Commutative and noncommutative representations of matrix-valued herglotz-nevanlinna functions

Operator realizations of matrix-valued Herglotz-Nevanlinna functions play an important and essential role in system theory, in the spectral theory of bounded nonselfadjoint operators, and in interpolation problems. Here, a generalization for realization results of the Brodskiǐ-Livsic type is given for Herglotz-Nevanlinna functions whose spectral measures are compactly supported.     

On locality in quantum general relativity and quantum gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.     

Periodic solutions of asymptotically linear Hamiltonian systems

We prove existence and multiplicity results for periodic solutions of time dependent and time independent Hamiltonian equations, which are assumed to be asymptotically linear. The periodic solutions are found as critical points of a variational problem in a real Hilbert space. By means of a saddle point reduction this problem is reduced to the problem of finding critical points of a function defined on a finite dimensional subspace. The critical points are then found using generalized Morse theory and minimax arguments.     

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems.     

Plastic deformation and performance of engineering polymer materials

The plastic deformation mechanism operating in polymer glasses is analyzed. The whole process consists of two main stages: nucleation of special shear defects, called PSTs (plastic shear transformations), and their disappearance. The important feature of plastic deformation of glasses is the storage of a large amount of internal energy ΔU_def upon straining. Such energy storage is the critical issue for mechanical performance of polymeric material: if the amount of stored energy is high, the appearance of macroscopic failure is very probable while glassy materials collecting a small amount of stored deformation energy are quite ductile. It is proposed that the rate of disappearance of PSTs is a key factor in dissipation of stored deformation energy. A parameter describing the dissipation ability of material upon deformation is introduced.     

Impurity optical absorption in parabolic quantum well

Optical absorption in GaAs parabolic quantum well in the presence of hydrogenic impurity is considered. The absorption coefficient associated with the transitions between the upper valence subband and donor ground state is calculated. The impurity ground state wave function and energy are obtained using the variational method. Dependence of the absorption spectra on impurity position in quantum well was investigated. It is shown, that along with quantum well width decrease the absorption threshold shifts to higher frequencies. Results obtained within frames of parabolic approximation are compared with results for rectangular infinite-barrier quantum well case. The acceptor state → conduction band transitions considered as well.     

Ligand Design for Site-Selective Metal Coordination: Synthesis of Transition-Metal Complexes with η6-Coordination of the Central Ring of Anthracene

A polycyclic aromatic ligand for site-selective metal coordination was designed by using DFT calculations. The computational prediction was confirmed by experiments: 2,3,6,7-tetramethoxy-9,10-dimethylanthracene initially reacts with [(C₅H₅)Ru(MeCN)₃]BF₄ to give the kinetic product with a [(C₅H₅)Ru]⁺ fragment coordinated at the terminal ring, which is then transformed into the thermodynamic product with coordination through the central ring. These isomeric complexes have markedly different UV/Vis spectra, which was explained by analysis of the frontier orbitals. At the same time, the calculations suggest that electrostatic interactions are mainly responsible for the site selectivity of the coordination.     

Diastereoselective cycloaddition of (S)-N-(1-phenylethylimino)trifluoropropionate and trifluoroethylphosphonate with diazomethane

The cycloaddition reaction of (S)-(α-phenylethylimino)trifluoropropionate with diazomethane leads to a diastereomeric mixture (4.5:1) of 5-trifluoromethyl-1,2,3-triazoline-5-carboxylates. Enantiopure diastereomers were isolated by column chromatography and converted into their respective non-racemic 2-trifluoromethyl-aziridine-2-carboxylates and carboxylic acids. The absolute configuration of newly formed stereogenic centers was determined by XRD analysis. The stereoselective reaction between (S)-N-(α-phenylethyl)trifluoroacetimidoylphosphonate and diazomethane produces a diastereomeric mixture (2.5:1) of 5-trifluoromethyltriazoline-5-phosphonates readily separated by column chromatography in diastereomerically pure forms.     

Effective flow of a viscous liquid through a helical pipe

We study the flow of a viscous fluid through a pipe with helical shape parameterized with , where the small parameter stands for the distance between two coils of the helix. The pipe has small cross-section of size . Using the asymptotic analysis of the microscopic flow described by the Navier–Stokes system, with respect to the small parameter that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe. To cite this article: E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).

Résumé

On considère un écoulement dans un tube de section circulaire et de forme hélicoïdale paramétré par , où est la distance entre deux tours de la spirale. Le rayon de la section du tube est lui aussi supposé égal à . A partir de l'écoulement microscopique décrit par le système de Navier–Stokes et en utilisant l'analyse asymptotique par rapport à ce petit paramètre on obtient l'écoulemment effectif décrit par une formule explicite de type Poiseuille associée à une petite déviation due à la géometrie du tube. Pour citer cet article : E. Marušić-Paloka, I. Pažanin, C. R. Mecanique 332 (2004).     

Influence of key parameters on the morphology of ethylcellulose microcapsules prepared via room-temperature spray drying

In this contribution, the morphology of ethylcellulose (EC) microspheres prepared with a room-temperature spray-drying technique is examined as a function of solution concentration, nozzle-to-target distance, and choice of solvent. Additionally, to determine the morphology of EC microspheres in the presence of an aqueous encapsulated material, a series of encapsulation measurements was conducted using hydrogen peroxide solution as the core component. It was observed that highly concentrated EC solutions lead to the formation of tail-like fibers adjacent to the sprayed microcapsules because of the high viscosity of solutions. Furthermore, when the solutions are sprayed from relatively short nozzle-to-target distances, porous EC films are formed on the target surface along with the EC microspheres. Three nozzle-to-target distances were tested (38, 69, and 115 cm), and the optimal one was found to be 115 cm. To determine how and to what extent the solvent used in room-temperature spray-drying experiments affects the morphology of resultant microspheres, EC was dissolved in either acetone or dichloromethane (DCM), and sprayed from the resultant solutions. While microcapsules prepared from the EC-in-DCM system exhibit even, but porous wall surfaces, microspheres prepared from the EC-in-acetone solution display irregular, but cavity-free wall-surfaces. Finally, as opposed to the pure EC capsules, the ones containing H₂O₂ solution exhibit very smooth wall surfaces; this effect was attributed to the plasticizing effect that the aqueous solution has on the ethylcellulose macromolecules.