Remarks on the analyticity of the free boundary for the one-dimensional Stefan problem

Sunto Si dimostra che nel problema di Stefan (con una o due fasi) nelle variabili x(-,+) e t0il contorno libero è una funzione analitica di t ^1/2 per t0,se il dato iniziale è assunto in una classe di fungioni intere. I coefficienti dello sviluppo del contorno libero in serie di poterne di t^1/2 sono determinati mediante formule ricorrenti. Un particolare esame è svolto per il caso in cui non c'è raccordo tra il dato iniziale e quello sul contorno libero, dimostrando l'esistenza di soluzioni dotate di contorno analitico, sotto opportune limitazioni sul salto tra i due dati; sono peró messi in evidenza anche casi in cui il problema non ammette soluzioni. Infine una breve analisi è svolta per i problemi in domini limitati, fornendo una dimostrazione della analiticità del contorno libero rispetto a t per t>0,alternativa a quella di [1].

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Work partially supported by the Italian CNR, while the first of the Authors was visiting the Mathematical Institute «U. Dini» of the University of Florence.     

Integral Moments of L-Functions

We give a new heuristic for all of the main terms in the integralmoments of various families of primitive L-functions. The resultsagree with previous conjectures for the leading order terms.Our conjectures also have an almost identical form to exactexpressions for the corresponding moments of the characteristicpolynomials of either unitary, orthogonal, or symplectic matrices,where the moments are defined by the appropriate group averages.This lends support to the idea that arithmetical L-functionshave a spectral interpretation, and that their value distributionscan be modelled using Random Matrix Theory. Numerical examplesshow good agreement with our conjectures. 2000 Mathematics SubjectClassification 11M26, 15A52.     

59Co NMR study of NdCo2, GdCo2, TbCo2 and HoCo2

We have observed the ⁵⁹Co spectra of the Laves phase Co compounds with Nd, Gd, Tb and Ho. We observe a spectrum consisting of a pair of lines for Nd, Tb and Ho compounds, because the Co sites are magnetically inequivalent in the presence of dipolar or pseudodipolar fields. For the heavy rare earth compounds, the magnitude of this splitting is comparable to the dipolar splitting produced by the neighboring spins, but for Nd it is much larger. The Nd compound is also anomalous in that the average hyperfine field is only 37.2 kOe while for the 3 heavy rare earth compounds it is about 60 kOe. The magnitude of the hyperfine field is discussed in terms of a simple model relating it to the cobalt moment and the rare earth spin.     

Comparing Heegaard splittings -the bounded case

In a recent paper we used Cerf theory to compare strongly irreducible Heegaard splittings of the same closed irreducible orientable 3-manifold. This captures all irreducible splittings of non-Haken 3-manifolds. One application is a solution to the stabilization problem for such splittings: If are the genera of two splittings, then there is a common stabilization of genus . Here we show how to obtain similar results even when the 3-manifold has boundary.

     

Cusp structures of alternating links

Summary An alternating link is canonically associated with every finite, connected, planar graph . The natural ideal polyhedral decomposition of the complement of is investigated. Natural singular geometric structures exist onS ³– , with respect to which the geometry of the cusp has a shape reflecting the combinatorics of the underlying link projection. For the class of balanced graphs, this induces a flat structure on peripheral tori modelled on the tessellation of the plane by equilateral triangles. Examples of links containing immersed, closed ₁-injective surfaces in their complements are given. These surfaces persist after most surgeries on the link, the resulting closed 3-manifolds consequently being determined by their fundamental groups.Oblatum 20-V-1991     

The Steiner ratio conjecture for cocircular points

A Steiner minimal treeS is a network of shortest possible length connecting a set ofn points in the plane. LetT be a shortest tree connecting then points but with vertices only at these points.T is called a minimal spanning tree. The Steiner ratio conjecture is that the length ofS divided by the length ofT is at least 3/2. In this paper we use a variational approach to show that if then points lie on a circle, then the Steiner ratio conjecture holds.     

Synthesis and reactions of the Diels-Alder adduct of thebaine with 4-phenyl-1,2,4-triazoline-3,5-dione

The title compound was prepared. Upon treatment with HCl a rearrangement occurred and the “open” compound 5 was obtained as its colorless hydrochloride. This salt readily lost HCl and gave the betaine 5. The rearranged “closed” compound 6 was obtained from 5.Quaternary salts 13 and 14 may be formed in methanolic solution from thebaine and codeine and tetracyanoethylene. The salt 13 reacts with the title dienophile and affords the “open” adduct 15.