Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.34 (2002)

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https://www.openstarts.units.it/handle/10077/4158

CONTENTS

Edoardo Ballico
On the minimal free resolution of multiple curves

Giuseppe Dattoli, Paolo E. Ricci and Laura Marinelli
Generalized truncated exponential polinomyals and applications

Jan Hamhalter
Noncommutative phenomena in measure theory on operators algebras

Annamaria Miranda
Cardinal invariants for function spaces

Sania Marušić
Asymptoptic behaviour of Sobolev constants for thin curved rods or pipes

Céline Azizieh
Symmetry and monotonicity results for positive solutions of p-Laplace systems

Filippo Gazzola
The sharp exponent for a Liouville-type theorem for an elliptic inequality

Yuri Bozhkov and Antonio Carlos Gilli Martins
On the symmetry group of a differential equation and the Liouville-Gelfand problem

Wolfgang Desch and Krista W. Homan
Pointwise versions of solutions to Cauchy problems in L^p-spaces

Luisa Di Piazza
A Riemann-type minimal integral for the classical problem of primitives

Heinz König
Measure and Integration: an attempt at unified systematization

Antonella Nannicini
Twistor methods in conformal almost symplectic geometry

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Editorial policy The journal Rendiconti dell’Istituto di Matematica dell’università di Trieste publishes original articles in all areas of mathematics. Special regard is given to research papers, but attractive expository papers may also be considered for publication. The journal usually appears in one issue per year. Additional issues may however be published. In particular, the Managing Editors may consider the publication of supplementary volumes related to some special events, like conferences, workshops, and advanced schools. All submitted papers will be refereed. Manuscripts are accepted for review with the understanding that the work has not been published before and is not under consideration for publication elsewhere. Our journal can be obtained by exchange agreements with other similar journals.

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Now showing 1 - 5 of 12

Twistor methods in conformal almost symplectic geometry
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2002)
Nannicini, Antonella
Given a 2n-dimensional almost symplectic manifold $\left(M,\omega\right)$, we consider the conformal class of $\omega$ and to each symplectic connection, $\nabla$, we associate, in a natural way, a $e^{2\sigma}\omega$-symplectic connection, $\nabla^{\sigma}$. We prove that the twistor bundle $Z\left(M,\omega\right):=\frac{P\left(M,Sp\left(2n\right)\right)}{U(n)}$, with its canonical almost complex structure induced by $\nabla$, is an invariant of the conformal class of $\left(\omega,\nabla\right)$. Then we study the interplay between conformal properties of $\left(M,\omega\right)$ and complex properties of $Z\left(M,\omega\right)$, passing trough the existence of special symplectic connections. Finally we prove that, in the case of a special K$\ddot{\textrm{a}}$hler manifold, the section of $Z\left(M,\omega\right)$ defined by the complex structure of M is an almost complex submanifold with respect to a certain almost complex structure on $Z\left(M,\omega\right)$.
1167 557
Cardinal invariants for function spaces
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2002)
Miranda, Annamaria
Several function space topologies can be generated by a procedure defined by two parameters: a network on the domain and topology on the hyperspace of the range. Results about cardinal functions and metrizability for a particular class of such spaces are given.
947 384
Asymptoptic behaviour of Sobolev constants for thin curved rods or pipes
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2002)
Marušić, Sania
We study the Sobolev imbedding inequality in a curved rod or pipe with a smooth central curve $\gamma$. Using the variational approach and the two-scale convergence for thin domains we find the limit of the Sobolev imbedding constant W$^{1,r}\hookrightarrow L^{q}$ as $\epsilon$, the ratio between cross section diameter and the lenght of the rod, tends to 0.
602 389
Measure and Integration: an attempt at unified systematization
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2002)
König, Heinz
The Fundamentals for Set Functions. The Outer and Inner Extension Theorems. Consequences and Applications. The Fundamentals for Functionals. Comparison with the Traditional Daniell-Stone and Bourbaki Procedures.
717 597
Noncommutative phenomena in measure theory on operators algebras
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2002)
Hamhalter, Jan
The aim of this paper is to to review the basic principles of the measure theory built on operator algebras and to summarize recent progress in this field. We concentrate on those results which demonstrate considerable difference between the classical measure theory and its operator-algebraic counterpart. In particular, we show that the functional-analytic structure of a a given operator algebra A, the lattice-theoretic properties of measures on the projection lattice of A, the facial structure of the convex set of all states on A, and the continuity properties of states on A are connected in a way has no analogy in the standard measure theory.
877 445

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