A systematic formula for the asymptotic expansion of singular integrals

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.

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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.

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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     

Rate constants from the reaction path Hamiltonian. I. Reactive flux simulations for dynamically correct rates

As ab initio electronic structure calculations become more accurate, inherent sources of error in classical transition state theory such as barrier recrossing and tunneling may become major sources of error in calculating rate constants. This paper introduces a general method for diabatically constructing the transverse eigensystem of a reaction path Hamiltonian in systems with many degenerate transverse frequencies. The diabatically constructed reaction path Hamiltonian yields smoothly varying coupling constants that, in turn, facilitate reactive flux calculations. As an example we compute the dynamically corrected rate constant for the chair to boat interconversion of cyclohexane, a system with 48 degrees of freedom and a number of degenerate frequencies. The transmission coefficients obtained from the reactive flux simulations agree with previous results that have been calculated using an empirical potential. Furthermore, the calculated rate constants agree with experimental values. Comparison to variational transition state theory shows that, despite finding the true bottleneck along the reaction pathway, variational transition state theory only accounts for half of the rate constant reduction due to recrossing trajectories.     

Rapid analysis of triterpenic acids by liquid chromatography using porous graphitic carbon and evaporative light scattering detection

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.     

Investigation of the formation process of MCs+-molecular ions during sputtering

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.     

Third-order nonlinear optical figure of merits for conjugated TTF-quinone molecules

We have revealed a substantial enhancement of third-order optical figure of merits by the synthesis of a compact molecule possessing the tetrathiafulvalene (TTF) group with two backside C=O groups. Addition of the saturated methylene chain substantially suppresses the third-order optical figure of merits and even local optical hyperpolarizabilities at lambda = 532 nm. Another TTF-derivative molecule possessing ethylenic and acetylenic chains demonstrates large hyperpolarizabilities; however, generally, the figure of merit factor decreases due to the increasing optical losses as a consequence of enhanced linear absorption. At the same time, both of the chromophores have a large nonlinear optical response. General approaches for search and design of the third-order optical materials with improved properties are given.     

Synthesis of functionalized rab GTPases by a combination of solution- or solid-phase lipopeptide synthesis with expressed protein ligation

Prenylated proteins with non-native functionalities are generally very difficult to obtain by recombinant or enzymatic means. The semisynthesis of preparative amounts of prenylated Rab guanosine triphosphatases (GTPases) from recombinant proteins and synthetic prenylated peptides depends largely on the availability of functionalised prenylated peptides corresponding to the proteins' native structure or modifications thereof. Here, we describe and compare solution-phase and solid-phase strategies for the generation of peptides corresponding to the prenylated C terminus of Rab7 GTPase. The solid-phase with utilisation of a hydrazide linker emerges as the more favourable approach. It allows a fast and practical synthesis of pure peptides and gives a high degree of flexibility in their modification. To facilitate the analysis of semisynthetic proteins, the synthesised peptides were equipped with a fluorescent group. Using the described approach, we introduced fluorophores at several different positions of the Rab7 C terminus. The position of the incorporated fluorescent groups in the peptides did not influence the protein-ligation reaction, as the generated peptides could be ligated onto thioester-tagged Rab7. However, it was found that the positioning of the fluorescent group had an influence on the functionality of the Rab7 proteins; analysis of the interaction of the semisynthetic Rab7 proteins with REP (Rab escort protein) and GDI (guanosine diphosphate dissociation inhibitor) molecules revealed that modification of the peptide side chains or of the C-terminal isoprenoid did not significantly interfere with complex formation. However, functionalisation of the C terminus was found to have an adverse effect on complex formation and stability, possibly reflecting low structural flexibility of the Rab GDI/REP molecules in the vicinity of the lipid-binding site.     

Kinetics of adsorption of the cobalt ions on the "electrolytic solution/gamma-alumina" interface

In the present work we studied, for the first time, the kinetics of adsorption of the Co(H(2)O)(6)(2+) species on the "electrolytic solution/gamma-Al(2)O(3)" interface at pH = 7 and 25 degrees C for a very broad range of Co(II) surface concentrations ranged from 0.03 to 6 theoretical Co(H(2)O)(6)(2+) surface layers. Moreover, we studied the surface dissolution of gamma-alumina in the presence of the Co(H(2)O)(6)(2+) ions in the impregnating solution, the contribution of the Co(II) desorption on the whole deposition process and the deposition isotherm. It was found that under the conditions where the deposition has taken place, the dissolution of the gamma-alumina surface is negligible even in the presence of the Co(H(2)O)(6)(2+) species in the impregnating solution. It was, moreover, inferred that the Co(II) desorption does not participate significantly to the whole deposition process. It was found that the deposition kinetics may be described by the following kinetic expression r(Co,bulk) = k'C(Co,bulk)(2), which relates the rate of disappearance of the Co(H(2)O)(6)(2+) ions from the impregnating solution, r(Co,bulk,) with their concentration C(Co,bulk). This kinetic expression may be derived assuming the following deposition scheme: nS + 2[Co(H(2)O)(6)(2+)] --> S(n) - [Co(H(2)O)(x,x)(<)(6)(2+)](2), where S represents the surface reception sites. The above expressions indicated that two Co(H(2)O)(6)(2+) ions are involved, from the side of the interface, in the reaction with the reception sites. It seems probable that the deposition step involves the simultaneous adsorption and dimerization of the two interfacial Co(H(2)O)(6)(2+) ions through (hydr)oxobridges. On the other hand, the sigmoidal form of the deposition isotherm and the dependence of the apparent rate constant, k', on the interfacial Co(II) concentration suggested that the already deposited Co(II) species may be involved in the reception sites, S, promoting the adsorption and resulting to the formation of multinuclear complexes and Co(II) surface precipitates. Finally, reasonable interface potential values for oxides were determined for the first time using kinetic results.     

Separation strategy for acidic chiral pharmaceuticals with capillary electrochromatography on polysaccharide stationary phases

The effect of five factors on the capillary electrochromatographic enantioseparation of acidic compounds was studied using an experimental design. The studied factors were pH, acetonitrile content in the mobile phase, temperature, buffer concentration, and applied voltage. These experiments allowed defining a generic separation strategy applicable on acidic compounds with chemical and structural diversity. The starting screening conditions consist of a 45 mM ammonium formate electrolyte at pH 2.9 mixed with 65% acetonitrile, an applied voltage of 15 kV, and a temperature of 25 degrees C. The screening phase occasionally can be followed by an optimization procedure. Evaluation of the proposed strategy pointed out that it allows achieving baseline resolution within a relatively short time when a beginning of separation is obtained at the starting conditions. This strategy revealed enantioselectivity for 11 compounds out of 15, of which 10 could be baseline-separated after the proposed optimization steps.