We study the rational Cherednik algebra attached to complex reflection group G(r, 1, 2). Each irreducible representation Sλ of 2) corresponds a standard module Δ(λ) for algebra. give necessary and sufficient conditions existence morphism between two these modules explicit formulas them when they exist.

Recently, a previous contributor showed how the delta-wye conversion may be applied to find the equivalent capacitance of five capacitors arranged in a bridge configuration. In fact, that contributor gave an algorithm for this purpose which showed that the equivalent capacitance depends upon all five capacitors. However, in this paper, we point out that there is a special case where the equival...

Abstract In this study, the multiple-factor analysis of dehumidification performance and flow resistance for cross-flow membrane module was carried out based on orthogonal test. Three operating four structural parameters were selected as independent variables two test indicators, i.e., rate ( γ ) account per unit pressure drop (Δ φ /Δ p ). The influence seven factors indicators ranked by single...

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_{...

Current carbon and sulphur isotope ratios (δ(13)C and δ(34)S) suggest there were major shifts in partitioning between reduced and oxidised reservoirs of carbon and sulphur during the Early Cretaceous. However, the δ(13)C and δ(34)S records are composed from different Ocean Drilling Program sites and are hard to correlate at high resolution. We present high-resolution Aptian δ(13)C(org) and δ(34...

The voltage-gated calcium channel subunit α(2)δ plays a fundamental role in propagation of excitatory signals associated with release of glutamate and neuropeptides substance P (SP) and calcitonin gene-related protein (CGRP). It can be selectively inhibited by gabapentinoids. Hence, investigation of the α(2)δ subunit may predict the efficacy of gabapentinoid therapy in neuropathic pain. Since s...

This work focuses on a mechanism (and software) which communicates (via MathLink protocol) and provides compatibility between the representation of nonlinear functions specified as Mathematica expressions and objects of suitable classes supported by the C-XSC automatic differentiation modules. The application of the developed communication software is demonstrated by MathLink compatible program...

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field k of positive characteristic p. The main result proves that Weyl modules have (cogood) p-filtrations subject to restrictions on p. In case the high weight of the Weyl module is p-regular, the p-filtration is compatible with theG1-radical series of the module. This is a preliminary...