The Borsuk�CUlam theorem for homotopy spherical space forms

In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk–Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known.     

Estimation of Jc(B) dependence from self-field alternating current (AC) losses measured on Bi-2223/Ag tapes

Transport AC losses measured in self-field conditions on multifilamentary Bi-2223 tapes are often found to be lower than those calculated within the framework of the critical state model for a bulk wire with elliptical cross section, though generally higher than predicted for a strip. This effect is sometimes ascribed to the non-ideal geometry of the tapes, which does not exactly reproduce either shape. Here we propose an alternative explanation assuming that the critical current density of superconducting material depends on magnetic field. In practice, we analyzed the AC loss curve and deduced different I_c values for the individual data points, using the standard Norris equation for elliptical conductor. This gives the relation between ‘calculated' I_c and the self-field associated to AC transport current, which can be regarded as an alternative way to qualify the dependence of J_c on magnetic field. Important is that this procedure covers the range of fields below the self-field at I_c where the measurement in background DC field can not be used to determine J_c(B).     

An iterative construction of Gorenstein ideals

In this paper, we present a method to inductively construct Gorenstein ideals of any codimension We start from a Gorenstein ideal of codimension contained in a complete intersection ideal of the same codimension, and we prove that under suitable hypotheses there exists a new Gorenstein ideal contained in the residual ideal We compare some numerical data of the starting and the resulting Gorenstein ideals of the construction. We compare also the Buchsbaum-Eisenbud matrices of the two ideals, in the codimension three case. Furthermore, we show that this construction is independent from the other known geometrical constructions of Gorenstein ideals, providing examples.

     

Magic Numbers in Boson 4He Clusters: The Auger Evaporation Mechanism

The absence of magic numbers in bosonic ⁴He clusters predicted by all theories since 1984 has been challenged by high-resolution matter-wave diffraction experiments. The observed magic numbers were explained in terms of enhanced growth rates of specific cluster sizes for which an additional excitation level calculated by diffusion Monte Carlo is stabilized. The present theoretical study provides an alternative explanation based on a simple independent particle model of the He clusters. Collisions between cluster atoms in excited states within the cluster lead to selective evaporation via an Auger process. The calculated magic numbers as well as the shape of the number distributions are in quite reasonable agreement with the experiments.     

Linear systems, singularity and not too ramified morphisms

Given a smooth k-variety Y (where k is a field of arbitrary characteristic) and a linear systemL on Y we study the dimension of the singular locus of the general element ofL, both inside and outside the base locus B ofL. We interpret these results from the point of view of the transversality theory, and we improve a result by Speiser about the not too ramified morphisms. Moreover, we show that our results can be applied in some cases where a criterion by Zhang, for the smoothness of the general element ofL, fails. Entrata in Redazione il 15 settembre 1997, e in versione definitiva il 28 ottobre 1999.     

On the α-ketols obtained from α,β-unsaturated aromatic aldehydes and bakers'yeast

From α-methylcinnamaldehyde (1b), acetaldehyde and fermenting bakers'yeast, at pH 5, the $\text{R}$ α-ketol (6) is obtained in $\text{ca}$. 15% yield, togheter with unreacted (1b); from cinnamaldehyde (1a), under identical conditions, optically inactive (5) has been isolated as the only transformation product.     

Spectral Analysis and Zeta Determinant on the Deformed Spheres

We consider a class of singular Riemannian manifolds, the deformed spheres , defined as the classical spheres with a one parameter family g[k] of singular Riemannian structures, that reduces for k = 1 to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian , we study the associated zeta functions . We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in . An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular and . We give explicit formulas for the zeta regularized determinant in the low dimensional cases, N = 2,3, thus generalizing a result of Dowker [25], and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter k. Partially supported by FAPESP: 2005/04363-4