I. A Review of China's Judicial Protection for Human Rights To effectively protect human rights, a country needs to specify in its laws a complete series of basic rights its citizens shall enjoy. Meanwhile, the lega...I. A Review of China's Judicial Protection for Human Rights To effectively protect human rights, a country needs to specify in its laws a complete series of basic rights its citizens shall enjoy. Meanwhile, the legal rights for an individual citizen would be meaningless even though such rights are prescribed in laws if, when the person's rights are infringed upon, he or she has no access to judicial relief. Administration of justice is the last resort, in fact the most effective, means.展开更多
Adozen experts of law gathered on April 1, 2003 to share their views on protection of the workers’ right to remuneration for their work in accordance with the Labor Law of the People’s Republic of China. That took p...Adozen experts of law gathered on April 1, 2003 to share their views on protection of the workers’ right to remuneration for their work in accordance with the Labor Law of the People’s Republic of China. That took place at a seminar jointly sponsored by the Human Rights and the Beijing-based Democracy and Law magazines and the Branch of Labor and Social Security Laws of the Beijing Society of Law. Participants were from the All-China Federation of Trade Unions,展开更多
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTE...The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in ℚ, marked ⊕and +α,β, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in ℝand ℂ. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned.展开更多
The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the ...The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the first fundamental form (FFF) and the partial Noether operator's determining equations are derived. These determining equations are then used to construct the partial Noether operators and conserved vectors for the wave equation on different surfaces. The conserved vectors for the wave equation on the sphere, cone and fiat space are simplified using the Lie point symmetry generators of the equation and conserved vectors with the help of the symmetry conservation laws relation.展开更多
Finding that in the formula of expansion of a function into a series of wave-like functions ?the coefficients are its Fourier transforms, if existed, we deduce mathematically all the principles and hypothesis that ill...Finding that in the formula of expansion of a function into a series of wave-like functions ?the coefficients are its Fourier transforms, if existed, we deduce mathematically all the principles and hypothesis that illustrated physicists utilized to build quantum mechanics a century ago, beginning with the duality particle-wave principle of Planck and including the Schrödinger equations. By the way, we find a simple Fourier transform relation between Dirac momentum and position bras and a useful permutation relation between operators in phase and Hilbert spaces. Moreover, from the found particle-wave duality formula we prove and obtain again essentially by mathematical analysis all the laws of wave optics concerning reflections, refractions, polarizations, diffractions by one or many identical 3D objects with various forms and dimensions.展开更多
In this paper,sine trigonometry operational laws(ST-OLs)have been extended to neutrosophic sets(NSs)and the operations and functionality of these laws are studied.Then,extending these ST-OLs to complex neutrosophic se...In this paper,sine trigonometry operational laws(ST-OLs)have been extended to neutrosophic sets(NSs)and the operations and functionality of these laws are studied.Then,extending these ST-OLs to complex neutrosophic sets(CNSs)forms the core of thiswork.Some of themathematical properties are proved based on ST-OLs.Fundamental operations and the distance measures between complex neutrosophic numbers(CNNs)based on the ST-OLs are discussed with numerical illustrations.Further the arithmetic and geometric aggregation operators are established and their properties are verified with numerical data.The general properties of the developed sine trigonometry weighted averaging/geometric aggregation operators for CNNs(ST-WAAO-CNN&ST-WGAO-CNN)are proved.A decision making technique based on these operators has been developed with the help of unsupervised criteria weighting approach called Entropy-ST-OLs-CNDM(complex neutrosophic decision making)method.A case study for material selection has been chosen to demonstrate the ST-OLs of CNDM method.To check the validity of the proposed method,entropy based complex neutrosophic CODAS approach with ST-OLs has been executed numerically and a comparative analysis with the discussion of their outcomes has been conducted.The proposed approach proves to be salient and effective for decision making with complex information.展开更多
In this paper, we conduct research on the operation mechanism of claim in civil procedure law and the applications on the court trial way reform. The ultimate goal of the rule of law lies in identifying and protecting...In this paper, we conduct research on the operation mechanism of claim in civil procedure law and the applications on the court trial way reform. The ultimate goal of the rule of law lies in identifying and protecting the rights of citizens. Way to protect the rights of citizens is diverse, but the judicial relief is the most basic and important form of insurance. Everyone can “into” the court and get the impartiality of the judicial relief, is a measure of a country judicial level height and the rule of law implementation degree of important yardstick. Judicial system and judicial procedure to build and build a better, if the subject of litigation rights are not being met and the safeguard, can’t get through the door and it is the legislators and legal scholars over the many efforts are meaningless, under this basic condition, we propose the new perspective on the corresponding issues that is necessary.展开更多
Exploring the inner law of the economic operation of urbanization can understand the regulation mechanism of the optimal distribution of urban resource allocation. In this regard, we propose to explore and analyze the...Exploring the inner law of the economic operation of urbanization can understand the regulation mechanism of the optimal distribution of urban resource allocation. In this regard, we propose to explore and analyze the inner law of urbanization economic operation and its application. The study found that the urbanization economy originated from the urban agglomeration effect, which includes the agglomeration economic operation mechanism and spillover effect operation mechanism, based on which three kinds of inner laws of urbanization economic operation are explored, combined with the economic operation law, the non-equilibrium state of the declining cities are regulated and applied, and the results show that the analysis of the inner laws of urbanization economic operation has a direct significance in guiding the real economic process.展开更多
Currently,the water inrush hazards during tunnel construction,the water leakage during tunnel operation,and the accompanying disturbances to the ecological environment have become the main problems that affect the str...Currently,the water inrush hazards during tunnel construction,the water leakage during tunnel operation,and the accompanying disturbances to the ecological environment have become the main problems that affect the structural safety of tunnels in water-rich regions.In this paper,a tunnel seepage model testing system was used to conduct experiments of the grouting circle and primary support with different permeability coefficients.The influences of the supporting structures on the water inflow laws and the distribution of the water pressure in the tunnel were analyzed.With the decrease in the permeability coefficient of the grouting circle or the primary support,the inflow rate of water into the tunnel showed a non-linear decreasing trend.In comparison,the water inflow reduction effect of grouting circle was much better than that of primary support.With the increase of the permeability coefficient of the grouting ring,the water pressure behind the primary lining increases gradually,while the water pressure behind the grouting ring decreases.Thus,the grouting of surrounding rock during the construction of water-rich tunnel can effectively weaken the hydraulic connection,reduce the influence range of seepage,and significantly reduce the decline of groundwater.Meanwhile,the seepage tests at different hydrostatic heads and hydrodynamic heads during tunnel operation period were also conducted.As the hydrostatic head decreased,the water pressure at each characteristic point decreased approximately linearly,and the water inflow rate also had a gradual downward trend.Under the action of hydrodynamic head,the water pressure had an obvious lagging effect,which was not conducive to the stability of the supporting structures,and it could be mitigated by actively regulating the drainage rate.Compared with the hydrostatic head,the hydrodynamic head could change the real-time rate of water inflow to the tunnel and broke the dynamic balance between the water pressure and water inflow rate,thereby affecting the stress state on the supporting structures.展开更多
In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statisti...In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.展开更多
Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and ...Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.展开更多
For centuries, groups of people desiring to supply themselves with goods, to market their products, or to obtain services of various kinds on a co-operative basis, have made increasing use of co-operative associations...For centuries, groups of people desiring to supply themselves with goods, to market their products, or to obtain services of various kinds on a co-operative basis, have made increasing use of co-operative associations to achieve these purposes. Duringthe period, legislation designed especially for the incorporation and conduct of such associations has been enacted by different counties. Since a co-operative is established and carried on by and for the use of its members, this essay makes a comparison between Canadian and Chinese co-operative laws in terms of membership in the aspects of qualifications, rights and obligations and withdrawal of membership, so as to probe the function of co-operative legislation and find some enlightment from it.展开更多
Taking into account the fact that the computer systems, as the implementations of Turing machine, are physical devices, the paper shows considerations in which hard drive behavior will be presented in terms of statist...Taking into account the fact that the computer systems, as the implementations of Turing machine, are physical devices, the paper shows considerations in which hard drive behavior will be presented in terms of statistical mechanics. Because computer is a machine, its analysis cannot be based only on mathematical models apart of physical conditions. In the paper it will be presented a very narrow part this problem – an analysis of hard drive behavior in the context of the power-law distributions. We will focus only on four selected hard drive parameters, i.e. the rate of transfer bytes to or from the disk during the read or write, the number of pending requests to the disk and the rate of read operations. Our research was performed under the Windows operating system and this allows to make a statistical analysis for the possible occurrence of power-laws representing the lack of characteristic scale for considered processes. This property will be confirmed in all analyzed cases. A presented study can help describing the behavior of the whole computer system in terms of physics of computer processing.展开更多
In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are ...In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.展开更多
ON April 3, 1992, the Law of the PRC on the Protection of Rights and Interests of Women (Protection Law), the first basic law for protecting rights and interests of women and promoting equality between men and women i...ON April 3, 1992, the Law of the PRC on the Protection of Rights and Interests of Women (Protection Law), the first basic law for protecting rights and interests of women and promoting equality between men and women in China, was adopted at the fifth session of the Seventh National People’s Congress (NPC), and entered into force on October 1 of the same year.展开更多
Du Fort-Frankel finite difference method(FDM)was firstly proposed for linear diffusion equations with periodic boundary conditions by Du Fort and Frankel in 1953.It is an explicit and unconditionally von Neumann stabl...Du Fort-Frankel finite difference method(FDM)was firstly proposed for linear diffusion equations with periodic boundary conditions by Du Fort and Frankel in 1953.It is an explicit and unconditionally von Neumann stable scheme.However,there has been no research work on numerical solutions of nonlinear Schrödinger equations with wave operator by using Du Fort-Frankel-type finite difference methods(FDMs).In this study,a class of invariants-preserving Du Fort-Frankel-type FDMs are firstly proposed for one-dimensional(1D)and two-dimensional(2D)nonlinear Schrödinger equations with wave operator.By using the discrete energy method,it is shown that their solutions possess the discrete energy and mass conservative laws,and conditionally converge to exact solutions with an order of for ofο(T^(2)+h_(x)^(2)+(T/h_(x))^(2))1D problem and an order ofο(T^(2)+h_(x)^(2)+h_(Y)^(2)+(T/h_(X))^(2)+(T/h_(y))^(2))for 2D problem in H1-norm.Here,τdenotes time-step size,while,hx and hy represent spatial meshsizes in x-and y-directions,respectively.Then,by introducing a stabilized term,a type of stabilized invariants-preserving Du Fort-Frankel-type FDMs are devised.They not only preserve the discrete energies and masses,but also own much better stability than original schemes.Finally,numerical results demonstrate the theoretical analyses.展开更多
文摘I. A Review of China's Judicial Protection for Human Rights To effectively protect human rights, a country needs to specify in its laws a complete series of basic rights its citizens shall enjoy. Meanwhile, the legal rights for an individual citizen would be meaningless even though such rights are prescribed in laws if, when the person's rights are infringed upon, he or she has no access to judicial relief. Administration of justice is the last resort, in fact the most effective, means.
文摘Adozen experts of law gathered on April 1, 2003 to share their views on protection of the workers’ right to remuneration for their work in accordance with the Labor Law of the People’s Republic of China. That took place at a seminar jointly sponsored by the Human Rights and the Beijing-based Democracy and Law magazines and the Branch of Labor and Social Security Laws of the Beijing Society of Law. Participants were from the All-China Federation of Trade Unions,
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
文摘The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in ℚ, marked ⊕and +α,β, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in ℝand ℂ. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned.
文摘The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the first fundamental form (FFF) and the partial Noether operator's determining equations are derived. These determining equations are then used to construct the partial Noether operators and conserved vectors for the wave equation on different surfaces. The conserved vectors for the wave equation on the sphere, cone and fiat space are simplified using the Lie point symmetry generators of the equation and conserved vectors with the help of the symmetry conservation laws relation.
文摘Finding that in the formula of expansion of a function into a series of wave-like functions ?the coefficients are its Fourier transforms, if existed, we deduce mathematically all the principles and hypothesis that illustrated physicists utilized to build quantum mechanics a century ago, beginning with the duality particle-wave principle of Planck and including the Schrödinger equations. By the way, we find a simple Fourier transform relation between Dirac momentum and position bras and a useful permutation relation between operators in phase and Hilbert spaces. Moreover, from the found particle-wave duality formula we prove and obtain again essentially by mathematical analysis all the laws of wave optics concerning reflections, refractions, polarizations, diffractions by one or many identical 3D objects with various forms and dimensions.
基金the Rajamangala University of Technology Suvarnabhumi.
文摘In this paper,sine trigonometry operational laws(ST-OLs)have been extended to neutrosophic sets(NSs)and the operations and functionality of these laws are studied.Then,extending these ST-OLs to complex neutrosophic sets(CNSs)forms the core of thiswork.Some of themathematical properties are proved based on ST-OLs.Fundamental operations and the distance measures between complex neutrosophic numbers(CNNs)based on the ST-OLs are discussed with numerical illustrations.Further the arithmetic and geometric aggregation operators are established and their properties are verified with numerical data.The general properties of the developed sine trigonometry weighted averaging/geometric aggregation operators for CNNs(ST-WAAO-CNN&ST-WGAO-CNN)are proved.A decision making technique based on these operators has been developed with the help of unsupervised criteria weighting approach called Entropy-ST-OLs-CNDM(complex neutrosophic decision making)method.A case study for material selection has been chosen to demonstrate the ST-OLs of CNDM method.To check the validity of the proposed method,entropy based complex neutrosophic CODAS approach with ST-OLs has been executed numerically and a comparative analysis with the discussion of their outcomes has been conducted.The proposed approach proves to be salient and effective for decision making with complex information.
文摘In this paper, we conduct research on the operation mechanism of claim in civil procedure law and the applications on the court trial way reform. The ultimate goal of the rule of law lies in identifying and protecting the rights of citizens. Way to protect the rights of citizens is diverse, but the judicial relief is the most basic and important form of insurance. Everyone can “into” the court and get the impartiality of the judicial relief, is a measure of a country judicial level height and the rule of law implementation degree of important yardstick. Judicial system and judicial procedure to build and build a better, if the subject of litigation rights are not being met and the safeguard, can’t get through the door and it is the legislators and legal scholars over the many efforts are meaningless, under this basic condition, we propose the new perspective on the corresponding issues that is necessary.
文摘Exploring the inner law of the economic operation of urbanization can understand the regulation mechanism of the optimal distribution of urban resource allocation. In this regard, we propose to explore and analyze the inner law of urbanization economic operation and its application. The study found that the urbanization economy originated from the urban agglomeration effect, which includes the agglomeration economic operation mechanism and spillover effect operation mechanism, based on which three kinds of inner laws of urbanization economic operation are explored, combined with the economic operation law, the non-equilibrium state of the declining cities are regulated and applied, and the results show that the analysis of the inner laws of urbanization economic operation has a direct significance in guiding the real economic process.
基金supported by the Chongqing Natural Science Foundation(No.cstc2020jcyjmsxm X0904)the Chongqing Talent Plan(No.CQYC2020058263)+3 种基金the Chongqing Technology Innovation and Application Development Project(No.cstc2021ycjh-bgzxm0246)the China Postdoctoral Science Foundation(No.2021M693739)the Sichuan Science and Technology Program(No.2021YJ0539)the Natural Science foundation of Jiangsu higher education institutions of China(Grant No.19KJD170001)。
文摘Currently,the water inrush hazards during tunnel construction,the water leakage during tunnel operation,and the accompanying disturbances to the ecological environment have become the main problems that affect the structural safety of tunnels in water-rich regions.In this paper,a tunnel seepage model testing system was used to conduct experiments of the grouting circle and primary support with different permeability coefficients.The influences of the supporting structures on the water inflow laws and the distribution of the water pressure in the tunnel were analyzed.With the decrease in the permeability coefficient of the grouting circle or the primary support,the inflow rate of water into the tunnel showed a non-linear decreasing trend.In comparison,the water inflow reduction effect of grouting circle was much better than that of primary support.With the increase of the permeability coefficient of the grouting ring,the water pressure behind the primary lining increases gradually,while the water pressure behind the grouting ring decreases.Thus,the grouting of surrounding rock during the construction of water-rich tunnel can effectively weaken the hydraulic connection,reduce the influence range of seepage,and significantly reduce the decline of groundwater.Meanwhile,the seepage tests at different hydrostatic heads and hydrodynamic heads during tunnel operation period were also conducted.As the hydrostatic head decreased,the water pressure at each characteristic point decreased approximately linearly,and the water inflow rate also had a gradual downward trend.Under the action of hydrodynamic head,the water pressure had an obvious lagging effect,which was not conducive to the stability of the supporting structures,and it could be mitigated by actively regulating the drainage rate.Compared with the hydrostatic head,the hydrodynamic head could change the real-time rate of water inflow to the tunnel and broke the dynamic balance between the water pressure and water inflow rate,thereby affecting the stress state on the supporting structures.
文摘In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.
文摘Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.
文摘For centuries, groups of people desiring to supply themselves with goods, to market their products, or to obtain services of various kinds on a co-operative basis, have made increasing use of co-operative associations to achieve these purposes. Duringthe period, legislation designed especially for the incorporation and conduct of such associations has been enacted by different counties. Since a co-operative is established and carried on by and for the use of its members, this essay makes a comparison between Canadian and Chinese co-operative laws in terms of membership in the aspects of qualifications, rights and obligations and withdrawal of membership, so as to probe the function of co-operative legislation and find some enlightment from it.
文摘Taking into account the fact that the computer systems, as the implementations of Turing machine, are physical devices, the paper shows considerations in which hard drive behavior will be presented in terms of statistical mechanics. Because computer is a machine, its analysis cannot be based only on mathematical models apart of physical conditions. In the paper it will be presented a very narrow part this problem – an analysis of hard drive behavior in the context of the power-law distributions. We will focus only on four selected hard drive parameters, i.e. the rate of transfer bytes to or from the disk during the read or write, the number of pending requests to the disk and the rate of read operations. Our research was performed under the Windows operating system and this allows to make a statistical analysis for the possible occurrence of power-laws representing the lack of characteristic scale for considered processes. This property will be confirmed in all analyzed cases. A presented study can help describing the behavior of the whole computer system in terms of physics of computer processing.
文摘In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.
文摘ON April 3, 1992, the Law of the PRC on the Protection of Rights and Interests of Women (Protection Law), the first basic law for protecting rights and interests of women and promoting equality between men and women in China, was adopted at the fifth session of the Seventh National People’s Congress (NPC), and entered into force on October 1 of the same year.
基金supported by the National Natural Science Foundation of China(Grant No.11861047)by the Natural Science Foundation of Jiangxi Province for Distinguished Young Scientists(Grant No.20212ACB211006)by the Natural Science Foundation of Jiangxi Province(Grant No.20202BABL 201005).
文摘Du Fort-Frankel finite difference method(FDM)was firstly proposed for linear diffusion equations with periodic boundary conditions by Du Fort and Frankel in 1953.It is an explicit and unconditionally von Neumann stable scheme.However,there has been no research work on numerical solutions of nonlinear Schrödinger equations with wave operator by using Du Fort-Frankel-type finite difference methods(FDMs).In this study,a class of invariants-preserving Du Fort-Frankel-type FDMs are firstly proposed for one-dimensional(1D)and two-dimensional(2D)nonlinear Schrödinger equations with wave operator.By using the discrete energy method,it is shown that their solutions possess the discrete energy and mass conservative laws,and conditionally converge to exact solutions with an order of for ofο(T^(2)+h_(x)^(2)+(T/h_(x))^(2))1D problem and an order ofο(T^(2)+h_(x)^(2)+h_(Y)^(2)+(T/h_(X))^(2)+(T/h_(y))^(2))for 2D problem in H1-norm.Here,τdenotes time-step size,while,hx and hy represent spatial meshsizes in x-and y-directions,respectively.Then,by introducing a stabilized term,a type of stabilized invariants-preserving Du Fort-Frankel-type FDMs are devised.They not only preserve the discrete energies and masses,but also own much better stability than original schemes.Finally,numerical results demonstrate the theoretical analyses.