教学课程资源库 更多>>

关键词： 数学分析   形象思维   严格推导  

摘要： 《数学分析》 是现代数学的基础理论之一.在 《数学分析》 的教学中, 培养学生的形象思维能力和严格推导能力是非常重要的两个方面.本文通过一些典型的例子, 讨论了形象思维和严格推导在 《数学分析》 的教学中的重要作用以及这两者之间的紧密关系.

关键词： 直流断路器   强制换流   拓扑结构   数学分析  

摘要： 作为高压直流输电的关键设备之一,直流断路器受到了广泛的关注。混合直流断路器继承了机械断路器通态损耗低与固态断路器开断迅速的特点,是目前直流断路器研究的主要方向。文中着重分析了影响基于全控型电力电子器件的强制换流型混合直流断路器开断速度的因素,针对辅助换流电路中缓冲电容放电回流影响机械断路器动作时间以及能量吸收电路吸收能量的时间问题,提出一种强制换流型混合断路器方案,该方案能够防止缓冲电容电流回流,同时减少避雷器吸收能量所用时间。对该断路器各个工作阶段的数学模型进行了数值分析,通过Pscad/EMTDC软件对故障状态混合断路器开断过程进行仿真,并且与典型强制混合直流断路器开断过程进行比较,验证了该方案切实可行。

关键词： Photosystem II   Chl fluorescence   Induction   Electron transport   Mathematical model  

摘要： The OJDIP rise in chlorophyll fluorescence during induction at different light intensities was mathematically modeled using 24 master equations describing electron transport through photosystem II (PSII) plus ordinary differential equations for electron budgets in plastoquinone, cytochrome f, plastocyanin, photosystem I, and ferredoxin. A novel feature of the model is consideration of electron in- and outflow budgets resulting in changes in redox states of Tyrosine Z, P680, and Q(A) as sole bases for changes in fluorescence yield during the transient. Ad hoc contributions by transmembrane electric fields, protein conformational changes, or other putative quenching species were unnecessary to account for primary features of the phenomenon, except a peculiar slowdown of intra-PSII electron transport during induction at low light intensities. The lower than F (m) post-flash fluorescence yield F (f) was related to oxidized tyrosine Z. The transient J peak was associated with equal rates of electron arrival to and departure from Q(A) and requires that electron transfer from Q(A) (-) to Q(B) be slower than that from Q(A) (-) to Q(B) (-). Strong quenching by oxidized P680 caused the dip D. Reduced plastoquinone, a competitive product inhibitor of PSII, blocked electron transport proportionally with its concentration. Electron transport rate indicated by fluorescence quenching was faster than the rate indicated by O-2 evolution, because oxidized donor side carriers quench fluorescence but do not transport electrons. The thermal phase of the fluorescence rise beyond the J phase was caused by a progressive increase in the fraction of PSII with reduced Q(A) and reduced donor side.

关键词： Time-fractional diffusion-wave equation   Caputo fractional derivative   Cauchy problem   Mittag-Leffler function   Mainardi function   Fourier transform  

摘要： This paper deals with a theoretical mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation in the upper half-plane, , , where the Caputo fractional derivative of order is considered. An explicit solution to this Cauchy problem is obtained via separation of variables. A first proof of the validity of the obtained results is provided for a certain kind of initial conditions. Throughout this work a new expression of the solution to this problem and its utility for carrying out rigurous proofs are presented. Finally, several new properties of the solution are obtained.

关键词： 高等教学   研究生   入学考试   题解  

ISBN: (数字)9787111589914 ISBN: (纸本)9787111589914

摘要： 全书共分八讲。讲介绍极限的思想、各种求解方法和证明极限存在的各种技巧；第二讲介绍函数一致连续性的思想和证明方法及技巧；第三讲介绍与微分中值定理（包括泰勒公式）有关的思想和解决问题的方法；第四讲介绍定积分的重要计算技巧和证明函数可积性的方法；第五讲介绍各类级数收敛性的判别方法和技巧，并对函数项级数和函数性质进行了详尽的讨论；第六讲介绍多元函数的各种性质及应用；第七讲介绍各类积分的计算方法和技巧，特别是第二类曲面积分；第八讲介绍证明不等式的常用方法和技巧。

关键词： Cavitation   Rayleigh-Plesset equation   Approximation scheme   Mathematical analysis   Numerical solution  

摘要： In the paper we introduce a new approximation scheme for modelling a spherical cloud of cavitation bubbles based upon a model developed in (Wang and Brennen in J. Fluids Eng. 121(4):872-880, 1999) which consists of fully nonlinear continuum mixture equations coupled with the Rayleigh-Plesset equation for dynamics of the bubbles. We prove existence of a unique, local-in-time solution to the equations using the Banach fixed-point theorem which also provides us with the convergent scheme for a numerical simulation of the solution. We further demonstrate acquired numerical results.

关键词： Bacterial chemotaxis   Signalling pathway   Adaptation   Equilibrium   Stability analysis   Overshoot  

摘要： We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an Escherichia coli cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions the system may exhibit oscillatory-type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins do. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions in the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our paper closes by discussing intercell variability of total protein concentration as a means of ensuring the overall survival of a population as cells are subjected to different environments.

关键词： 公费师范生   数学分析   教学实践  

摘要： 针对初中起点公费师范生的知识结构和能力水平,以及《数学分析》课程的特点,公费师范生的培养目标和定位,从教学内容选取,教学技术的使用和基本的解决问题能力和数学思维习惯的养成等教学实践进行探讨,寻找有效的《数学分析》的教学方式。

关键词： Mathematical model   Bioethanol production   The stability analysis   Settling unit  

摘要： Bioethanol generated from biomass and bioenergy crops has been promulgated as one of the most feasible alternatives to fossil fuel, as it is considered to be clean, green and of course renewable. In this paper, we develop a nonlinear chemostat model for bioethanol production. The growth rate is given by a modified Andrew expression with inhibition by ethanol, which is often used to model the growth of biomass. Then the uniqueness, invariance and dissipation of solutions of the model are established. Steady state solutions of the model and their stability are also determined as a function of the residence time. We also investigate the effects of the model parameters on a physically valid region. Finally, we compare the performance of a reactor, using a recycling process, against that of without recycling process. With a substrate feed concentration of 100 g/L, there is a critical value of the residence time which identifies a turning point in the reactor performance for the removal of substrate. (c) 2018 Elsevier Ltd. All rights reserved.

关键词： 高中生   数学   分析   解决问题   能力  

摘要： 分析和解决问题的能力是指能阅读、理解对问题进行陈述的材料;能综合应用所学数学知识、思想和方法解决问题,包括解决在相关学科、生产、生活中的数学问题,并能用数学语言正确地加以表述。它是逻辑思维能力、运算能力、空间想象能力等基本数学能力的综合体现。由于高考数学科的命题原则是在考查基础知识的基础上,注重对数学思想和方法的考查,注重数学能力的考查,强调了综合性。这就对考生分析和解决问题的能力提出了更高的要求,也使试卷的题型更新,更具有开放性。纵观近几年的高考,学生在这一方面失分的普遍存在,如07年的理科24题、08年的理科24题、09年的理科23、24题、2010年的文科21题,这就要求我们教师在平时教学中注重分析和解决问题能力的培养,以减少在这一方面的失分。我就分析和解决问题能力的组成及培养谈几点刍见。