‎let $i$ denote an ideal of a noetherian ring $r$‎. ‎the purpose of‎ ‎this article is to introduce the concepts of quintasymptotic‎ ‎sequences over $i$ and quintasymptotic cograde of $i$‎, ‎and to show that they play a role analogous to quintessential sequences‎ ‎over $i$ and quintessential cograde of $i$‎. ‎we show that‎, ‎if $r$ is‎ ‎local‎, ‎then the quintasymptotic cograde of $i$ is una...

‎Let $I$ denote an ideal of a Noetherian ring $R$‎. ‎The purpose of‎ ‎this article is to introduce the concepts of quintasymptotic‎ ‎sequences over $I$ and quintasymptotic cograde of $I$‎, ‎and to show that they play a role analogous to quintessential sequences‎ ‎over $I$ and quintessential cograde of $I$‎. ‎We show that‎, ‎if $R$ is‎ ‎local‎, ‎then the quintasymptotic cograde of $I$ is una...

paris polyphylla smith var. yunnanensis (liliaceae) is an important traditional medicinal plant of the yunnan province in china. however, the genomic information regarding this plant is limited. to further understand its molecular background, we conducted illumina hiseq 2000 second-generation sequencing of this plant species. approximately 30,198,679 reads with an average length of 202 bases we...

bioinformatics, through the sequencing of the full genomes for many species, is increasingly relying on efficient global alignment tools exhibiting both high sensitivity and specificity. many computational algorithms have been applied for solving the sequence alignment problem. dynamic programming, statistical methods, approximation and heuristic algorithms are the most common methods applied t...

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.