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  • Strongly Mackey topologies and Radon vector measures
    Port. Math. (IF 0.517) 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)

  • On the discriminant locus of a rank $n-1$ vector bundle on $\mathbb P^{n-1}$
    Port. Math. (IF 0.517) 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

  • Metastability of the proximal point algorithm with multi-parameters
    Port. Math. (IF 0.517) 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

  • Homoclinic tangency and variation of entropy
    Port. Math. (IF 0.517) Pub Date : 2020-12-22
    Marcus Bronzi; Ali Tahzibi

    In this paper we study the e¤ect 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

  • Weak König’s lemma in herbrandized classical second-order arithmetic
    Port. Math. (IF 0.517) 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.

  • Compensated compactness and corrector stress tensor for the Einstein equations in $\mathbb T^2$ symmetry
    Port. Math. (IF 0.517) Pub Date : 2020-12-22
    Bruno Le Floch; Philippe G. LeFloch

    We consider the Einstein equations in $\mathbb T^2$ symmetry, either for vacuum spacetimes or coupled to the Euler equations for a compressible fluid, and we introduce the notion of $\mathbb T^2$ areal flows on $\mathbb T^3$ with finite total energy. By uncovering a hidden structure of the Einstein equations, we establish a compensated compactness framework which allows us to solve the global evolution

  • Endowing evolution algebras with properties of discrete structures
    Port. Math. (IF 0.517) 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.

  • On the eigenvalues of quantum graph Laplacians with large complex $\delta$ couplings
    Port. Math. (IF 0.517) Pub Date : 2020-10-14
    James B. 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 Re$\alpha \to -\infty$

  • Overdetermined constraints and rigid synchrony patterns for network equilibria
    Port. Math. (IF 0.517) 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

  • State dependent nonconvex sweeping processes in smooth Banach spaces
    Port. Math. (IF 0.517) 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

  • Constructing separable Arnold snakes of Morse polynomials
    Port. Math. (IF 0.517) Pub Date : 2020-10-14
    Miruna-Ştefana Sorea

    We give a new and constructive proof of the existence of a large class of univariate polynomials whose graphs have preassigned shapes. By definition, all the critical points of a Morse polynomial function are real and simple and all its critical values are distinct. Thus to any Morse polynomial we can associate an alternating permutation called Arnold snake, given by the relative positions of its critical

  • A generalized one phase Stefan problem as a vanishing viscosity limit
    Port. Math. (IF 0.517) Pub Date : 2020-10-14
    Kelei Wang

    We study the vanishing viscosity limit of a nonlinear di¤usion equation describing chemical reaction interface or the spatial segregation interface of competing species, where the di¤usion 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

  • The supremum-involving Hardy-type operators on Lorentz-type spaces
    Port. Math. (IF 0.517) 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

  • Convergence of a full discrete finite element method for the Korteweg–de Vries equation
    Port. Math. (IF 0.517) 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

  • Global existence for a one-dimensional non-relativistic Euler model with relaxation
    Port. Math. (IF 0.517) 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

  • Motivic volumes of fibers of tropicalization
    Port. Math. (IF 0.517) 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 consider 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

  • The Bruhat order on classes of isotopic Latin squares
    Port. Math. (IF 0.517) 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

  • On generalized Bregman nonspreading mappings and zero points of maximal monotone operator in a reflexive Banach space
    Port. Math. (IF 0.517) 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

  • Some existence results for a quasilinear problem with source term in Zygmund-space
    Port. Math. (IF 0.517) 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), \\ -\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 $L^\infty(\Omega)$, $H(x,s,\xi)$

  • A fast method for solving a block tridiagonal quasi-Toeplitz linear system
    Port. Math. (IF 0.517) 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

  • Stein–Weiss inequalities for radial local Morrey spaces
    Port. Math. (IF 0.517) 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.

  • On the Hilbert vector of the Jacobian module of a plane curve
    Port. Math. (IF 0.517) Pub Date : 2020-06-30
    Armando Cerminara; Alexandru Dimca; Giovanna Ilardi

    We identify several classes of complex projective plane 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

  • On a local systolic inequality for odd-symplectic forms
    Port. Math. (IF 0.517) 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

  • Remarks on the Bohnenblust–Hille inequalities
    Port. Math. (IF 0.517) 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.

  • The impact of a lower order term in a Dirichlet problem with a singular nonlinearity
    Port. Math. (IF 0.517) 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 $$\begin{cases} -\div(a(x)|\nabla u|^{p-2} \nabla u) + u|u|^{r-1} = \dfrac{f(x)}{u^{\theta}} & \mbox{in $\Omega$,} \\ u > 0 & \mbox{in $\Omega$,} \\ u = 0 & \mbox{on $\partial\Omega$} \\ \end{cases}$$ proving that the lower order term $ u|u|^{r-1}$ has some regularizing effects on the solutions.

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