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关键词： 复变函数   数学分析   极限   积分  

摘要： 复变函数是研究数域为复数域的函数,本文通过对复变函数与数学分析之间若干问题的比较,而阐述复变函数与数学分析的相近之处及不同之处,进而实现知识的理解加深,找到两学科之间的联系和区别,从而更深刻的理解两类数学问题。

关键词： 工程技术   应用数学  

摘要： 进入21世纪以来,我国的经济飞速发展,城市化进程也在不断加深,为配合城市化的发展,对工程技术的需求越来越大,为保证广大工程技术人员和科研工作者的工作质量,增强他们对运用电子计算技术解决工程问题的意识,需要在实践中,充分利用数学课程的理论知识和工程实际问题相结合,重视工程技术应用数学的重要性。本文的主要内容就是对工程技术应用数学进行相关分析。

关键词： 适配体   富集水平   数学分析   SELEX  

摘要： 指数富集的配基系统进化(SELEX)方法是一种新颖的筛选技术,能从人工合成的DNA/RNA文库中筛选得到核酸适配体.根据SELEX原理,与靶标亲和性最强的核酸适配体应该具有最高的富集水平.然而,SELEX实验很少出现这种现象.本文采用数学方法,论证了在满足一定实验条件时,与靶标亲和性最强的核酸适配体并不具有最高的富集水平,并指出了较大的靶标浓度、较低的分离效率会促使这种现象的产生.

关键词： Systems pharmacology   Feedback   Antibody   Receptor rebound   Pharmacokinetics   Pharmacodynamics  

摘要： We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after the application of an antibody drug using a target-mediated drug disposition model. It is assumed that the receptor synthesis rate experiences homeostatic feedback from the receptor levels. It is shown for a very fast feedback response, that the occurrence of rebound is determined by the ratio of the elimination rates, in a very similar way as for no feedback. However, for a slow feedback response, there will always be rebound. This result is illustrated with an example involving the drug efalizumab for patients with psoriasis. It is shown that slow feedback can be a plausible explanation for the observed rebound in this example.

关键词： Epidemic model   vaccination and treatment controls   basic reproduction number   isolation   global stability   37N25   92D30   34K20  

摘要： In this article, we consider a susceptible-infectious-recovered (SIR) type epidemic model with some isolation to the susceptible, treatment for infectives, and vaccination to the newly recruited individuals. The basic reproduction number is obtained, and both the existence and stability of the disease-free and endemic equilibrium are discussed. We study the influence of isolation on infected individuals. We also study the existence of optimal control for both vaccination and treatment to minimize both the infected population and the costs required to control the disease. All the theoretical results are verified through numerical simulations and some of the key findings are given at the end of the article.

关键词： 数学分析   高等学校   教材  

ISBN: (数字)9787567219656 ISBN: (纸本)9787567219656

摘要： 实数集与函数、数列极限、函数极限、函数的连续性、导数与微分、微分中值定理及其应用、实数的完备性、不定积分、定积分等。

关键词： SIQR model   Imperfect quarantine   Equilibria   Stability analysis   Hopf bifurcation   Uniform persistence  

摘要： The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.

关键词： 数学分析   实变函数   理念   方法  

摘要： 高等教育是一个国家可持续发展的重要组成部分,而数学教育又是高等教育的基石。课堂教学是数学教育中传授知识和技能的重要渠道。丰富的教学活动和良好的教学效果强烈依赖于明确的教学理念和有效的教学方法。以"数学分析"和"实变函数"两门课程的教学为例,结合自己多年来的教学经历和体会,阐述普通高等学校数学类课程的教学理念,并围绕着教学理念探究教学措施和方法,希望以己拙见抛砖引玉。