浅谈高等数学习题课教学

探讨习题课教学应注意的问题．首先明确指出习题课的目的和意义,之后从重视对数学概念的理解运用、习题的选择、课堂互动等方面阐述如何提高课堂教学效率,以达到不断渗透数学思想、数学方法的目的,从而培养学生良好的思维品质．     

浅析ETA物理认知模型在中学物理习题教学中的应用

物理习题教学是中学物理教学的重要环节,能够帮助学生提高运用物理知识解决实际问题的能力.基于ETA物理认知模型,针对理论物理认知题型、实验物理认知到理论物理认知题型和应用物理认知题型3类题型的习题特点,总结出每类题型具体的应对策略.在习题教学过程中教师需要强化学生的物理基本知识和理论,帮助学生做好从实践到构建物理模型的过渡,引导学生做好理论与实际生活联系,为提升习题教学的有效性提供参考.     

Exercising QS: quantitative skills in an exercise science course

This study seeks to bring the discipline of exercise science into the discussion of Quantitative Skills (QS) in science. The author's experiences of providing learning support to students and working with educators in the field are described, demonstrating the difficulty of encouraging students to address their skills deficit. A survey of students’ perceptions of their own QS and of that required for their course, demonstrates the difficulties faced by students who do not have the prescribed assumed knowledge for the course. Limited results from academics suggest that their perceptions of students’ QS deficits are even direr than those of the under-prepared students.     

Evidence of Improvement in Various Impairments by Exercise Interventions in Patients with Knee Osteoarthritis: A Systematic Review and Meta-analysis of Randomized Clinical Trials

Purpose: To investigate improvement in various impairments by exercise interventions in patients with knee osteoarthritis (OA). Methods: We collected data on randomized controlled trials (RCTs) comparing the effects of exercise intervention with those of either nonintervention or psychoeducational intervention in patients with knee OA. Data on pain, stiffness, muscle strength, range of motion, flexibility, maximal oxygen uptake, and position sense were synthesized. The Grading of Recommendations Assessment, Development, and Evaluation system was used to determine the quality of the evidence. Results: Thirty-three RCTs involving 3,192 participants were identified. Meta-analysis provided highquality evidence that exercise intervention improves maximal oxygen uptake, and moderate-quality evidence that exercise intervention also improves pain, stiffness, knee extensor and flexor muscle strength, and position sense. The evidence that exercise intervention improves knee extension and flexion range of motion was deemed as undetermined-quality. Conclusion: In patients with knee OA, improvement in pain, stiffness, muscle strength, maximal oxygen uptake, and position sense with the use of exercise intervention can be expected. Although the quality of evidence of the effect of exercise intervention on range of motion was inconclusive, exercise intervention should be recommended for patients with knee OA to improve various impairments.     

Pricing American currency options in an exponential Lévy model

In this article the problem of the American option valuation in a Lévy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying process at the exercise boundary (i.e. with positive jumps in the call case), original results are derived by relying on first passage time and overshoot associated with a Lévy process. For finite life American currency calls, the formula derived by Bates or Zhang, in the context of a negative jump size, is tested. It is basically an extension of the one developed by Mac Millan and extended by Barone‐Adesi and Whaley. It is shown that Bates' model generates pretty good results only when the process is continuous at the exercise boundary.     

如何将发散思维应用在习题课中

习题课教学过程中充分发挥学生的发散思维,有助于对物理概念的理解和创新能力的培养,本通过对一道典型力学题的分析,阐述了如何将发散思维应用在习题课教学中。     

The American Foreign Exchange Option in Time-Dependent One-Dimensional Diffusion Model for Exchange Rate

The classical Garman-Kohlhagen model for the currency exchange assumes that the domestic and foreign currency risk-free interest rates are constant and the exchange rate follows a log-normal diffusion process. In this paper we consider the general case, when exchange rate evolves according to arbitrary one-dimensional diffusion process with local volatility that is the function of time and the current exchange rate and where the domestic and foreign currency risk-free interest rates may be arbitrary continuous functions of time. First non-trivial problem we encounter in time-dependent case is the continuity in time argument of the value function of the American put option and the regularity properties of the optimal exercise boundary. We establish these properties based on systematic use of the monotonicity in volatility for the value functions of the American as well as European options with convex payoffs together with the Dynamic Programming Principle and we obtain certain type of comparison result for the value functions and corresponding exercise boundaries for the American puts with different strikes, maturities and volatilities. Starting from the latter fact that the optimal exercise boundary curve is left continuous with right-hand limits we give a mathematically rigorous and transparent derivation of the significant early exercise premium representation for the value function of the American foreign exchange put option as the sum of the European put option value function and the early exercise premium. The proof essentially relies on the particular property of the stochastic integral with respect to arbitrary continuous semimartingale over the predictable subsets of its zeros. We derive from the latter the nonlinear integral equation for the optimal exercise boundary which can be studied by numerical methods.     

Spectral Method for the Black-Scholes Model of American Options Valuation

In this paper, we devote ourselves to the research of numerical methods for American option pricing problems under the Black-Scholes model. The optimal exercise boundary which satisfies a nonlinear Volterra integral equation is resolved by a high-order collocation method based on graded meshes. For the other spatial domain boundary, an artificial boundary condition is applied to the pricing problem for the effective truncation of the semi-infinite domain. Then, the front-fixing and stretching transformations are employed to change the truncated problem in an irregular domain into a one-dimensional parabolic problem in [−1,1]. The Chebyshev spectral method coupled with fourth-order Runge-Kutta method is proposed for the resulting parabolic problem related to the options. The stability of the semi-discrete numerical method is established for the parabolic problem transformed from the original model. Numerical experiments are conducted to verify the performance of the proposed methods and compare them with some existing methods.     

Valuing American options under the CEV model by Laplace-Carson transforms

This paper investigates American option pricing under the constant elasticity of variance (CEV) model. Taking the Laplace-Carson transform (LCT) to the corresponding free-boundary problem enables the determination of the optimal early exercise boundary to be separated from the valuation procedure. Specifically, a functional equation for the LCT of the early exercise boundary is obtained. By applying Gaussian quadrature formulas, an efficient method is developed to compute the early exercise boundary, American option price and Greeks under the CEV model.     

Effect of Home-based Exercise Therapy for Peripheral Arterial Disease Patients Underwent Endovascular Treatment: A Clinical Controlled Design

Objective: This study aimed to clarify the effect of home-based exercise therapy on physical activity in peripheral arterial disease (PAD) patients after EVT. Methods: Study design was controlled clinical design. The subjects were 30 patients (76.6% men) who underwent EVT in the Sakakibara Heart Institute of Okayama. Patients with EVT meeting the inclusion criteria were divided into two groups, intervention group (Home-based exercise) and control group. Patients'' basic characteristics, the number of steps walked and QOL questionnaire (WIQ, SEPA, Vascu QOL) were assessed before surgery and, at the 3 month after discharge. A two-way analysis of variance (ANOVA) was performed to compare number of steps walked and QOL questionnaire. Results: Interaction effect were observed in the number of steps walked (F (1,28) =13.89, p<0.01). A multiple comparison test confirmed a significant increase between results of before surgery and at three months after surgery in the intervention group (p<0.01). An interaction between the presence and absence of intervention was found for the WIQ pain score (F(1,28) = 5.86, p=0.01), speed score (F(1,28) = 3.80, p=0.04) and SEPA (F(1,28) = 4.99, p=0.03). In a multiple comparison study, there was a significant increase in WIQ pain and speed scores in both groups before and 3 months after discharge from the hospital. Conclusion: Home-based exercise therapy using physical activity indices has the potential to improve number of steps and quality of life in patients with PAD after EVT.