Pattern formation in the Schlögl model of nonlinear kinetics

To study the effect of a local, spatial inhomogeneity on the progress of a chemical reaction which may exhibit a nonequilibrium phase transition, we have studied a (slightly) generalized version of a model proposed originally by Schlögl. Focusing on that regime of parameter space where the reaction sequence A + 2X[lrarr2]3X and B + X[lrarr2]C allows a first-order transition, we consider the consequences of introducing a spatially-varying diffusion coefficient characterized by a correlation length which calibrates the region over which the spatial inhomogeneity persists. We find that if the inhomogeneity is localized, only small quantitative differences are found between the exact solution reported earlier by Schlögl and the solutions generated here. However, as the correlation length becomes larger, abruptly at a certain critical value, a qualitative change in the nature of the solutions is found, with apparent oscillations produced in the concentration variable of the problem. We interpret this behavior as indicating the onset of pattern formation, and suggest that this behavior may be of importance in those radiation-induced phenomena where high-energy intermediates are produced.     

Slow and fast quarks in nucleons

Using light-front dynamics, and the notion of the running effective quark mass, we propose a model of the three-quark nucleon wave function, which accounts simultaneously both for the low and the high energy experimental data. Our wave function is a product of a spinor part, inferred from the QCD sum rules, and a gaussian scalar factor, taken for simplicity. Including all three Ioffe currents we get from one wave function both the negative neutron charge radius 〈r²〉_neutron=-0.108 fm² and the decreasing d/u ratio in the proton for x_Bj increasing from 0.5 to 1.     

Fourier transform infrared investigations of phosphate-silicate coatings on iron

The influence of silica addition and of the annealing on the structure and properties of phosphate coatings are investigated. It has been observed that silica stabilizes phosphates and reduces the transport of iron towards the surface.     

On factorization structures and epidense hulls

Characterizations of epidense subcategories of topological categories and of existence of epidense hulls have been described in [2, 3, 4]. In this paper a similar characterization is given in a much more general setting; for example the category need not have products. The relationship between finite factorization structures and existence of epidense hulls is investigated. It is found to be analogous to the relationship between general factorization structures and epireflective hulls.     

The crystal and molecular structure of chlorobis(N-ethyl-1 3-imidazolidine-2-thione)copper(I)

Summary The crystal structure of the title compound has been determined from x-ray diffractometer data by the heavy-atom method and refined anisotropically by least-squares calculations. Crystals are monoclinic, space groupP 2₁/c, with unit cell dimensions:a=7.321(1),b=14.622(2),c=14.827(2) Å,=92.95(2), Z=4. The finalR index is 4.6%. The copper coordination is trigonal, involving the sulphur atoms of twoN-ethyl-1,3-imidazolidine-2-thione molecules and one chlorine atom. The structure is held together by two intramolecular N-HCl hydrogen bonds and by normal van der Waals interactions.     

Osservazioni sulle caratteristiche dei grafi o singrammi

Riassunto Si introducono certi gruppi di numeri associati ad un grafo o singrammaG che vengono chiamati caratteristiche diG. Si studiano alcune proprietà delle caratteristiche e se ne fanno applicazioni a vari problemi sui grafi.

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Résumé On introduit certains groupes de nombres qui sont associés à un grapheG et qu’on appelle caractéristiques deG. Ou étudie quelques proprietés des caractéristiques et on en fait des applications a divers problèmes sur les graphes.

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Lavoro eseguito nell’ambito del Gruppo N. 26 del Comitato Naz. per la Mat. del C.N.R.     

Optimale Bestelltermine bei zufallsveränderlichen Lieferfristen

Zusammenfassung Ermittlung des günstigsten Bestellzeitpunktes, wenn die Zeitspanne zwischen der Bestellung und der Lieferung eine Zufallsveränderliche mit bekannter Verteilung ist.

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Summary Determination of the optimal time for placing orders in those cases where the time interval between order and supply is a random variable with known distribution.

     

N,N′-dialkylsubstituted Imidazolidine-2-thionecopper(I) complexes. X-ray analysis of chloro-bis(N,N′-dimethylimidazolidine-2-thione)copper(I)

Summary New complexes of copper(I) withN,N-dialkylsubstituted imidazolidine-2-thione ligands were prepared by reduction of CuX₂ (X = Cl or Br). The i.r. spectra show that in all the complexes the ligand coordinates through the sulphur atom. The crystal structure of chloro-bis(N,N-dimethylimidazolidine-2-thione)copper(I) has been determined from x-ray diffraction data. Crystals are monoclinic. space groupC ₂, with unit cell dimensions:a = 16.022(15),b = 9.942(10),c = 15.112(15) A, = 139.84(10)², Z = 4. The final R index is 5.2%. The copper coordination is trigonal, involving sulphur atoms of the two ligands and One chlorine atom. The steric effect of the two methyls imposes a rotation of the imidazolidine rings with respect to the coordination plane. The dihedral angle between the mean plane of thiourea moieties. parallel one with the other. and the coordination plane is 119.3°.This work was supported by the National Research Council (C.N.R.) of Rome.     

A new tricyclic triketone from tandem condensation reactions

Perhydrophenanthrene-1,5,10-trione (6) was isolated from the reaction of methyl 3-(carboxymethyl)cyclohexanone and cyclohexenone in a tandem Michael-Claisen reaction. NMR and X-ray analysis confirmed the structure of the product.