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关键词： 数学   恒等变换法   应用路径  

摘要： 在数学分析中恒等变换法是最常用的方法,主要用于有理式和无理式运算过程中的恒等变换,从而达到简化运算目的。对于某些作图题来说,利用恒等变换法,能使作图步骤得到简化,由此可见,恒等变换法在数学计算中具有非常重要的应用意义。为此,对恒等变换法在数学分析中的应用路径进行探讨,明确恒等变换法在数学分析中的作用。

关键词： BOLD contrast   energy metabolism   hemodynamics   mathematical modelling   kinetic modelling  

摘要： Blood oxygen level-dependent functional magnetic resonance imaging (BOLD-fMRI) is a standard clinical tool for the detection of brain activation. In Alzheimer's disease (AD), task-related and resting state fMRI have been used to detect brain dysfunction. It has been shown that the shape of the BOLD response is affected in early AD. To correctly interpret these changes, the mechanisms responsible for the observed behaviour need to be known. The parameters of the canonical hemodynamic response function (HRF) commonly used in the analysis of fMRI data have no direct biological interpretation and cannot be used to answer this question. We here present a model that allows relating AD-specific changes in the BOLD shape to changes in the underlying energy metabolism. According to our findings, the classic view that differences in the BOLD shape are only attributed to changes in strength and duration of the stimulus does not hold. Instead, peak height, peak timing and full width at half maximum are sensitive to changes in the reaction rate of several metabolic reactions. Our systems-theoretic approach allows the use of patient-specific clinical data to predict dementia-driven changes in the HRF, which can be used to improve the results of fMRI analyses in AD patients.

关键词： Fixed-rate mortgages   Obstacle problem   Uniformly parabolic operator   Strong solution  

摘要： In this paper, we address the mathematical analysis of a partial differential equation model for pricing fixed-rate mortgages with prepayment and default options, where the underlying stochastic factors are the house price and the interest rate. The mathematical model is posed in terms of a sequence of linked complementarity problems, one for each month of the loan life, associated with a uniformly parabolic operator. We study the existence of a strong solution to each one of the obstacle problems. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： 数学   分析和解决问题能力   策略  

摘要： 新课标明确指出,高中数学课程对于提高学生的分析和解决问题能力,形成理性思维,发展智力和创新思维起着基础性作用。就高中生的分析和解决问题能力的组成和培养谈几点浅见。

关键词： Radial basis functions   Repeated integrals of complementary error function   American options as free boundary problems   Artificial boundary conditions   Bernstein functions   Completely monotone functions  

摘要： In this paper, we introduce a new family of infinitely smooth and "nearly" locally supported radial basis functions (RBFs), derived from the general solution of a heat equation arising from the American option pricing problem. These basis functions are expressed in terms of "the repeated integrals of the complementary error function" and provide highly efficient tools to solve the free boundary partial differential equation resulting from the related option pricing model. We introduce an integral operator with a function-dependent lower limit which is employed as a basic tool to prove the radial positive definiteness of the proposed basis functions and could be of independent interest in the RBF theory. We then show that using the introduced functions as expansion bases in the context of an RBF-based meshless collocation scheme, we could exactly impose the transparent boundary condition accompanying the heat equation. We prove that the condition numbers of the resulting collocation matrices are orders of magnitude less than those arising from other popular RBF families used in current literature. Some other properties of these bases such as their Fourier transforms as well as some useful representations in terms of positive Borel measures will also be discussed. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Rate of energy change   Kinetic method   Kinematic method   Gait analysis  

摘要： Segmental power is used in human movement analyses to indicate the source and net rate of energy transfer between the rigid bodies of biomechanical models. Segmental power calculations are performed using segment endpoint dynamics (kinetic method). A theoretically equivalent method is to measure the rate of change in a segment's mechanical energy state (kinematic method). However, these two methods have not produced experimentally equivalent results for segments proximal to the foot, with the difference in methods deemed the "power imbalance." In a 6 degree-of-freedom model, segments move independently, resulting in relative segment endpoint displacement and non-equivalent segment endpoint velocities at a joint. In the kinetic method, a segment's distal end translational velocity may be defined either at the anatomical end of the segment or at the location of the joint center (defined here as the proximal end of the adjacent distal segment). Our mathematical derivations revealed the power imbalance between the kinetic method using the anatomical definition and the kinematic method can be explained by power due to relative segment endpoint displacement.. In this study, we tested this analytical prediction through experimental gait data from nine healthy subjects walking at a typical speed, The average absolute segmental power imbalance was reduced from 0.023 to 0.046 W/kg using the anatomical definition to <= 0.001 W/kg using the joint center definition in the kinetic method (95.56-98.39% reduction). Power due to relative segment endpoint displacement in segmental power analyses is substantial and should be considered in analyzing energetic flow into and between segments. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： 数学分析   行为主义学习   考评机制  

摘要： 针对近年来大学生数学能力不平衡的情况，从行为主义学习理论角度，提出了改变教学风格以及设计新的考评机制，用以改善数学分析课程“教与学”的行为有效性。通过调查发现，在教学改革方面充分利用错误习题、错误解答、悖论、反例以及一些研究性课题，有助提升学生数学能力和教学效果。

关键词： 数学分析   数学概念   数学技能  

摘要： 数学分析习题课是数学分析课程教学的重要组成部分,它既能加强对概念更深层次的理解,也能灵活的将数分课程中所涵盖的概念、定理及性质来进一步解决数学中的问题。习题课作为一种重要的教学补偿手段,在相对抽象、复杂、计算技巧多元化的数学分析课程中尤为重要。

关键词： 数学阅读   有效性   阅读能力   数学语言   小学   数学分析   自主学习   数学知识  

摘要： 古语云:“读书百遍,其义自见。”这说明阅读能力对一个人来说是多么的重要。良好的数学阅读,能帮助学生提高数学分析、抽象、推理的能力以及自主学习的能力,更有助于帮助学生获取数学知识,丰富数学语言,培养数学交流的能力。数学教师不但要培养学生的计算能力,更要注重对学生数学阅读兴趣的激发、数学阅读习惯的培养和阅读方法的指导,为学生的终身学习与发展奠定基础。一、数学语言的独特数学是一门科学,也是一种文化,更是一种语言。数学语言具有简洁、无歧义的特点,而数学符号往往内涵丰富。

关键词： 数学分析定理教学   MuPAD软件   高等院校  

摘要： 文章尝试将MuPAD软件的画图、计算等功能融入数学分析的定理教学过程中,使学生直观地理解数学分析的相关定理,提高教学的交互可视性,从而激发学生的学习和科研兴趣,并结合案例,介绍MuPAD软件辅助数学分析定理教学的思想。