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1.
Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003 相似文献
2.
G. Ullrich D. Herzog R. Liska P. Burtscher N. Moszner 《Journal of polymer science. Part A, Polymer chemistry》2004,42(19):4948-4963
Camphorquinone (CQ), a widely used photoinitiator (PI) in dental applications, was covalently bonded to aromatic amines to enhance the rate of electron and proton transfer effect due to the close vicinity of the diketone and the amine group. 10‐bromocamphorquinone and 10‐bromomethylcamphorquinone were selected as suitable precursors for esterification with the carboxyl group containing aromatic amines based on 4‐dimethylaminobenzoic acid. Properties of the new photoinitiating systems were investigated by UV spectroscopy and differential scanning photocalorimetry in lauryl acrylate. Compared to physical mixtures, in all cases similar or even better performance was obtained. Surprisingly, 10‐acetyl derivatives 7 – 9 and 18 especially, were found to be highly reactive. Compared to CQ/ethyl 4‐dimethylaminobenzoate, the rate of photopolymerization was increased by a factor of up to 2. Intramolecular reaction was confirmed by photo‐differential scanning calorimetry experiments with varying PI concentrations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4948–4963, 2004 相似文献
3.
This is the second in a two-part series of articles in which we analyze a system similar in structure to the well-known Zakharov equations from weak plasma turbulence theory, but with a nonlinear conservation equation allowing finite time shock formation. In this article we analyze the incompressible limit in which the shock speed is large compared to the underlying group velocity of the dispersive wave (a situation typically encountered in applications). After presenting some exact solutions of the full system, a multiscale perturbation method is used to resolve several basic wave interactions. The analysis breaks down into two categories: the nonlinear limit and the linear limit, corresponding to the form of the equations when the group velocity to shock speed ratio, denoted by ε, is zero. The former case is an integrable limit in which the model reduces to the cubic nonlinear Schrödinger equation governing the dispersive wave envelope. We focus on the interaction of a “fast” shock wave and a single hump soliton. In the latter case, the ε=0 problem reduces to the linear Schrödinger equation, and the focus is on a fast shock interacting with a dispersive wave whose amplitude is cusped and exponentially decaying. To motivate the time scales and structure of the shock-dispersive wave interactions at lowest orders, we first analyze a simpler system of ordinary differential equations structurally similar to the original system. Then we return to the fully coupled partial differential equations and develop a multiscale asymptotic method to derive the effective leading-order shock equations and the leading-order modulation equations governing the phase and amplitude of the dispersive wave envelope. The leading-order interaction equations admit a fairly complete analysis based on characteristic methods. Conditions are derived in which: (a) the shock passes through the soliton, (b) the shock is completely blocked by the soliton, or (c) the shock reverses direction. In the linear limit, a phenomenon is described in which the dispersive wave induces the formation of a second, transient shock front in the rapidly moving hyperbolic wave. In all cases, we can characterize the long-time dynamics of the shock. The influence of the shock on the dispersive wave is manifested, to leading order, in the generalized frequency of the dispersive wave: the fast-time part of the frequency is the shock wave itself. Hence, the frequency undergoes a sudden jump across the shock layer.In the last section, a sequence of numerical experiments depicting some of the interesting interactions predicted by the analysis is performed on the leading-order shock equations. 相似文献
4.
Holger Poths Erik Wischerhoff Rudolf Zentel Axel Sch nfeld Guido Henn Friedrich Kremer 《Liquid crystals》1995,18(5):811-818
Two new ferroelectric oligosiloxanes, a cyclic tetramer and a twin, have been synthesized. By a comparative study with their corresponding monomer and side chain polysiloxanes, the influence of oligo- and polymerization on the liquid crystalline and ferroelectric properties have been investigated. Polymerization leads to a stabilization of LC phases through increase of the clearing temperatures and suppression of crystallization. Oligomerization also leads to mesophase broadening, but, due to the low degree of polymerization, the effect is inferior to the linear polysiloxanes. The low viscosity of the oligosiloxanes ensures response times in the microsecond region, thus being comparable with their monomer and conventional LMWFLCs. It is found that polymerization increases the spontaneous polarization Ps. This is attributed to the density increase after polymerization, enhancing the inter-mesogenic interactions. The collective and local dynamics of the OFLCs are influenced differently with respect to their molecular structures. Each oligomer is already a good model for its corresponding polymer concerning the soft mode dynamics. For the local β-relaxation a similar temperature dependence of the relaxation times τ for the cyclic tetramer and for the side chain polysiloxanes is observed. The long axial rotation of the twin, having a very efficient decoupling, is significantly faster, thus resembling the monomer. 相似文献
5.
Jü rgen Herzog Takayuki Hibi Xinxian Zheng 《Transactions of the American Mathematical Society》2006,358(9):4119-4134
Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distributive lattice, the Alexander dual is computed.
6.
Gerd Herzog Christoph Schmoeger 《Proceedings of the American Mathematical Society》2003,131(11):3507-3509
We prove the converse of Raubenheimer and Rode's Banach algebra version of the Perron-Frobenius Theorem.
7.
Axel Ruhe 《BIT Numerical Mathematics》2007,47(2):239-240
8.
Axel Ruhe 《BIT Numerical Mathematics》2006,46(4):687-688
9.
A relatively simple procedure is described for the selective and highly sensitive determination of amitrole (3-amino-1,2,4-triazole) by ionpair HPLC with amperometric detection. The separation was achieved on a polar CN-column using hexane, propanol, water (62:36:2) with LiClO4 (2.5 g·l–1) and trichloroacetic acid (2 g·l–1) as electrolytes. The determination range lies between 500 pg and 500 ng and the limit of detection was found to be 200 pg (s.d.: 11%; N=9). The minimum detectability for the alternative UV-monitoring was 2.5 ng. The developed method may be helpful in production and quality control and for the selective determination of amitrole in commercial formulations. 相似文献
10.
A multilayer structure consisting of undoped GaAs and AlAs layers was incorporated into a buffer layer on GaAs substrates. This reduces the spreading of impurities from the substrate (e.g. tellurium) into layers deposited on top of the multilayer system as observed by SIMS and C/V profiling. Incorporation coefficients for tellurium in GaAs, AlAs and multilayers were calculated. 相似文献