Cinchoninium l-tartrate tetrahydrate

The title compound, (3R,4S,8R,9S)-cinchoninium (2R,3R)-tartrate tetrahydrate, C₁₉H₂₃N₂O⁺·C₄H₅O₆⁻·4H₂O, is a hydrated salt of cinchonine. In the cinchoninium cation, the geometry around the quinuclidinic N atom is typical of a protonated N atom, and the bond lengths and angles in the tartrate moiety clearly indicate the mono-ionized form. The relative orientation of the quinoline and quinuclidine systems is that most frequently observed in structures of cinchona salts and corresponds to one of the energy minima calculated for this type of mol­ecule in the gas phase. An extended network of intermolecular hydrogen bonds spreads parallel to the bc plane separating apolar layers.     

Countably generated prime ideals in <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript>

We confirm a twenty year old conjecture by showing that a nonzero prime ideal P in the algebra H^∞ of bounded analytic functions in the open unit disk is countably generated if and only if it is either a principal ideal generated by the polynomial z−z₀, |z₀|<1, or if P is generated by the n-th roots of an atomic inner function. The case of the algebra H^∞+C is also dealt with. Dedicated to the 70th birthday of Joseph Cima Research supported by the RIP-program Oberwolfach 2004.     

A Hopf Bundle Over a Quantum Four-Sphere from the Symplectic Group

We construct a quantum version of the SU(2) Hopf bundle S⁷→S⁴. The quantum sphere S⁷_q arises from the symplectic group Sp_q(2) and a quantum 4-sphere S⁴_q is obtained via a suitable self-adjoint idempotent p whose entries generate the algebra A(S⁴_q) of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere S⁴. We compute the fundamental K-homology class of S⁴_q and pair it with the class of p in the K-theory getting the value −1 for the topological charge. There is a right coaction of SU_q(2) on S⁷_q such that the algebra A(S⁷_q) is a non-trivial quantum principal bundle over A(S⁴_q) with structure quantum group A(SU_q(2)).     

Rational Design of Ag/TiO2 Nanosystems by a Combined RF‐Sputtering/Sol‐Gel Approach

The present work is devoted to the preparation of Ag/TiO₂ nanosystems by an original synthetic strategy, based on the radio‐frequency (RF) sputtering of silver particles on titania‐based xerogels prepared by the sol–gel (SG) route. This approach takes advantage of the synergy between the microporous xerogel structure and the infiltration power characterizing RF‐sputtering, whose combination enables the obtainment of a tailored dispersion of Ag‐containing particles into the titania matrix. In addition, the system′s chemico‐physical features can be tuned further through proper ex situ thermal treatments in air at 400 and 600 °C. The synthesized composites are extensively characterized by the joint use of complementary techniques, that is, X‐ray photoelectron and X‐ray excited Auger electron spectroscopies (XPS, XE‐AES), secondary ion mass spectrometry (SIMS), glancing incidence X‐ray diffraction (GIXRD), field emission scanning electron microscopy (FE–SEM), transmission electron microscopy (TEM), electron diffraction (ED), high‐angle annular dark field scanning TEM (HAADF–STEM), energy‐filtered TEM (EF–TEM) and optical absorption spectroscopy. Finally, the photocatalytic performances of selected samples in the decomposition of the azo‐dye Plasmocorinth B are preliminarily investigated. The obtained results highlight the possibility of tailoring the system characteristics over a broad range, directly influencing their eventual functional properties.     

Energy estimate and fundamental solution for degenerate hyperbolic Cauchy problems

The aim of this paper is to give an uniform approach to different kinds of degenerate hyperbolic Cauchy problems. We prove that a weakly hyperbolic equation, satisfying an intermediate condition between effective hyperbolicity and the C^∞ Levi condition, and a strictly hyperbolic equation with non-regular coefficients with respect to the time variable can be reduced to first-order systems of the same type. For such a kind of systems, we prove an energy estimate in Sobolev spaces (with a loss of derivatives) which gives the well-posedness of the Cauchy problem in C^∞. In the strictly hyperbolic case, we also construct the fundamental solution and we describe the propagation of the space singularities of the solution which is influenced by the non-regularity of the coefficients with respect to the time variable.     

Planar polynomials for commutative semifields with specified nuclei

We consider the implications of the equivalence of commutative semifields of odd order and planar Dembowski-Ostrom polynomials. This equivalence was outlined recently by Coulter and Henderson. In particular, following a more general statement concerning semifields we identify a form of planar Dembowski-Ostrom polynomial which must define a commutative semifield with the nuclei specified. Since any strong isotopy class of commutative semifields must contain at least one example of a commutative semifield described by such a planar polynomial, to classify commutative semifields it is enough to classify planar Dembowski-Ostrom polynomials of this form and determine when they describe non-isotopic commutative semifields. We prove several results along these lines. We end by introducing a new commutative semifield of order 3⁸ with left nucleus of order 3 and middle nucleus of order 3².