The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In this article, an analogue of the Grothendieck compactness principle is considered when the norm topology of a Banach space is replaced by its weak topology. It is shown that every weakly compact subset of a Banach space is contained in...

The (salen)Co(III)-catalyzed hydrolytic kinetic resolution (HKR) of terminal epoxides is a bimetallic process with a rate controlled by partitioning between a nucleophilic (salen)Co-OH catalyst and a Lewis acidic (salen)Co-X catalyst. The commonly used (salen)Co-OAc and (salen)Co-Cl precatalysts undergo complete and irreversible counterion addition to epoxide during the course of the epoxide hy...

We report ab initio generalized valence bond and Correlation-consistent configuration interaction studies of CO and NO interacting with Pd and Pt atoms. We find dramatically different bonding mechanisms for the two ligands, which are easily understood in terms of changes in the electronic structure of the metal and the ligand. CO bonds to both Pd and Pt by a u donor/* back-bonding mechanism, yi...

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

In this paper, a group shift is an expansive action of Zd on a compact metrizable zero dimensional group by continuous automorphisms. All group shifts factor topologically onto equal-entropy Bernoulli shifts; abelian group shifts factor by continuous group homomorphisms onto canonical equalentropy Bernoulli group shifts; and completely positive entropy abelian group shifts are weakly algebraica...

In this work we provide a characterization of distinct types (linear and non-linear) maps between Banach spaces in terms the differentiability certain class Lipschitz functions. Our results are stated an abstract bornological non-linear framework. Restricted to linear case, can apply our compact, weakly-compact, limited completely continuous operators. Moreover, yield Gelfand-Phillips recover s...

Carbon Monoxide (CO) is the most abundant air pollutant gas and accumulates rapidly to dangerous concentrations even in areas that seem to be well ventilated. Carbon monoxide detectors/alarm systems exist but people who are old, hearing impaired, partially sighted or heavy sleepers may not get the warning or find it difficult to wake up and get out in the event of dangerous concentration of CO ...

let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

What strategy profiles can be played when it is common knowledge that weakly dominated strategies are not played? A comparison to the case of strongly dominated strategy is in order. A common informal argument shows that if it is common knowledge that players do not play strongly dominated strategies then players can play only profiles that survive the iterative elimination of strongly dominate...