I heard the concept of the ”equal‐sum point” in a math summer camps and found it very interesting. After searching on the Internet,I found that the ”equal‐sum point” was associated with Soddy point. Soddy point is a magic point in plane geometry, which was found by British physicist, chemist Frederick.Soddy. Some research about the Soddy point has been done in foreign countries, but the properties are not comprehensive. In China, Teacher HuasongHuang raised the concept of the “equal‐sum point” and the “equal‐difference point” and drew some properties, I found that these two points were very similar to the Soddy point, but they did not link the two points with Soddy point. In this article ,I will connect the Soddy point with the “equal‐sum point” and the “equal‐difference point” and study their properties more deeply and find some new discoveries.

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Dijkstra and Bellman-ford are the two basic methods to solve Single-source shortest paths problem，and SPFA is the optimized version of Bellman-ford. However, since the algorithm time complexity is 0 (kn), SPFA’s time efficiency has some instabilities. This paper will compare the time efficiency between Dijkstra optimized with heap and three kinds of SPFA in different density graphs. Meanwhile, random data is created to test optimized Dijkstra and 3 types of SPFA. Finally, according to the calculation result of two methods’ time efficiency, some suggestion is given for their application under different situation.

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.

In this paper, we firstly re-present the results of Bondar et al. (2013). Then, following the approach taken in it, we use the method of Operational Dynamic Modeling (ODM) to deal with the situation where thebackground mechanics is varying between quantum and classical mechanics.