Gevrey properties of real planar singularly perturbed systems

By applying geometric techniques to real analytic singularly perturbed vector fields on the plane, we develop a way to give a bound on the Gevrey type of the Taylor development of canard manifolds at degenerate planar turning points. By blowing up the phase space at the turning point, we find asymptotic estimates even when such expansions w.r.t. traditional phase space variables do not exist. The asymptotic estimates are then used to give a sufficient and necessary condition on the existence of (local) canard solutions.     

Nonlinear optical properties of regioregular main‐chain polyesters

We have prepared new polyesters containing quadratic, nonlinear optical (NLO) active chromophores covalently incorporated into the main chain. In these polymers, the sequence of the chromophore units along the main chain is rigorously head to tail. All the polyesters are processable, both in the melt and in solution. For one polyester, a full second‐order NLO characterization has been performed. An out‐of‐resonance d₃₃ coefficient of 21 pm/V at 1368 nm has been measured. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2719–2725, 2007     

Carbide precipitates in solution-quenched PH13-8 Mo stainless steel: A small-angle neutron scattering investigation

This paper deals with the small-angle neutron scattering (SANS) investigation on solution-quenched PH13-8 Mo stainless steel. From the nature of the variation of the functionality of the profiles for varying specimen thickness and also from the transmission electron microscopy (TEM), it has been established that the small-angle scattering signal predominantly originates from the block-like metallic carbide precipitates in the specimen. The contribution due to double Bragg reflection is not significant in the present case. The single scattering profile has been extracted from the experimental profiles corresponding to different values of specimen thickness. In order to avoid complexity and non-uniqueness of the multi-parameter minimization for randomly oriented polydisperse block-like precipitate model, the data have been analyzed assuming randomly oriented polydisperse cylindrical particle model with a locked aspect ratio.     

Performance evaluation of fiber Bragg grating sensors by digital holographic technique, strain gauge measurement

In view of the growing interest for non-destructive tests of materials, geodynamical monitoring and in general remote sensing, there is a great effort to bring practical optical sensors from research labs to industrial and environmental applications. In this paper, we employ digital holographic technique as an efficient tool for evaluating the strain measurement capability of fiber Bragg gratings (FBG). A cantilever beam has been employed as a test structure under loading test. The strain measurements results obtained by fiber-based sensors have been compared to those obtained by using full-field digital holographic technique and point-wise strain gauge sensors glued on the same cantilever beam. A simple theoretical model is also presented to interpret and compare the experimental results coming from different techniques.     

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Seismic data is modeled in the high‐frequency approximation, using the techniques of microlocal analysis. We consider general, anisotropic elastic media. Our methods are designed to allow for the formation of caustics. The data is modeled in two ways. First, we give a microlocal treatment of the Kirchhoff approximation, where the medium is assumed to be piecewise smooth, and reflection and transmission occur at interfaces. Second, we give a refined view on the Born approximation based upon a linearization of the scattering process in the medium parameters around a smooth background medium. The joint formulation of Born and Kirchhoff scattering allows us to take into account general scatterers as well as the nonlinear dependence of reflection coefficients on the medium parameters. The latter allows the treatment of scattering up to grazing angles. The outcome of the analysis is a characterization of the singular part of seismic data. We obtain a set of pseudodifferential operators that annihilate the data. In the process we construct a Fourier integral operator and a reflectivity function such that the data can be represented by this operator acting on the reflectivity function. In our construction this Fourier integral operator becomes invertible. We give the conditions for invertibility for general acquisition geometry. The result is also of interest for inverse scattering in acoustic media. © 2002 John Wiley & Sons, Inc.     

On the chromatic polynomial of a graph

Let P(G,λ) be the chromatic polynomial of a graph G with n vertices, independence number α and clique number ω. We show that for every λ≥n, ()^α≤≤ () ^{n −ω}. We characterize the graphs that yield the lower bound or the upper bound.?These results give new bounds on the mean colour number μ(G) of G: n− (n−ω)() ^{n −ω}≤μ(G)≤n−α() ^α. Received: December 12, 2000 / Accepted: October 18, 2001?Published online February 14, 2002     

关于1+1维可积系统的代数结构与Riemann-Hilbert变换

1+1维经典可积系统的隐代数结构用Riemann-Hilbert变换进行一般性讨论。新的Loop代数用Yang-Baxter等式的解给出,并指出它与基本Poisson-Lie括号的一致性。系统的Virasoro代数结构由系统的共形不变性导出。     

A delta white noise functional

The additive renormalization% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabs7adaWgaaWcbaGaaeySdiaab6cacaqG0bqefeKCPfgBaGqb% diaa-bcaaeqaaOGaeyypa0Jaa8hiaiaacIcacaaIYaGaeqiWdaNaai% ykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaGqadOGa% a4hiaiGacwgacaGG4bGaaiiCaiaacIcacqGHsislcaqGXoWaaWbaaS% qabeaacaqGYaaaaOGaai4laiaaikdacaGGPaGaa4hiaiaacQdaciGG% LbGaaiiEaiaacchacqGHXcqSdaWadiqaaiabgkHiTiaadkeacaGGNa% GaaiikaiaadshacaGGPaWaaWbaaSqabeaacaaIYaaaaOGaai4laiaa% ikdacaGFGaGaey4kaSIaa4hiaiaabg7acaWGcbGaai4jaiaacIcaca% WG0bGaaiykaaGaay5waiaaw2faaiaacQdaaaa!6C5C!\[{\rm{\delta }}_{{\rm{\alpha }}{\rm{.t}} } = (2\pi )^{ - 1/2} \exp ( - {\rm{\alpha }}^{\rm{2}} /2) :\exp \pm \left[ { - B'(t)^2 /2 + {\rm{\alpha }}B'(t)} \right]:\]is shown to be a generalized Brownian functional. Some of its properties are derived. is shown to be a generalized Brownian functional. Some of its properties are derived.On leave from Universidade do Minho, Area de Matematica, Largo Carlos Amarante, P-4700 Braga, Portugal.     

北京七色光儿童艺术剧院的声学设计

北京七色光儿童艺术剧院是一个以演出儿童话剧为主，同时还可以进行歌舞、音乐等其他文艺形式的演出的多功能剧场，该剧院形式活泼，音质良好。本文从音质和噪声控制的几个方面对其声学设计进行了介绍。     

关于Hopf丛S3的几个论题

本文证明了Hopf主纤维丛S^3的几个相关的命题，指出底流形S^3上的Laplace算子在主丛上的提升是主丛S^3上的Laplace算子，以及主丛的嵌入截面具有不动点性质等。