The crucial importance of agostic interactions in intermediates formed in propylene polymerization using neutral salicyladiminato palladium(II) and nickel complexes as catalysts

The structures of intermediates formed in propylene polymerisation using neutral salicyladiminato palladium(II) and nickel(II) complexes as catalysts have been investigated using density functional theory. Calculations show that all low energy intermediates contain agostic interactions either between the metal and a hydrogen from the added propylene forming four- or five-membered chelate rings, or, when a phenyl ring is present, between the metal and an aromatic C-C bond. The agostic interactions with the metal are concomitant with changes in ligand dimensions and electronic properties. In particular when a metal to hydrogen bond is formed, there is a lengthening of the C-H bond. Significant differences are found for the agostic interactions with palladium and nickel in that for Pd there is a clear preference for specific intermediates but for Ni there are several different structures with similar energies which are likely to lead to a greater variety of products on further polymerisation. (c) 2007 Elsevier B.V. All rights reserved.

A DFT study of propylene polymerization using neutral salicyladiminato nickel(II) and palladium(II) as catalysts

Propylene polymerization using salicyladiminato metal catalalysts has been studied using density functional theory at the B3LYP/LANL2DZ level. In particular, the effects on the reaction mechanisms of changing the metal from Pd(II) to Ni(II) have been investigated. While the reaction mechanisms involving the salicyladiminato Ni(II) catalyst have been found to be similar to those established previously for the salicyladiminato Pd(II) catalyst, the nickel catalyst was found to differentiate the trans-O intermediate from the trans-.N intermediate with an energy difference of 46.63 U mol(-1) significantly more than the palladium catalyst for which the energy difference was calculated as 35.82 kJ mol(-1). The energy difference between the trans-O configuration and the trans-N configuration is decreased significantly when combining a molecule of propylene with the catalyst. For the Ni catalyst, the trans-O isomer is more stable than the trans-N isomer to a greater extent than for Pd, so that the insertion of propylene from 20 is relatively less favoured for Ni than for Pd. It is predicted that the mechanism of isomerization from 20 to 2N through a rotational transition state TS2O2N is more appropriate for the Ni catalyst system. The palladium system shows a larger preference for pi-coordination than its nickel counterpart, although the latter possesses a lower reaction barrier. It was found that the occupation of the trans-O position in the asymmetric salicyladiminato catalyst is also more favored by the alkene as it is by the alkyl so that insertion of the alkene may always start from a particular configuration so that specific products are obtained. (c) 2005 Elsevier B.V. All rights reserved.

Coordination-driven self-assembly of a novel carbonato-bridged heteromolecular neutral nickel(II) triangle by atmospheric CO2 fixation

Formation of a quasi-symmetrical mu(3)-carbonato-bridged self-assembled heteromolecular triangle of Ni(II), [(mu(3)-CO3){Ni-2(salmeNH)(2)(NCS)(2)}[Ni(salmeNH(2))(2)]center dot Et2O center dot H2O (HsalmeNH = 2-[(3-methylamino-propylimino)-methyl]-phenol) involves atmospheric CO2 uptake in a neutral medium, by spontaneous self-reorganization of the starting mononuclear Ni(II)-Schiff-base complex, [Ni(salmeNH)(2)]. The environment around Ni(II) in two of the subunits is different from the third one. The starting complex, (Ni(salmeNH)(2)], and one of the possible intermediate species, [Ni(salmeNH(2))(2)(NCS)(2)], which has a very similar coordination environment to that in the third Ni(II) center, have been characterized structurally. A plausible mechanism for the formation of such a triangle has also been proposed. The compound shows a very strong antiferromagnetic coupling. Fit as a regular triangular arrangement gave J = -53.1, g = 2.24, and R = 1.5 x 10(-4).

An efficient finite difference scheme for three-dimensional, non-equilibrium flows using operator splitting

An efficient finite difference scheme is presented for the inviscid terms of the three-dimensional, compressible flow equations for chemical non-equilibrium gases. This scheme represents an extension and an improvement of one proposed by the author, and includes operator splitting.

Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Modified level set method with Canny operator for image noise removal

The level set method is commonly used to address image noise removal. Existing studies concentrate mainly on determining the speed function of the evolution equation. Based on the idea of a Canny operator, this letter introduces a new method of controlling the level set evolution, in which the edge strength is taken into account in choosing curvature flows for the speed function and the normal to edge direction is used to orient the diffusion of the moving interface. The addition of an energy term to penalize the irregularity allows for better preservation of local edge information. In contrast with previous Canny-based level set methods that usually adopt a two-stage framework, the proposed algorithm can execute all the above operations in one process during noise removal.

Operator performance evaluation of controlled depth of field in a stereographically displayed virtual environment

Retinal blurring resulting from the human eye's depth of focus has been shown to assist visual perception. Infinite focal depth within stereoscopically displayed virtual environments may cause undesirable effects, for instance, objects positioned at a distance in front of or behind the observer's fixation point will be perceived in sharp focus with large disparities thereby causing diplopia. Although published research on incorporation of synthetically generated Depth of Field (DoF) suggests that this might act as an enhancement to perceived image quality, no quantitative testimonies of perceptional performance gains exist. This may be due to the difficulty of dynamic generation of synthetic DoF where focal distance is actively linked to fixation distance. In this paper, such a system is described. A desktop stereographic display is used to project a virtual scene in which synthetically generated DoF is actively controlled from vergence-derived distance. A performance evaluation experiment on this system which involved subjects carrying out observations in a spatially complex virtual environment was undertaken. The virtual environment consisted of components interconnected by pipes on a distractive background. The subject was tasked with making an observation based on the connectivity of the components. The effects of focal depth variation in static and actively controlled focal distance conditions were investigated. The results and analysis are presented which show that performance gains may be achieved by addition of synthetic DoF. The merits of the application of synthetic DoF are discussed.

Vekua theory for the Helmholtz operator

Vekua operators map harmonic functions defined on domain in \mathbb R2R2 to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally, we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical, and plane waves.

Operator space structure of JC*-triples and TROs, I

We embark upon a systematic investigation of operator space structure of JC*-triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a JC*-triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension

On the operator space structure of Hilbert spaces

Operator spaces of Hilbertian JC∗ -triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite-dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite-dimensional subspaces. Injective envelopes are explicitly computed.

Effect of mountain breeze in ventilating the city under calm and neutral atmospheric environment: Interaction of airflow structures and ventilation efficiency

Many modern cities locate in the mountainous areas, like Hong Kong, Phoenix City and Los Angles. It is confirmed in the literature that the mountain wind system developed by differential heating or cooling can be very beneficial in ventilating the city nearby and alleviating the UHI effect. However, the direct interaction of mountain wind with the natural-convection circulation due to heated urban surfaces has not been studied, to our best knowledge. This kind of unique interaction of two kinds of airflow structures under calm and neutral atmospheric environment is investigated in this paper by CFD approach. A physical model comprising a simple mountain and three long building blocks (forming two street canyons) is firstly developed. Different airflow structures are identified within the conditions of different mountain-building height ratios (R=Hm/Hb) by varying building height but fixing mountain height. It is found that the higher ventilation rate in the street canyons is expected in the cases of smaller mountain-building ratios, indicating the stronger natural convection due to increasing heated building surfaces. However, there is the highest air change rate (ACH) in the lowest-building-height case and most of the air is advective into the street canyon through the top open area, highlighting the important role played by the mountain wind. In terms of the ventilation efficiency, it is shown that the smallest R case enjoys the best air change efficiency followed by the highest R case, while the worst ventilative street canyons occur at the middle R case. In the end, a gap across the streets is introduced in the modeling. The existence of the gap can greatly channel the mountain wind and distribute the air into streets nearby. Thus the ACH can be doubled and air quality can be significantly improved.

Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.