Spectral approximation of variationally-posed eigenvalue problems by nonconforming methods

This paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems. It is an extension to more general situations of known previous results about nonconforming methods. As an application of the present theory, convergence and optimal order error estimates are proved for the lowest order Crouzeix–Raviart approximation of the eigenpairs of two representative second-order elliptical operators.     

A maschke type theorem for weak Hopf algebras

In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke＇s Theorem for （H, B）-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.     

Synthesis and subsequent reactivity of 1-amino-2-aza-1,3-butadienes derived from β-amino esters

A high yield preparation of 1-amino-2-aza-1,3-butadienes derived from β-amino esters from N-unsubstituted amidines and acetylenic esters is described. These substrates are efficient starting material for the preparation of dihydrotriazines and 5-amino pyrrolidin-3-ones.     

Contact Relative Differential Invariants for Non Generic Parabolic Monge-Ampère Equations

We find relative differential invariants of different orders for non generic parabolic Monge-Ampère equations (MAE’s). They are constructed in terms of some tensors associated with the derived flag of the characteristic distribution. The vanishing of such invariants allows one to determine the classes of each non generic parabolic MAE with respect to contact transformations.     

Kinetics and mechanism of the reaction of an arenediazonium ion with hydrophilic aminocarboxylic acids in aqueous buffered solution

The reaction of 4‐nitrobenzenediazonium ion, 4NBD, with the aminocarboxylic acids (AA) glycine and serine was studied under acidic conditions by using Linear Sweep Voltammetry (LSV), which allows simultaneous monitoring of 4NBD loss and product formation. Voltammograms of the reaction mixture are complex, showing up to five reduction peaks. The reduction peaks at E_p = ?0.5 and ?1.0 V, not detected in the absence of AA, are associated to products formed in the course of the reaction. The variation of their peak current, i_p, with time shows a complex behavior; that of i_p (E_p = ?1.0 V) follows a biphasic profile with i_p increasing with time up to a maximum after which a decrease is detected, suggestive of formation and subsequent decomposition of a transient intermediate, meanwhile i_p (E_p = ?0.5 V) increases with time after an induction period. The peaks at E_p = ?0.1 and ?0.8 V are associated to the reduction of the diazonium group of 4NBD and, in the presence of AA ([AA] >>> [4NBD]), their peak currents decrease exponentially with time following clean first‐order kinetics for more than 3t_1/2. The variation of k_obs with [AA] at a given pH is linear with an intercept equal to zero and that of log(k_obs) with pH at constant [AA] is also linear. Kinetic evidence is consistent with a reaction mechanism involving an irreversible, rate‐limiting bimolecular step which leads to the formation of an unstable triazene, which further decomposes yielding 4‐nitroaniline among other reaction products. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of Correlation Dimension to Evaluate Cognitive Performance in Schizophrenic Patients Using a New Computer Technique

A new cognitive-motor, computer-administered instrument, the Random Rhythm Generation test (ARG), measured the schizophrenics' and control subjects' capacity of performing random (aleatory) rhythms. The interval frequencies between subjects' responses and chaotic dynamic attractor of the generated series, expressed in the phase space and correlation dimension, were analyzed. Results showed that schizophrenic patients (SG) generated more regular and rhythmic series than those of the control group (CG) when performing the ARG (correlation dimension in SG = 2.796 ± 0.47, in CG = 3.842 ± 0.51, p < 0.01). Therefore, the ARG may be usefull for the estimation and quantification of the cognitive-motor dysfunction in schizophrenic patients and possible definitions of treatments of cognitive and psychomotor dysfunctions. Our results also suggest that schizophrenic patients are characterized by more regular and rhythmic patterns than control subjects.