The aim of this paper is to apply systematically to AdS 4 some modern tools in the representation theory of Lie algebras which are easily generalised to the supersymmetric and quantum group settings and necessary for applications to string theory and integrable models. Here we introduce the necessary representations of the AdS 4 algebra and group. We give explicitly all singular (null) vectors ...

Two different possible mechanisms of water gas shift reaction including formate and redox mechanisms on the Ag5 cluster were investigated using DFT computations. All the elementary steps involved in both mechanisms were considered. It was observed that dissociation of H2Oads and OHads, as well as formation of CO2(ads), required activation e...

Automated Driving Systems ( ADS ) have made great achievements in recent years thanks to the efforts from both academia and industry. A typical is composed of multiple modules, including sensing, perception, planning, control, which brings together latest advances different domains. Despite these achievements, safety assurance significance, since unsafe behavior can bring catastrophic consequen...

let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

A muscle synergy is a coordinative structure of muscles that has been proposed as a strategy to reduce the number of variables that the central nervous system (CNS) has to address in motor tasks. In this article, the mechanical contribution of muscle synergies and coordinative structures of muscles in voluntary multi-directional postural control were investigated. The task for healthy, young su...

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].