The $$L^p$$ L p -Calderón–Zygmund inequality on non-compact manifolds of positive curvature

Annals of Global Analysis and Geometry - We construct, for $$p>n$$ , a concrete example of a complete non-compact n-dimensional Riemannian manifold of positive sectional curvature which does...     

On the Spectral Rigidity of Hopf Manifolds

We characterize Hopf manifolds of complex dimension 3 (resp. 2) in the class of compact locally conformal Kaehler manifold ( resp. Hermitian manifold ) by the spectrum of the Laplacian acting on functions.     

A calorimetric study of the different thermal behaviour of DNA in the isotropic and liquid-crystalline states

A difference between the thermal behaviour of the isotropic and liquid-crystalline state of sonicated DNA in aqueous salt solution containing poly(ethyleneglycol)(PEG) has been demonstrated. On cooling, a different degree of renaturation of thermally denaturated DNA is observed between samples which form the isotropic state and more concentrated samples which on cooling form the cholesteric state.     

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- , .

     

Catalysis in aromatic nucleophilic substitution. Note II. Piperidino substitution reactions of some 2-l-3-nitrothiophenes and 2-l-5-nitrothiophenes in methanol and benzene

The rates of piperidino substitution of some 2-L-3-nitrothiophenes (I) and 2-L-5-nitrothiophenes (II) (L = Cl, Br, I, OC₆H₄NO₂-p, and SO₂Ph) have been measured in methanol and in benzene at various piperidine concentrations. The reactivity of compounds (I) is not affected by the piperidine concentration in both methanol and benzene, except for the case of L = I (Ic). Probably due to association effects, the reactivity of Ic in benzene decreases as the piperidine concentration is increased. The reactions of compounds II follow overall second order kinetics in methanol while in benzene a different behaviour is observed as a function of the nature of the leaving group. In fact, the piperidino substitutions of IIa-c (L = Cl, Br, I) are mildly accelerated at high piperidine concentrations (a moderate solvent effect); on the contrary the reactivity of IId and e shows a strong dependence on the piperidine concentration, pointing out a genuine base catalysis.     

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.     

On finite {1,2,3}-semiaffine planes

In this paper, we investigate {1,2,3}-semiaffine planes. All such planes of order n >51 shall be classified. It turns out that they are embeddable into projective planes of the same order n in the most natural way.Work supported by National Research Project on Strutture Geometriche Combinatoria, loro applicazioni of Italian M.P.I. and G.N.S.A.G.A. of C.N.R.     

Amphiphilic cyclodextrin carriers embedding porphyrins: charge and size modulation of colloidal stability in heterotopic aggregates

The interaction between the anionic 5,10,15,20-tetrakis(4-sulfonatophenyl)-21H,23H-porphyrin (TPPS) and cationic vesicles formed by heptakis(2-omega-amino-O-oligo(ethylene oxide)-6-hexylthio)-beta-cyclodextrin (SC6CDNH2) has been investigated in detail through a combination of elastic light scattering (ELS), quasi-elastic light scattering (QELS), zeta potential measurements, and time-resolved fluorescence anisotropy. ELS experiments provided the first structural characterization of these cationic vesicles both in the absence and in the presence of TPPS porphyrin, modeling the system as a spherical particle described by a single thin shell form factor. The structure of mixed hetero-aggregates is modulated by charge and size of the two components as function of different porphyrin/cyclodextrin (CD) molar ratios. At the limiting molar ratio studied, the absolute value of zeta potential (/zeta/ = 12.5 mV) seems to be a reference value for the formation of stable colloidal CD vesicular aggregates at thermodynamic equilibrium. New insights on the structure of these heterotopic colloids have been obtained by analysis of rotational correlation times at different molar ratios exploiting time-resolved fluorescence anisotropy experiments. At high porphyrin loads, the anisotropy decays behave as monoexponentials and the rotational correlation times (1-2 ns) together with the r(0) values close to zero suggest the presence of small amounts of TPPS embedded in a hydrophobic environment either in monomeric or in aggregated form. At the lower porphyrin/CD molar ratios, the anisotropy decays exhibit a double-exponential behavior showing a predominant component with a slow rotational correlation time (20-25 ns) and limiting anisotropy values of approximately 0.15. This component has been assigned to molecules that are more stabilized onto the CD vesicles, that is, porphyrins embedded into the oligo-ethylene "wall" of the CD vesicles. Scanning near-field optical microscopy of the samples evaporated on glass surfaces gave further insights on the morphology and optical properties of these systems, confirming the embedding of TPPS on the vesicles and evidencing the role of the solvent.