Grazing‐incidence X‐ray diffraction study of rubrene epitaxial thin films

The growth of organic semiconductors as thin films with good and controlled electrical performances is nowadays one of the main tasks in the field of organic semiconductor‐based electronic devices. In particular it is often required to grow highly crystalline and precisely oriented thin films. Here, thanks to grazing‐incidence X‐ray diffraction measurements carried out at the ELETTRA synchrotron facility, it is shown that rubrene thin films deposited by organic molecular beam epitaxy on the surface of tetracene single crystals have the structure of the known orthorhombic polymorph, with the (2 0 0) plane parallel to the substrate surface. Moreover, the exact epitaxial relationship between the film and the substrate crystalline structures is determined, demonstrating the presence of a unique in‐plane orientation of the overlayer.     

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.     

A convenient synthesis of aromatic thiols from unactivated aryl halides

Aromatic thiols are obtained in good yields from unactivated aryl halides and excess MeSNa in HMPA.