- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 06:54:58
10
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PM&vol=65&iss=2&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)
65
2008
2
Weak theorems on differential inequalities for two-dimensional functional differential systems
Jiri
Sremr
Czech Academy of Sciences, BRNO, CZECH REPUBLIC
System of functional differential equations, Cauchy problem, theorems on differential inequalities
New theorems on differential inequalities for two-dimensional systems of linear functional differential equations are established. Differential systems with argument deviations are considered in more detail, in which case further results are obtained.
Ordinary differential equations
General
157
189
10.4171/PM/1804
http://www.ems-ph.org/doi/10.4171/PM/1804
On the Cauchy problem in Sobolev spaces for nonlinear Schrödinger equations with potential
Rémi
Carles
Mathématiques, CC 051, MONTPELLIER CEDEX 5, FRANCE
Nonlinear Schrödinger equation, external potential, Cauchy problem, well-posedness, ill-posedness, semiclassical analysis
We consider the Cauchy problem for nonlinear Schrödinger equations in the presence of a smooth, possibly unbounded, potential. No assumption is made on the sign of the potential. If the potential grows at most linearly at infinity, we construct solutions in Sobolev spaces (without weight), locally in time. Under some natural assumptions, we prove that the H
Partial differential equations
General
191
209
10.4171/PM/1805
http://www.ems-ph.org/doi/10.4171/PM/1805
τ(p;q)-summing mappings and the domination theorem
Ximena
Mujica
Universidade Federal do Paraná, CURITIBA, PR, BRAZIL
Summing, domination
We extend the concept of τ-summing operators presented by Pietsch in his monograph on Operator Ideals to multilinear mappings and polynomials. We also present a domination theorem for τ(p)-summing mappings and polynomials, showing their relation with p-semi-integral mappings and polynomials.
Functional analysis
General
211
226
10.4171/PM/1806
http://www.ems-ph.org/doi/10.4171/PM/1806
Every strict sum of cubes in F4[t] is a strict sum of 6 cubes
Luis
Gallardo
Université de Brest, BREST CEDEX 3, FRANCE
Waring's problem, polynomials, forms, cubes, cubic forms, characteristic two, finite fields
It is easy to see that an element P(t) ∈ F4[ t ] is a strict sum of cubes if and only if P(t) ∈ M(4) where M(4) = { P(t) ∈ F4[ t ] | P(r) ∈ {0,1} for all r ∈ F4 and such that either 3 does not divide deg(P(t)), or 3 does divide deg(P(t)) and P(t) is monic }. We say that P(t) is a “strict” sum of cubes A1(t)3 +···+ Ag(t)3 if deg(Ai3) < deg(P) + 3 for each i, and we define g(3,F4[ t ]) as the least g such that every element of M(4) is a strict sum of g cubes. The main result is that g(3,F4[ t ]) ≤ 6. This improves an earlier result of the author that g(3,F4[ t ]) ≤ 9.
Number theory
General
227
236
10.4171/PM/1807
http://www.ems-ph.org/doi/10.4171/PM/1807
Steiner's invariants and minimal connections
Stephen
Ducret
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
Marc
Troyanov
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
Metric geometry, Steiner invariant
The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the one-dimensional Hausdorff measure.
Geometry
General
237
242
10.4171/PM/1808
http://www.ems-ph.org/doi/10.4171/PM/1808
Bivariate classical and q-series transformations
Wenchang
Chu
Università del Salento, LECCE, ITALY
Cangzhi
Jia
Northeastern University, SHENYANG, CHINA
Inverse series relations, q-series, classical hypergeometric series
By means of bivariate inverse series relations, we review several bivariate classical hypergeometric series transformation formulae and establish their q-analogues.
Special functions
General
243
256
10.4171/PM/1809
http://www.ems-ph.org/doi/10.4171/PM/1809
An exact multiplicity result for a class of symmetric problems
Philip
Korman
University of Cincinnati, CINCINNATI, UNITED STATES
Exact multiplicity of solutions
We consider positive solutions of a class of semilinear problems u'' + λa(x)f(u) = 0, −1 < x < 1, u(−1) = u(1) = 0, with even and positive a(x), depending on a positive parameter λ. In case f(u) is convex, an exact multiplicity result was given in P. Korman, Y. Li and T. Ouyang [6]; see also P. Korman [4] for the details. It was observed by P. Korman and J. Shi [7] that convexity requirement can be relaxed for large u (see also [5]). We show that convexity requirement can also be relaxed for small u.
Ordinary differential equations
General
257
260
10.4171/PM/1810
http://www.ems-ph.org/doi/10.4171/PM/1810
On radicals and polynomial rings
Sodnomkhorloo
Tumurbat
National University of Mongolia, ULAAN BAATAR, MONGOLIA
Deolinda Isabel
Mendes
Universidade da Beira Interior, COVILHÃ, PORTUGAL
Abish
Mekei
National University of Mongolia, ULAAN BAATAR, MONGOLIA
Kurosh–Amitsur radical, essential left ideal, upper radical, polynomial rings
For any class ℳ of rings, it is shown that the class ℰℓ(ℳ) of all rings each non-zero homomorphic image of which contains either a non-zero left ideal in ℳ or a proper essential left ideal is a radical. Some characterizations and properties of these radicals are presented. It is also shown that, for radicals γ under certain constraints, one can obtain a strictly decreasing chain of radicals γ = γ(1) ⊃ γ(2) ⊃ ··· ⊃ γ(n) ⊃ ··· where, for each positive integer n, γ(n) is the radical consisting of all rings A such that A[ x1, … ,xn ] is in γ, thus giving a negative answer to a question posed by Gardner. Moreover, classes ℳ of rings are constructed such that there exist several such radicals γ in the interval [ ℰℓ(0),ℰℓ(ℳ) ] .
Associative rings and algebras
General
261
273
10.4171/PM/1811
http://www.ems-ph.org/doi/10.4171/PM/1811
Wedderburn quasialgebras
Helena
Albuquerque
Universidade de Coimbra, COIMBRA, PORTUGAL
Alberto
Elduque
Universidad de Zaragoza, ZARAGOZA, SPAIN
José María
Pérez-Izquierdo
Universidad de la Rioja, LOGRONO - LA RIOJA, SPAIN
Nonassociative algebras, group graded algebras, Wedderburn algebras
The Wedderburn–Artin Theorem for G-graded quasialgebras is proved. This provides new examples of quasialgebras.
Nonassociative rings and algebras
Associative rings and algebras
General
275
283
10.4171/PM/1812
http://www.ems-ph.org/doi/10.4171/PM/1812
The Fourier–Borel transform between spaces of entire functions of a given type and order
Vinícius
Vieira Fávaro
Universidade Federal de Uberlândia, UBERLÂNDIA, MG, BRAZIL
Fourier–Borel transform, quasi-nuclear polynomial, (s;m(r,q ))-summing polynomial
In this article we study the Fourier–Borel transform between the dual of ExpkÑ,(s;( r,q)),A(E), the space of entire functions on E of (s;(r,q))-quasi-nuclear order k and (s;(r,q))-quasi-nuclear type strictly less than A, and the space Expk'(s',m(r';q')),0,(θ(k)A)−1(E') of entire functions on E' of (s',m(r';q'))-summing order k and (s',m(r';q'))-summing type less than or equal to (θ(k)A)−1. This mapping identifies algebraically and topologically these two spaces. On the dual space it is considered the strong topology. This generalizes results of Matos [4] and Martineau [3].
Functional analysis
General
285
309
10.4171/PM/1813
http://www.ems-ph.org/doi/10.4171/PM/1813