On positive invertibility of operators and their decompositions

In Banach spaces ordered by a normal cone that contains interior points the positive invertibility of operators is studied. If there exists a uniformly positive functional then any positively invertible operator A possesses a B -decomposition, i.e., a positive decomposition A = U – V with the properties: U^–1 exists, VU^–1 ≥ 0, Ax ≥ 0, U x ≥ 0 imply x ≥ 0 and r (VU^–1) < 1. Earlier it was shown that the existence of a B -decomposition with r (VU^–1) < 1 is sufficient for the positive invertibility of the operator A. Peris' result is obtained as a special case of the main theorem. The decomposition is demonstrated for a positively invertible operator in a Banach space ordered by an ice cream cone (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pseudodifferential parabolic equations in uniform spaces

The paper is devoted to local and global solvability in locally uniform spaces and to the existence of a global attractor for a parabolic problem containing fractional power of the minus Laplace operator. Several useful technical tools and estimates are also collected in this paper.     

二氧化碳对同质外延生长单晶金刚石内应力的影响

本文研究了在反应气体中引入不同浓度的CO₂对微波等离子体化学气相沉积(MPCVD)法同质外延生长单晶金刚石内应力的影响，并对其作用机理进行了分析。研究发现，随着CO₂浓度增加，单晶金刚石内应力逐渐减小，这是由于添加的CO₂提供了含氧基团，可以有效刻蚀金刚石生长过程中的非金刚石碳，并能够降低金刚石中杂质的含量，从而避免晶格畸变，减少生长缺陷，并最终表现为单晶金刚石内应力的减小，其中金刚石内应力以压应力的形式呈现。此外反应气体中加入CO₂可以降低单晶金刚石的生长速率和沉积温度，且在合适的碳氢氧原子比(5∶112∶4)下能够得到杂质少、结晶度高的单晶金刚石。     

Nickel N‐heterocyclic carbene complexes in the vinyl polymerization of norbornene

Vinyl polymerized norbornene has some useful properties such as good mechanical strength, optical transparency and heat resistance. Several transition metal complexes have been described in the literature as active catalysts for the vinyl polymerization of norbornene. We now report the use of three types of nickel(II) complexes with N‐heterocyclic carbene (NHC) ligands in the catalytic vinyl polymerization of norbornene under a range of conditions. Specifically, two nickel complexes bearing a chelating bis(NHC) ligand, two nickel complexes bearing two chelating anionic N‐donor functionalized NHC ligands as well as one diiodidonickel(II) complex with two monodentate NHC ligands were tested. The solid‐state structure of bis(1,3‐dimethylimidazol‐2‐ylidene)diiodidonickel(II), as determined by X‐ray crystallography, is presented. The highest polymerization activity of 2.6 × 10⁷ g (mol cat)^?1 h^?1 was observed using the latter nickel complex as catalyst, activated by methylaluminoxane. The norbornene polymers thus obtained are of high molecular weight but with rather low polydispersity. Copyright © 2010 John Wiley & Sons, Ltd.     

Term rank preservers of Boolean matrices

We obtain some characterizations of linear operators that preserve the term rank of Boolean matrices. That is, a linear operator over Boolean matrices preserves the term rank if and only if it preserves the term ranks 1 and k(≠1) if and only if it preserves the term ranks 2 and l(≠2). Other characterizations of term rank preservers are given.