A characterization of dilatation analytic integral kernels

We characterize integral operators belonging to B(L ² (ℝ³))which are dilatation analytic in the Cartesian product of two sectors S _a ⊂ ℂ as analytic functions from S _a×S_a into B(L ²(Ω)), the space of bounded operators on square integrable functions on the unit sphere Ω, which satisfy certain norm estimates uniformly on every subsector.     

Sui coefficienti di Fourier di una funzione rispetto al sistema dei polinomi ultrasferici

Sunto Si trova al n. 1 del Lavoro stesso. A Giovanni Sansone per il suo 70^mo compleanno. Lavoro eseguito nell' Istituto Nazionale per le Applicazioni del Calcolo.     

Preparation and crystal structure of a copper(II) homobinuclear chelate

Summary The structure of the homobinuclear complex Cu₂(aapen)H₂O, where aapen is the tetraanionic ligand derived from the condensation of 1,2-diaminocthane witho-acetoacetylphenol, has been determined from diffractometer data and refined to R = 6.1%. The crystals are monoclinic,P2₁/c, witha = 12.991(5),b = 8.530(4),c = 18.546(6) Å, and = 104.10(4)°; Z = 4. The ligand employed has two different coordination sets of atoms, N₂O₂ and O₂O₂, two oxygen atoms being common to both donor sets. In the complex, one copper atom is retained in the plane of the inner N₂O₂ chamber whilst the other, which is incorporated in the outer O₂O₂ chamber, is five-coordinate, being axially bonded to a water molecule.     

Thermodynamic parameters for the protonation of carboxylic acids in aqueous tetraethylammonium iodide solutions

The protonation constants of 21 carboxylic acids (formic, acetic, propionic, benzoic, phenoxyacetic, salicylic, oxalic, malonic, succinic, itaconic, malic, tartaric, oxydiacetic, thiodiacetic, thiodipropionic, phthalic, maleic, citric, 1,2,3-tricarboxylic, 1,2,4-tricarboxylic and 1,2,4,5-tetracarboxylic), have been determined potentiometrically, by pH-metric measurements, at several temperatures and ionic strengths, 5T55°C, 0<11 mol-dm^–3, using tetraethylammonium iodide as background salt. General equations for the dependence on ionic strength of thermodynamic parameters have been found. The statistical significance of results and the possibility of using a simple model for the thermodynamics of carboxylic acids protonation, is discussed.     

Multipliers of L which vanish at infinity

The main results of this paper are as follows.

1.

(i) If p ≠ 2, there exists a continuous multiplier (function) of L^p(Rⁿ) which vanishes at infinity, but which is not in the closure, in the multiplier norm, of the space of Fourier transforms of integrable functions.     

Which pi-clamped conjugated monocycles exhibit ring currents?

Quenching/survival of ring currents in pi-clamped conjugated monocycles is controlled by the match or mismatch in parity between the frontier orbitals of the central pi-conjugated 4n+2/4n monocycle and those of the clamps. Changes in ring current are not primarily caused by bond alternation or 'Mills-Nixon' effects; current and geometry changes on clamping are both consequences of electronic structure.     

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to instabilities with mound formation whose typical linear size L increases with time (coarsening process). In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening is known to be logarithmic in the absence of noise ( L(t) ∼ ln t) and to follow a power law ( L(t) ∼t ^1/3) when noise is present. If the surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stages of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster : if α is the exponent describing the steepening of the maximal slope M of mounds ( M ^α∼L) we find that L(t) ∼t ⁿ: n is equal to for 1≤α≤2 and it decreases from to for α≥2, according to n = α/(5α - 2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t) ∼t ^1/4, irrespectively of α. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model α = 1, both in the absence and in the presence of noise. Received 28 September 2001 and Received in final form 21 November 2001