate the local and global conservation properties of the multisymplectic discretization based on Fourier pseudospectral approximations. The local and global spatial conservation of energy is proved. The error estimates of local energy conservation law are also derived. Numerical experiments are presented to verify the theoretical predications.
文摘The higher order wave equation of KdV type, which describes many important physical phenomena, has been investigated widely in last several decades. In this work, multi- symplectic formulations for the higher order wave equation of KdV type are presented, and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is calculated by the multi-symplectic Fourier pseudospectral scheme. Numerical experiments are carried out, which verify the efficiency of the Fourier pseudospectral method.
