Higher homotopy of groups definable in o-minimal structures

It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L. As a consequence, we obtain that all abelian definably compact groups of a given dimension are definably homotopy equivalent, and that their universal covers are contractible.     

Cluster formation in opinion dynamics: a qualitative analysis

In this paper we formulate a discrete version of the bounded confidence model (Deffuant et al. in Adv Complex Syst 3:87–98, 2000; Weisbuch et al. in Complexity 7:55–63, 2002), which is representable as a family of ordinary differential equation systems. Then, we analytically study these systems. We establish the existence of equilibria which correspond to opinion profiles displaying a finite number of isolated clusters. We prove the asymptotic stability of some of these equilibria and show that they represent the asymptotic trend of the solutions of the systems under consideration. For a particular case, we also characterize the initial profiles that lead to different cluster configurations.     

Anomalous Behavior in an Effective Model of Graphene with Coulomb Interactions

We analyze by exact Renormalization Group (RG) methods the infrared properties of an effective model of graphene, in which two-dimensional (2D) massless Dirac fermions propagating with a velocity smaller than the speed of light interact with a 3D quantum electromagnetic field. The fermionic correlation functions are written as series in the running coupling constants, with finite coefficients that admit explicit bounds at all orders. The implementation of Ward Identities in the RG scheme implies that the effective charges tend to a line of fixed points. At small momenta, the quasi-particle weight tends to zero and the effective Fermi velocity tends to a finite value. These limits are approached with a power law behavior characterized by non-universal critical exponents.     

Ipso nitration. Nitrodeformylation reactions in nitrothiophenealdehydes

Nitration of 4-nitro-2-thiophenealdehyde afforded 2,4-dinitrothiophene and small quantities of 4,5-dinitro-2-thiophenealdehyde; 5-nitro-2-thiophenealdehyde gave instead 3,5-dinitro-2-thiophenealdehyde as the main product and some 2,5-dinitrothiophene. The two dinitrothiophenes form through a nitrodeformylation reaction which represents an interesting example of the nitration at an ipso position in a strongly deactivated substrate.     

Misure euclidee,hermitiane, simplettiche e potenze esterne di uno spazio vettoriale quaternionale

Riassunto SiaV _n uno spazio vettoriale quaternionale destro n-dimensionale e V_4n lo spazio vettoriale reale ? immagine reale ? diV _n. Una metrica hermitiana inV _n e le metriche euclidea e simplettica ad essa associate danno luogo (attraverso la considerazione di determinanti sul corpo dei quaternioni) a tre diversi tipi di metriche per i multivettori semplici di ∧^t V_4n. Le nozioni introdotte permettono, tra l’altro, di associare ad ogni sottospazio V_t di V_4n un ben determinato angolo (deviavione caratteristica assoluta di V_t) e di generalizzare ai multivettori la disuguaglianza di Cauchy-Schwarz. Lavoro eseguito nell’ambito dell’attività del Contratto di Ricerca n. 9 del Comitato per la matematica del C.N.R. Entrata in Redaz’one il 25 giugno 1970.     

Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction‐diffusion equations invading an unstable equilibrium

We revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction‐diffusion equations with one linearly stable and one linearly unstable equilibrium. For a wide class of initial data this problem reduces to finding the minimal speed of the monotone traveling wave solutions connecting these two equilibria in one space dimension. We introduce a variational characterization of these traveling wave solutions and give a necessary and sufficient condition for linear versus nonlinear selection mechanism. We obtain sufficient conditions for the linear and nonlinear selection mechanisms that are easily verifiable. Our method also allows us to obtain efficient lower and upper bounds for the propagation speed. © 2004 Wiley Periodicals, Inc.     

Monoterpene alkaloids from Argylia radiata

Argylia radiata (L.) D. Don (Bignoniaceae) represents an important source of secondary metabolites, largely unexplored. The paper presents the isolation from the plant root of two new monoterpene alkaloids, 10-acetoxy-actinidine and 4-nor-7,8-dehydro-10-hydroxy-skytanthine, whose structures were elucidated by Mass spectrometry and 1H-NMR data.     

Optimal strategy to model the electrodialytic recovery of a strong electrolyte

In this work, mostly Nernst–Planck derived relationships were used to simulate the electrodialytic recovery of a strong electrolyte, namely sodium chloride. To this end, it was set up a five-step experimental procedure consisting of zero-current leaching, osmosis, and dialysis, electro-osmosis, desalination, current–voltage and validation tests. The contribution of leaching and solute diffusion across the electro-membranes was found to be negligible with respect to the electro-migration. On the contrary, solvent diffusion tended to be important as the solute concentration difference at the membrane sides increased or current density was reduced. The electro-osmosis and desalination tests yielded the water and solute transport numbers.

By performing several limiting current tests at different solute concentrations and feed flow rates using anionic or cationic membranes, it was possible to determine simultaneously the limiting current intensity, the ratio of the differences between the counter-ion transport numbers in the anion- and cation-exchange membranes and solution, the overall resistance of the electro-membranes, the effective membrane surface area, and the solute mass transfer coefficient.

All these process and design parameters allowed the time course of the solute concentration in the concentrating (C) and diluting (D) compartments, as well as the voltage applied to the electrodes, to be reconstructed quite accurately without any further correction factors. The capability of the above parameters to simulate the performance of the electrodialysis (ED) unit was checked by resorting to a few validation tests, that were performed in quite different operating conditions from those used in the training tests, that is by filling tank C with a low feed volume with a low solute concentration and applying a constant current intensity to magnify the effect of electro-osmosis or by changing the current intensity step-wisely to simulate the continuous-mode operation of a multistage ED unit. Finally, a parameter sensitivity analysis made the different contribution of the process and design parameters to be assessed, thus yielding a straightforward procedure for designing or optimising accurately ED desalination units up to a final salt concentration of about 1.7 kmol m⁻³.