Published electronically January 10, 2023

DOI: 10.1137/21S1454110

**Authors:** Feng Jiang (University of Nottingham Ningbo China), Zhengyang Guo (University of Nottingham Ningbo China), Dongâ€™ang Liu (University of Nottingham Ningbo China), and Yanghao Wang (University of Nottingham Ningbo China) **Project Advisors:** Behrouz Emamizadeh (University of Nottingham Ningbo China) and Amin Farjudian (University of Nottingham Ningbo China)

**Abstract:** This note is concerned with the qualitative properties of the solutions of a class of linear ordinary differential equations. The existence and uniqueness of solutions are addressed, and properties of the graph of the solution when imposing some restrictions are derived. A new notion of derivative, called the force derivative, is introduced and an orthogonality result, between the force derivative of the solution and the force function, is obtained. All the important results are verified by numerical examples using MATLAB. Finally, an inequality result reminiscent of the famous G. Talenti's inequality is proved.

Published electronically March 9, 2023

DOI: 10.1137/22S1504445

**Authors:** Garrett Kepler (California State University, East Bay), Maria Palomino (California State University, East Bay) **Project Advisor:** Andrea Arauza Rivera (California State University, East Bay)

**Abstract:** Food deserts are regions where people lack access to healthy foods. In this article we use k-means clustering to cluster the food deserts in two Bay Area counties. The centroids (means) of these clusters are optimal locations for intervention sites (such as food pantries) since they minimize the distance that a person within a food desert cluster would need to travel to reach the resources they require. We present the results of both a standard and a weighted k-means clustering algorithm. The weighted algorithm takes into account the poverty levels in each food desert when determining the placement of a centroid. We find that this weighting can make significant changes to the proposed locations of intervention sites.