1,720,962 research outputs found
On a one-phase Stefan problem
No full textIn this paper we introduce a new way to approach the one-phase Stefan problem
partial_t(u +chi) = Delta u + fchi, u(0) = g, chiin H(u(t)),
with both g and f non-negative and where H : R
ightarrow P([0; 1]) is the usual
maximal monotone Heavyside graph. Our idea is to introduce a discrete
in time approximation scheme involving, step by step, suitable one-phase
Hele-Shaw problems. With natural regularity hypotheses on data we are
able to solve them, by means of results similar to a joint work of the second author with P. Tilli.
Using the qualitative behavior of these solutions we can then construct a discrete in
time approximate solution for the Stefan problem endowed with suitable
a-priory estimates. So we can ̄finally pass to the limit, getting existence of
solutions, uniqueness, monotonicity and regularity results
On the L^1-relaxed area of graphs of BV piecewise constant maps taking three values
No full textGiven a bounded open connected set Omega subset of R-2 with Lipschitz boundary, we consider the class of piecewise constant maps u taking three fixed values alpha , beta , gamma is an element of R-2, vertices of an equilateral triangle; for any u in this class, using a weak notion of Jacobian determinant valid for BV functions, we give a precise description of Det (del u) and show that the relaxed graph area of u is bounded from above by a quantity related to the flat norm of Det (del u) . The provided upper bound allows to show the validity of a De Giorgi conjecture regarding the relaxed area functional when one restricts to this class of piecewise constant functions
Matematica Generale. Esercizi e problemi con soluzioni e svolgimenti. Seconda edizione aggiornata.
No full textCon il moltiplicarsi dei corsi di laurea nei quali è presente l’esame propedeutico di Matematica Generale si è assistito a una proliferazione di pubblicazioni che illustrano le principali nozioni di Algebra, Analisi e Geometria. Questi testi, se da un lato rappresentano un efficace strumento di supporto alle lezioni teoriche, dall'altro non forniscono tutti gli strumenti necessari per superare effettivamente l'esame finale.
Il presente volume nasce con il tentativo di ovviare a tale inconveniente fornendo abbondante materiale su tutti i principali argomenti di un esame di Matematica Generale: insiemi, funzioni, successioni, limiti e integrali, sia nella loro veste classica che in quella applicativa. Infine, a tutti coloro che vivono la matematica come un'interessante sfida intellettuale, con la quale confrontarsi e divertirsi, è dedicata l'ultima sezione che vi lasciamo piacevolmente scoprire
Non-standard probability, coherence and conditional probability on many-valued events
No full textThe usual coherence criterion by de Finetti is extended both to many-valued events and to
conditional probability. Special attention is paid to assessments in which the betting odds
for conditioning events are zero. This case is treated bymeans of infinitesimal probabilities.
We propose a rationality criterion, called stable coherence, which is stronger than coherence
in the sense of no sure loss
A representation of Keynes’s long-term expectation in financial markets
Full text linkThis paper advances an intuitive representation of Keynes's notion of long-term expec-
tation. We introduce the epsilon-contamination approach and represent the conventional
judgment by the Steiner point of agents' common probability set. We anticipate a change
in conventional judgment by updating the Steiner point
Regularity and convergence of critical points of an Ambrosio-Tortorelli functional with linear growth and of its Γ-limit
Full text linkIn the one-dimensional setting we consider an Ambrosio-Tortorelli functional Fε(u,v) which has linear growth with respect to u′. We prove that under suitable conditions on the fidelity term, minimizers and critical points of Fε are Sobolev regular, and that the same is true for the Γ-limit F of Fε. As a corollary, we obtain that the functional Aw(u) computing the length of the generalized graph of a function of bounded variation u, under the same conditions on the fidelity term, admits a unique minimizer of class C1. This partially solves a conjecture by De Giorgi [16] in the one-dimensional case
Covers, soap films and BV functions
No full textIn this paper we review the double covers method with constrained BV functions for solving the classical Plateau’s problem. Next, we carefully analyze some interesting examples of soap films compatible with covers of degree larger than two: in particular, the case of a soap film only partially wetting a space curve, a soap film spanning a cubical frame but having a large tunnel, a soap film that retracts to its boundary, and various soap films spanning an octahedral frame
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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