let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various Hilbert-Schmidt isomorphisms of the form tr(A−), are expressed in terms of dual adjunctions, and maps between them. Of particular interest is the connection with quantum s...

Let Λ and Γ be artin algebras and ΛUΓ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of k-Gorenstein modules with respect to ΛUΓ and then establish the left-right symmetry of the notion of k-Gorenstein modules, which develops a classical result of Auslander. As an application, we study the properties of dual modules relative to Gorenstein bimodules. ...

Schur polynomials are special cases of Schubert polynomials, which in turn dual characters flagged Weyl modules. The principal specialization and has a long history, with Macdonald famously expressing the any polynomial terms reduced words. We prove lower bound on Our result yields an alternative proof conjecture Stanley about originally proved by Weigandt.

A module M is called square-free if it contains nonon-zero omorphic submodules and B with A∩B= 0. Dually, Mis dual-square-free has no proper M=A+B M/A∼=M/B. In this paper we show that M=⊕i∈I Mi, then iff each Mi Mj ⊕j=i∈I are orthogonal. M=⊕ni=1Mi, dual-square-free, 1⩽i⩽n, ⊕ni=jMi factor-orthogonal. Moreover, in the finite case, weshow M=⊕i∈ISi a direct sum of non-is simple modules, dual-square...

The use of a dual-ended readout PET detector module based on Geiger-mode avalanche photodiodes (GAPDs) with large-area microcells was proposed to obtain high photon detection efficiency (PDE) and overcome energy non-linearity problems. A simulation study was performed and experimental measurement were taken for the singleand dual-ended PET detector modules consisting of the two types of GAPDs w...

We define exact functors from categories of Harish-Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of these functors. In particular, we show that they map irreducible spherical representations to irreducible spherical representations and, moreover, that they...