{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:37:05Z","timestamp":1759970225979,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T00:00:00Z","timestamp":1736380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>For each n-dimensional real Banach space X, each positive integer m, and each bounded set A\u2286X with diameter greater than 0, let \u03b2X(A,m) be the infimum of \u03b4\u2208(0,1] such that A\u2286X can be represented as the union of m subsets of A, whose diameters are not greater than \u03b4 times the diameter of A. Estimating \u03b2X(A,m) is an important part of Chuanming Zong\u2019s quantitative program for attacking Borsuk\u2019s problem. However, estimating the partitioning functionals of general convex bodies in finite dimensional Banach spaces is challenging, so we will begin with the estimation of partitioning functionals for special convex bodies. In this paper, we prove a series of inequalities about partitioning functionals of convex cones. Several estimations of partitioning functionals of the convex hull of (A+u)\u222a(A\u2212u) and (A+u)\u222a(\u2212A\u2212u) are also presented, where A\u2286Rn\u22121\u00d7{0} is a convex body with the origin o in its interior, and u\u2208Rn\u2216(Rn\u22121\u00d7{0}). These results contribute to the study of Borsuk\u2019s problem through Zong\u2019s program.<\/jats:p>","DOI":"10.3390\/axioms14010048","type":"journal-article","created":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T09:54:27Z","timestamp":1736416467000},"page":"48","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Partitioning Functional of a Class of Convex Bodies"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3335-9223","authenticated-orcid":false,"given":"Xinling","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"177","DOI":"10.4064\/fm-20-1-177-190","article-title":"Drei S\u00e4tze \u00fcber die n-dimensionale euklidische Sph\u00e4re","volume":"20","author":"Borsuk","year":"1933","journal-title":"Fund. 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