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Algebraic cycles and Fano threefolds of genus 8 Port. Math. (IF 0.8) Pub Date : 2022-01-17 Robert Laterveer
We show that prime Fano threefolds $Y$ of genus 8 have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, a certain tautological subring of the Chow ring of powers of $Y$ injects into cohomology.
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Denumerable cellular families in $\mathbf{ZF}$ Port. Math. (IF 0.8) Pub Date : 2022-01-17 Kyriakos Keremedis, Eliza Wajch
A denumerable cellular family of a topological space $\mathbf{X}$ is a countably infinite collection of pairwise disjoint non-empty open sets of $\mathbf{X}$. $\mathbf{IQDI}$ is the sentence: For every infinite set $X$, the set of all finite subsets of $X$ has a countably infinite subset. Among other results, the following are proved in $\mathbf{ZF}$: (i) $\mathbf{IQDI}$ iff every infinite 0-dimensional
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Note on Lisbon integrals and their associated $D$-modules Port. Math. (IF 0.8) Pub Date : 2022-01-17 Daniel Barlet
The aim of this article is to specify the links between the three kinds of Lisbon integrals, trace functions and trace forms with the corresponding $D$-modules.
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Finite-element approximation of a phase field model for tumour growth Port. Math. (IF 0.8) Pub Date : 2022-01-17 Joe Eyles, Robert Nürnberg, Vanessa Styles
We consider a fully practical finite-element approximation of a diffuse interface model for tumour growth that takes the form of a degenerate parabolic system. In addition to showing stability bounds for the approximation, we prove convergence, and hence existence of a solution to this system in two space dimensions. Several numerical experiments demonstrate the practicality and robustness of the proposed
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A note on a bilevel problem for parameter learning for inverse problems with the wave equation Port. Math. (IF 0.8) Pub Date : 2022-01-17 Wiebke Günther, Axel Kröner
In this paper we consider a bilevel problem for determining the optimal regularization parameter in an inverse problem with the linear wave equation transferring results from Holler, Kunisch, and Barnard (2018), where a general function space setting and applications to (bilinear) elliptic problems have been addressed. We analyze the well-posedness and derive the optimality conditions for the bilevel
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Well-posedness and long time behavior for a general class of Moore–Gibson–Thompson equations with a memory Port. Math. (IF 0.8) Pub Date : 2022-01-17 Serge Nicaise, Hizia Bounadja
We consider the well-posedness and the long time behavior of the Moore– Gibson–Thompson equation with memory in the critical case. We first find general sufficient conditions that guarantee a (optimal) polynomial decay of the system. Then by comparing the behavior of the resolvent of the Moore–Gibson–Thompson system with the one of the resolvent of the wave equation with a frictional interior damping
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Sparse versions of the Cayley–Bacharach theorem Port. Math. (IF 0.8) Pub Date : 2021-08-18 Laura Felicia Matusevich, Bruce Reznick
We give combinatorial generalizations of the Cayley–Bacharach theorem and induced map.
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The set of numerical semigroups of a given multiplicity and Frobenius number Port. Math. (IF 0.8) Pub Date : 2021-08-18 Manuel B. Branco, Ignacio Ojeda, José Carlos Rosales
We study the structure of the family of numerical semigroups with fixed multiplicity and Frobenius number. We give an algorithmic method to compute all the semigroups in this family. As an application we compute the set of all numerical semigroups with given multiplicity and genus.
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On Gaussian curvatures and singularities of Gauss maps of cuspidal edges Port. Math. (IF 0.8) Pub Date : 2021-08-18 Keisuke Teramoto
We show a relation between sign of Gaussian curvature of a cuspidal edge and geometric invariants via singularities of Gauss maps. Moreover, we define and characterize positivity/negativity of cusps of Gauss maps by geometric invariants, and show a relation between the signs of cusps and the Gaussian curvature.
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Analysis of a bulk-surface thermistor model for large-area organic LEDs Port. Math. (IF 0.8) Pub Date : 2021-08-18 Annegret Glitzky, Matthias Liero, Grigor Nika
The existence of a weak solution for an effective system of partial differential equations describing the electrothermal behavior of large-area organic light-emitting diodes (OLEDs) is proved. The effective system consists of the heat equation in the threedimensional bulk glass substrate and two semilinear equations for the current flow through the electrodes coupled to algebraic equations for the
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On a free boundary model for three-dimensional MEMS with a hinged top plate: Stationary case Port. Math. (IF 0.8) Pub Date : 2021-08-18 Katerina Nik
A stationary free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at different voltages. The model couples a nonlocal fourth-order equation for the deformation of the top plate to a Laplace equation for the electrostatic potential in the
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The Talbot effect as the fundamental solution to the free Schrödinger equation Port. Math. (IF 0.8) Pub Date : 2021-08-18 Daniel Eceizabarrena
The Talbot effect is usually modeled using the Helmholtz equation, but its main experimental features are captured by the solution to the free Schrödinger equation with the Dirac comb as initial datum. This simplified description is a consequence of the paraxial approximation in geometric optics. However, it is a heuristic approximation that is not mathematically well justified, so K. I. Oskolkov raised
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Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip Port. Math. (IF 0.8) Pub Date : 2021-06-02 Pierre Bérard, Bernard Helffer, Rola Kiwan
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions. In previous works, many examples have been analyzed corresponding to squares, rectangles, disks, triangles, tori, .... A natural toy model for further
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Stability conditions for reversible and partially integrable systems Port. Math. (IF 0.8) Pub Date : 2021-06-02 Claudio A. Buzzi, Luci Any F. Roberto, Marco A. Teixeira
The purpose of this paper is to provide results like Peixotos Theorem inside a class $\mathfrak{X}$ of 3-dimensional reversible systems. We deal with reversible systems associated to an involution $\varphi_1$ such that $\operatorname{Dim}\operatorname{Fix}(\varphi_1)$ is equal to one. We further assume the existence of a first integral for any $X\in\mathfrak{X}$ that leaves invariant any sphere centered
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The cost of approximate controllability of heat equation with general dynamical boundary conditions Port. Math. (IF 0.8) Pub Date : 2021-06-02 Idriss Boutaayamou, Salah-Eddine Chorfi, Lahcen Maniar, Omar Oukdach
We consider the heat equation with dynamic boundary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and some optimization techniques, we obtain explicit bounds of the minimal norm control. We consider the linear and the semilinear cases.
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On the asymptotic behavior of high order moments for a family of Schrödinger equations Port. Math. (IF 0.8) Pub Date : 2021-06-02 Nikolay Tzvetkov, Nicola Visciglia
We study upper bounds and the asymptotic behavior of high order moments for solutions to a family of linear and nonlinear Schrödinger equations.
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Strongly Mackey topologies and Radon vector measures Port. Math. (IF 0.8) Pub Date : 2020-12-22 Marian Nowak
Let $X$ be a topological Hausdorff space and $\mathcal B o$ be the $\sigma$-algebra of Borel sets in $X$. Let $B(\mathcal B o)$ be the space of all bounded $\mathcal B o$-measurable scalar functions on $X$, equipped with the Mackey topology $\tau(B(\mathcal B o),M(X))$, where $M(X)$ denotes the Banach space of all scalar Radon measures on $X$. It is proved that $(B(\mathcal B o),\tau(B(\mathcal B o)
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On the discriminant locus of a rank $n-1$ vector bundle on $\mathbb P^{n-1}$ Port. Math. (IF 0.8) Pub Date : 2020-12-22 Hirotachi Abo
In this paper, we show that if a vector bundle of rank $n-1$ on projective $(n-1)$-space is very ample and if its top Chern class is greater than one, then the discriminant locus of the vector bundle, the locus of singular sections of the vector bundle, is an irreducible hypersurface and that the degree of the hypersurface can be expressed as a function of invariants of the vector bundle. As applications
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Weak König’s lemma in herbrandized classical second-order arithmetic Port. Math. (IF 0.8) Pub Date : 2020-12-22 Fernando Ferreira
This is a short paper describing how a herbrandized functional interpretation can give a new treatment of some issues in classical second-order arithmetic. It is perhaps worthy of note that, in our interpretation, second-order variables are interpreted by finite sets of natural numbers.
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Endowing evolution algebras with properties of discrete structures Port. Math. (IF 0.8) Pub Date : 2020-12-22 Rafael González-López, Juan Núñez
In this paper, we introduce new results on evolution algebras obtained by following a relatively new line of research on these objects. It consists of the use of certain properties of graphs to facilitate the study of evolution algebras and reciprocally.
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Metastability of the proximal point algorithm with multi-parameters Port. Math. (IF 0.8) Pub Date : 2020-12-22 Bruno Dinis, Pedro Pinto
In this article we use techniques of proof mining to analyse a result, due to Yonghong Yao and Muhammad Aslam Noor, concerning the strong convergence of a generalized proximal point algorithm which involves multiple parameters. Yao and Noor's result ensures the strong convergence of the algorithm to the nearest projection point onto the set of zeros of the operator. Our quantitative analysis, guided
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Homoclinic tangency and variation of entropy Port. Math. (IF 0.8) Pub Date : 2020-12-22 Marcus Bronzi, Ali Tahzibi
In this paper we study the effect of a homoclinic tangency in the variation of the topological entropy. We prove that a diffeomorphism with a homoclinic tangency associated to a basic hyperbolic set with maximal entropy is a point of entropy variation in the $C^{\infty}$-topology. We also prove results about variation of entropy in other topologies and when the tangency does not correspond to a basic
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Compensated compactness and corrector stress tensor for the Einstein equations in $\mathbb T^2$ symmetry Port. Math. (IF 0.8) Pub Date : 2020-12-22 Bruno Le Floch, Philippe LeFloch
We consider the Einstein equations in T2 symmetry, either for vacuum spacetimes or coupled to the Euler equations for a compressible fluid, and we introduce the notion of T2 areal flows on T3 with finite total energy. By uncovering a hidden structure of the Einstein equations, we establish a compensated compactness framework and solve the global evolution problem for vacuum spacetimes as well as for
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Overdetermined constraints and rigid synchrony patterns for network equilibria Port. Math. (IF 0.8) Pub Date : 2020-10-14 Ian Stewart
In network dynamics, synchrony between nodes defines an equivalence relation, usually represented as a colouring. If the colouring is balanced, meaning that nodes of the same colour have colour-isomorphic inputs, it determines a subspace that is flow-invariant for any ODE compatible with the network structure. Therefore any state lying in such a subspace has the synchrony pattern determined by that
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State dependent nonconvex sweeping processes in smooth Banach spaces Port. Math. (IF 0.8) Pub Date : 2020-10-14 Djalel Bounekhel, Messaoud Bounkhel, Mostafa Bachar
In the setting of 2-uniformly smooth and $q$-uniformly convex Banach spaces, we prove the existence of solutions of the following multivalued differential equation: $$-\frac{d}{dt} J(u(t)) \in N^C(C(t,u(t));u(t)) \mbox{ a.e. in } [0,T]. \:\:\: \mathrm{(SDNSP)}$$ This inclusion is called State Dependent Nonconvex Sweeping Process (SDNSP). Here $N^C(C(t,u(t)); u(t))$ stands for the Clarke normal cone
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On the eigenvalues of quantum graph Laplacians with large complex $\delta$ couplings Port. Math. (IF 0.8) Pub Date : 2020-10-14 James Kennedy, Robin Lang
We study the location of the spectrum of the Laplacian on compact metric graphs with complex Robin-type vertex conditions, also known as $\delta$ conditions, on some or all of the graph vertices. We classify the eigenvalue asymptotics as the complex Robin parameter(s) diverge to $\infty$ in $\mathbb{C}$: for each vertex $v$ with a Robin parameter $\alpha \in \mathbb{C}$ for which $\mathrm{\Re}\,\alpha
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Constructing separable Arnold snakes of Morse polynomials Port. Math. (IF 0.8) Pub Date : 2020-10-14 Miruna-Ştefana Sorea
We give a new and constructive proof of the existence of a special class of univariate polynomials whose graphs have preassigned shapes. By definition, all the critical points of a Morse polynomial function are real and distinct and all its critical values are distinct. Thus we can associate to it an alternating permutation: the so-called Arnold snake, given by the relative positions of its critical
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A generalized one phase Stefan problem as a vanishing viscosity limit Port. Math. (IF 0.8) Pub Date : 2020-10-14 Kelei Wang
We study the vanishing viscosity limit of a nonlinear diffusion equation describing chemical reaction interface or the spatial segregation interface of competing species, where the diffusion rate for the negative part of the solution converges to zero. As in the standard one phase Stefan problem, we prove that the positive part of the solution converges uniformly to the solution of a generalized one
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The supremum-involving Hardy-type operators on Lorentz-type spaces Port. Math. (IF 0.8) Pub Date : 2020-09-09 Qinxiu Sun, Xiao Yu, Hongliang Li
Given measurable functions $u, \sigma$ on an interval $(0,b)$ and a kernel function $k(x,y)$ on $(0,b)^2$ satisfying Oinarov condition, the supremum-involving Hardy-type operators $$Rf(x)=\sup_{x\leq\tau < b}u(\tau)\int_0^\tau k(\tau,y)\sigma (y)f(y)dy, x > 0$$ in Orlicz-Lorentz spaces are investigated. We obtain sufficient conditions of boundedness of $R: \Lambda_{u_0}^{G_0}(w_0)\\ \rightarrow \L
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Convergence of a full discrete finite element method for the Korteweg–de Vries equation Port. Math. (IF 0.8) Pub Date : 2020-09-09 Pengzhan Huang
In this paper, we put emphasis on discussing a full discrete finite element scheme for the Korteweg–de Vries equation, where nonlinear term is dealt with a semi-implicit scheme and temporal term is discreted by the Euler scheme. Theoretical analysis is based on error splitting technique, i.e., error function is split as temporal error function plus spatial error function, and then unconditionally optimal
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Global existence for a one-dimensional non-relativistic Euler model with relaxation Port. Math. (IF 0.8) Pub Date : 2020-09-09 Shuyang Xiang, Yangyang Cao
We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the domain of definition, allowing the existence of shock waves. Our proof relies on a well-balanced random choice method called Glimm method which preserves the fluid equilibria and we construct a sequence of approximate
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The Bruhat order on classes of isotopic Latin squares Port. Math. (IF 0.8) Pub Date : 2020-09-09 Rosário Fernandes, Henrique F. da Cruz, Domingos Salomão
In a previous paper, the authors introduced and studied the Bruhat order in the class of Latin squares of order n. In this paper, we investigate the restriction of the Bruhat order in a class of isotopic Latin squares. We present equivalent conditions for two Latin squares be related by the Bruhat order when one of them is obtained from the other by interchanging rows or columns or symbols. The cover
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Motivic volumes of fibers of tropicalization Port. Math. (IF 0.8) Pub Date : 2020-09-09 Jeremy Usatine
Let $T$ be an algebraic torus over an algebraically closed field, let $X$ be a smooth closed subvariety of a $T$-toric variety such that $U = X \cap T$ is not empty, and let $\mathscr{L}(X)$ be the arc scheme of $X$. We define a tropicalization map on $\mathscr{L}(X) \setminus \mathscr{L}(X \setminus U)$, the set of arcs of $X$ that do not factor through $X \setminus U$. We show that each fiber of
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On generalized Bregman nonspreading mappings and zero points of maximal monotone operator in a reflexive Banach space Port. Math. (IF 0.8) Pub Date : 2020-07-15 Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomo
The purpose of this paper is to investigate the existence and approximation of fixed points of generalized Bregman nonspreading mapping which are also the zero points of maximal monotone operator in a real reflexive Banach space. Without assuming the ‘AKTT’ condition, we prove a strong convergence theorem for approximating a common element in the set of fixed points of system of generalized Bregman
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A fast method for solving a block tridiagonal quasi-Toeplitz linear system Port. Math. (IF 0.8) Pub Date : 2020-07-15 Skander Belhaj, Fahd Hcini, Yulin Zhang
This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [10], we propose a more general algorithm for such systems. The algorithm is based on a block decomposition for block tridiagonal quasi-Toeplitz matrices and the Sherman–Morrison–Woodbury inversion formula. We also compare the proposed approach to the standard block $LU$ decomposition method and
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Stein–Weiss inequalities for radial local Morrey spaces Port. Math. (IF 0.8) Pub Date : 2020-07-15 Kwok-Pun Ho
This paper establishes a generalization of the celebrated Stein–Weiss inequalities for the fractional integral operators on radial functions in local Morrey spaces. We find that some conditions can be relaxed for the Stein–Weiss inequalities on radial local Morrey spaces.
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Some existence results for a quasilinear problem with source term in Zygmund-space Port. Math. (IF 0.8) Pub Date : 2020-07-15 Boussad Hamour
In this paper we study the existence of solution to the problem \begin{equation*} \left\{\begin{array}{l} u\in H_{0}^{1}(\Omega), \\[4pt] -\textrm{div}\,(A(x)Du)=H(x,u,Du)+f(x)+a_{0}(x)\, u\quad \text{in} \quad\mathcal{D}'(\Omega), \end{array} \right. \end{equation*} where $\Omega$ is an open bounded set of $\mathbb{R}^{2}$, $A(x)$ a coercive matrix with coefficients in $L^\infty(\Omega)$, $H(x,s,\xi)$
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On a local systolic inequality for odd-symplectic forms Port. Math. (IF 0.8) Pub Date : 2020-07-15 Gabriele Benedetti, Jungsoo Kang
The aim of this paper is to formulate a local systolic inequality for odd-symplectic forms (also known as Hamiltonian structures) and to establish it in some basic cases. Let $\Omega$ be an odd-symplectic form on an oriented closed manifold $\Sigma$ of odd dimension. We say that $\Omega$ is Zoll if the trajectories of the flow given by $\Omega$ are the orbits of a free $S^1$-action. After defining
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Remarks on the Bohnenblust–Hille inequalities Port. Math. (IF 0.8) Pub Date : 2020-07-15 Djair Paulino, Daniel Pellegrino, Joedson Santos
We revisit the Bohnenblust--Hille multilinear and polynomial inequalities and prove some new properties. Our main result is a multilinear version of a recent result on polynomials whose monomials have a uniformly bounded number of variables.
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The impact of a lower order term in a Dirichlet problem with a singular nonlinearity Port. Math. (IF 0.8) Pub Date : 2020-07-15 Lucio Boccardo, Gisella Croce
In this paper we study the existence and regularity of solutions to the following Dirichlet problem −div(a(x)|∇u| p−2 ∇u) + u|u| r−1 = f (x) u θ in Ω, u > 0 in Ω, u = 0 on ∂Ω proving that the lower order term u|u| r−1 has some regularizing effects on the solutions. Mathematics Subject Classification (2010). 35J66, 35J75
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On the Hilbert vector of the Jacobian module of a plane curve Port. Math. (IF 0.8) Pub Date : 2020-06-30 Armando Cerminara, Alexandru Dimca, Giovanna Ilardi
We identify several classes of curves $C:f=0$, for which the Hilbert vector of the Jacobian module $N(f)$ can be completely determined, namely the 3-syzygy curves, the maximal Tjurina curves and the nodal curves, having only rational irreducible components. A result due to Hartshorne, on the cohomology of some rank 2 vector bundles on $\mathbb{P}^2$, is used to get a sharp lower bound for the initial
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Varieties of regular semigroups with uniquely defined inversion Port. Math. (IF 0.8) Pub Date : 2020-02-13 João Araújo,Michael Kinyon,Yves Robert
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Joint differential invariants of binary and ternary forms Port. Math. (IF 0.8) Pub Date : 2020-02-13 Gülden Gün Polat, Peter Olver
We use moving frames to construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated
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A noninequality for the fractional gradient Port. Math. (IF 0.8) Pub Date : 2020-02-13 Daniel Spector
In this paper we give a streamlined proof of an inequality recently obtained by the author: For every $\alpha \in (0,1)$ there exists a constant $C=C(\alpha,d)>0$ such that \begin{align*} \|u\|_{L^{d/(d-\alpha),1}(\mathbb{R}^d)} \leq C \| D^\alpha u\|_{L^1(\mathbb{R}^d;\mathbb{R}^d)} \end{align*} for all $u \in L^q(\mathbb{R}^d)$ for some $1 \leq q
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On the Hadamard product of degenerate subvarieties Port. Math. (IF 0.8) Pub Date : 2020-02-13 Gabriele Calussi, Enrico Carlini, Giuliana Fatabbi, Anna Lorenzini
We consider generic degenerate subvarieties $X_i\subset\mathbb{P}^n$. We determine an integer $N$, depending on the varieties, and for $n\geq N$ we compute dimension and degree formulas for the Hadamard product of the varieties $X_i$. Moreover, if the varieties $X_i$ are smooth, their Hadamard product is smooth too. For $n
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Large deviations for dynamical systems with stretched exponential decay of correlations Port. Math. (IF 0.8) Pub Date : 2020-02-13 Romain Aimino, Jorge Milhazes Freitas
We obtain large deviations estimates for systems with stretched exponential decay of correlations, which improve the ones obtained in \cite{AFLV11}. As a consequence we obtain better large deviations estimates for Viana maps and get large deviations estimates for a class of intermittent maps with stretched exponential loss of memory.
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$C^1$-generic sectional Axiom A flows have only trivial symmetries Port. Math. (IF 0.8) Pub Date : 2019-09-30 Wescley Bonomo,Paulo Varandas
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Courant-sharp Robin eigenvalues for the square and other planar domains Port. Math. (IF 0.8) Pub Date : 2019-09-30 Katie Gittins, Bernard Helffer
This paper is devoted to the determination of the cases where there is equality in Courant's nodal domain theorem in the case of a Robin boundary condition. For the square, we partially extend the results that were obtained by Pleijel, B\'erard--Helffer, Helffer--Persson--Sundqvist for the Dirichlet and Neumann problems. After proving some general results that hold for any value of the Robin parameter
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The universal bound property for a class of second order ODEs Port. Math. (IF 0.8) Pub Date : 2019-09-30 Mama Abdelli, Alain Haraux
We consider the scalar second order ODE u + |u | $\alpha$ u + |u| $\beta$ u = 0, where $\alpha$, $\beta$ are two positive numbers and the non-linear semi-group S(t) generated on IR 2 by the system in (u, u). We prove that S(t)IR 2 is bounded for all t > 0 whenever 0 0, u (t) 2 + |u(t)| $\beta$+2 $\le$ C max{t -- 2 $\alpha$ , t -- ($\alpha$+1)($\beta$+2) $\beta$--$\alpha$ }.
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Invariant measures for the two-dimensional averaged-Euler equations Port. Math. (IF 0.8) Pub Date : 2019-09-30 Alexandra Symeonides
We define a Gaussian invariant measure for the two-dimensional averaged-Euler equation and show the existence of its solution with initial conditions on the support of the measure. An invariant surface measure on the level sets of the energy is also constructed, as well as the corresponding flow. Poincare recurrence theorem is used to show that the flow returns infinitely many times in a neighbourhood
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Slowly non-dissipative equations with oscillating growth Port. Math. (IF 0.8) Pub Date : 2019-06-06 Phillipo Lappicy,Juliana Pimentel
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An extremal property of lattice polygons Port. Math. (IF 0.8) Pub Date : 2019-06-06 Nikolai Bliznyakov,Stanislav Kondratyev
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Three-dimensional registration and shape reconstruction from depth data without matching: A PDE approach Port. Math. (IF 0.8) Pub Date : 2019-06-06 Diogo Gomes,João Costeira,João Saúde
The widespread availability of depth sensors like the Kinect camera makes it easy to gather three-dimensional (3D) data. However, accurately and efficiently merging large datasets collected from different views is still a core problem in computer vision. This question is particularly challenging if the relative positions of the views are not known, if there are few or no overlapping points, or if there
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Fourier approximation methods for first-order nonlocal mean-field games Port. Math. (IF 0.8) Pub Date : 2019-06-06 Levon Nurbekyan, João Saúde
In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a convex optimization problem over a finite-dimensional subspace of continuous curves. Furthermore, we perform a time-discretization for this optimization problem
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Rigidity for perimeter inequalities under symmetrization: State of the art and open problems Port. Math. (IF 0.8) Pub Date : 2019-06-06 Filippo Cagnetti
We review some classical results in symmetrization theory, some recent progress in understanding rigidity, and indicate some open problems.
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Nitsche’s method for unilateral contact problems Port. Math. (IF 0.8) Pub Date : 2019-06-06 Tom Gustafsson, Rolf Stenberg, Juha Videman
We derive optimal a priori and a posteriori error estimates for Nitsche's method applied to unilateral contact problems. Our analysis is based on the interpretation of Nitsche's method as a stabilised finite element method for the mixed Lagrange multiplier formulation of the contact problem wherein the Lagrange multiplier has been eliminated elementwise. To simplify the presentation, we focus on the
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Homogenization of obstacle problems in Orlicz–Sobolev spaces Port. Math. (IF 0.8) Pub Date : 2019-06-06 Diego Marcon, José Francisco Rodrigues, Rafayel Teymurazyan
We study the homogenization of obstacle problems in Orlicz-Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the $p(\cdot)$-Laplacian type. Our approach is based on the Lewy-Stampacchia inequalities, which then give access to a compactness argument. We also prove the convergence of the coincidence sets under non-degeneracy conditions.
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Accuracy of a coupled mixed and Galerkin finite element approximation for poroelasticity Port. Math. (IF 0.8) Pub Date : 2019-06-06 Silvia Barbeiro
In this paper, we consider a coupling mixed finite element and continuous Galerkin finite element formulation for a coupled flow and geomechanics model. We use the lowest order Raviart-Thomas space for the spatial approximation of the flow variables and continuous piecewise linear finite elements for the deformation variable while we consider the backward Euler method for the time discretization. This
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On flows generated by vector fields with compact support Port. Math. (IF 0.8) Pub Date : 2018-12-12 Olivier Kneuss,Wladimir Neves
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Towards a pseudoequational proof theory Port. Math. (IF 0.8) Pub Date : 2018-12-12 Jorge Almeida, Ondřej Klima
A new scheme for proving pseudoidentities from a given set {\Sigma} of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when {\Sigma} defines a locally finite variety, a pseudovariety of groups, more generally, of completely simple semigroups, or of commutative monoids. Many further examples when the scheme is complete are given when {\Sigma} defines