tailieunhanh - Báo cáo hóa học: " Research Article On Star Duality of Mixed Intersection Bodies"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Star Duality of Mixed Intersection Bodies | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 39345 12 pages doi 2007 39345 Research Article On Star Duality of Mixed Intersection Bodies Lu Fenghong Mao Weihong and Leng Gangsong Received 7 July 2006 Revised 22 October 2006 Accepted 30 October 2006 Recommended by Y. Giga A new kind of duality between intersection bodies and projection bodies is presented. Furthermore some inequalities for mixed intersection bodies are established. A geometric inequality is derived between the volumes of star duality of star bodies and their associated mixed intersection integral. Copyright 2007 Lu Fenghong et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and main results Intersection bodies were first explicitly defined and named by Lutwak 1 . It was here that the duality between intersection bodies and projection bodies was first made clear. Despite considerable ingenuity of earlier attacks on the Busemann-Petty problem it seems fair to say that the work of Lutwak 1 represents the beginning of its eventual solution. In 1 Lutwak also showed that if a convex body is sufficiently smooth and not an intersection body then there exists a centered star body such that the conditions of Busemann-Petty problem hold but the result inequality is reversed. Following Lutwak the intersection body of order i of a star body is introduced by Zhang 2 . It follows from this definition that every intersection body of order i of a star body is an intersection body of a star body and vice versa. As Zhang observes the new definition of intersection body allows a more appealing formulation namely the Busemann-Petty problem has a positive answer in M-dimensional Euclidean space if and only if each centered convex body is an intersection body. The intersection body .