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A class of fractional refinable functions
No full textStarting from a family of centrally symmetric, totally positive and
compactly supported (GP) refinable functions and introducing a fractional
exponent in the discrete Fourier transform, new functions, that are
proved to be still refinable, are generated. Even if, for non integer,
they are not compactly supported anymore they exhibit a decay that
allows them to belong to L2(R); moreover, for certain values of their
parameters they reduce to the fractional B-splines, while, for integer,
they interpolate the GP refinable functions. Also, these refinable functions
can be characterized by a convolution relation between suitable minimally
supported GP refinable functions and suitable fractional B-splines
Su un modello di Hele-Shaw dipendente dalla temperatura.
No full textSi costruisce un modello per l'iniezione di un fluido in una cella di Hele-Shaw. Si studiano le proprietà di esistenza ed unicità
della soluzione del problema di equazioni differenziali di tipo parabolico e di trasporto, con condizione integro differenziale sull'interfaccia, che descrivono il problema fisico.We constructed a model for the injection of a fluid in a Hele-Shaw cell and we study the properties of existence and uniqueness of the differential problem solution. These equations are of parabolic and transport kind, with an integral differential condition on the interface
On a New Class of Multiresolution Analyses Generated by Fractional Refinable Functions.
No full textA new class of refinable functions extending the GP class is
presented. It is characterized by a symbol with fractional
exponent that gives rise to non-compactly supported refinable
functions with decay and the stability properties of these refinable functions allow them to generate a multiresolution analysis (MRA) of L^2(R). The fractional refinable functions introduced here show a surprising order of exactness
Metodo diretto per lo studio delle biforcazioni alla Hopf per un flusso alla Poiseuille.
No full textSi studiano le soluzioni di stabilità di un sistema di evoluzione, dipendente da parametro R e le condizioni di non unicità della soluzione
Fractional GP refinable functions
Get PDFA new class of refinable functions extending the GP class introduced
in [12] is presented. It is characterized by a symbol with fractional exponent that gives
rise to non-compactly supported refinable functions. Nevertheless, the decay and stability
properties of these refinable functions allow them to generate a multiresolution
analysis (MRA) of L2(R). For suitable values of their parameters these refinable functions
reduce to the fractional B-splines introduced in [16], while, for integer α, they
interpolate the GP refinable functions. Furthermore, this class of refinable functions is
proved to be closed with respect to convolution and fractional differentiation, allowing
for its convenient the applicability to Sobolev spaces. The fractional refinable functions
introduced here show an useful order of polynomial exactness
A new class of biorthogonal wavelets on the interval
No full textConsidering the class of the refinable GP functions, I construct a class of biorthogonal bases on the interval with any prescribed order of polynomial exactness. Numerical results are compared with respect to the B-spline bases and show better performances
On a Temperature-dependent Hele-Shaw flow in one dimension.
No full textSi presenta un modello per un flusso di Hele-Shaw con temperatura variabile in una dimensione spaziale. Il problema da risolvere è un problema a frontiera libera per un'equazione parabolica con una condizione al contorno non lineare e non locale. Si dimostrano esistenza e unicità
Accurate Hopf points for the Poiseuille flow of a Bingham fluid.
No full textSi studiano i punti di biforcazione (di non unicitá) della soluzione del sistema differenziale ottenuto, per modellizzazione, da un flusso piano di Poiseuille per un fluido viscoso alla Bingham
Cardinal Filters
No full textSi analizza un particolare filtro basato su funzioni raffinabili e lo si utilizza per l'analisi di segnali
Galerkin Method Based on Refinable Functions
No full textThe aim of this paper is to study the shape preserving properties of B-bases on a finite interval. These bases are obtained by the integer translates of totally positive compactly supported refinable functions. We shall prove that the constructed B-bases generate, on the interval, multiresolution analyses which reproduce polynomials up to a certain degree
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