1-Meixner Random Vectors

Journal of Theoretical Probability - A definition of d-dimensional n-Meixner random vectors is given first. This definition involves the commutators of their semi-quantum operators. After that we...     

On the spectral norm of algebraic numbers

In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $.     

Inversion of adjunction for non-degenerate hypersurfaces

 We prove a precise inversion of adjunction formula for the log variety (ℂ ^{d +1},X), where X is a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded by dimension. Received: 17 September 2002 / Revised version: 22 November 2002 Published online: 14 February 2003 Current address: DPMMS, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, England. e-mail: f.ambro@dpmms.cam.ac.uk Mathematics Subject Classification (2000): Primary 14B05; Secondary 14M25, 52B20     

The set of toric minimal log discrepancies

We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points. This work is supported by a 21st Century COE Kyoto Mathematics Fellowship, and a JSPS Grant-in-Aid No 17740011.     

Extreme behavior of bivariate elliptical distributions

This paper exploits a stochastic representation of bivariate elliptical distributions in order to obtain asymptotic results which are determined by the tail behavior of the generator. Under certain specified assumptions, we present the limiting distribution of componentwise maxima, the limiting upper copula, and a bivariate version of the classical peaks over threshold result.     

Soft X-ray resonant magnetic scattering studies on Fe/CoO exchange bias system

We have used soft X-ray resonant magnetic scattering (XRMS) to search for the presence of an effective ferromagnetic moment belonging to the antiferromagnetic (AF) layer which is in close contact with a ferromagnetic (F) layer. Taking advantage of the element specificity of the XRMS technique, we have measured hysteresis loops of both Fe and CoO layers of a CoO(40 Å)/Fe (150 Å) exchange bias bilayer. From these measurements we have concluded that the proximity of the F layer induces a magnetic moment in the AF layer. The F moment of the AF layer has two components: one is frozen and does not follow the applied magnetic field and the other one follows in phase the ferromagnetic magnetization of the F layer. The temperature dependence of the F components belonging to the AF layer is shown and discussed.     

New vertex invariants and topological indices of chemical graphs based on information on distances

By applying information theory to the set of topological distances from one vertex to all other graph vertices, one obtains four new types of vertex invariants (u _i,v _i,x _i,Y _i) which are real numbers (as opposed to integers). They may be combined in many ways to afford new topological indices. One such type leads to indicesU, V, X andY which show no degeneracy for alkanes with up to 15 vertices.     

Continuous-time Markov model for geriatric patients behavior. Optimization of the bed occupancy and computer simulation

Previous research has shown that the flow of patients around departments of geriatric medicine and ex-patients in the community may be modelled by the application of a mixed-exponential distribution. In this paper we considered a five-compartment model using a continuous-time Markov process to describe the flow of patients. Using a M/Ph/c queuing model, we present a way of optimizing the number of beds in order to maintain an acceptable delay probability at a sufficiently low level. Finally, we constructed a Java computer simulation, using data from St George’s Hospital, London.     

Subbundles of maximal degree of the normal bundle of algebraic space curves almost complete intersection of special type

Summary LetX⊂P ³ be an irreducible smooth curve which is not a complete intersection. The main result of this paper shows that whenX is an a.c.i. of special type, i.e. its homogeneous ideal is generated by three polynomial of the same degreem, and additionallym>2, the subbundles of maximal degree of the normal bundle ofX inP ³ correspond to the singular points of maximal multiplicity of a plane curve which is the image ofX by a map (the linear system of the surfaces of minimal degree throughX). In particular this normal bundle is stable. The initial case of this family of curves, i.e. form=3, has been studied by E. Ballico-Ph. Ellia with different methods.

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Riassunto SiaX⊂P ³ una curva irriducibile e liscia che non è una completa intersezione. Il risultato principale di questa Nota mostra che quandoX è una almost completa intersezione di tipo speciale, cioè il suo ideale omogeneo è generato minimamente da 3 polinomi dello stesso gradom, e, inoltre,m>2, i sottofibrati di grado massimo del fibrato normale diX inP ³ corrispondono ai punti singolari di molteplicità massima di una curva piana che è l’immagine diX tramite una mappa (il sistema lineare delle superficie di grado minimo passanti perX). In particolare questo fibrato normale è stabile. Il caso iniziale di questa famiglia di curve, i.e. perm=3, è stato studiato da E. Ballico-Ph. Ellia con differenti metodi.

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This research is supported by GNSAGA (Italy).

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The main results of this paper have been the object of a talk at the meeting on ?Curves in Projective Space? held at Rocca di Papa in june 1985.