【摘要】：本文以星體的對(duì)偶Orlicz Hausdorff度量的刻畫問(wèn)題和星體的對(duì)偶混合亮度積分及其極值問(wèn)題為主要研究對(duì)象。我們引進(jìn)了星體的對(duì)偶Orlicz Hausdorff度量的概念,并將其與經(jīng)典的對(duì)偶Hausdorff度量和對(duì)偶1Hausdorff度量進(jìn)行了比較。進(jìn)而討論了這一新度量的一些基本性質(zhì)。這一度量為計(jì)算Orlicz空間中星體之間的距離提供了便利。我們還對(duì)星體引進(jìn)了對(duì)偶混合亮度積分的概念,進(jìn)而研究了其相關(guān)極值問(wèn)題,建立了對(duì)不同指數(shù)的循環(huán)不等式,以及它與星體的截面體體積之間的重要聯(lián)系。
[Abstract]:In this paper, we focus on the characterization of dual Orlicz Hausdorff metric of stars and the dual mixed luminance integral and its extremum of stars. We introduce the concept of dual Orlicz Hausdorff metric of stars and compare it with the classical dual Hausdorff metric and dual 1Hausdorff metric. Then some basic properties of this new metric are discussed. This metric facilitates the calculation of distances between stars in Orlicz space. We also introduce the concept of dual mixed luminance integral to the star, and then study its correlation extremum problem, establish the cyclic inequality for different exponents and the important relation between it and the volume of the cross section body of the star.
【學(xué)位授予單位】：重慶師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O186.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 ZHOU Yanping;WANG Weidong;FENG Yibin;;The Brunn-Minkowski Type Inequalitiesfor Mixed Brightness-Integrals[J];Wuhan University Journal of Natural Sciences;2014年04期

2 何日高;;p-Hausdorff度量[J];應(yīng)用數(shù)學(xué)與計(jì)算數(shù)學(xué)學(xué)報(bào);2011年01期

，

本文編號(hào)：2241919