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 ...

In this note we study the generalized Hilbert series operator H?, induced by a positive Bore measure ? on [0,1), between weighted sequence spaces. We characterize measures for which H? is bounded different Finally, certain special measures, obtain sharp norm estimates of operators and establish some new inequalities with best constant factors.

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 ...

In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...

Abstract We present a conjecture about the reduced Hilbert series of coordinate ring simple polyomino in terms particular arrangements non-attacking rooks that can be placed on polyomino. By using computational approach, we prove above holds for all polyominoes up to rank 11. In addition, true class parallelogram polyominoes, by looking at those as planar distributive lattices. Finally, give co...