Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a ...Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.展开更多
Being professional teacher is a process of acting and self empowering of teachers collectively and continuously. A teacher is not merely transferring knowledges and subject matters to the students but also internalizi...Being professional teacher is a process of acting and self empowering of teachers collectively and continuously. A teacher is not merely transferring knowledges and subject matters to the students but also internalizing the values; professionalism, knowledge laedership, community empowerment, etc. Partnership, professional development, and learning community are possibly gained by the teachers through lesson study implementasion interconnectedly and mutually. This paper aims at elaborating on the experience of State Junior High School 1 Srandakan Bantul Yogyakarta in implementing lesson study as a break-through to enhance the teachers＇ professional development incorporating the three mechanisms of lesson study. This school has conducted lesson study for about three years. The study resulted that 80 percent of teachers achieve their competence in planning, doing, and reflecting the lesson through observing other teachers performance and being observed interchangeably.展开更多
The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysi...The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.展开更多
This paper deals with an inverse problem for the unknown source term in a nonlinear evolution equation. Firstly, the authors change the initial boundary value problem (IBVP) for the equation into a Cauchy problem for ...This paper deals with an inverse problem for the unknown source term in a nonlinear evolution equation. Firstly, the authors change the initial boundary value problem (IBVP) for the equation into a Cauchy problem for a certain nonlinear evolution equation. Secondly, using the semigroup theory, the authors establish the existence and uniqueness of the solution for the inverse problem. Finally, they take advantage of the fixed point method for some contraction mapping and get the solvability of the inverse problem for the evolution equation.展开更多
Consider the Navier-Stokes equations in IRn×(0, T), for n≥3. Let 1 < a≤min{2, n/(n-2)} and define β by (2/a)+ (n/β) = 2. Set α′= α/(α-1). It is proved that Dv belongs to C(0, T; Lα′) ∩ Lα′ (0, T;...Consider the Navier-Stokes equations in IRn×(0, T), for n≥3. Let 1 < a≤min{2, n/(n-2)} and define β by (2/a)+ (n/β) = 2. Set α′= α/(α-1). It is proved that Dv belongs to C(0, T; Lα′) ∩ Lα′ (0, T; L2β/(n-2)) whenever Dv ∈ Lα(0, T; Lβ). In pwticular, v is a regular solution. This results is the natural extensinn to α ∈ (1, 2] of the classical sufficient condition that establishes that Lα(0, T; Lγ) is a regularity class if (2/α)+(n/γ) = 1. Even the borderline case α = 2 is significat. In fact, this result states that L2(0, T; W1,n) is a regularity class if n≤ 4. Since W1,n→L∞ is false, this result does not follow from the classical one that states that L2(0, T; L∞) is a regularity class.展开更多
A worldwide consensus on reducing greenhouse gas emissions has been reached at the technical and political level. However, as the issue involves economic costs and developmental interests, the international institutio...A worldwide consensus on reducing greenhouse gas emissions has been reached at the technical and political level. However, as the issue involves economic costs and developmental interests, the international institutional framework for addressing global greenhouse gas emissions has consistently failed to balance the demands of equity and sustainability. But the sustainability of carbon budget proposal is undoubtedly achievable if the total global carbon budget （the total amount of carbon permitted by climate security） is made an absolute constraint. If an initial allocation is made among all members of the global village on a per capita basis, a limited total budget could not only meet basic needs but also ensure equity. Taking into account historical emission levels and future needs, we should implement carbon budget transfer payments and devise a corresponding financial mechanism to ensure efficient allocation. Unlike the phase-by-phase progress and provisional goals of the Kyoto Protocol, the carbon budget proposal presented here is a comprehensive and holistic package. Due to the politicization of the climate change question, however, many technical issues can only be worked out through international political and diplomatic negotiations.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.
文摘Being professional teacher is a process of acting and self empowering of teachers collectively and continuously. A teacher is not merely transferring knowledges and subject matters to the students but also internalizing the values; professionalism, knowledge laedership, community empowerment, etc. Partnership, professional development, and learning community are possibly gained by the teachers through lesson study implementasion interconnectedly and mutually. This paper aims at elaborating on the experience of State Junior High School 1 Srandakan Bantul Yogyakarta in implementing lesson study as a break-through to enhance the teachers＇ professional development incorporating the three mechanisms of lesson study. This school has conducted lesson study for about three years. The study resulted that 80 percent of teachers achieve their competence in planning, doing, and reflecting the lesson through observing other teachers performance and being observed interchangeably.
基金supported by the"Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues"of the Chinese Academy of Sciences (Grant No.XDA01020304)
文摘The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.
基金Supported by tile Post-doctorate Science Foundation and tile National NSF ofChina.
文摘This paper deals with an inverse problem for the unknown source term in a nonlinear evolution equation. Firstly, the authors change the initial boundary value problem (IBVP) for the equation into a Cauchy problem for a certain nonlinear evolution equation. Secondly, using the semigroup theory, the authors establish the existence and uniqueness of the solution for the inverse problem. Finally, they take advantage of the fixed point method for some contraction mapping and get the solvability of the inverse problem for the evolution equation.
文摘Consider the Navier-Stokes equations in IRn×(0, T), for n≥3. Let 1 < a≤min{2, n/(n-2)} and define β by (2/a)+ (n/β) = 2. Set α′= α/(α-1). It is proved that Dv belongs to C(0, T; Lα′) ∩ Lα′ (0, T; L2β/(n-2)) whenever Dv ∈ Lα(0, T; Lβ). In pwticular, v is a regular solution. This results is the natural extensinn to α ∈ (1, 2] of the classical sufficient condition that establishes that Lα(0, T; Lγ) is a regularity class if (2/α)+(n/γ) = 1. Even the borderline case α = 2 is significat. In fact, this result states that L2(0, T; W1,n) is a regularity class if n≤ 4. Since W1,n→L∞ is false, this result does not follow from the classical one that states that L2(0, T; L∞) is a regularity class.
文摘A worldwide consensus on reducing greenhouse gas emissions has been reached at the technical and political level. However, as the issue involves economic costs and developmental interests, the international institutional framework for addressing global greenhouse gas emissions has consistently failed to balance the demands of equity and sustainability. But the sustainability of carbon budget proposal is undoubtedly achievable if the total global carbon budget （the total amount of carbon permitted by climate security） is made an absolute constraint. If an initial allocation is made among all members of the global village on a per capita basis, a limited total budget could not only meet basic needs but also ensure equity. Taking into account historical emission levels and future needs, we should implement carbon budget transfer payments and devise a corresponding financial mechanism to ensure efficient allocation. Unlike the phase-by-phase progress and provisional goals of the Kyoto Protocol, the carbon budget proposal presented here is a comprehensive and holistic package. Due to the politicization of the climate change question, however, many technical issues can only be worked out through international political and diplomatic negotiations.
