10 Dicembre, 2003 14:30

Sezione di Probabilità e Statistica Matematica

Dependence orderings for order statistics

Subhash Kochar, Indian Statistical Institute, New Delhi

Aula seminari III piano

10 Dicembre, 2003 17:00

Seminario Matematico e Fisico di Milano

Semigruppi di operatori per equazioni di evoluzione

Klaus Engel, Università de L'Aquila

Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Aula 3 (piano terra)

abstract

abstract

Nell'ambito dell'analisi funzionale, la teoria dei semigruppi di operatori fornisce uno strumento molto potente per lo studio delle equazioni di evoluzione. La prima parte del seminario dà una breve introduzione di questa teoria. In particolare vengono richiamati risultati sulla generazione e sul comportamento asintotico di semigruppi, partendo da alcuni spunti storici. Nella seconda parte viene dimostrato come questi risultati astratti possono essere applicati a problemi concreti come equazioni integro-differenziali, equazioni differenziali con ritardo oppure sistemi con condizioni dinamiche al bordo. In particolare vengono presentati risultati recenti sulla buona positura ed il comportamento asintotico delle soluzioni dei sistemi sopra citati.

5 Dicembre, 2003 12:30

Seminari di Cultura Matematica

Crittogrsfis s chiave pubblica

R. Betti, Dip. di Matematica

Aula B.21

Nell'ambito dell'analisi funzionale, la teoria dei semigruppi di operatori fornisce uno strumento molto potente per lo studio delle equazioni di evoluzione. La prima parte del seminario dà una breve introduzione di questa teoria. In particolare vengono richiamati risultati sulla generazione e sul comportamento asintotico di semigruppi, partendo da alcuni spunti storici. Nella seconda parte viene dimostrato come questi risultati astratti possono essere applicati a problemi concreti come equazioni integro-differenziali, equazioni differenziali con ritardo oppure sistemi con condizioni dinamiche al bordo. In particolare vengono presentati risultati recenti sulla buona positura ed il comportamento asintotico delle soluzioni dei sistemi sopra citati.

3 Dicembre, 2003 15:00

Sezione di Fisica Matematica

Equazioni Solitoniche Nascoste

Paolo Casati, Università di Milano Bicocca

Aula Seminari MOX-6° piano dip. di matematica

abstract

abstract

Nel seminario saranno presentate alcune
equazioni non lineari alle derivate parziali
note nella letteratura come equazioni di Korteweg de Vries nascoste. Si
mostrera come queste equazioni possano essere ottenute mediante un
processo di riduzione di un sistema dinamico definito sugli strati
singolari (o nascosti) della Grassmaniana infinito dimensionale di Sato.
Inoltre verrano discusse le loro proprieta multihamiltoniane.
Infine si accennera brevemente come si pensa di usare la teoria delle
rappresentazioni delle algebre di Lie per costruire le loro soluzioni
multisolitoniche.

3 Dicembre, 2003 17:00

Seminario Matematico e Fisico di Milano

Fluxes of mechanical quantities across fractal boundaries

Miroslav Silhavy, Akademie ved Ceske Republiky, Praha (Rep. Ceca)

Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza

abstract

abstract

This seminar deals with fluxes of quantities across parts of the boundary of a body R with fractal boundary. A broad interpretation of the notion of a fractal boundary is employed here to mean any bounded subset R of Rn whose boundary dR is so complicated that the outer normal n to R is not defined for a.e. point of dR. Here a.e. means almost everywhere with respect to the n-1 dimensional Hausdorff measure (area) Hn-1. For a fractal body, Hn-1(dR) is infinite, since otherwise R is a set of finite perimeter with an Hn-1 a.e. defined normal. The paper is concerned with determining the net flux F(q,T) of a scalar quantity (such as the heat flux) across a subset T of dR, where the quantity is represented by a continuous field of the flux vector q on Rn with integrable distributional divergence. The paper examines basic properties of the functional F: (1) On the negative side, it is shown that if Hn-1(dR) is infinite, then F(q, . ) does not extend to a measure unless q is in some sense trivial. (2) On the positive side, it is proved that each R can be approximated by a sequence Rj of sets of finite perimeter such that the classical Cauchy formula holds in some limiting sense. (3) Consequences are derived of the situation when a given T insulates under q in the sense that the flux through each trace S of T vanishes. (4) Conditions are given on dR for the locality of F (so that the value F(q,T) depends on the values of q on T). (5) Classes of flux vector fields are described to which F(q,T) can be extended.

28 Novembre, 2003 12:30

Seminari di Cultura Matematica

L'entropia e la freccia del tempo

P. Biscari, Dip. di Matematica

aula seminari III piano

This seminar deals with fluxes of quantities across parts of the boundary of a body R with fractal boundary. A broad interpretation of the notion of a fractal boundary is employed here to mean any bounded subset R of Rn whose boundary dR is so complicated that the outer normal n to R is not defined for a.e. point of dR. Here a.e. means almost everywhere with respect to the n-1 dimensional Hausdorff measure (area) Hn-1. For a fractal body, Hn-1(dR) is infinite, since otherwise R is a set of finite perimeter with an Hn-1 a.e. defined normal. The paper is concerned with determining the net flux F(q,T) of a scalar quantity (such as the heat flux) across a subset T of dR, where the quantity is represented by a continuous field of the flux vector q on Rn with integrable distributional divergence. The paper examines basic properties of the functional F: (1) On the negative side, it is shown that if Hn-1(dR) is infinite, then F(q, . ) does not extend to a measure unless q is in some sense trivial. (2) On the positive side, it is proved that each R can be approximated by a sequence Rj of sets of finite perimeter such that the classical Cauchy formula holds in some limiting sense. (3) Consequences are derived of the situation when a given T insulates under q in the sense that the flux through each trace S of T vanishes. (4) Conditions are given on dR for the locality of F (so that the value F(q,T) depends on the values of q on T). (5) Classes of flux vector fields are described to which F(q,T) can be extended.

25 Novembre, 2003 11:00

Sezione di Geometria, Algebra e loro applicazioni

Nuove tendenze in crittografia

Angelo Sonnino, Università della Basilicata

Dipartimento di Matematica - Politecnico di Milano

This seminar deals with fluxes of quantities across parts of the boundary of a body R with fractal boundary. A broad interpretation of the notion of a fractal boundary is employed here to mean any bounded subset R of Rn whose boundary dR is so complicated that the outer normal n to R is not defined for a.e. point of dR. Here a.e. means almost everywhere with respect to the n-1 dimensional Hausdorff measure (area) Hn-1. For a fractal body, Hn-1(dR) is infinite, since otherwise R is a set of finite perimeter with an Hn-1 a.e. defined normal. The paper is concerned with determining the net flux F(q,T) of a scalar quantity (such as the heat flux) across a subset T of dR, where the quantity is represented by a continuous field of the flux vector q on Rn with integrable distributional divergence. The paper examines basic properties of the functional F: (1) On the negative side, it is shown that if Hn-1(dR) is infinite, then F(q, . ) does not extend to a measure unless q is in some sense trivial. (2) On the positive side, it is proved that each R can be approximated by a sequence Rj of sets of finite perimeter such that the classical Cauchy formula holds in some limiting sense. (3) Consequences are derived of the situation when a given T insulates under q in the sense that the flux through each trace S of T vanishes. (4) Conditions are given on dR for the locality of F (so that the value F(q,T) depends on the values of q on T). (5) Classes of flux vector fields are described to which F(q,T) can be extended.

21 Novembre, 2003 

Sezione di Geometria, Algebra e loro applicazioni

Expert systems for decision-making (verification, synthesis, time estimation)

Alexander Frolov, Moscow Power Engineering Univ., Moscow

Dip. di Matem. F. Brioschi , Pol. di Milano

This seminar deals with fluxes of quantities across parts of the boundary of a body R with fractal boundary. A broad interpretation of the notion of a fractal boundary is employed here to mean any bounded subset R of Rn whose boundary dR is so complicated that the outer normal n to R is not defined for a.e. point of dR. Here a.e. means almost everywhere with respect to the n-1 dimensional Hausdorff measure (area) Hn-1. For a fractal body, Hn-1(dR) is infinite, since otherwise R is a set of finite perimeter with an Hn-1 a.e. defined normal. The paper is concerned with determining the net flux F(q,T) of a scalar quantity (such as the heat flux) across a subset T of dR, where the quantity is represented by a continuous field of the flux vector q on Rn with integrable distributional divergence. The paper examines basic properties of the functional F: (1) On the negative side, it is shown that if Hn-1(dR) is infinite, then F(q, . ) does not extend to a measure unless q is in some sense trivial. (2) On the positive side, it is proved that each R can be approximated by a sequence Rj of sets of finite perimeter such that the classical Cauchy formula holds in some limiting sense. (3) Consequences are derived of the situation when a given T insulates under q in the sense that the flux through each trace S of T vanishes. (4) Conditions are given on dR for the locality of F (so that the value F(q,T) depends on the values of q on T). (5) Classes of flux vector fields are described to which F(q,T) can be extended.

17 Novembre, 2003 15:30

Seminario Matematico e Fisico di Milano

Struttura riemanniana e sub-riemanniana sul gruppo di Heisenberg e analisi dei rispettivi (sub-)laplaciani

Fulvio Ricci, Scuola Normale Superiore (Pisa)

Dipartimento di Matematica e Applicazioni - Università degli Studi di Milano Bicocca - Via Bicocca degli Arcimboldi, 8

abstract

abstract

Il gruppo di Heisenberg costituisce l'esempio più semplice di varietà dotata di metrica sub-riemanniana. Tale struttura è stata ampiamente studiata per il suo interesse in analisi armonica, analisi complessa, geometria conforme, teoria geometrica della misura. Per altri aspetti, diversi lavori di geometria differenziale trattano un'altra metrica sul gruppo di Heisenberg, questa volta riemanniana, che è strettamente collegata alla precedente. In un certo senso, le due metriche hanno lo stesso andamento asintotico. Questa affinità viene riscontrata anche nell'analisi degli operatori differenziali più significativi in ciascuna struttura: il sub-laplaciano nel primo caso, e l'operatore di Laplace-Beltrami nel secondo. Più complessa è la relazione tra le due strutture quando si passa ad analizzare operatori che agiscono su forme differenziali. Verranno indicati alcuni risultati recenti e problemi aperti di teoria spettrale in questo contesto.

3 Novembre, 2003 14:30

Seminario Matematico e Fisico di Milano

Simulating Cloth at the Computer

Marzia Fontana, Università degli studi di Parma

Aula seminari MOX - 6° piano dip. Mat.

abstract

abstract

The intent of the present talk is to introduce cloth modelling, as an area of increasing interest for computer graphics and CAD modelling applications. Drapes and garments are, in fact, visualization elements recurrently appearing in animated movies and videogames, or virtual reality scenes (e.g., virtual catwalks). Besides, a strong impulse comes from industry, e.g. for apparel, upholstery and fabric furniture production, increasingly demanding CAD tools driving the process of cloth design.
A survey on some famous cloth models proposed by the computer graphics community is presented. While purely geometric cloth models can be adequate for animation tasks, discrete or continuous physical formulations need to be used to accurately predict cloth shape behaviour for simulation purposes, e.g. functional analysis, virtual cloth prototyping, etc. We particularly focus on physics-based approaches, taking into account structural global properties depending on the considered textile materials, as well as interactions with the external environment. Some continuous PDE formulations inherited by structural mechanics approaches have been proposed in the literature, more convenient under static conditions and small displacements. However, differently from continuous textile engineering approaches, computer graphics’ community involved in physics-based cloth modelling tends to prefer discrete ODE models, typically formulated through Lagrangian or Newtonian dynamics, formally simpler and computationally less expensive. Particle-based models are the most frequently considered discrete cloth representations. These are, somehow, a coherent representation of the intrinsic “discrete” nature of textiles as interlaced plots of threads, particularly efficient for global shape visualization/simulation under dynamic conditions and large cloth deformations. The main characteristics and some numerical issues around particle-based cloth modelling are singled out.
As an application, we present some results on discrete physics-based cloth modelling and simulation, as obtained by the KAEMaRT group of Dipartimento di Meccanica, Politecnico di Milano and Dipartimento di Ingegneria Industriale, Università di Parma. Our research is aiming to extend a particle-based Newtonian cloth model originally proposed for simple cloth geometries to complex-shaped textile configurations such as garments or functional textiles, presenting several levels of design complexities (e.g., multi-layered fabric composition, seams and other construction constraints, etc.) for CAD design, simulation and virtual prototyping purposes. Examples and test cases are shown.