Nuclearity of a nonnegative definite integral kernel on a separable metric space

The aim of this paper is to characterize the nuclearity of an integral operator, defined by a continuous non-negative definite square integrable kernel on a separable metric space, in terms of the integrability of the trace of the kernel function. Nuclearity here plays a role forU-statistics.     

Topological influence of the presence of fully-λ-bases in locally convex spaces

This article reveals the topological impact of fully--bases in locally convex spaces where carries either the traditional normal topology or the fairly generalized-topology of Ruckle. It has been established that the generalized nuclearity of plays a significant role in influencing the topology of the space. Further, the equivalence of normal topology and the topology arising out of the fully--base ( being equipped with normal topology or-topology) has been investigated.We acknowledge with thanks the suggestions of the referee.     

Amenability and exactness for dynamical systems and their -algebras

We study the relations between amenability (resp. amenability at infinity) of -dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.

     

Boosting Benzene Oxidation with a Spin-State-Controlled Nuclearity Effect on Iron Sub-Nanocatalysts

A fundamental understanding of the nature of nuclearity effects is important for the rational design of superior sub-nanocatalysts with low nuclearity, but remains a long-standing challenge. Using atomic layer deposition, we precisely synthesized Fe sub-nanocatalysts with tunable nuclearity (Fe₁–Fe₄) anchored on N,O-co-doped carbon nanorods (NOC). The electronic properties and spin configuration of the Fe sub-nanocatalysts were nuclearity dependent and dominated the H₂O₂ activation modes and adsorption strength of active O species on Fe sites toward C−H oxidation. The Fe₁-NOC single atom catalyst exhibits state-of-the-art activity for benzene oxidation to phenol, which is ascribed to its unique coordination environment (Fe₁N₂O₃) and medium spin state (t_2g⁴e_g¹); turnover frequencies of 407 h⁻¹ at 25 °C and 1869 h⁻¹ at 60 °C were obtained, which is 3.4, 5.7, and 13.6 times higher than those of Fe dimer, trimer, and tetramer catalysts, respectively.     

Crossed products of operator systems

In this paper we introduce the crossed product construction for a discrete group action on an operator system. In analogy to the work of E. Katsoulis and C. Ramsey, we describe three canonical crossed products arising from such a dynamical system. We describe how these crossed product constructions behave under G-equivariant maps, tensor products, and the canonical $C^{?}$-covers. We show that hyperrigidity is preserved under two of the three crossed products. Finally, using A. Kavruk's notion of an operator system that detects $C^{?}$-nuclearity, we give a negative answer to a question on operator algebra crossed products posed by Katsoulis and Ramsey.     

Effects of the substituents of pyrazole/thiazine ligands on nuclearity of Cu(II) nitrate complexes

[Cu(H₂O)(PzTz)₂](NO₃)₂ (1), [Cu(μ-NO₃)(NO₃)(DMPzTz)] _n (2), and [{Cu(NO₃)(DPhPzTz)}₂(μ-NO₃)₂] (3) [PzTz?=?2-(1-pyrazolyl)-1,3-thiazine, DMPzTz?=?2-(3,5-dimethyl-1-pyrazolyl)-1,3-thiazine, DPhPzTz?=?2-(3,5-diphenyl-1-pyrazolyl)-1,3-thiazine] have been prepared and characterized by elemental analysis, electronic spectroscopy, IR spectroscopy, electron paramagnetic resonance spectroscopy, magnetic susceptibility measurements, and single-crystal X-ray diffraction. Influence of ligand size on coordination to Cu(II) has been analyzed. The three complexes are five-coordinate and the coordination geometry can be described as a distorted trigonal bipyramid for 1 or a distorted square pyramid for 2 and 3. As a consequence of the strain induced by the ligands, 1 is a monomeric complex cation whereas 2 is a polymer and 3 is a dimer.     

A novel oxovanadate structural type – Synthesis,single crystal structure and magnetic properties of a mixed-valence polyoxovanadate formed by {V17O40(Cl)} and {V15O36(Cl)} clusters

A novel polyoxovanadate structural type, with an average nuclearity of V₁₆, formed by a mixture of two different polyoxovananadates: {V₁₅O₃₆(Cl)} and{V₁₇O₄₀(Cl)} has been synthesized and characterized. The title compound, formulated as [Ni(phen)₃]₂{[V₁₅O₃₆(Cl)]_0.5[V₁₇O₄₀(Cl)]_0.5} · H₂O (1) (phen = 1,10′-phenanthroline), presents two different polyoxovanadate architectures: {V₁₅O₃₆(Cl)} and {V₁₇O₄₀(Cl)}, with the last one representing a new framework type in polyoxovanadate chemistry. Here, we present the synthesis of this novel polyoxovanadate under hydrothermal conditions and its characterization by IR and XPS spectroscopies, elemental and thermogravimetric analysis, redox titration, magnetic measurements and single-crystal X-ray diffraction.