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关键词： 数学分析   高等学校   教材  

ISBN: (纸本)9787563456260

摘要： 本书是华东师大数学系编《数学分析》(第四版，高等教育出版社)上册的配套用书。其章节内容与教材一致，讲

关键词： Applied mathematics   Behavioral and social aspects of health   Biology   Complex systems   Computational biology   Crime and criminology   Economics   Homicide   Law   Mathematics   Medicine   Operations research   Policy models   Political aspects of health   Political science   Population biology   Population modeling   Public health   Public policy   Research Article   Social and behavioral sciences   Socioeconomic aspects of health   Sociology  

摘要： In the USA, the relationship between the legal availability of guns and the firearm-related homicide rate has been debated. It has been argued that unrestricted gun availability promotes the occurrence of firearm-induced homicides. It has also been pointed out that gun possession can protect potential victims when attacked. This paper provides a first mathematical analysis of this tradeoff, with the goal to steer the debate towards arguing about assumptions, statistics, and scientific methods. The model is based on a set of clearly defined assumptions, which are supported by available statistical data, and is formulated axiomatically such that results do not depend on arbitrary mathematical expressions. According to this framework, two alternative scenarios can minimize the gun-related homicide rate: a ban of private firearms possession, or a policy allowing the general population to carry guns. Importantly, the model identifies the crucial parameters that determine which policy minimizes the death rate, and thus serves as a guide for the design of future epidemiological studies. The parameters that need to be measured include the fraction of offenders that illegally possess a gun, the degree of protection provided by gun ownership, and the fraction of the population who take up their right to own a gun and carry it when attacked. Limited data available in the literature were used to demonstrate how the model can be parameterized, and this preliminary analysis suggests that a ban of private firearm possession, or possibly a partial reduction in gun availability, might lower the rate of firearm-induced homicides. This, however, should not be seen as a policy recommendation, due to the limited data available to inform and parameterize the model. However, the model clearly defines what needs to be measured, and provides a basis for a scientific discussion about assumptions and data.

关键词： 弹簧振子   摩擦   滑阻运动  

摘要： 本文系统地探讨了以恒定速度牵引弹簧振子时弹簧振子的运动规律,给出了弹簧振子运动速度的解析解,静摩擦因数大于动摩擦因数导致弹簧振子做滑阻运动。

关键词： 数学分析   多媒体   课后辅导  

摘要： 《数学分析》是数学专业的重要基础课程,它跨时长,难度也比较大。该文针对数学专业的专科生提出了几点教学想法。

关键词： 高等代数   数学分析  

摘要： 高等代数与数学分析在理论、具体问题、解题思路及处理方法上都是不同的，但两者在一些方面又有着密切联系。本文通过实例对高等代数在通过数学分析中的应用进行分析探讨，从而引出两门专业基础课程有关问题的互通与融合，相互密切的关联。

关键词： Stock loans   Kolmogorov equation   Obstacle problems   Anisotropic regularity   Characteristics time discretization   Finite elements   Augmented Lagrangian active set method  

摘要： In this paper the mathematical analysis of a model for pricing stock loan contracts, when the accumulative dividend yield associated to the stock is returned by the lender to the borrower on redemption, is carried out. More precisely, the model is formulated in terms of an obstacle problem associated to a Kolmogorov equation and the existence and uniqueness in the set of solutions with polynomial growth are obtained. Also some regularity properties of the solution are analyzed. Next, for the numerical solution of the problem the combination of Crank-Nicolson Lagrange-Galerkin with the augmented Lagrangian active set method is described. Finally, some numerical examples illustrate the theoretical properties of the optimal redeeming boundary previously stated in the literature. (C) 2013 Elsevier Inc. All rights reserved.