An integer partition λ ` n corresponds, via its Ferrers diagram, to an artinian monomial ideal I ⊂ C[x, y] with dimC C[x, y]/I = n. If λ corresponds to an integrally closed ideal we call it concave . We study generating functions for the number of concave partitions, unrestricted or with at most r parts. 1. concave partitions By an integer partition λ = (λ1, λ2, λ3, . . . ) we mean a weakly dec...

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 ...

[Purpose] This study investigated upper-extremity muscle activities in natural, ideal, and corrected head positions. [Subjects and Methods] Forty subjects with a forward head posture and rounded shoulder were recruited and randomly assigned to the natural head position group (n = 13), ideal head position group (n = 14), or corrected head position group (n = 13). Muscle activities were measured ...

We find two Fσδ ideals on N neither of which is Fσ whose quotient Boolean algebras are homogeneous but nonisomorphic. This solves a problem of Just and Krawczyk (1984). We consider Boolean algebras of the form P(N)/I, where I is an ideal on N containing the ideal Fin of finite sets. In [3] Just and Krawczyk formulated several conditions on the ideals I,J that guarantee their quotients P(N)/I an...

We investigate the convergence of GMRES for an n by n Jordan block J . For each k that divides n we derive the exact form of the kth ideal GMRES polynomial and prove the equality max ‖v‖=1 min p∈πk ‖p(J)v‖ = min p∈πk max ‖v‖=1 ‖p(J)v‖, where πk denotes the set of polynomials of degree at most k and with value one at the origin, and ‖ · ‖ denotes the Euclidean norm. In other words, we show that ...