Let $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal ...

t h e s p e c i a l c o n c e n t r i c a l l y b r a c e d f r a m e (s c b f) i s a c o m m o n t y p e o f s t e e l s t r u c t u r a l s y s t e m f o r r e s i s t i n g l a t e r a l l o a d i n g. t h i s t y p e o f s y s t e m p r o v i d e s t h e r e q u i r e d s t i f f n e s s a n d s t r e n g t h a t r e l a t i v e l y l o w c o s t. d e s i g n c o d e s, b a s e d o n p a s ...

let $ m , n in mathbb{n}$, $d$ be a division ring, and $m_{m times n}(d)$ denote the bimodule of all $m times n$ matrices with entries from $d$. first, we characterize one-sided submodules of $m_{m times n}(d)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $d$. next, we introduce the notion of a nest module of matrices with entries from $d$. we ...

Our ultimate concern is the mapping between representations in the Language of Thought (in the sense of Fodor 1975) and representations at LF in some version of the Minimalist Program (Chomsky 1995). We argue on a variety of grounds that such a mapping is direct and that both these levels of representation must meet the (same) condition of compositionality. We argue that Copy theory, in particu...