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也谈“平行四边形的面积”的教学 被引量:1
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作者 廖运章 《中小学课堂教学研究》 2017年第Z2期13-15,79,共4页
运用数方格(在方格纸中数单位正方形的个数)和割补法推证平行四边形的面积公式,是我国小学数学教学的传统,被现行多数课标数学教科书及课堂教学采用,但教材设计和教学实践出现了偏差。本文在析因的基础上,认为'数方格'是一种建... 运用数方格(在方格纸中数单位正方形的个数)和割补法推证平行四边形的面积公式,是我国小学数学教学的传统,被现行多数课标数学教科书及课堂教学采用,但教材设计和教学实践出现了偏差。本文在析因的基础上,认为'数方格'是一种建模方法,其操作应合理、得当、科学,并阐释数方格方法求平行四边形面积的逻辑顺序。同时,基于出入相补原理在平行四边形面积公式推导当中的核心地位,归纳出入相补原理推证平行四边形面积公式的常见方法,促进小学'平行四边形的面积'课堂教学的有效性。 展开更多
关键词 平行四边形面积 数方格方法 出入相补原理
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3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization 被引量:2
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作者 Tiril P Gurholt Xuecheng Tai 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2009年第4期403-420,共18页
Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmenta... Segmentation of three-dimensional(3D) complicated structures is of great importance for many real applications.In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model.Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations.Instead,the minimum cut on a special designed graph need to be computed.The method is tested on data with complicated structures.It is rather stable with respect to initial value and the algorithm is nearly parameter free.Experiments show that it can solve large problems much faster than traditional approaches. 展开更多
关键词 Piecewise constant level set method energy minimization graph cut SEGMENTATION three-dimensional.
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Casimir Effect of Massive Scalar Field with Hybrid Boundary Condition in(1+1)-Dimensional Spacetime
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作者 HE Xiao-Kai LIU Wen-Biao QIU Wei-Gang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第5期845-848,共4页
The Casimir energy of massive scalar field with hybrid (Diriehlet-Neumann) boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green's function... The Casimir energy of massive scalar field with hybrid (Diriehlet-Neumann) boundary condition is calculated. In order to regularize the model, the typical methods named as mode summation method and Green's function method are used respectively. It is found that the regularized zero-point energy density depends on the scalar field's mass. When the field is massless, the result is consistent with previous literatures. 展开更多
关键词 Casimir effect boundary condition massive scalar field REGULARIZATION
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Magnetic Properties of Ferromagnetic Double Layers with Ferrimagnetic Interlayer Coupling at Zero Temperature
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作者 JIANG Wei ZHU Cheng-Bo WANG Wei ZHANG Fan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第2期349-352,共4页
Spin-wave theory is used to study magnetic properties of ferromagnetic double layers with a ferrimagnetic interlayer coupling at zero temperature. The spin-wave spectra and four sublattices magnetizations and internal... Spin-wave theory is used to study magnetic properties of ferromagnetic double layers with a ferrimagnetic interlayer coupling at zero temperature. The spin-wave spectra and four sublattices magnetizations and internal energy are calculated by employing retarded Green function technique. The sublattice magnetizations at ground state are smaller than their classical values, owing to the zero-point quantum fluctuations of the spins. 展开更多
关键词 spin-wave theory ferromagnetic double layers zero-point quantum fluctuation ferrimagnetic interlay coupling
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Heterogeneous Responses of Chinese Cities' Housing Prices to Monetary Policies
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作者 闫妍 王延颋 朱晓武 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第10期791-796,共6页
This works examine the responses of housing prices to the monetary policies in various Chinese cities. Thirty-five large and medium sized Chinese cities are classified into six clusters applying the minimum variance c... This works examine the responses of housing prices to the monetary policies in various Chinese cities. Thirty-five large and medium sized Chinese cities are classified into six clusters applying the minimum variance clustering method according to the calculated correlation coefficients between the housing price indices of every two cities.Time difference correlation analysis is then employed to quantify the relations between the housing price indices of the six clusters and the monetary policies.It is suggested that the housing prices of various cities evolved at different paces and their responses to the monetary policies are heterogeneous,and local economic features are more important than geographic distances in determining the housing price trends. 展开更多
关键词 monetary policy housing price heterogeneous responses cluster
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Relativistic Continuum Random Phase Approximation and Applications I. Formalism
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作者 杨丁 曹李刚 马中玉 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第4期716-722,共7页
A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed in terms of the Green's function technique. In this method the contribution of the continuum spectrum to nuclear excitatio... A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed in terms of the Green's function technique. In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function, which includes also the negative states in the Dirac sea in the no sea approximation. The theoretical formalism of RCRPA and numerical details are presented. The single particle Green's function is calculated numerically by a proper product of regular and irregular solutions of the Dirac equation. The numerical details and the formalism of RCRPA in the momentum representation are presented. 展开更多
关键词 Hartree-Fock and random-phase approximations giant resonances nuclear matter
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LBE-DEM coupled simulation of gas-solid two-phase cross jets 被引量:6
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作者 GUI Nan XU WenKai +1 位作者 GE Liang YAN Jie 《Science China(Technological Sciences)》 SCIE EI CAS 2013年第6期1377-1386,共10页
This paper establishes a lattice Boltzmann equation-discrete element method (LBE-DEM) coupled simulation method under the Eulerian-Lagrangian framework at first, and applies it to simulating a two-dimensional gas-soli... This paper establishes a lattice Boltzmann equation-discrete element method (LBE-DEM) coupled simulation method under the Eulerian-Lagrangian framework at first, and applies it to simulating a two-dimensional gas-solid two-phase cross jet. The gas phase is simulated by the lattice-Boltzmann method via the TD2G9 model; the solid phase is traced by the Lagrangian method and the inter-particle collision is calculated by the DEM method. Three values of the Stokes number St=10, 25, and 50 are simulated under the same mass loading. This paper focuses on the characteristics of vortex structure, particle distribution, and the reverse-flow/rebounding rate in cross jets. We analyze the characteristics of fluid vortex motion, particle cluster distribution, rebounding rate of particles and the influencing factors for them. The results show the existence of joint distribution of discrete clusters and discrete particles in cross jets. Meanwhile, it shows that a larger concentration of particles in the early stage of jet evolution or a smaller Stokes number under the same mass loading can produce a larger rebounding rate. However, the rebounding rate of particles at the late stage, in general, is stable. 展开更多
关键词 gas-solid flow cross jet lattice Boltzmann discrete element method inter-particle collision
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