- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 15:02:33
5
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PM&vol=70&iss=1&update_since=2024-03-29
Portugaliae Mathematica
Port. Math.
PM
0032-5155
1662-2758
General
10.4171/PM
http://www.ems-ph.org/doi/10.4171/PM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2008)
70
2013
1
Outerplanarity without accumulation in the cylinder and the Möbius Band
Luis
Boza
Universidad de Sevilla, SEVILLA, SPAIN
Eugenio
Fedriani
Universidad Pablo de Olavide, SEVILLA, SPAIN
Juan
Núñez
Universidad de Sevilla, SEVILLA, SPAIN
Graph embeddings, infinite graphs, tubular surfaces
In this paper we explicitly characterize the outer-embeddings without vertex accumulation points in the open cylinder and in the Möbius strip. In the first case, the list of forbidden minors consists of 11 graphs. In the second, we provide the list of 92 forbidden minors as well as the list of 182 forbidden subgraphs.
Combinatorics
General
1
10
10.4171/PM/1922
http://www.ems-ph.org/doi/10.4171/PM/1922
Another approach on an elliptic equation of Kirchhoff type
Anderson Luis
Albuquerque de Araujo
Universidade Federal de Viçosa, VIÇOSA-MG, BRAZIL
Leray–Schauder’s fixed point theorem, nonlocal problems, Kirchhoff equation, subcritical growth
This paper is concerned with the existence of solutions to the class of nonlocal boundary value problems of the type \[ -M\left(\int_{\Omega}|\nabla u|^2\right)\Delta u = f(x,u), \text { in } \Omega, \ u=0, \text{ on } \partial \Omega, \] where $\Omega$ is a smooth bounded domain of $\mathbb{R}^N$ and $M$ is a positive continuous function. By assuming that $f(x, u)$ is a Carathéodory function which growths at most $|u|^{\frac{N}{N-2}}$, $N \geq 3$, and under a suitable growth condition on $M$, one proves an existence result by applying the Leray–Schauder fixed point theorem.
Partial differential equations
General
11
22
10.4171/PM/1923
http://www.ems-ph.org/doi/10.4171/PM/1923
Convergence of a finite difference method for the KdV and modified KdV equations with $L^2$ data
Paulo
Amorim
Universidade de Lisboa, LISBOA, PORTUGAL
Mário
Figueira
Universidade de Lisboa, LISBOA, PORTUGAL
Korteweg–de Vries equation, KdV equation, finite difference scheme
We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in $L^2$), without size restrictions. Our approach uses a fourth order (in space) stabilization term and a special conservative discretization of the nonlinear term. Convergence follows from a smoothing effect and energy estimates. We illustrate our results with numerical experiments, including a numerical investigation of an open problem related to uniqueness posed by Y. Tsutsumi.
Numerical analysis
Partial differential equations
General
23
50
10.4171/PM/1924
http://www.ems-ph.org/doi/10.4171/PM/1924
When every principal ideal is flat
Fatima
Cheniour
Université Sidi Mohamed Ben Abdellah, FES, MOROCCO
Najib
Mahdou
Université Sidi Mohamed Ben Abdellah, FES, MOROCCO
PF-ring, direct product, localization, Dedekind domain, homomorphic image, amalgamated duplication of a ring along an ideal, pullback
This paper deals with the well-known notion of PF-rings, that is, rings in which principal ideals are flat. We give a new characterization of PF-rings. Also we provide a necessary and sufficient condition for $R\bowtie I$ (resp. $R/I$ when $R$ is a Dedekind domain or $I$ is a primary ideal) to be a PF-ring. The article includes a brief discussion of the scope and precision of our results.
Commutative rings and algebras
General
51
58
10.4171/PM/1925
http://www.ems-ph.org/doi/10.4171/PM/1925
Tropical Severi varieties
Jihyeon Jessie
Yang
McMaster University, HAMILTON, ONTARIO, CANADA
Severi varieties, tropicalization, subdivisions of polygons
We study the tropicalizations of Severi varieties, which we call tropical Severi varieties. In this paper, we give a partial answer to the following question: “Describe the tropical Severi varieties explicitly.” We obtain a description of tropical Severi varieties in terms of regular subdivisions of polygons. As an intermediate step, we construct explicit parameter spaces of curves. These parameter spaces are much simpler objects than the corresponding Severi variety and they are closely related to flat degenerations of the Severi variety, which in turn describes the tropical Severi variety. As an application, we understand G. Mikhalkin’s correspondence theorem for the degrees of Severi varieties in terms of tropical intersection theory. In particular, this provides a proof of the independence of point-configurations in the enumeration of tropical nodal curves.
General
59
91
10.4171/PM/1926
http://www.ems-ph.org/doi/10.4171/PM/1926