A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

Novel scaling behavior of directed polymers: Disorder distribution with long tails

We study the problem of directed polymers (DP) on a square lattice. The distribution of disorder is assumed to be independent but non-Gaussian. We show that for distributions with a power-law tailP() 1/||¹⁺ , where>2, so that the mean and variance are well defined, the scaling exponentv of the DP model depends on in a continuous fashion.     

On the dehydration enthalpies of some beta-aluminas

The energetics of the dehydration reaction of single crystal (Na, Na 50%-Li, Li) and ceramic Na beta-aluminas have been studied.From the dependence of the dehydration enthalpy values on the water content it has been deduced that lattice water can be bound in two different ways i.e. by ion-dipole interactions with conducting cations and by hydrogen bonds with spinel block oxygens. As expected, the first one gives binding energies depending on the nature of the monovalent cation (H=84.5 and 59.4 kJ/mol H₂O for Li and Na beta-alumina respectively). In contrast, the enthalpy change associated with the second one is identical for the three beta-aluminas (H=15.1 kJ/mol H₂O). The ceramic Na beta-alumina undergoes a surface reaction too (with CO₂) leading to the formation of carbonates and bicarbonates.

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Zusammenfassung Die Energetik der Dehydratisierungsreaktion von Einkristallen von Na-, Na (50%)/Li- und Li- sowie von Na--Aluminiumoxid wurde untersucht. Aus der Abhängigkeit der Dehydratisierungsenthalpie vom Wassergehalt ergibt sich, daß Wasser auf zwei verschiedene Weisen gebunden ist, nämlich durch Ion-Dipol-Wechselwirkung mit leitenden Kationen und durch Wasserstoffbrückenbindungen mit Sauerstoffatomen. Wie zu erwarten war werden für die ersteren von der Natur der einwertigen Kationen abhängige Bindungsenergien (H=84.1 kJ/Mol H₂O bzw. 59.4 kJ/Mol H₂O für Li- bzw. Na--Alumina) erhalten. Die auf die zweite Wechselwirkung zurückzuführenden Enthalpieänderung ist dagegen für die drei-Aluminiumoxide identisch (H=15.1 kJ/Mol H₂O). Das keramische Na--Aluminiumoxid zeigt auch eine Oberflächenreaktion mit CO₂, die zur Bildung von Carbonaten und Bicarbonaten führt.

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(Na, Na 50%-Li, Li)- -- . , - . , Li — Na-- , , 84.5 59.4 / ₂. , - 15.1 / ₂. Na- , .

     

Crystal and molecular structure of nitrosyl(1,10-phenanthroline)-bis(triphenylphosphine)iridium(I) Dihexafluorophosphate, [Ir(NO)(phen)(PPh3)2][PF6]2

Summary The structure of [Ir(NO)(phen)(PPh₃)₂][PF₆]₂ has been determined from x-ray diffractometer data. The compound crystallizes in space groupPnam with four molecules in a unit cell witha = 19.924(12),b = 14.793(9) andc = 16.348(9) A. Full-matrix least-squares refinement has led to a final R value of 0.061 for the 4796 observed reflections. The structure consists of well-separated ions, and the geometry around the metal is trigonal bipyramidal with nitrosyl and bidentate 1,10-phenanthroline (in spite of the very narrow bite angle of 75.8°) ligands occupying the equatorial positions and the triphenylphosphine ligands the axial positions. The cation has an imposed crystallographicm symmetry. Important bond lengths are as follows: Ir-P, 2.391(3): Ir-N (nitrosyl) 1.700(12): Ir-N (1,10-phenanthroline) 2.103(12) and 2.142(11): N-O, 1.201(18)A. The nitrosyl ligand is linear [Ir-N-O = 179.9(9)°] so that this complex can be formulated as an NO⁺ complex of iridium(I).     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.     

Spectrophotometric titration of mercury(II) with ethylenedithiodiacetic acid

Summary Mercuric ions may be determined by titration with ethylenedithiodiacetic acid at a wavelength of 260 nm at any pH less than 1. The method is simple, rapid, and selective, and is applicable in solutions of high electrolyte concentration. Mercury(II) can be determined down to 1.5×10^–5 M with a relative standard deviation less than 2%.

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Zusammenfassung Quecksilber (II) läßt sich mit Äthylendithiodiessigsäure bei 260 nm und pH1 titrieren. Das Verfahren ist einfach, rasch und selektiv. Es läßt sich auch für Lösungen mit hoher Elektrolytkonzentration anwenden. Hg(II)-Konzentrationen über 1,5×10^–5 M sind mit einer relativen Standardabweichung unter 2% bestimmbar.

     

On the 2 and the 3-connectedness of ample divisors on a surface

Let X be a nonsingular complex projective surface and let D be an ample divisor on X such that the associated invertible sheaf is spanned by its global sections. We prove that D is 2-connected apart from a few cases we explicitly describe. We also provide a corresponding result for the 3-connectedness when D²10 and for the 4-connectedness when D²17 and D is very ample.     

Ond-folds whose canonical bundle is not numerically effective,according to Mori and Kawamata

Sunto In questo lavoro si studiano le varietà non singolari di dimensione d il cui divisore canonico non è numericamente effettivo e si estendono alcuni dei risultati ottenuti da Mori nel caso d=3. CiÒ viene ottenuto mediante un uso sistematico della teoria di Mori dei raggi estremali e di un forte teorema di Kawamata-Shokurov. Quest'ultimo risultato fornisce una varietà normale Y e un morfismo : X Y che contrae un raggio estremale R e che dá la struttura di X. Se R è numericamente effettivo, dimY