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21.
Jean Luc Guermond 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1987,38(5):717-729
Asymptotic theories like the lifting-line, the slender body or the slender ship lead to lineintegrals with singular kernels. Sometimes these integrals are improper, that is to say that they are defined only by their Finite Part. To find asymptotic expansions of these integrals, the Matched Asymptotic Expansion Method is widely used along with other more specific methods depending on the kernel type. The first method is laborious and not systematic, and the other methods are sometimes too much specific to treat general cases. Moreover, all of them are not well adapted to deal with Finite Part integrals.Here, a new method is proposed to avoid the previous difficulties. This method is systematic for homogeneous kernels and gives approximations up to any order, as long as the derivative of the weight function exists at this given order. Moreover the occurrence of logarithmic terms in the expansion is explained and easily predictable. An elliptic integral and the classical lifting-line theory are treated to illustrate the ease of this method.
Nomenclature D domain of integration - f(x) weight function - FP Finite Part - h(x) weight function - I ,I o bounded intervals - j, J integers - K(x, ) singular kernel - L, L integers - M integer defining the approximation order - P k (x) Legendre polynomial - R set of real numbers - R(ß) equals 1 if is an integer and 0 if not - R f, J ,R K, L remainders of Taylor developments - S () equals either 1 or the sign function:sgn() - t, u, v, x variable of integration - , real numbers - homogeneity order of the kernel - F () Euler's integral (gamma function) - small parameter - [.] integer part of 相似文献
Résumé Les théories asymptotiques telles que la ligne portante, le corps élancé ou le navire de grand allongement conduisent à des intégrales curvilignes à noyaux singuliers. Parfois, ces intégrales sont impropres c'est à dire qu'elles sont définies en Parties Finies. Différentes méthodes ont été mises au point pour trouver les développements asymptotiques de ces intégrales. Généralement elles dépendent fortement de la nature du noyau, et c'est finalement la méthode des développements raccordés qui est utilisées quand le noyau est trop compliqué. Cependant, cette méthode est laborieuse et comme les précèdentes non adaptée aux intégrales défines par leur Partie Finie.Une nouvelle méthode est proposée pour surmonter ces difficultés. Cette méthode est systématique pour les noyaux homogènes et donne les approximations à tout ordre pourvu que les dérivées de la fonction poids existent jusqu'à cet ordre. De plus la présence de termes logarithmiques dans le développement est expliquée et aisément prédictible.Une intégrale elliptique, ainsi que la fameuse théorie de la ligne portante sont traités pour illustrer les possibilités de la méthode.
Nomenclature D domain of integration - f(x) weight function - FP Finite Part - h(x) weight function - I ,I o bounded intervals - j, J integers - K(x, ) singular kernel - L, L integers - M integer defining the approximation order - P k (x) Legendre polynomial - R set of real numbers - R(ß) equals 1 if is an integer and 0 if not - R f, J ,R K, L remainders of Taylor developments - S () equals either 1 or the sign function:sgn() - t, u, v, x variable of integration - , real numbers - homogeneity order of the kernel - F () Euler's integral (gamma function) - small parameter - [.] integer part of 相似文献
22.
Summary We first give a new proof of a conjecture of J.-P. Serre on the homotopy of finite complexes, which was recently proved by C. McGibbon and J. Neisendorfer. The emphasis is on a property of the mod. 2 homology of certain spaces: their quasi-boundedness as right modules over the Steenrod algebra. This property is preserved when one goes from a simply connected space to its loop space and also when one takes a covering of anH-space. Then we show that this notion of quasi-boundedness simplifies H. Miller's proof of D. Sullivan's conjecture on the contractibility of the space of pointed maps from the classifying space of the groupe /2 into a finite complex. 相似文献
23.
The molecular energy of the complex (η5-C5H5)2TiCl2 has been calculated for experimental geometry and for several hypothetical forms by a semi-empirical CNDO/2 approach. The energy difference between experimental (quasi-tetrahedral) geometry and a planar geometry is ca. 20 kcal mol?1. This difference is sufficiently high to explain the difficulty of the inversion process. 相似文献
24.
Urs P. Wild Hans J. Griesser Vo Dinh Tuan Jean F.M. Oth 《Chemical physics letters》1976,41(3):450-455
The emission spectra of the second excited singlet state of [18] annulene and of monofluoro [18] annulene (in a 3-methylpentane glass at 4 K) are reported. The large energy gap between the first and second excited singlet states inhibits fast internal conversion and favours the appearance of S2 → S0 emission. In addition, fluorescence from the S1 state can be observed in monofluoro [13] annulene by exciting into the S2 or directly into the S1 absorption. 相似文献
25.
The optically active methylphenyl-α-naphthylsilane racemises quickly in tetrahydrofuran in the presence of LiAlH4.Kinetic results show a different behaviour of the hydride depending on its concentration. Activation parameters have been obtained and mechanisms proposed. 相似文献
26.
Claude Balny Jennifer Canva Pierre Douzou Jean Bourdon 《Photochemistry and photobiology》1969,10(6):375-382
Abstract— Chemiluminescence and photochemiluminescence of systems generating excited (singlet) molecular oxygen has been studied at low temperature in fluid media. A possible interpretation is proposed: that dimers of singlet oxygen are directly or indirectly responsible for the observed emission, the species [1 δg +1 σg+ ] predominating. Energy transfer to a fluorescent molecule is possible only when conditions of spectral overlap, required for transfer by inductive resonance, are fulfilled. Evidence is also presented for the formation of a transient complex between oxygen and a sensitiser or acceptor molecule [S…O2 ], which is the precursor of singlet oxygen in these systems. However, other possible mechanisms cannot be excluded. 相似文献
27.
The examination of 19F chemical shifts for ca. 650 F-alkylated compounds of general formula CF3(CF2)nCF2X led to the following conclusions: the CF2 groups α to X are very sensitive to the nature of X, and are spread over a range of 85 ppm. The effect of the length of the F-alkyl chain decreases rapidly, so that δCF2(α) can already be considered as characteristic of X for n = 1 or 2 for most practical purposes. Solvent effects (in 9 different solvents having ε = 1.8 to 52.1) were found to be rather small except for the F-alkyl iodides. A chart which indicates the domain in which the CF2(α) resonance signal is to be expected is given for 42 different series of F-alkylated compounds; it is expected to provide the synthetic chemist with a useful tool for the identification and characterization of such compounds. 相似文献
28.
Harold C. Beachell Jean C. Peterson 《Journal of polymer science. Part A, Polymer chemistry》1969,7(8):2021-2029
A linear polyurethane of high molecular weight was prepared in solution by the polyaddition of equimolar amounts of ethylene glycol and methylene bis(4-phenyl isocyanate). The polymer was fractionated by using a direct sequential extraction procedure, with a solvent–nonsolvent system consisting of N,N′-dimethylformamide (DMF) and acetone (A). The resulting fractions were characterized by viscosity and lightscattering measurements. The relationship between the intrinsic viscosity and molecular weight was found in DMF at 25°C. to be [η] = 3.64 × 10?4M0.71. The unperturbed polymer chain dimensions were determined from intrinsic viscosity measurements carried out under experimentally determined theta conditions. 相似文献
29.
When European laboratories decided to develop a digital sound broadcasting system (DSB), they specified three main conditions to fulfil:
- quality improvement up to the level of ‘CD’ sound, even in difficult reception conditions (mobile vehicles, etc)
- additional significant digital data transmissions in order to transform sound broadcasting into a really new service
- the possibility of a common system for satellite and terrestrial transmissions.
30.
Jean Bourgain 《Communications in Mathematical Physics》1996,176(2):421-445
Consider the2D defocusing cubic NLSiu
t+u–u|u|2=0 with Hamiltonian
. It is shown that the Gibbs measure constructed from the Wick ordered Hamiltonian, i.e. replacing ||4 by ||4 :, is an invariant measure for the appropriately modified equationiu
t
+ u‒ [u|u
2–2(|u|2
dx)u]=0. There is a well defined flow on thesupport of the measure. In fact, it is shown that for almost all data the solutionu, u(0)=, satisfiesu(t)–e
it C
Hs
(), for somes>0. First a result local in time is established and next measure invariance considerations are used to extend the local result to a global one (cf. [B2]). 相似文献