Electrochemical reduction of 1-([(4-halophenyl)imino]methyl)-2-naphthols in aprotic media.

The electrochemical reduction of 1-([(4-halophenyl)imino]methyl)-2-naphthols on graphite electrodes was studied using cyclic voltammetry, chronoamperometry, constant-potential coulometry and preparative constant-potential electrolysis techniques. The data revealed that the reduction on graphite was irreversible and followed an EC mechanism. The diffusion coefficients and the number of electrons transferred were determined using the chronoamperometric Cottrell slope and the ultramicro disc Pt-electrode steady-state current. The number of electrons was also determined by bulk electrolysis. The compounds were subjected to constant-potential preparative electrolysis and the electrolysis products were purified and identified by spectroscopic methods. Based on these findings, a mechanism for the electro-reduction process is proposed.     

On the Convenience to Form Coalitions or Partnerships in Simple Games

A partnership in a cooperative game is a coalition that possesses an internal structure and, simultaneously, behaves as an individual member. Forming partnerships leads to a modification of the original game which differs from the quotient game that arises when one or more coalitions are actually formed. In this paper, the Shapley value is used to discuss the convenience to form either coalitions or partnerships. To this end, the difference between the additive Shapley value of the partnership in the partnership game and the Shapley alliance value of the coalition, and also between the corresponding value of the internal and external players, are analysed. Simple games are especially considered. Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.     

Lagrangian flows: The dynamics of globally minimizing orbits

The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications.We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].Reprinted by permission of Addison Wesley Longman Ltd.     

A simple stereoselective one-pot synthesis of C-nucleosides by 1,3-dipolar cycloaddition of chiral azomethine imines prepared in situ

The NH,NH-dihydrocycloadduct 1 (6-chloro-9,9-dimethyl-7,8-dihydro-9H-pyrazolo[4,3-d]tetrazolo[1,5-b]-pyridazine) obtained by the cycloaddition of 2-diazopropane to 6-chlorotetrazolo[1,5-b]pyridazine, is transformed with protected or unprotected carbohydrates 2, 5, 7,9, 11, 13 and 15 in the presence of methyl acrylate ( 3 ) into the corresponding C-nucleosides 4,6,8,10,12,14 and 16 . In this one-pot synthesis two new chiral centers are formed stereoselectively, dependent on the chirality at C-atom next to aldehydo group in the carbohydrate.     

Modulated DSC for gas hydrates analysis

Modulated DSC has been applied to the study of methane, ethane and propane hydrates at different hydrate and ice concentrations. The reversing component of the TMDSC curves, makes it possible to characterize such hydrates. Methane and ethane hydrates show the melting-decomposition peak at a temperatures higher than the ice contained in the sample, while propane hydrate melts and decomposes at lower temperature than the ice present in the sample. The hydrate peaks tend to disappear if the hydrate is stored at atmospheric pressure. Guest size and cavity occupation fix the heat of dissociation and stability of the hydrates, as confirmed by parallel tests on tetrahydrofurane hydrates.     

Diagram Literacy in Preservice Math Teachers, Computer Science Majors, and Typical Undergraduates: The Case of Matrices, Networks, and Hierarchies

According to the National Council of Teachers of Mathematics (2000), children need to learn how to create and use mathematical diagrams to represent and reason about phenomena in the world. The author proposes a model of diagram literacy that includes six types of knowledge required for diagrammatic competence - implicit, construction, similarity, structural, metacognitive, and translational. A study is reported that examined college students' diagram literacy for three interrelated mathematical diagrams - matrices, networks, and hierarchies. Three groups of students participated: preservice, secondary-level, math teachers; computer science majors; and typical undergraduates. The results of the study are reassuring in some ways concerning the level of diagram literacy possessed by students at the culmination of current K through 12 instruction and by teachers of future secondary students. However, the results also point to areas in which preservice math teachers should be better prepared if the goals for students' diagram literacy are to be met.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.