We show that given a finitely generated standard graded algebra of dimension d over an infinite field, its graded Noether normalizations obey a certain kind of ‘generic exchange’, allowing one to pass between any two of them in at most d steps. We prove analogous generic exchange theorems for minimal reductions of an ideal, minimal complete reductions of a set of ideals, and minimal complete re...

A simple formulation for studying the free vibration of shear-deformable functionally graded plates of different shapes with different cutouts using the finite element method is presented. The aim is to fill the void in the available literature with respect to the free vibration results of functionally graded plates of different shapes with different cutouts. The material properties of the plat...

We compute the Hilbert coefficients of a graded module with pure resolution and discuss lower and upper bounds for these coefficients for arbitrary graded modules.

An important theorem by Beilinson describes the bounded derived category of coherent sheaves on P, yielding in particular a resolution of every coherent sheaf on P in terms of the vector bundles Ω Pn (j) for 0 ≤ j ≤ n. This theorem is here extended to weighted projective spaces. To this purpose we consider, instead of the usual category of coherent sheaves on P(w) (the weighted projective space...

We prove that the classes of graded monoids, regular monoids and Kleene monoids coincide for submonoids of free groups. We also prove that it is decidable whether or not a finitely generated submonoid of a free group is graded, and solve the homomorphism and isomorphism problems for graded submonoids of free groups. This generalizes earlier results for submonoids of free monoids. MSC: 20E05; 20...

Alter Breath-hold duration Increasing parallel-imaging factors (up to x 4 routinely) will reduce breath-hold with minimal impact on SSFP quality. Reduce spatial resolution small reductions in phase resolution will significantly reduce breath-hold Increasing the echo train/segments shorten breathhold, with slight decrease in temporal resolution Increase the number of averages(3-5) for free-breat...