High rank elliptic curves with prescribed torsion group over quadratic fields

There are 26 possibilities for the torsion groups of elliptic curves defined over quadratic number fields. We present examples of high rank elliptic curves with a given torsion group which set the current rank records for most of the torsion groups. In particular, we show that for each possible torsion group, except maybe for \(\mathbb {Z}/15\mathbb {Z}\) , there exists an elliptic curve over some quadratic field with this torsion group and with rank \(\ge 2\) .     

On the Sobolev trace Theorem for variable exponent spaces in the critical range

In this paper, we study the Sobolev trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then, we give local conditions on the exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to satisfy such conditions and therefore to ensure the existence of extremals.     

Effective permittivity of a fiber-reinforced composite with transversely isotropic constituents

Simple closed-form expressions for effective permittivity of fiber-reinforced composites with transversely isotropic constituents are found using asymptotic homogenization. Circular cylindrical fibers are distributed in a square array. The analysis considers four orientations of constituents transverse symmetry axis relative to fibers direction. Local problems defined on a periodic square unit cell are solved by means of complex potential theory using Weierstrassian and Natanzon's functions, assuming that the contrast of permittivities is small. Derived closed-form formulas are compared with finite element calculations and, in the isotropic case, with standard mixture rules and classical bounds, obtaining excellent results even when contrast is large.     

Quasi-classical rate constants for the inelastic process O2(υi≫ 1) + O2 → O2(υf) + O2

Rate constants have been calculated using quasi-classical trajectories (QCT) for the vibrational relaxation of highly excited O₂:O₂(X³Σ?,v_i) + O₂(X³Σ?,0) → O₂(X³Σ?,v_f) + O₂(X³Σ?) with 22 ≤v_i≤28. The present full-dimensional QCT results agree very well with recent quantum reduced dimensionality calculations, giving further support to the hypothesis that the observed experimental jump in depletion rates would be due partially to enhanced vibrational relaxation.     

The calculation of the L 2-norm of the index of a plane curve and related formulas

We provide formulas for calculating the L ²-norm of the index function of a rectifiable closed curve in the complex plane. Some applications to isoperimetric inequalities are given. The main tool used is the decomposition of a rectifiable closed curve into a sequence of Jordan curves, curves with null index functions, and an exceptional set.     

A MALDI‐TOF MS study of lanthanide(III)‐cored poly(phenylenevinylene) dendrimers

An extensive study by matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectrometry (MS) of some first‐generation and second‐generation lanthanide(III)‐cored poly(phenylenevinylene) dendrimers is described. The complexes were obtained by self‐assembly of suitably functionalized carboxylate dendrons around the lanthanide ion (La³⁺, Er³⁺). Fourier transform infrared (FT‐IR) spectroscopy gave reasonable evidence for the proposed structures. However, MS was used to ascertain unequivocally the complex formation. The most reliable results were found in the negative reflector mode, using 2‐[(2E)‐3‐(4‐tert‐butylphenyl)‐2‐methylprop‐2‐enylidene]malononitrile (DCTB) as matrix. Well‐defined and highly resolved base peaks corresponding to negative ions of [Gn₄La]^? and [Gn₄Er]^? were found in all cases, with an excellent match between the theoretical and observed isotope distributions. However, the 3 : 1 stoichiometry used in the synthesis guarantees an empirical formula Gn₃Ln for the complexes. Copyright © 2008 John Wiley & Sons, Ltd.     

Asymptotic behavior of the eigenvalues of the one-dimensional weighted<Emphasis Type="Italic">p</Emphasis>-Laplace operator

In this paper we study the spectral counting function for the weightedp-laplacian in one dimension. First, we prove that all the eigenvalues can be obtained by a minimax characterization and then we show the existence of a Weyl-type leading term. Finally we find estimates for the remainder term. The first author is supported by Universidad de Buenos Aires grant TX48, by ANPCyT PICT No. 03-05009. The second author is supported by CONICET and Universidad de San Andres.