Tranversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near L2 in the restricted three-body problem

The restricted three-body problem is considered for values of the Jacobi constant C near the value C₂ associated to the Euler critical point L₂. A Lyapunov family of periodic orbits near L₂, the so-called family (c), is born for C = C₂ and exists for values of C less than C₂. These periodic orbits are hyperbolic. The corresponding invariant manifolds meet transversally along homoclinic orbits. In this paper the variation of the transversality is analyzed as a function of the Jacobi constant C and of the mass parameter μ. Asymptotical expressions of the invariant manifolds for C ? C₂ and μ ? 0 are found. Several numerical experiments provide accurate information for the manifolds and a good agreement is found with the asymptotical expressions. Symbolic dynamic techniques are used to show the existence of a large class of motions. In particular the existence of orbits passing in a random way (in a given sense) from the region near one primary to the region near the other is proved.     

Hochauflösende29Si-Festkörper-NMR-Spektroskopie: Einfluß des Si-O-Si-Bindungswinkels auf die isotrope chemische Verschiebung von t- und h-Y2Si2O7

Starting from high-resolution solid-state²⁹Si NMR spectra of two modifications of Y₂Si₂O₇ with different Si-O-Si bond angles it was verified that increasing bond angles cause high-field isotropic²⁹Si chemical shifts.

     

A method for measuring the proportion of different plane orientations in metal supported catalysts by gas chemisorption

A method is presented, which allows us to calculate the percentage of metal surface atoms with different coordination numbers, on metal supported catalysts. This method is based on gas-metal stoichiometry values reported for the chemisorption of H₂, O₂ and CO on well defined monocrystals, and on gas chemisorption measurements on metal supported catalysts. It has here been applied to a series of Pd/SiO₂ catalysts.     

Molecular orbital theory and tunnelling currents

Summary The parameters appearing in an effective tight-binding Hamiltonian are shown to be simply related to the tunnelling currents and the overlap between the different orbitals of the constituent atoms. Different systems are considered and the results show that our approach applies both to molecular and condensed-matter systems.

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Riassunto Si mostra che i parametri presenti in una hamiltoniana efficace a legame forte sono correlati semplicemente alle correnti di tunnel e alla sovrapposizione tra i diversi orbitali degli atomi costituenti. Si considerano diversi sistemi e i risultati mostrano che il nostro approccio si applica sia a sistemi molecolari che di materia condensata.

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Резюме ПоказЫвается, что параметрЫ, появляющиеср в эффективном Гамильтониане в приближении силъной связи, связнЫ с туннелънЫми токами и перекрЫтием между разяичнЫми орбиталями составляюших атомов. Рассматриваются различнЫе системЫ. ПолученнЫе результатЫ показЫвают, что наш подход применим к молекулярнЫм системам и к конденсироваииому веществу.

     

Diffusion of MgCl2 through nuclepore membranes of polycarbonate

Summary Diffusion of MgCl₂ through six different types of nuclepore membranes of polycarbonate has been studied. The change of concentration with time was determined by a conductivitymeter on line with a microcomputer. The measurements were carried out at temperatures between 20 and 50°C at 10°C intervals and at different concentrations in the range 2·10⁻⁴÷10⁻¹ equiv l⁻¹. The salt permeabilityP _ms of the membrane system, formed by the membrane itself and the two adjacent layers of diffusion, is obtained through methematical treatment of the concentrationvs. time results. We have studied the variation ofP _ms with concentration of solutions, the characteristics of the membrane and the temperature. Finally, we have estimated the activation energy of the diffusion process by using a kinetic model of the permeation.

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Riassunto Si è studiata la diffusione di MgCl₂ attraverso sei diversi tipi di membrane Nuclepore di policarbonato. Il cambiamento di concentrazione nel tempo è stato determinato da un misuratore di conduttività collegato con un microcomputer. Le misurazioni sono state effettuate a temperatura tra 20 e 50°C ad intervalli di 10°C e a differenti concentrazioni nell’intervallo 2·10⁻⁴÷10⁻¹ equiv l⁻¹. La permeabilità al saleP _ms del sistema membrana, formato dalla membrana stessa e da due strati adiacenti di diffusione è ottenuta attraverso la trattazione matematica dei risultati di concentrazionivs. il tempo. Si sono studiate la variazioneP _ma con la concentrazione delle soluzioni, le caratteristiche della membrana e la temperatura. Infine si è stimata l’energia di attivazione del processo di diffusione usando un modello cinetico di permeazione.

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Резюме Исследуется диффузия MgCl₂ через шесть различных типов ядерных мембран из поликарбоната. Изменение концентрации со временем определяется с помощью измерения проводимости в линию с микрокомпьютером. Измерения проводятся при температурах от 20 до 50°C с интервалом 10°C и при различных концентрациях в области 2.10⁻⁴÷10⁻¹. Проницаемость солиP _ms через мембранную систему, образованную самой мембраной и двумя соседними слоями диффузии, получается с помощью математической обработки зависимости концентрации от времени. Мы исследовали изменениеP _ms в зависимости от концентрации растворов, характеристик мембран и температуры. Б заключение, мы оцениваем энергию активации процесса диффузии, используя кинетическую модель проникновения.

     

Level–wise Approximation of a Markov Process Associated to the Boundary of an Infinite Tree

We study an approximation of a Markov process associated to the boundary of an infinite rooted tree. This approximation is constructed by projecting the infinitesimal generator of the original process (defined on the boundary) onto the spaces associated to the filtration spanned by the successive levels of the rooted tree. S. Martínez and J. San Martín acknowledge the support by Nucleus Millenium Information and Randomness P04-069-F. D. Remenik current address: Center for Applied Mathematics, Cornell University, 657 Rhodes Hall, Ithaca, NY 14853. The author acknowledges the partial support by Nucleus Millenium Information and Randomness P01-005 for his work in his undergraduate thesis at Universidad de Chile.     

Hydroxyapatite coating on porous polyurethane facilitated by tetraethoxysilane

Biomimetic growth of calcium phosphate compounds on porous polyurethane (PU) treated with tetraethoxysilane (TEOS) and soaked in simulated body fluid (SBF) solution was studied using scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDAX), and Fourier transformed infrared spectroscopy–attenuated total reflectance (FTIR–ATR). Polyurethane was treated with TEOS in order to produce silanol groups which stimulated the growth of hydroxyapatite when immersed in SBF solution. Polyurethanes that were not treated with TEOS did not show calcium phosphate growth upon immersion in SBF solution. The Ca and P determined by EDAX and inductively coupled plasma spectroscopy (ICP) analysis revealed that the surface layer was not stoichiometric hydroxyapatite, but carbonated, containing hydroxyapatite with a Ca/P ratio of 1.5–1.6. This was confirmed by FTIR–ATR.     

Synthesis of anacardic acids by nucleophilic substitution on 2-aryloxazolines

A new direct synthesis for anacardic acids based in a nucleophilic substitution of a methoxy group in 2-aryloxazolines by long-chained Grignard reagents is reported.