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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.
Bérangère C Caussarieu N Morin P Morin-Allory L Lafosse M 《Journal of separation science》2004,27(12):964-970
An original system which uses Porous Graphitic Carbon as support and a mixture of organic solvents as mobile phase is proposed for the analysis of triterpenic acids by liquid chromatography. The separation of betulinic acid, ursolic acid, oleanolic acid, and 18alpha- and 18beta-glycyrrhetinic acids was carried out within a short time and monitored by evaporative light scattering detection as universal detection method. Molecular modelling studies show that the main contribution to the selectivity comes from the electrostatic interaction characterised by the dipole moment of the products. 相似文献
89.
Vlekken J D'Olieslaeger M Knuyt G Vandervorst W De Schepper L 《Journal of the American Society for Mass Spectrometry》2000,11(7):650-658
In secondary ion mass spectrometry, the detection of MCs+ clusters (with M an element of the specimen) under a Cs bombardment is frequently used for the quantification of major elements. Despite some very good results obtained by this method, some problems still remain. In order to gain some more insight into these problems, the formation mechanism of the MCs+ clusters is investigated using a Monte Carlo model. It is shown that the majority of the constituent particles of the formed clusters are initially first or second neighbor atoms at the surface and that the velocity distribution of the MCs+ clusters becomes broader and peaked at higher velocities with increasing surface binding energy of the M atom. In addition, it is demonstrated that the interaction potential between the M and Cs+ particle has no influence on the velocity distribution of the MCs+ clusters. On the other hand, the cluster formation probability, defined as the probability that a sputtered M and Cs+ particle will form a MCs+ cluster, is extremely sensitive to this interaction potential. It is also shown that the cluster formation probability decreases with increasing surface binding energy. Finally, a good correspondence is obtained between the calculated and experimental velocity distributions of MCs+ clusters sputtered from different monoatomic materials. As a consequence, the Monte Carlo model and the discussed results can be validated. 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