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enResonance tongues in the linear Sitnikov equation [Analysis & Diff. Eqs.]
http://cmafcio.ciencias.ulisboa.pt/node/104
<span>Resonance tongues in the linear Sitnikov equation [Analysis & Diff. Eqs.]</span>
<div><time datetime="2017-12-05T13:30:00Z">Tue, 12/05/2017 - 13:30</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Wed, 11/29/2017 - 14:16</span>
<div><p><strong>Mauricio Misquero</strong> (Universidade de Granada)</p>
<p>It is studied a Hill's equation, depending on two parameters e∈[0,1) and Λ>0, that has applications to some problems in Celestial Mechanics of the Sitnikov-type. Due to the nonlinearity of the eccentricity parameter e and the coexistence problem, the stability diagram in the (e,Λ)-plane presents unusual resonance tongues emerging from points (0,(n/2)<sup>2</sup> ), n=1,2,…. The tongues bounded by curves of eigenvalues corresponding to 2π-periodic solutions collapse into a single curve of coexistence (for which there exist two independent 2π-periodic eigenfunctions), whereas the remaining tongues have no pockets and are very thin.</p>
<p>Unlike most of the literature related to resonance tongues and Sitnikov-type problems, the study of the tongues is made from a global point of view in the whole range of e∈[0,1). We apply the stability diagram of our equation to determine the regions for which the equilibrium of a Sitnikov (N+1)-body problem is stable in the sense of Lyapunov and the regions having symmetric periodic solutions with a given number of zeros.</p>
<p> </p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Wed, 29 Nov 2017 14:16:48 +0000pjmendes@fc.ul.pt104 at http://cmafcio.ciencias.ulisboa.ptOn Goodman realizability [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/102
<span>On Goodman realizability [Math. Logic]</span>
<div><time datetime="2017-11-24T15:00:00Z">Fri, 11/24/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 11/20/2017 - 15:43</span>
<div><p><strong>Emanuele Frittaion</strong> (Universidade De Lisboa)</p>
<p>Goodman's theorem (after Nicholas D. Goodman) asserts that adding the axiom of choice to intuitionistic arithmetic in all finite types yields a system which is conservative over Heyting arithmetic. This is in contrast with classical arithmetic in all finite types. In fact, the combination of choice with classical logic results in a system as strong as full second-order arithmetic.</p>
<p>There are several proofs of this result. The most direct proof was given by Goodman in his paper "Relativized realizability in intuitionistic arithmetic of all finite types", J. Symbolic Logic 43 (1978) and is based on a realizability interpretation which combines Kleene recursive realizability with Kripke semantics. I will discuss this notion of realizability and then present a modified version of Goodman realizability that shows that intuitionistic arithmetic in all finite types augmented with both choice and extensionality is also conservative over Heyting arithmetic. The only proof of this result is due to Michael Beeson.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Mon, 20 Nov 2017 15:43:29 +0000pjmendes@fc.ul.pt102 at http://cmafcio.ciencias.ulisboa.ptWhat is a substructural logic? [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/101
<span>What is a substructural logic? [Math. Logic]</span>
<div><time datetime="2017-11-17T15:00:00Z">Fri, 11/17/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 11/13/2017 - 09:59</span>
<div><p><strong>Jean-Yves Béziau</strong> (University of Brazil, Rio De Janeiro and École Normale Supérieure, Paris)</p>
<p>This talk is about the nature and definition of the notion of "substructural logic" from the point of view of universal logic. I will discuss the connections and differences between a general approach of logical systems based on sequent systems and the Polish logic methodology based on consequence operator or consequence relation, analyzing some phenomena like cut. I will study various examples of logics, in particular I will examine in which sense intuitionistic logic can be considered as a substructural logic or not.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Mon, 13 Nov 2017 09:59:25 +0000pjmendes@fc.ul.pt101 at http://cmafcio.ciencias.ulisboa.ptOn polynomials with given Hilbert function [Geometry]
http://cmafcio.ciencias.ulisboa.pt/node/100
<span>On polynomials with given Hilbert function [Geometry]</span>
<div><time datetime="2017-11-17T14:00:00Z">Fri, 11/17/2017 - 14:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Tue, 10/24/2017 - 09:25</span>
<div><p><strong>Pedro Marques</strong> (Universidade de Évora)</p>
<p>The rank of a homogeneous polynomial F of degree d is the minimal number of summands when it is written as a sum of powers of linear forms. In terms of apolarity the rank is the minimal length of a smooth finite apolar subscheme, i.e. a subscheme whose homogeneous ideal is contained in the annihilator of the form in the ring of differential operators. We define the cactus rank of F as the minimal degree of any scheme apolar to F (not necessarily smooth). The cactus variety of degree d forms is the closure of the family of degree d forms with cactus rank r.</p>
<p>Bernardi and Ranestad proved that the cactus rank of a general cubic form F in n+1 variables is at most 2n+2 and conjectured that this upper bound is attained for n≥8. In a joint work with these authors and Jelisiejew, we present a decomposition of the cactus variety of cubic forms based on sets of Gorenstein Artinian algebras defined by polynomials with given Hilbert functions, with the aim of takling its dimension and thus give an approach to computing the cactus rank of a general cubic.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Tue, 24 Oct 2017 09:25:58 +0000pjmendes@fc.ul.pt100 at http://cmafcio.ciencias.ulisboa.ptPolynomially bounded C-minimal valued fields [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/99
<span>Polynomially bounded C-minimal valued fields [Math. Logic]</span>
<div><time datetime="2017-10-27T16:30:00Z">Fri, 10/27/2017 - 16:30</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 10/23/2017 - 10:55</span>
<div><p><strong>Pablo Cubides Kovacsics</strong> (Université de Caen)</p>
<p>After introducing C-minimal expansions of valued fields, the aim of the talk is to show that every C-minimal valued field having a value group which is Q-linearly bounded is uniformly polynomially bounded. As a corollary, we obtain that any C-minimal expansion of valued fields like C_p, Falg((tQ)) and, in general, of any valued field having Q as its value group, is uniformly polynomially bounded. This is a joint work with Françoise Delon.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Mon, 23 Oct 2017 10:55:40 +0000pjmendes@fc.ul.pt99 at http://cmafcio.ciencias.ulisboa.ptAn introduction to logics with probability operators [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/98
<span>An introduction to logics with probability operators [Math. Logic]</span>
<div><time datetime="2017-10-27T15:00:00Z">Fri, 10/27/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 10/23/2017 - 10:47</span>
<div><p><strong>Zoran Ognjanovic</strong> (Mathematical Institute of the Serbian Academy of Sciences and Arts)</p>
<p>The problems of representing, and working with, uncertain knowledge are ancient problems dating, at least, from Leibnitz. In the last decades there is a growing interest in the field connected with applications to computer science and artificial intelligence. Researchers from those areas have studied uncertain reasoning using different methods. Some of the proposed formalisms for handling uncertain knowledge are based on logics with probability operators. The aim of this presentation is to provide an introduction to such formal systems. The main focus is related to mathematical techniques for infinitary probability logics used to obtain results about proof-theoretical and model-theoretical issues: axiomatizations, completeness, compactness, decidability.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Mon, 23 Oct 2017 10:47:01 +0000pjmendes@fc.ul.pt98 at http://cmafcio.ciencias.ulisboa.ptSchottky Principal Bundles over Riemann surfaces [Geometry]
http://cmafcio.ciencias.ulisboa.pt/node/97
<span>Schottky Principal Bundles over Riemann surfaces [Geometry]</span>
<div><time datetime="2017-11-03T14:00:00Z">Fri, 11/03/2017 - 14:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Thu, 10/19/2017 - 09:47</span>
<div><p><strong>Susana Ferreira</strong> (Instituto Politécnico de Leiria)</p>
<p>The Schottky uniformization theorem states that every Riemann surface X can be written as a quotient of a domain in the Riemann sphere by a Schottky group. On the other hand, the Narasimhan-Seshadri and Ramanathan well-known theorems can be viewed as uniformization results for vector and principal bundles over X.</p>
<p>In this presentation, motivated by a tentative Schottky uniformization for bundles, we introduce Schottky principal G-bundles over compact Riemann surfaces generalizing, to principal G-bundles, the notion of Schottky vector bundle given by Florentino, with G a connected reductive algebraic group.</p>
<p>We describe a correspondence between the character variety of a certain type of Schottky representations to the moduli space of flat semistable principal bundles with trivial topological type. We prove that this correspondence, under certain conditions, is locally surjective. Moreover, we show that the topological type of every Schottky principal bundle is trivial.</p>
<p>At the end we consider two special cases where the Schottky map is surjective.</p>
<p>This is joint work with A. C. Casimiro and C. Florentino.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Thu, 19 Oct 2017 09:47:05 +0000pjmendes@fc.ul.pt97 at http://cmafcio.ciencias.ulisboa.ptSign-changing solutions of the nolinear heat equation with positive initial value [Analysis & Diff. Eqs.]
http://cmafcio.ciencias.ulisboa.pt/node/96
<span>Sign-changing solutions of the nolinear heat equation with positive initial value [Analysis & Diff. Eqs.]</span>
<div><time datetime="2017-11-09T13:30:00Z">Thu, 11/09/2017 - 13:30</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 10/16/2017 - 15:47</span>
<div><p><strong>Fred Weissler</strong> (Institut Galilée - Université Paris 13)</p>
<p>We consider the nonlinear heat equation u<sub>t </sub>- Δu = |u|<sup>α</sup> u on R<sup>N</sup>, where α > 0. It is well known that the Cauchy problem is locally well-posed in a variety of spaces. For instance, for every α > 0, it is well-posed in the space C<sub>0</sub>(R<sup>N</sup>) of continuous functions that converge to 0 at infinity. It is also well-posed in L<sup>p</sup>(R<sup>N</sup> ) for p > 1, p > Nα / 2, but not well-posed in L<sup>p</sup> for 1 ≤ p < Nα / 2 if α > 2 / N. In particular, for such p there exist positive initial values u<sub>0 </sub>∈ L<sup>p</sup> for which there is no local in time positive solution. Also, if one considers the initial value u<sub>0</sub>(x) = c |x|<sup>-2 / α</sup> for all x ∈ R<sup>N</sup>∖{0}, with c > 0, it is known that if c is small, there exists a global in time (positive) solution with u<sub>0</sub> as initial value, and in fact this solution is self-similar. On the other hand, if c is large, there is no local in time positive solution, self-similar or otherwise. We prove that in the range 0 < α < 4 / (N - 2), for every c > 0, there exists infinitely many self-similar solutions to the Cauchy problem with initial value u<sub>0</sub>(x) = c |x|<sup>-2 / α</sup>. Of course, these solutions are all sign-changing if c is sufficiently large. Also, in the range 2 / N < α < 4 / (N - 2), we prove the existence of local in time sign-changing solutions for a class of nonnegative initial values u<sub>0 </sub>∈ L<sup>p</sup>, for 1 ≤ p < Nα / 2, for which no local in time positive solution exists.</p>
<p>This is joint work with T. Cazenave, F. Dickstein and I. Naumkin.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Mon, 16 Oct 2017 15:47:57 +0000pjmendes@fc.ul.pt96 at http://cmafcio.ciencias.ulisboa.ptProof mining in convex optimization and nonlinear analysis [Math. Logic]
http://cmafcio.ciencias.ulisboa.pt/node/95
<span>Proof mining in convex optimization and nonlinear analysis [Math. Logic]</span>
<div><time datetime="2017-10-20T15:00:00Z">Fri, 10/20/2017 - 15:00</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Mon, 10/16/2017 - 09:36</span>
<div><p><strong>Laurentiu Leustean</strong> (University of Bucharest and Simion Stoilow Institute of Mathematics of the Romanian Academy)</p>
<p>The research program of proof mining in mathematical logic – first suggested by G. Kreisel in the 1950s as ‘unwinding of proofs’ and developed by U. Kohlenbach in the 1990s and afterwards – is a field of study that aims to analyze, using proof-theoretic tools, the proofs of existing mathematical theorems in order to obtain their hidden quantitative content. The new information is both of quantitative nature, such as algorithms and effective bounds, as well as of qualitative nature, such as uniformities in the bounds. In this talk we give an introduction to proof mining and present some recent applications in convex optimization and nonlinear analysis.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Mon, 16 Oct 2017 09:36:52 +0000pjmendes@fc.ul.pt95 at http://cmafcio.ciencias.ulisboa.ptFractionary powers of Laplacians in Fluid Mechanics [Math. Physics]
http://cmafcio.ciencias.ulisboa.pt/node/94
<span>Fractionary powers of Laplacians in Fluid Mechanics [Math. Physics]</span>
<div><time datetime="2017-10-20T13:30:00Z">Fri, 10/20/2017 - 13:30</time></div>
<span><span lang="" about="http://cmafcio.ciencias.ulisboa.pt/user/13" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">pjmendes@fc.ul.pt</span></span>
<span>Wed, 10/11/2017 - 14:03</span>
<div><p><strong>Antonio Córdoba</strong> (Universidad Autónoma de Madrid)<br /><br />
Fractional powers of Laplacians play an important role in the evolution of fluid interphases and atmospheric fronts. There are several useful, and to some extend surprising, new pointwise inequalities satisfied by those operators which help us to understand the nature of several models in Fluid Mechanics, such as SQG, Hele-Shaw cells or Muskat´s problem.</p>
<p><a href="https://www.google.pt/maps/place/Edificio+C6+-+Faculdade+de+Ci%C3%AAncias+da+Universidade+de+Lisboa/@38.7557128,-9.1593984,17z">Room 6.2.33</a> [⤴]<img alt="Fundação para a Ciência e Tecnologia" data-entity-type="file" data-entity-uuid="2e09c74e-2138-4d43-8d43-3b0d8e16af3d" src="http://cmafcio.ciencias.ulisboa.pt/sites/cmafcio/files/inline-images/2015_FCT_H_cinza_1.jpg" class="align-right" /></p></div>
Wed, 11 Oct 2017 14:03:01 +0000pjmendes@fc.ul.pt94 at http://cmafcio.ciencias.ulisboa.pt