1,722,050 research outputs found
A note on standard completeness for some extensions of uninorm logic
Full text linkWe prove standard completeness for uninorm logic extended with knotted axioms. This is done following a proof-theoretical approach, based on the elimination of the density rule in suitable hypersequent calculi
A Whitney extension theorem for functions taking values in scales of Banach spaces
No full textWe introduce a modified version of the Whitney extension operators for collections of functions from a closed subset of Rn into scales of Banach spaces with smoothing operators. We prove an extension theorem for collections whose elements take values in different spaces of the scale. A motivation for considering this kind of collections comes from very basic observations on the composition of functions of more than one real variable. The idea at the base of the proof is rather natural in the context of scales of Banach spaces, and consists in introducing smoothing operators in the construction of the extension, with smoothing parameters related to the diameter of each Whitney dyadic cube. Classical examples of scales of Banach spaces with smoothing operators are also given, and new related observations are proved
Calcolo delle Probabilità
No full textIl libro si rivolge agli studenti di calcolo delle probabilità dei corsi di laurea in Informatica, in Matematica e di quelli delle Facoltà di Ingegneria e di Statistica. Particolare attenzione, nell'organizzazione degli argomenti, è stata rivolta alle esigenze didattiche dei nuovi ordinamenti.
Il testo introduce agli elementi di base del Calcolo delle Probabilità, senza trascurare di sottolineare gli elementi di connessione tra la teoria e le applicazioni. Anche a questo scopo esso si avvale di un ampio materiale di esercizi, oltre duecento, di cui una metà completamente risolti
Longer lifespan for many solutions of the Kirchhoff equation
No full textWe consider the Kirchhoff equation on the d-dimensional torus T^d, and its Cauchy problem with initial data of size epsilon in the Sobolev class. The effective equation for the dynamics at the quintic order, obtained in previous papers by quasilinear normal form, contains resonances corresponding to nontrivial terms in the energy estimates. Such resonances cannot be avoided by tuning external parameters (simply because the Kirchhoff equation does not contain parameters). In this paper we introduce nonresonance conditions on the initial data of the Cauchy problem and prove a lower bound epsilon^{-6} for the lifespan of the corresponding solutions (the standard local theory gives epsilon^{-2}, and the normal form for the cubic terms gives epsilon^{-4}). The proof relies on the fact that, under these nonresonance conditions, the growth rate of the "superactions" of the effective equations on large time intervals is smaller (by a factor epsilon^2) than its a priori estimate based on the normal form for the cubic terms. The set of initial data satisfying such nonresonance conditions contains several nontrivial examples that are discussed in the paper
Fourier coefficients of invariant random fields on homogeneous spaces of compact Lie groups
Full text linkLet T be a random field invariant under the action of a compact group G. We investigate properties of the Fourier coefficients as orthogonality and Gaussianity. In particular we give conditions ensuring that independence of the random Fourier coefficients implies Gaussianity. As a consequence, in general, it is not possible to simulate a non-Gaussian invariant random field through its Fourier expansion using independent coefficients. end{abstract
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