Search results for " Matematica"
showing 10 items of 1345 documents
Generalized frame operator, lower semiframes, and sequences of translates
2023
Given an arbitrary sequence of elements $\xi =\lbrace \xi _n\rbrace _{n\in \mathbb {N}}$ of a Hilbert space $(\mathcal {H},\langle \cdot ,\cdot \rangle )$, the operator $T_\xi$ is defined as the operator associated to the sesquilinear form $\Omega _\xi (f,g)=\sum _{n\in \mathbb {N}} \langle f , \xi _n\rangle \langle \xi _n , g\rangle$, for $f,g\in \lbrace h\in \mathcal {H}: \sum _{n\in \mathbb {N}}|\langle h , \xi _n\rangle |<^>2<\infty \rbrace$. This operator is in general different from the classical frame operator but possesses some remarkable properties. For instance, $T_\xi$ is always self-adjoint with regard to a particular space, unconditionally defined, and, when xi is a lo…
A blow-up result for a nonlinear wave equation on manifolds: the critical case
2021
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.
Nonstandard variational calculus with applications to classical mechanics. 2. The inverse problem and more
1999
In this paper we continue analyzing the possible applications of nonstandard analysis to variational problems, with particular interest in classical mechanics. In particular, we adapt various techniques of numerical analysis to solve the nonstandard version of the Euler-Lagrange equation for both one-and multidimensional systems. We also start an introductory analysis of the inverse problem of the calculus of variation, identifying a class of nonstandard difference equations for which a first-order Lagrangian can be obtained.
MR2888559 Muratov, M. A.; Chilin, V. I. (o)-topology in ∗-algebras of locally measurable operators. Ukrainian Math. J. 61 (2009), no. 11, 1798–1808. …
2012
An operatorial approach to stock markets
2009
We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real market, and by the existence of conserved quantities, like the total number of shares or some linear combination of cash and shares. The same framework as the one used in the description of a gas of interacting bosons is adopted.
Metafora ed Analogia in Didattica della Matematica
2014
This paper is a report that concerns two experiments that I proposed in nine secondary school classes (pupils from fourteen to eighteen years old) in order to test some hypotesis concerning the use of metaphor during teaching-learning processes. I begin by analyzing the different significances of the concepts of metaphor and analogy that can be found in literature. Then I try to frame these concepts within the framework of semiotic mediation. I show some excerpts taken from the experimentations, and I try to interpret some of pupil’s utterances (words, gestures) as metaphors which offer to the teacher a possible way (by analogies) to introduce mathematical contents. I conclude with some ope…
Differential of metric valued Sobolev maps
2020
We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when the target is $\mathbb{R}$.
A PU-integral on a compact Hausdorff space.
2002
MR2817222 Ursescu, Corneliu, A mean value inequality for multifunctions. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 54(102) (2011), no. 2, 193–200
2011
The paper is devoted to extend some mean value inequalities from the function setting to the multifunction one. Let (M,d) be a metric space, let F be a multifunctions defined on D \subset R and taking values in the family of nonempty subsets of M, and let g: D\rightarrow R be a strictly increasing function. The author proves the following inequality: \frac{\delta(F(b),F(a))}{g(b)-g(a)} \leq \sup_{s\in [a,b)\cap D} \sup_{S\in F(s)} \sup_{t\in (s,b)\cap D} \frac{\delta(F(t),S)}{g(t)-g(s)}, where a and b are two points of D with a<b and, if Q and P are nonempty subsets of M, then \delta(Q,P)=\sup_{p\in P} \inf_{q\in Q}d(q,p). An application of the previous inequality to the Dini derivatives of…