It is shown that for every p ∈ (1,∞) there exists a Banach space X of finite cotype such that the projective tensor product lp⊗̂X fails to have finite cotype. More generally, if p1, p2, p3 ∈ (1,∞) satisfy 1 p1 + 1 p2 + 1 p3 6 1 then lp1⊗̂lp2⊗̂lp3 does not have finite cotype. This is a proved via a connection to the theory of locally decodable codes.

in this paper, we consider locally graded groups in which every non-permutable subgroup is soluble of bounded derived length.

An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is aGCD domain for every maximal ideal $M$ of $D$. We study somering-theoretic properties of locally GCD domains. E.g., we show that $%D$ is a locally GCD domain if and only if $aDcap bD$ is locally principalfor all $0neq a,bin D$, and flat overrings of a locally GCD domain arelocally GCD. We also show that the t-class group...

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

BACKGROUND The lower risk of cancer in the areas inhabited by the German minority in the region of Opole, Poland, at the turn of the 1980's and 1990's has been already reported. A reanalysis of the present-day data was conducted. PATIENTS AND METHODS All the cancer cases (at all sites combined) registered within the years 2008-2012 with data collected by the Regional Cancer Registry in Opole ...

Inspired by recent construction of high-rate locally correctable codes with sublinear query complexity due to Kopparty, Saraf and Yekhanin (2010) we address the similar question for locally testable codes (LTCs). In this note we show a construction of high-rate LTCs with sublinear query complexity. More formally, we show that for every , ρ > 0 there exists a family of LTCs over the binary field...

CURRENT SCIENCE, VOL. 86, NO. 4, 25 FEBRUARY 2004 518 N. S. Murthy is in the Institute for Cytology and Preventive Oncology, Maulana Azad Medical College Campus, BSZ Marg, New Delhi 110 002, India; Aleyamma Mathew is in the Division of Epidemiology and Cancer Research, Regional Cancer Centre, Medical College Campus, Thiruvananthapuram 695 011, India *For correspondence. (e-mail: nsmurthy44@yaho...

We survey the state of the art in constructions of locally testable codes, locally decodable codes and locally correctable codes of high rate.