A note concerning a sole sufficient operator.

A note on inequalities for Tsallis relative operator entropy

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

A Note on Hilberts Operator

LEMMA L 1 When Kp< oo, then &fis a continuous (bounded) linear transformation with both domain and range Lp( — <*> , oo ), and § 2 / = — ƒ. LEMMA 2. Whenf(t)ÇzLi(— <*>, oo), then §ƒ exists for almost all x in ( — oo , co ), but does not necessarily belong to Li(a, b), where a, b are arbitrary numbers(— oo ^a<b^ oo) ; however (l+x)~\ &f\ÇzLi(— oo , co) when 0<q<l. When f and ^f belong to Li(— oo...

A note concerning Primary Source Knowledge

We add a small increment to understanding the notion of ‘Primary Source Knowledge’ (PSK). PSK is knowledge that the non-expert and the citizen can acquire by assiduously reading the primary scientific journal literature without being embedded in the cultural life of the corresponding technical specialty (Collins and Evans 2007). This comes from exposing four papers to the automated computer fil...

A Note concerning Completely Regular Gyspaces1

A note on sufficient dimension reduction

In this paper, we presented a theoretical result and then discussed possible applications of our result to SDR problems. In addition to providing insights into existing SDR methods when Y is univariate; our theorem also applies to multivariate responses, especially when the response takes the form of ðY ;W Þ, where Y is a continuous variable and W is categorical. r 2007 Elsevier B.V. All rights...