In this paper we present an overview on logarithmic Sobolev inequalities. These inequalities have become a subject of intense research activity during the past years, from analysis and geometry in finite and infinite dimension, to probability and statistical mechanics, and of course many others developments and applications are expected. We have divided this paper into three parts. The first pa...

We are interested in the quantitative analysis of compaction ratio for two classical families trees: recursive trees and plane binary increasing trees. These typical representatives tree models with a small depth. Once size n is compacted by keeping only one occurrence all fringe subtrees appearing resulting graph contains nodes. This result must be compared to results simply generated trees, w...

purpose: e is a commonly use letter for illiterates or those who could not read english to measure visual acuity. the e chart is the mainly used charts in iran. however, they do not have the standards. they are in different format, fixed for 6 meter test, with or without lighting, with unequal number of letters in each line and different contrasts. as a result, there is an essential need for a ...