International Journal of Applied Science <p>International Journal of Applied Science (IJAS) is an international, double-blind peer-reviewed, open-access journal, published by IDEAS SPREAD INC. It publishes original research, applied, and educational articles in all areas of applied science. It provides an academic platform for professionals and researchers to contribute innovative work in the field.<br>Authors are encouraged to submit complete, unpublished, original works that are not under review in any other journals. The scopes of the journal include, but are not limited to, the following fields: Agriculture, Biological Engineering and Application, Applied Mathematics and Statistics, Applied Physics and Engineering, Applied Chemistry and Materials Sciences, Civil Engineering and Architecture, Computer and Information Sciences and Application, Energy, Environmental Science and Engineering, Mechanics, Metrology, Military Science, Space Science, Sports Science, Ergonomics, Health Sciences, Fisheries science, Food Science, Forestry and all the fields related to applied science.<br>The journal is published in both print and online versions. The online version is free access and download.</p> IDEAS SPREAD INC en-US International Journal of Applied Science 2576-7240 <p>Copyright for this article is retained by the author(s), with first publication rights granted to the journal.<br>This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (</p> On Stability Estimate of Optimal Transport Maps Using m-th Polynomial Convexity <p>In 1781, Gaspard Monge first proposed the practical problem of relocating building materials while minimizing workers’ effort. Mathematically, the problem can be reiterated as finding a mapping T0 that transforms a random variable (<em>X</em>) following probability measure (μ) into a random variable (<em>Y</em>) following probability measure (<em>ν</em>), with minimal cost. Afterward, it has been widely studied and applied in statistics, machine learning, and economics, which concern the study of “distance” between usually a pair of probability distributions. The focus of this paper is centered on investigating and generalizing stability estimates for optimal transport plans, particularly through the lens of strong polynomial convexity. Building on previous research using plug-in estimators to strengthen the convergence rate of discrete or semi-discrete estimators for optimal transport plans, this paper introduces a novel stability estimate leveraging L-Lipschitz continuity and a paradigmatic methodology based on polynomial convexity, the understanding of which remains limited.</p> Kei Leong Chen ##submission.copyrightStatement## 2024-05-27 2024-05-27 7 1 p1 p1 10.30560/ijas.v7n1p1