‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

Dynamic reorganization of signaling systems frequently accompanies pathway perturbations, yet quantitative studies of network remodeling by pathway stimuli are lacking. Here, we report the development of a quantitative proteomics platform centered on multiplex absolute quantification (AQUA) technology to elucidate the architecture of the cullin-RING ubiquitin ligase (CRL) network and to evaluat...

In this mostly expository note we give a down-to-earth introduction to the V-filtration of M. Kashiwara and B. Mal-grange on D-modules. We survey some applications to generalized Bernstein-Sato polynomials, multiplier ideals, and monodromy of vanishing cycles. The V filtration on D-modules was introduced by M. Kashiwara and B. Malgrange to construct vanishing cycles in the category of (regular ...

In this paper, we present an automatic translation from synchronous guarded actions to SystemC. Synchronous guarded actions are often used as intermediate code representation of synchronous languages like Esterel and Quartz. The obtained SystemC modules can be seamlessly integrated into existing simulation environments, e. g. for fast simulation or the generation of virtual hardware prototypes....

we investigate the problem of the existence of a frame forright ideals of a c*-algebra a, without the use of the kasparov stabilizationtheorem. we show that this property can not characterize a as a c*-algebraof compact operators.

Reliability of software counts on its fault-prone modules. This means that the less software consists of fault-prone units the more we may trust it. Therefore, if we are able to predict the number of fault-prone modules of software, it will be possible to judge the software reliability. In predicting software fault-prone modules, one of the contributing features is software metric by which one ...

let $ m , n in mathbb{n}$, $d$ be a division ring, and $m_{m times n}(d)$ denote the bimodule of all $m times n$ matrices with entries from $d$. first, we characterize one-sided submodules of $m_{m times n}(d)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $d$. next, we introduce the notion of a nest module of matrices with entries from $d$. we ...

We introduce sequentially Sr modules over a commutative graded ring and sequentially Sr simplicial complexes. This generalizes two properties for modules and simplicial complexes: being sequentially Cohen-Macaulay, and satisfying Serre’s condition Sr . In analogy with the sequentially CohenMacaulay property, we show that a simplicial complex is sequentially Sr if and only if its pure i-skeleton...