Matching families are one of the major ingredients in the construction of locally decodable codes (LDCs) and the best known constructions of LDCs with a constant number of queries are based on matching families. The determination of the largest size of any matching family in Zm, where Zm is the ring of integers modulo m, is an interesting problem. In this paper, we show an upper bound of O((pq)...

it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...

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.

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...

Oleo-gum-resin of Boswellia serrata Roxb. (Burseraceae) locally called ‘Kundur’, is one of the ingredients in certain Unani formulations used in renal diseases. In the present study, the effect of Kundur and its methanol soluble (MS), and methanol insoluble (MINS) fractions were investigated on Gentamicin induced nephrotoxicity in Albino rats. The renal effects of Kundur and its fractions were ...

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...