Abstract Let be a regular local ring and non‐zero element of . A theorem due to Knörrer states that there are finitely many isomorphism classes maximal Cohen–Macaulay (CM) ‐modules if only the same is true for double branched cover , is, hypersurface which defined by in We consider an analogue this statement case instead In particular, we show hypersurface, refer as ‐fold has finite CM represen...

Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (τ -covers). We deal with two types of combinatorial questions which arise from this study. (1) Two new cardinals introduced in the topological study are expressed in terms of well known cardinals characteristics of the continuum. (2) We study the additiv...

Motivated by the minimal tower problem, an earlier work studied diagonalizations of covers where the covers are related to linear quasiorders (τ -covers). We deal with two types of combinatorial questions which arise from this study. 1. Two new cardinals introduced in the topological study are expressed in terms of well known cardinals characteristics of the continuum. 2. We study the additivit...

approximately all sequenced archaeal and half of eubacterial genomes have some sort of adaptive immune system, which enables them to target and cleave invading foreign genetic elements by an rnai-like pathway. crispr–cas (clustered regularly interspaced short palindromic repeats–crispr-associated proteins) systems consist of the crispr loci with multiple copies of a short repeat sequence separa...

information on different rangeland plants’ nutritive values during variousphonological stages is of importance for the rangelands management. this information helpsrangeland managers to choose proper grazing times to achieve higher animal performancewith no detrimental effects on the rangeland vegetations. effects of various plant parts’phenological stages and vegetation types on reserve carboh...