We study the super-resolution (SR) problem of recovering point sources consisting of a collection of isolated and suitably separated spikes from only the low frequency measurements. If the peak separation is above a factor in $(1, 2)$ of the Rayleigh length (physical resolution limit), L1 minimization is guaranteed to recover such sparse signals. However, below such critical length scale, especially the Rayleigh length, the $L_1$ certificate no longer exists. We show several local properties (local minimum, directional stationarity, and sparsity) of the limit points of minimizing two $L_1$ based nonconvex penalties, the difference of $L_1$ and $L_2$ norms $(L_{1-2})$ and capped $L_1 (CL_1)$, subject to the measurement constraints. In one and two dimensional numerical SR examples,the local optimal solutions from dierence of convex function algorithms outperform the global L1 solutions near or below Rayleigh length scales either in the accuracy of ground truth recovery or in nding a sparse solution satisfying the constraints more accurately.

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.