On Integral Metrics and Trajectory Classification

In this project, we explore distance in the context of metrics. More specifically, we take a look at an integral metric that is used to determine the distance between sets. The motivation behind this project is to determine that the integral metric we use is meaningful in the context of our data set. The data set we useconsists of trajectories of cars along a portion of the I5 highway. Through training, testing, and evaluating this model on the data set, we can reach conclusions on the structure of the data and the success of this integral metric in terms of a classifier. In the end, we can both determine whether or not this integral metric fits with the data set chosen and explore other areas where the metric could possibly succeed or where it might fail.

On one property of zeros of polynomials of the least $$$(\alpha; \beta)$$$-deviation from zero in weighted space $$$L_p$$$

We prove the property of monotonity of zeros of polynomials of the least $$$(\alpha; \beta)$$$-deviation from zero in the space with integral metrics with weight.