模糊连通度与模糊核度

本文给出了衡量模糊连通性的三个工量：模糊连通度，模糊边连通度与模糊核度及其相关的性质。与普通图连通性的分析相比较，由于考虑了模糊性，这三个量能更好，更深入地刻划出不同的图在连通性方面的微妙差异。     

PrO-C*-代数的顺从性和核性

研究了Pro—C^*-代数的顺从性和核性．主要证明了(1)顺从Pro—C^*代数的闭理想是顺从的；(2)核Pro—C^*代数类对归纳极限封闭；(3)交换σ-C^*-代数和核C^*-代数都是核，σ-C^*-代数并且核σ-C^*-代数类对于商运算、张量积运算和可数逆向极限封闭．进一步得到核，σ-C^*-代数的扩张保持核性的条件。     

{Nb288O768(OH)48(CO3)12}: A Macromolecular Polyoxometalate with Close to 300 Niobium Atoms

A protein‐sized (ca. 4.2×4.2×3.6 nm³) non‐biologically derived molecule {Nb₂₈₈O₇₆₈(OH)₄₈(CO₃)₁₂} ( Nb₂₈₈ ) containing up to 288 niobium atoms has been obtained, which is by far the largest and the highest nuclearity polyoxoniobate (PONb). Particularly, in terms of metal nuclearity number, Nb₂₈₈ is the second largest cluster so far reported in classic polyoxometalate chemistry (V, Mo, W, Nb, and Ta). Nb₂₈₈ can be described as a giant windmill‐like cluster aggregate of six nanoscale high‐nuclearity PONb units {Nb₄₇O₁₂₈(OH)₆(CO₃)₂} ( Nb₄₇ ) joined together by six additional Nb ions. Interestingly, the 47‐nuclearity Nb₄₇ units generated in situ can be isolated and bridged by copper complexes to form an inorganic–organic hybrid three‐dimensional PONb framework, which exhibits effective catalytic activity for hydrolyzing nerve agent simulant of dimethyl methylphosphonate. The unique Nb₄₇ cluster also provides a new type of topology to very limited family of Nb‐O clusters.     

Λ0-Nuclear Operators and Λ0-Nuclear Spaces in p-adic Analysis

For a Köthe sequence space, the classes of ₀-nuclear spaces and spaces with the ₀-property are introduced and studied and the relation between them is investigated. Also, we show that, for ₀c ₀, these classes of spaces are in general different from the corresponding ones for ₀=c ₀, which have been extensively studied in the non-archimedean literature (see, for example, [1]–[6]).     

Rkk (X)-nucléarité (d‘après; G. Skandalis)

We define a notion of nuclearity for C(X)-C^*-algebras yielding the same results of semi-exactness, for Kasparovs bifunctor RKK(X), as those obtained by Skandalis in the case X=. We connect explicitly this new notion of nuclearity with those already known.     

Vanadium(V) Complexes of O,N,O-Donor Tridentate Ligands Containing the {VVO(OMe)}2+ Unit: Syntheses,Structures and Properties

Abstract

Syntheses, characterisation and properties of two complexes containing the oxovanadium(V) methoxide unit have been described. Deprotonated benzoylhydrazones of 2–hydroxy–5–methoxy‐benzaldehyde (H₂bhsOMe) and 2–hydroxy–5–chlorobenzaldehyde (H₂bhsCl) were used as coligands. Crystal structures of both the complexes were determined. In solid state one of them is a dinuclear species [VO(bhsOMe)(OMe)]₂ (1) whereas the other one is a mononuclear complex [VO(bhsCl)(OMe)(HOMe)](2). The dinegative ligands coordinate the metal ions via phenolate–O, imine–N and deprotonated amide–O atoms. In 1, the metal ions of two square pyramidal VO(bhsOMe)(OMe) units share the methoxide groups to form a dinuclear species. The oxygen of a methanol molecule completes the hexacoordination of the metal centre in 2. In each of the two distorted octahedral VO₅N moieties of 1 the bridging methoxide oxygen and in that of 2 the methanol oxygen is trans to the corresponding oxo group. Both the complexes are redox active. The VO³⁺ to VO²⁺ reduction potentials (vs Ag/AgCl) of 1 and 2 are observed at ?0.25 and ?0.04 V, respectively. The band positions in the electronic spectra and the redox potentials reflect the influence of the substituents present on the ligands.     

Quantum Correlations,Nuclearity, and Spacetime Curvature

It is proved for a Haag–Araki–Kastler quantum field theory, that gravitation reduces the correlations in the vacuum state. Secondly, we prove Bell's inequalities by nuclearity assumptions. The so-called -content of certain compact mappings restricts the size of the set of measurements which violate Bell's inequalities.     

Cobalt(II) chloride adducts with acetonitrile,propan‐2‐ol and tetrahydrofuran: considerations on nuclearity,reactivity and synthetic applications

High‐spin cobalt(II) complexes are considered useful building blocks for the synthesis of single‐molecule magnets (SMM) because of their intrinsic magnetic anisotropy. In this work, three new cobalt(II) chloride adducts with labile ligands have been synthesized from anhydrous CoCl₂, to be subsequently employed as starting materials for heterobimetallic compounds. The products were characterized by elemental, spectroscopic (EPR and FT–IR) and single‐crystal X‐ray diffraction analyses. trans‐Tetrakis(acetonitrile‐κN )bis(tetrahydrofuran‐κO )cobalt(II) bis[(acetonitrile‐κN )trichloridocobaltate(II)], [Co(C₂H₃N)₄(C₄H₈O)₂][CoCl₃(C₂H₃N)]₂, (1), comprises mononuclear ions and contains both acetonitrile and tetrahydrofuran (thf) ligands, The coordination polymer catena‐poly[[tetrakis(propan‐2‐ol‐κO )cobalt(II)]‐μ‐chlorido‐[dichloridocobalt(II)]‐μ‐chlorido], [Co₂Cl₄(C₃H₈O)₄], (2′), was prepared by direct reaction between anhydrous CoCl₂ and propan‐2‐ol in an attempt to rationalize the formation of the CoCl₂–alcohol adduct (2), probably CoCl₂(HOⁱPr)_m . The binuclear complex di‐μ‐chlorido‐1:2κ⁴Cl :Cl‐dichlorido‐2κ²Cl‐tetrakis(tetrahydrofuran‐1κO )dicobalt(II), [Co₂Cl₄(C₄H₈O)₄], (3), was obtained from (2) after recrystallization from tetrahydrofuran. All three products present cobalt(II) centres in both octahedral and tetrahedral environments, the former usually less distorted than the latter, regardless of the nature of the neutral ligand. Product (2′) is stabilized by an intramolecular hydrogen‐bond network that appears to favour a trans arrangement of the chloride ligands in the octahedral moiety; this differs from the cis disposition found in (3). The expected easy displacement of the bound solvent molecules from the metal coordination sphere makes the three compounds good candidates for suitable starting materials in a number of synthetic applications.     

Cluster of clusters: Structural rules for vertex-sharing icosahedral supraclusters

Structural rules for supraclusters based on vertex-sharing icosahedra are developed. These simple rules are useful in elucidating the structural relationships of these clusters of clusters.     

A bipyridine‐ligated zinc(II) complex with bridging flavonolate ligation: synthesis,characterization, and visible‐light‐induced CO release reactivity

Metal–flavonolate compounds are of significant current interest as synthetic models for quercetinase enzymes and as bioactive compounds of importance to human health. Zinc–3‐hydroxyflavonolate compounds, including those of quercetin, kampferol, and morin, generally exhibit bidentate coordination to a single Zn^II center. The bipyridine‐ligated zinc–flavonolate compound reported herein, namely bis(μ‐4‐oxo‐2‐phenyl‐4H‐chromen‐3‐olato)‐κ³O ³:O ³,O ⁴;κ³O ³,O ⁴:O³‐bis[(2,2′‐bipyridine‐κ²N ,N ′)zinc(II)] bis(perchlorate), {[Zn₂(C₁₅H₉O₃)₂(C₁₀H₈N₂)₂](ClO₄)₂}_n , ( 1 ), provides an unusual example of bridging 3‐hydroxyflavonolate ligation in a dinuclear metal complex. The symmetry‐related Zn^II centers of ( 1 ) exhibit a distorted octahedral geometry, with weak coordination of a perchlorate anion trans to the bridging deprotonated O atom of the flavonolate ligand. Variable‐concentration conductivity measurements provide evidence that, when ( 1 ) is dissolved in CH₃CN, the complex dissociates into monomers. ¹H NMR resonances for ( 1 ) dissolved in d₆‐DMSO were assigned via HMQC to the H atoms of the flavonolate and bipyridine ligands. In CH₃CN, ( 1 ) undergoes quantitative visible‐light‐induced CO release with a quantum yield [0.004 (1)] similar to that exhibited by other mononuclear zinc–3‐hydroxyflavonolate complexes. Mass spectroscopic identification of the [(bpy)₂Zn(O‐benzoylsalicylate)]⁺ ion provides evidence of CO release from the flavonol and of ligand exchange at the Zn^II center.