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41.
42.
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
43.
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
44.
Gilles Gosselin Jean Louis Imbach Leroy B. Townsend Raymond P. Panzica 《Journal of heterocyclic chemistry》1979,16(6):1185-1191
Ribosylation of the trimethylsilyl derivative ( 1b ) of imidazole-2-thione ( 1a ) using either stannic chloride or silver perchlorate as catalyst resulted in the formation of the acylated derivatives of 1-(β-D-ribofuranosyl)imidazole-2-thione ( 3c ) and 1,3-di-(β-D-ribofuranosyl)imidazole-2-thione ( 4c ) with the latter predominating ( 4c:3c , ca. 2:1 ). The diribosylated nucleoside 4c was shown to be the N,N-disubstituted product rather than the N,S-disubstituted product by 1H nmr and 13C nmr spectroscopy. Employment of the iodine-catalyzed fusion procedure reversed the aforementioned product ratios and provided the monoriboside 3c in excellent yield. When the trimethylsilyl derivative ( 5b ) of 2-methylthioimidazole ( 5a ) was reacted with 2,3,5-tri-O-benzoyl-D-ribofuranosyl bromide ( 2d ) in acetonitrile, the major product was 1,3-di-(2,3,5-tri-O-benzoyl-β-D-ribofuranosyl)-imidazole-2-thione ( 4b ). The formation of 4b in this reaction is thought to arise via the Hilbert-Johnson mechanism. 相似文献
45.
The solid-phase synthesis of the octapeptide 1 AcGly-Ala-Lys-Arg-His-Arg-Lys-ValOMe, which represents the fragment 14-21 of the amino acid sequence of the chromosomal histone H4, as well as of the structurally related nonapeptide 2 AcGly-Ala-Lys-Leu-Arg-His-Arg-Lys-ValOMe, is described using a new polyacrylic resin containing a glycolamide ester linkage(resin-NHCO-CH2-OCO-peptide) acting as a labile anchoring moiety between the resin and the peptide.After elongation of the polypeptide chain using classical protecting groups, i.e. t-butyloxycarbonyl for the α-NH2 function, benzyloxycarbonyl, nitro and 2,4-dinitrophenyl groups for the side-chains of Lys, Arg and His respectively, both peptides 1 and 2 were obtained in good yields and with a high purity as shown by high-pressure liquid chromatography, by amino-acid analysis and by high-field proton NMR spectroscopy.This work demonstrates the ability of the newly introduced polyacrylic resin to act as a convenient support for solid-phase peptide synthesis. 相似文献
46.
The voltammogram of aryldiazonium tetrafluoroborates in acetonitrile (ACN), at low concentration, shows a first one-electron wave followed at a more negative potential by a small second wave; this last one corresponds to the reduction of the radical formed at the level of the first wave. Simulation of the voltammogram permits one to determine the standard redox potential of the radical/anion couple Eo(Ph./Ph-) = 0.05 V/SCE and the reduction mechanism of the diazonium cation. An electron transfer concerted with the cleavage of the C-N bond furnishes the aryl radical; this radical undergoes two competitive reactions: reduction at the electrode and H-atom transfer. 相似文献
47.
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
48.
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
49.
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
50.
Electron attachment to polar molecules and their non-covalent complexes can lead to different kinds of anions which differ from their excess electron localization. Spectroscopic methods for studying anion structures are reviewed. In many cases, the neutral and anion structures are identical and can be deduced from the electron attachment properties. Examples are given for complexes containing polar solvents or building blocks of biomolecules (nucleobases, amino acid residues...). 相似文献