5 Aprile, 2004 17:00

Seminario Matematico e Fisico di Milano

On Highly Dispersive Partial Differential Equations

Peter Markowich, Universität Wien (Vienna, Austria)

Dipartimento di Matematica - Politecnico di Milano - Via Bonardi 9 - Milano - Aula Seminari VI piano

abstract

abstract

Partial differential equations with highly oscillatory solutions occur in many areas of science like quantum mechanics and acoustics, with important spin-offs to semiconductors, nanotechnology and low-temperature physics. These equations pose a great challenge to mathematical and numerical analysis. Recently a new mathematical technique has been developed to treat highly oscillatory PDEs, namely Wigner transforms. They allow deep new insights into high-frequency asymptotics. The state-of-the-art is reported in the lecture, with emphasis on applications in Bose­Einstein condensation.

2 Aprile, 2004 12:30

Seminari di Cultura Matematica

Viaggi nel tempo: le nuove frontiere della fisica

F. De Felice, Univ. di Padova

Aula B.21

Partial differential equations with highly oscillatory solutions occur in many areas of science like quantum mechanics and acoustics, with important spin-offs to semiconductors, nanotechnology and low-temperature physics. These equations pose a great challenge to mathematical and numerical analysis. Recently a new mathematical technique has been developed to treat highly oscillatory PDEs, namely Wigner transforms. They allow deep new insights into high-frequency asymptotics. The state-of-the-art is reported in the lecture, with emphasis on applications in Bose­Einstein condensation.

1 Aprile, 2004 11:00

Sezione di Probabilità e Statistica Matematica

Il processo gaussiano inverso normalizzato nei processi di mistura

Dott. Antonio Lijoi, dell Universita degli Studi di Pavia

Aula B55

abstract

abstract

Nel seminario viene presentata una particolare misura di probabilita'aleatoria ottenuta normalizzando gli incrementi di un processo gaussiano inverso. Tale misura di probabilita' aleatoria definisce una distribuzione iniziale per l'inferenza bayesiana nonparametrica. Si
dimostra che essa gode di proprieta' analoghe a quelle del processo di Dirichlet e vengono evidenziati i vantaggi derivanti dal suo
impiego nei modelli mistura gerarchici. Nell'ipotesi che le osservazioni
siano scambiabili, e' possibile ottenere una rappresentazione delle
leggi predittiva ed una caratterizzazione della distribuzione finale del
processo gaussiano inverso normalizzato. Infine vengono illustrate due
applicazioni a misture di normali allo scopo di effettuare un confronto
diretto con il processo di Dirichlet: la prima fa riferimento a dati
simulati e la seconda riguarda il ben noto data set sulle velocita'
relative delle galassie.

29 Marzo, 2004 17:00

Sezione di Geometria, Algebra e loro applicazioni

Algorithms for Reconstructing Shapes from Support-Type Function

Richard Gardner, Western Washington University

Dipartimento di Matematica - Politecnico di Milano

Nel seminario viene presentata una particolare misura di probabilita'aleatoria ottenuta normalizzando gli incrementi di un processo gaussiano inverso. Tale misura di probabilita' aleatoria definisce una distribuzione iniziale per l'inferenza bayesiana nonparametrica. Si
dimostra che essa gode di proprieta' analoghe a quelle del processo di Dirichlet e vengono evidenziati i vantaggi derivanti dal suo
impiego nei modelli mistura gerarchici. Nell'ipotesi che le osservazioni
siano scambiabili, e' possibile ottenere una rappresentazione delle
leggi predittiva ed una caratterizzazione della distribuzione finale del
processo gaussiano inverso normalizzato. Infine vengono illustrate due
applicazioni a misture di normali allo scopo di effettuare un confronto
diretto con il processo di Dirichlet: la prima fa riferimento a dati
simulati e la seconda riguarda il ben noto data set sulle velocita'
relative delle galassie.

29 Marzo, 2004 17:00

Sezione di Geometria, Algebra e loro applicazioni

Algorithms for Reconstructing Shapes from Support-Type Functions

Richard Gardner, Western Washington University (Washington, Stati Uniti)

Dipartimento di Matematica - Politecnico di Milano - Via Bonardi 9 - Milano - Aula Seminari VI piano

abstract

abstract

"There are several natural ways to take measurements of an unknown object. One is by means of the support function, which gives for any direction the (signed) distance from some fixed point (usually the origin) to the hyperplane supporting the object orthogonal to that direction. Another is by the distance between the two supporting hyperplanes orthogonal to a given direction. There is also the possibility of measuring the brightness function, which for an n-dimensional object gives the (n-1)-dimensional volumes of its orthogonal projections onto hyperplanes

25 Marzo, 2004 

Sezione di Probabilità e Statistica Matematica

Harmonic Analysis, Quadratic Forms and Risk Management

Prof. Kaj Nyström, Umea University

Aula Seminari III piano

"There are several natural ways to take measurements of an unknown object. One is by means of the support function, which gives for any direction the (signed) distance from some fixed point (usually the origin) to the hyperplane supporting the object orthogonal to that direction. Another is by the distance between the two supporting hyperplanes orthogonal to a given direction. There is also the possibility of measuring the brightness function, which for an n-dimensional object gives the (n-1)-dimensional volumes of its orthogonal projections onto hyperplanes

24 Marzo, 2004 

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Square functions, uniform rectifiability and regularity of parabolic free boundary problems

Kay Nyström, Umeå University, Sweden

"There are several natural ways to take measurements of an unknown object. One is by means of the support function, which gives for any direction the (signed) distance from some fixed point (usually the origin) to the hyperplane supporting the object orthogonal to that direction. Another is by the distance between the two supporting hyperplanes orthogonal to a given direction. There is also the possibility of measuring the brightness function, which for an n-dimensional object gives the (n-1)-dimensional volumes of its orthogonal projections onto hyperplanes

24 Marzo, 2004 

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Long-time stabilization of solutions to phase-field systems with memory

Hana Petzeltova, Mathematical Institute of the Academy of Sciences of the Czech Republic, Praga

"There are several natural ways to take measurements of an unknown object. One is by means of the support function, which gives for any direction the (signed) distance from some fixed point (usually the origin) to the hyperplane supporting the object orthogonal to that direction. Another is by the distance between the two supporting hyperplanes orthogonal to a given direction. There is also the possibility of measuring the brightness function, which for an n-dimensional object gives the (n-1)-dimensional volumes of its orthogonal projections onto hyperplanes

19 Marzo, 2004 12:30

Seminari di Cultura Matematica

Che cos'e' la curvatura?

F.G. Lastaria, Dip. di Matematica

Aula B.21

"There are several natural ways to take measurements of an unknown object. One is by means of the support function, which gives for any direction the (signed) distance from some fixed point (usually the origin) to the hyperplane supporting the object orthogonal to that direction. Another is by the distance between the two supporting hyperplanes orthogonal to a given direction. There is also the possibility of measuring the brightness function, which for an n-dimensional object gives the (n-1)-dimensional volumes of its orthogonal projections onto hyperplanes

18 Marzo, 2004 17:00

Seminario Matematico e Fisico di Milano

Carleman estimates and their applications to inverse problems

Victor Isakov, Wichita State University (Kansas, Stati Uniti)

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

abstract

abstract

We consider Carleman type estimates for general second order partial differential operators with real-valued coefficients. We include boundary terms. We give a derivation of these estimates, examples for elliptic and hyperbolic equations. As applications we consider uniqueness and stability in the Cauchy problem (in particular increased stability for the Helmholtz equation) and identification of coefficients and source terms of hyperbolic equations from the lateral Cauchy data.