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81.
82.
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
83.
Jean Bricmont Joel L. Lebowitz Christian Maes 《Journal of statistical physics》1987,48(5-6):1249-1268
We derive a number of new results for correlated nearest neighbor site percolation onZ
d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance –, has a nontrivial percolation behavior: sites on whichS
x
h percolate if and only ifh
c
. with0
c
< . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility. 相似文献
84.
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
85.
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
86.
A new and easy protocol for the formation of substituted 4,5-dihydro-1,2,4-triazin-6(1H)-ones was developed on solid support. The heterocyclic compounds were formed by nucleophilic reaction of hydrazine on thioamide esters. As cyclization was concomitant with cleavage from the support, substituted 4,5-dihydrotriazinones were obtained in high purity. 相似文献
87.
Alig Robin Karine Julienne Jean Claude Meslin David Deniaud 《Tetrahedron letters》2004,45(52):9557-9559
Substituted pyridones and pyridines have been synthesised efficiently by employing iminium salt as a key precursor. These compounds were prepared using tandem [4+2] cycloaddition/deamination between azabutadiene and dienophiles. 相似文献
88.
2-iodobenzonitrile, its derivatives, and various heterocyclic analogues undergo palladium(0)-catalyzed annulation onto diarylacetylenes or bicyclic alkenes to afford 2,3-diarylindenones and polycyclic aromatic ketones in very good to excellent yields. This reaction represents one of the first examples of the addition of an organopalladium moiety to the carbon-nitrogen triple bond of a nitrile. The reaction is compatible with a number of functional groups. A reaction mechanism, as well as a model accounting for the electronic effects of substituents on the aromatic ring of the nitrile, is proposed. 相似文献
89.
Fonseca GS Umpierre AP Fichtner PF Teixeira SR Dupont J 《Chemistry (Weinheim an der Bergstrasse, Germany)》2003,9(14):3263-3269
Stable transition-metal nanoparticles of the type [M(0)](n) are easily accessible through the reduction of Ir(I) or Rh(III) compounds dissolved in "dry" 1-n-butyl-3-methylimidazolium hexafluorophosphate ionic liquid by molecular hydrogen. The formation of these [M(0)](n) nanoparticles is straightforward; they are prepared in dry ionic liquid whereas the presence of the water causes the partial decomposition of ionic liquid with the formation of phosphates, HF and transition-metal fluorides. Transmission electron microscopy (TEM) observations and X-ray diffraction analysis (XRD) show the formation of [Ir(0)](n) and [Rh(0)](n) nanoparticles with 2.0-2.5 nm in diameter. The isolated [M(0)](n) nanoparticles can be redispersed in the ionic liquid, in acetone or used in solventless conditions for the liquid-liquid biphasic, homogeneous or heterogeneous hydrogenation of arenes under mild reaction conditions (75 degrees C and 4 atm). The recovered iridium nanoparticles can be reused several times without any significant loss in catalytic activity. Unprecedented total turnover numbers (TTO) of 3509 in 32 h, for arene hydrogenation by nanoparticles catalysts, have been achieved in the reduction of benzene by the [Ir(0)](n) in solventless conditions. Contrarily, the recovered Rh(0) nanoparticles show significant agglomeration into large particles with a loss of catalytic activity. The hydrogenation of arenes containing functional groups, such as anisole, by the [Ir(0)](n) nanoparticles occurs with concomitant hydrogenolysis of the C-O bond, suggesting that these nanoparticles behave as "heterogeneous catalysts" rather than "homogeneous catalysts". 相似文献
90.
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