Synthesis and characterization of new aromatic polyamides bearing crown ethers or their dipodal counterparts in the pendant structure. II. Benzo‐15‐crown‐5 and ortho‐bis[2‐(2‐ethoxyethoxy)ethoxy]benzene

This article describes the synthesis and characterization of two diacid monomers, each containing a benzo‐15‐crown‐5 subunit or its dipodal counterpart. Both novel monomers were reacted with technical aromatic diamines with Yamazaki's direct polyamidation method to render modified polyisophthalamides with high molecular weights containing side moieties of cyclic and acyclic ethylene oxide sequences. All the polymers were soluble in aprotic polar solvents and showed high glass‐transition temperatures in the range of 190–345 °C. The polymers with side crown ethers showed much higher glass‐transition temperatures than those with acyclic linear side ethylene oxide arms. The chemical composition, particularly with respect to the diamine and the open or closed character of the pendent ethylene oxide sequence, also affected other general properties such as the mechanical resistance, mechanical modulus, or water absorption. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4063–4075, 2006     

ON THE SUM OF THE FIRST n PRIMES

In this note, we show that the set of n such that the arithmeticmean of the first n primes is an integer is of asymptotic densityzero. We use the same method to show that the set of n suchthat the sum of the first n primes is a square is also of asymptoticdensity zero. We also prove that both the arithmetic mean ofthe first n primes as well as the square root of the sum ofthe first n primes are well distributed modulo 1.     

Spin relaxation in nanophased manganites

We present recent results obtained by DC and AC susceptibility, muon spin relaxation and neutron spin echo experiments in magnetically ordered La_0.7Pb_0.3MnO₃ and disordered La_0.7Pb_0.3Mn_0.8Fe_0.2O₃. These results aim to cover an extraordinary equivalent frequency range (from quasi-static experiments to almost the THz region) and give an overall picture of the processes within. The different relaxations observed are related either to the macroscopic long-ranged interactions among magnetic clusters (susceptibility techniques) and to short-ranged intracluster spin diffusion processes (muon and neutron techniques).     

A direct approach to second order conditions for mixed equality constraints

In this paper we consider an optimal control problem posed over piecewise continuous controls and involving state-control (mixed) equality constraints. We provide an explicit derivation of second order necessary conditions simpler than others available in the literature, yielding a clear understanding of how to define a set of “differentially admissible variations” where a certain quadratic form is nonnegative.     

Minimal large sets for cooperative games

We analyze the concept of large set for a coalitional game v introduced by Martínez-de-Albéniz and Rafels (Int. J. Game Theory 33(1):107–114, 2004). We give some examples and identify some of these sets. The existence of such sets for any game is proved, and several properties of largeness are provided. We focus on the minimality of such sets and prove its existence using Zorn’s lemma. Institutional support from research grants (Generalitat de Catalunya) 2005SGR00984 and (Spanish Government and FEDER) SEJ2005-02443/ECON is gratefully acknowledged, and the support of the Barcelona Economics Program of CREA.     

A Bohmian total potential view to quantum effects. II: decay of temporarily trapped states

Formation, persistence and decay of temporarily trapped states, the time-dependent generalization of resonances, are analysed within the framework of Bohmian Mechanics. More specifically, the so-called Bohm’s total potential, the sum of classical plus Bohm’s quantum potential, is used. It is found that both formation and decay are triggered by the frequency in the oscillations of the total potential. These oscillations have been studied at the specific locations where the classical potential displays maxima, i.e. the ‘walls’ temporarily capturing the system’s density. Our main result is that the total potential oscillation frequency is solely dependent on the steepness of the classical potential ramp and, surprisingly, independent of the classical barrier height and width, well depth and width, collision energy or wavepacket width.     

Very Colorful Theorems

We prove several colorful generalizations of classical theorems in discrete geometry. Moreover, the colorful generalization of Kirchberger’s theorem gives a generalization of the theorem of Tverberg on non-separated partitions.     

Salt Stress Proteins Identified by a Functional Approach in Yeast

Summary. We have performed functional genomics of salt stress by overexpression of gene libraries in yeast and selection for salt tolerance. Thirty halotolerance genes were isolated from yeast, Arabidopsis, and sugar beet. The results indicate that Na⁺ transport (uptake, efflux, and compartmentation), sulfate activation, RNA processing, and protein synthesis are crucial for salt tolerance.Received September 3, 2002; accepted September 16, 2002 Published online June 12, 2003     

Novel phthalocyaninatobis(alkylcarboxylato)silicon(IV) compounds: NMR data and X-ray structures to study the spacing provided by long hydrocarbon tails that enhance their solubility

The reaction between trans-PcSiCl2 (1) and the potassium salts of six fatty acids (2 a-2 f) led to the trans-PcSi[OOC(CH2)nCH3]2 compounds (3 a-3 f), which were characterised by elemental analysis, IR, UV/Vis and 1H, 13C, and 29Si NMR spectroscopy. From a detailed study of the NMR spectra, the strong anisotropic currents of the Pc macrocycle were found to have an effect on up to the sixth methylenic group. As expected, the length of the hydrocarbon tail does not affect the chemical shift of the 29Si nucleus of any of the compounds, appearing at around -222.6. The structures of PcSi[OOC(CH2)nCH3]2, where n = 7, 10, 12, 13 and 20, were determined by X-ray crystallography. All the compounds were found to be triclinic with a P1 space group. In all cases the observed crystallographic pseudosymmetry is Ci and the asymmetric unit consists of half a molecule. The silicon atom is at the centre of a distorted octahedron and hence its coordination number is six. The carboxylate fragments are in a trans configuration with respect to the Pc macrocycle. The supramolecular structures are discussed in detail herein. The correlation between the 1H NMR chemical shifts and the position of the corresponding carbon atoms in the hydrocarbon tail reveals that the dicarboxylate substituents exhibit a spacer-like behaviour that enhances the solubility. A detailed study of the tail variable allowed us to evaluate the loss of radial shielding along the Pc2- ligand.