publication . Article . 2016

Isoperimetric inequalities in surround system and space science

Wen, JiaJin; Yuan, Jun; Wu, ShanHe;
Open Access English
  • Published: 01 Feb 2016 Journal: Journal of Inequalities and Applications (issn: 1029-242X, Copyright policy)
  • Publisher: SpringerOpen
Abstract
By means of the algebraic, analysis, convex geometry, computer, and inequality theories we establish the following isoperimetric inequality in the centered 2-surround system $S^{(2)} \{P,\varGamma ,l \}$ : $$\begin{aligned}& \biggl(\frac{1}{|\varGamma |} \oint_{\varGamma }\bar{r}_{P}^{p} \biggr)^{1/p}\leqslant\frac{|\varGamma |}{4\pi}\sin\frac{l\pi}{|\varGamma |} \biggl[ \csc \frac{l\pi}{|\varGamma |}+\cot^{2} \frac{l\pi}{|\varGamma |} \ln \biggl(\tan \frac{l\pi}{|\varGamma |}+\sec\frac{l\pi}{|\varGamma |} \biggr) \biggr], \\& \quad \forall p\leqslant -2. \end{aligned}$$ As an application of the inequality in space science, we obtain the best lower bounds of the...
Subjects
free text keywords: p-power mean, centered 2-surround system, l-central region, λ-gravity function, Mathematics, QA1-939, Applied Mathematics, Analysis, Discrete Mathematics and Combinatorics, Combinatorics, Isoperimetric inequality, Pure mathematics, Mathematical analysis
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publication . Article . 2016

Isoperimetric inequalities in surround system and space science

Wen, JiaJin; Yuan, Jun; Wu, ShanHe;