Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 909261, 22 pages
http://dx.doi.org/10.5402/2011/909261
Research Article

Theories and Inequalities on the Satellite System

College of Mathematics and Information Science, Chengdu University, Chengdu 610106, China

Received 18 January 2011; Accepted 13 February 2011

Academic Editors: D. Han and G. Schimperna

Copyright ยฉ 2011 Chaobang Gao and Jiajin Wen. 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.

Abstract

We define the satellite system without any central, the satellite system with a central, and the satellite system of single point with a central. For the satellite system without any central ๐‘†{ฮ“,ฮ“๐‘}, we establish the inequality: โˆฎฮ“โˆฎ๐‘‘๐‘ ฮ“๐‘|๐‘ƒ๐‘„|๐‘‘๐‘ ๐‘„โ‰ค(๐‘|ฮ“|3/4๐œ‹2)sin(2๐œ‹/๐‘). For the satellite system with a central ๐‘†{๐‘‚,ฮ“,ฮ“๐‘}, we establish the following inequality under the proper hypothesis: โˆฎฮ“๐‘€๐‘[๐‘ก](๐‘Ÿ)๐‘‘๐‘ โ‰ค(|ฮ“|2/2๐œ‹)cos(๐œ‹/๐‘)(โˆ€๐‘กโˆˆ]โˆ’โˆž,โˆ’2]). As an application, we get the inequalities โˆฎฮ“๐œŒ๐‘ƒโˆฎ๐‘‘๐‘ โ‰ฅฮ“๐‘Ÿ๐‘ƒ๐‘‘๐‘ โ‰ฅ2|๐ท(ฮ“)|, for the satellite system of single point with a central ๐‘†{๐‘‚,ฮ“,๐‘ƒ}. For these results, there are generalized backgrounds in the fields of differential geometry and space science.