Free kicks play an important role in a modern soccer match. A skillful soccer player usually uses the opportunity of a free kick to score a goal. There are mainly two ways to give a free kick, falling ball and banana ball. The last thesis analyzes the path of falling soccer in two-dimensional plane. This thesis mainly focuses on using geometrical ways to generate a graph in three-dimensional coordinate system to analyze the path of banana ball and find out the most suitable distance to give a free kick.

Based on Leslie Matrix, the paper tries to predict the population fluctuation of Nanjing by considering the regional distinction and latest policy impacts, and hereby comes up with four conclusions: a) The population of Nanjing will see a relatively rapid growth between 2013 and 2020; b) Given the situation, the elderly population of the city will experience a much faster increase in the next 40 years, causing an elderly bulge that not only poses heavy burden to social welfare but also gives rise to a disproportionate population structure; c) The proposed retirement age extension in theory, will reduce the pressure on pension system by retaining active labors, and thus alleviating the problems of aging population to some extent; d) The newly-issued Two-Child Policy will not change the trends in or transform the population structure, therefore its effects on population aging is rather limited.

This paper proposes an Integrated Obesity Index (IOI) based on height, weight, waist, and hip, physical indexes that can be accessed through regular physical examinations, on top of common obesity standards, including Body Mass Index (BMI), Waist‐Hip Ratio (WHR), and Body Fat Percentage (BFP). Integrated Obesity Index is aimed to be feasible and convenient under application, as well as comprehensive, compensating for the limitations of existing classifications of obesity. Thus, this paper proposes and examines the application formula of the IOI by establishing geometric models. Adopting the data from epidemiological survey, this papers brings physical indicators, gender, BFP and other variables into the model for data analysis, applies linear regression on the resulting images, and obtains the IOI cut‐off point. By conducting comprehensive data analyses to various obesity classifications, the paper demonstrates that the IOI has significant advantages over BMI, WHP, or BFP and will compensate for the deficiencies of the existing obesity classifications to a certain extent in application.

This article applies functional knowledge and computer software to describe the relation between people distribution and evacuation efficency and safety in high-rise buildings.The people distribution contains two parts:the allocation of people in different storeys and the distribution of people in a certain storey. Through this mathematical model,we attempt to find the optimum plan of people distribution and use it to guide the distribution of different functional areas in high-rise buildings.

It is well known that group is a set with an algebra operation, which is often denoted by G . A simple group is the group which has only the 2 trivial normal subgroups. The importance of the simple groups may analogue to the prime numbers in the number theory. The classification of the finite simple groups was the central problem of 20th century’s’ algebra. In this research report, we use Sylow theorem, Burnside theorem, group action and some other elementally group theory methods to obtain some criteria of simple group . By using these criteria we determine the possible simple groups whose order less than 700. Generalizes the results in the reference [1]，[2]， [3]，[4].We conclude that Theorem A group G of order less or equal than 700 could not be simple except for |G|∈{60,168,360,504,660 and all primes}.