高中物理“教-学-评一体化”课堂教学探索——以“示波器的原理——带电粒子在电场中的偏转”为例

"教-学-评一体化"的课堂是指围绕教学目标,教师的教学、学生的学习以及教师对学生的评价组成一个有机的、整体的有效课堂.教学"有效"的唯一证据在于目标的达成,在于学生学习结果的质量,在于何以证明学生学会了什么.因此,教学中要关注对学生的评价.本文以"示波器的原理——带电粒子在电场中的偏转"为例,论述在"教-学-评一体化"的课堂中如何用评价促进学生思维发展.     

Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems

An equality has recently been shown relating the free energy difference between two equilibrium ensembles of a system and an ensemble average of the work required to switch between these two configurations. In the present paper it is shown that this result can be derived under the assumption that the system's dynamics is Markovian and microscopically reversible.     

边界元素法中有关积分的计算方法(Ⅱ)柱状边界条件下对曲面积分及椭圆积分的计算

在柱状边界条件下将对柱侧面的曲面积分表示成一维积分，同时还给出了椭圆积分的计算方法，由对空间立体角积分的算例可知，其计算的速度有了显著的提高．     

High-Order Hamilton＇s Principle and the Hamilton＇s Principle of High-Order Lagrangian Function

In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton＇s principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton＇s principle. Finally, the Hamilton＇s principle of high-order Lagrangian function is given.     

弹性半空间地基上圆形基础板的位移场和应力场

针对弹性半空间地基上圆形基础底板的弯曲问题,根据地基土壤的受力特性和已有实验研究成果,假设圆形基础底板底部与地基土壤之间是由竖向集中荷载引起的接触应力分布形式,采用板的弯曲理论和通过数值积分及最小二乘法拟合的方法,推导出完全满足边界条件的弹性半空间地基上圆形基础底板上部受集中力作用、下部受幂函数形式连续分布荷载作用时的位移场、径向和环向应力场的表达式。尽管圆形基础板属于中厚度板,但是该表达式的计算精度和可靠性得到了有限元分析软件ANSYS验证。     

Interpolatory integration rules and orthogonal polynomials with varying weights

We investigate which types of asymptotic distributions can be generated by the knots of convergent sequences of interpolatory integration rules. It will turn out that the class of all possible distributions can be described exactly, and it will be shown that the zeros of polynomials that are orthogonal with respect to varying weight functions are good candidates for knots of integration rules with a prescribed asymptotic distribution.Research supported by the Deutsche Forschungsgemeinschaft (AZ: Sta 299/4-2).     

Riccati方法与微分方程的渐近积分

考虑二阶常微分方程x″ f(t)x=0,t≥a,(1)假设应用Riccati方法得到方程(1)的主解(principal solution)的一个渐近积分并研究其副解(nonprincipal solutions)的三种不同的渐近性质.主要结果如下:定理1 若(Ⅰ)成立,则方程(1)有解x_1满足及另一解x_2满足x_2(t)=t[1 o(1)]. 反之,若方程(1)有解x(t)→1,t→∞,则(Ⅰ)成立. 定理2 设(Ⅰ)成立.(i)若(Ⅱ)成立,则方程(1)有解x_2使x_2’(t)=1 [tF(t) G(t)][1 o(1)] o(1). (ii) 反之,若方程(1)有解x使x’→1,t→∞,则(Ⅱ)成立. 定理3 若(Ⅲ)和(Ⅳ)成立,则方程(1)有解x_1满足(2)及解x_2满足     

工程施工中运输网络优化方案

施工工地运输方案的优化设计可以归结为 :按施工期要求设计运输线路或验证已有线路通行能力 ,计算总线路中影响提高流量的关键路段 ,取得最小费用最大流 .本文运用图论理论这一数学工具把实际问题抽象为有向网络 ,进而建立数学模型 .此方法理论上严密 ,解题步聚直观清晰 ,对水利、公路、水路、铁路等其它运输系统有普遍意义 .     

Strong tractability of multivariate integration using quasi-Monte Carlo algorithms

We study quasi-Monte Carlo algorithms based on low discrepancy sequences for multivariate integration. We consider the problem of how the minimal number of function evaluations needed to reduce the worst-case error from its initial error by a factor of depends on and the dimension . Strong tractability means that it does not depend on and is bounded by a polynomial in . The least possible value of the power of is called the -exponent of strong tractability. Sloan and Wozniakowski established a necessary and sufficient condition of strong tractability in weighted Sobolev spaces, and showed that the -exponent of strong tractability is between 1 and 2. However, their proof is not constructive.

In this paper we prove in a constructive way that multivariate integration in some weighted Sobolev spaces is strongly tractable with -exponent equal to 1, which is the best possible value under a stronger assumption than Sloan and Wozniakowski's assumption. We show that quasi-Monte Carlo algorithms using Niederreiter's -sequences and Sobol sequences achieve the optimal convergence order for any 0$"> independent of the dimension with a worst case deterministic guarantee (where is the number of function evaluations). This implies that strong tractability with the best -exponent can be achieved in appropriate weighted Sobolev spaces by using Niederreiter's -sequences and Sobol sequences.

     

On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order

We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.