Geometric quantization of topological gauge theories

We show that Abelian gauge theories in 2+1 space-time dimensions with the introduction of a topological Chern-Simons term can be quantized with the use of the symplectic formalism. The consistency of our results are verified by the agreement with the ones from the Dirac case.     

Localising gravity in composite monopole brane worlds without bulk cosmological constant

We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e., a defect composed of a 't Hooft–Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space–time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without a priori introduction of a bulk cosmological constant.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Photoinitiated curing of mono‐ and bifunctional epoxides by combination of active chain end and activated monomer cationic polymerization methods

Photoinitiated cationic polymerization of mono‐ and bifunctional epoxy monomers, namely cyclohexeneoxide (CHO), 4‐epoxycyclohexylmethyl‐3′,4′‐epoxycyclohexanecarboxylate (EEC), respectively by using sulphonium salts in the presence of hydroxylbutyl vinyl ether (HBVE) was studied. The real‐time FTIR spectroscopic, gel content determination, and thermal characterization studies revealed that both hydroxyl and vinyl ether functionalities of HBVE take part in the polymerization. During the polymerization, HBVE has the ability to react via both active chain end (ACE) and activated monomer mechanisms through its hydroxyl and vinyl ether functionalities, respectively. Thus, more efficient curing was observed with the addition of HBVE into EEC‐containing formulations. It was also demonstrated that HBVE is effective in facilitating the photoinduced crosslinking of monofunctional epoxy monomer, CHO in the absence of a conventional crosslinker. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4914–4920, 2007     

Diblock copolymers based on allyl methacrylate: Synthesis,characterization, and chemical modification

Different diblock copolymers constituted by one segment of a monomer supporting a reactive functional group, like allyl methacrylate (AMA), were synthesized by atom transfer radical polymerization (ATRP). Bromo‐terminated polymers, like polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(butyl acrylate) (PBA) were employed as macroinitiators to form the other blocks. Copolymerizations were carried out using copper chloride with N,N,N′,N″,N″‐pentamethyldiethylenetriamine (PMDETA) as the catalyst system in benzonitrile solution at 70 °C. At the early stage, the ATRP copolymerizations yielded well‐defined linear block copolymers. However, with the polymerization progress a change in the macromolecular architecture takes place due to the secondary reactions caused by the allylic groups, passing to a branched and/or star‐shaped structure until finally yielding gel at monomer conversion around 40% or higher. The block copolymers were characterized by means of size exclusion chromatography (SEC), ¹H NMR spectroscopy, and differential scanning calorimetry (DSC). In addition, one of these copolymers, specifically P(BA‐b‐AMA), was satisfactorily modified through osmylation reaction to obtain the subsequent amphiphilic diblock copolymer of P(BA‐b‐DHPMA), where DHPMA is 2,3‐dihydroxypropyl methacrylate; demonstrating the feasibility of side‐chain modification of the functional obtained copolymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3538–3549, 2007     

A note on continuously decomposed evolving exchange economies

It is routine to demonstrate in the exchange economy framework that small changes of individual preferences and endowments always result in small changes of the derived excess demand functions as one should expect. Though being as desirable for reasons of the consistency of the whole approach, however, a precise proof of the converse direction so far is still open to question. The present paper shows that it is actually true. We use a decomposition method for aggregate excess demand functions developed by Mas-Colell which is derived from the well-known decomposition method developed by Sonnenschein and perfected by Debreu and Mantel. Our result fills in a notorious gap in the line of economic justification usually given for this decomposition, or disaggregation, method in that comparative static analysis would be restricted if the decomposition of excess demand functions would not be continuous.     

Obstruction à la transversalité de lagrangiens

In this Note, we give a necessary and sufficient condition for Lagrangians in a symplectic vector bundle to be deformed stably into transversal Lagrangians. In the case of three Lagrangians, we show that the associated Grothendieck group can be identified with a Hermitian K-theory group. To cite this article: M. Karoubi, M.L. Lapa de Souza, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Tesla变压器型电子束加速器初步实验

 介绍了一种Tesla变压器型的强流电子束加速器。当变压器初级输入20kV左右的电压时，加速器二极管输出电压500kV，电流9kA，信号脉宽大约50ns，该装置具有结构简单，安装方便，运行可靠等特点。     

Optical properties of in situ doped and undoped titania nanocatalysts and doped titania sol-gel nanofilms

In this paper we present spectroscopic properties of doped and undoped titanium dioxide (TiO₂) as nanofilms prepared by the sol-gel process with rhodamine 6G doping and studied by photoacoustic absorption, excitation and emission spectroscopy. The absorption spectra of TiO₂ thin films doped with rhodamine 6G at very low concentration during their preparation show two absorption bands, one at 2.3 eV attributed to molecular dimmer formation, which is responsible for the fluorescence quenching of the sample and the other at 3.0 eV attributed to TiO₂ absorption, which subsequently yields a strong emission band at 600 nm. The electronic band structure and optical properties of the rutile phase of TiO₂ are calculated employing a fully relativistic, full-potential, linearized, augmented plane-wave (FPLAPW) method within the local density approximation (LDA). Comparison of this calculation with experimental data for TiO₂ films prepared for undoped sol-gels and by sputtering is performed.