COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

Presentations for monoids of finite partial isometries

In this paper we give presentations for the monoid DPn of all partial isometries on {1,..., n} and for its submonoid ODPn of all order-preserving partial isometries.

Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).

Classical solutions of the leading-logarithm approximation with non-trivial topology

Exact solutions of the classical equations corresponding to the leading-logarithm approximation are obtained. They are classified by an (integer) topological number.

Trivial OnLine

Juego online basado en el conocido juego de preguntas y respuestas, que puede ser instalado en un servidor y atender peticiónes de multitud de jugadores. Incluye un chat y un visualizador de fotografías.

Tal om läsnings-werket, hållne wid examina anniversaria, i Björneborgs trivial-schola af Johan Kraftman rect. scholae

Arkit: A-B8 C4.

Tal om läsnings-werket, hållne wid examina anniversaria, i Björneborgs trivial-schola af Johan Kraftman rect. scholae

Arkit: A-B8 C4.

El gran joc : una barreja del joc de l'Oca, el Trivial i l??educaci?? f??sica.'El gran juego : una mezcla del juego de la Oca, el Trivial y la educaci??n f??sica??

Experiencia llevada a cabo en el CEIP Pompeu Fabra de Lloret de Mar. La experiencia parte de la uni??n de juegos de mesa con la actividad f??sica que han de realizar los alumnos de primaria. Se incluyen las normas del juego con la metodolog??a y material necesarios para que otros docentes puedan poner esta actividad en pr??ctica.

Nombres. Isometries. Plantejament i calcul d'expressions aritmétiques i algebràiques. Us de recursos per afrontar situacions problemàtiques. 'Números. Isometrías. Planteamiento y cálculo de expresiones aritméticas y algebráicas. Uso de recursos para afrontar situaciones problemáticas'.

Fecha finalización tomada del código del documento

Hispanoamérica en un trivial.

Título del encuentro: 'Hispanoamérica en el aula de ELE', organizado por el Instituto Cervantes de Nápoles

Integrable maps with non-trivial topology: application to divertor configurations

We explore a method for constructing two-dimensional area-preserving, integrable maps associated with Hamiltonian systems, with a given set of fixed points and given invariant curves. The method is used to find an integrable Poincare map for the field lines in a large aspect ratio tokamak with a poloidal single-null divertor. The divertor field is a superposition of a magnetohydrodynamic equilibrium with an arbitrarily chosen safety factor profile, with a wire carrying an electric current to create an X-point. This integrable map is perturbed by an impulsive perturbation that describes non-axisymmetric magnetic resonances at the plasma edge. The non-integrable perturbed map is applied to study the structure of the open field lines in the scrape-off layer, reproducing the main transport features obtained by integrating numerically the magnetic field line equations, such as the connection lengths and magnetic footprints on the divertor plate.

Parameterization technique for the continuation power flow using the trivial and tangent predictor

This paper presents efficient geometric parameterization techniques using the tangent and the trivial predictors for the continuation power flow, developed from observation of the trajectories of the load flow solution. The parameterization technique eliminates the Jacobian matrix singularity of load flow, and therefore all the consequent problems of ill-conditioning, by the addition of the line equations which pass through the points in the plane determined by the variables loading factor and the real power generated by the slack bus, two parameters with clear physical meaning. This paper also provides an automatic step size control around the maximum loading point. Thus, the resulting method enables not only the calculation of the maximum loading point, but also the complete tracing of P-V curves of electric power systems. The technique combines robustness with ease of understanding. The results to the IEEE 300-bus system and of large real systems show the effectiveness of the proposed method. © 2012 IEEE.

Chaotic planar piecewise smooth vector fields with non-trivial minimal sets

In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. Some relations between minimality and orientable minimality are also investigated and the existence of new kinds of non-trivial minimal sets in chaotic systems is observed. The approach is geometrical and involves the ordinary techniques of non-smooth systems.

A countably compact free Abelian group of size continuum that admits a non-trivial convergent sequence

We show that it is consistent with ZFC that the free Abelian group of cardinality c admits a topological group topology that makes it countably compact with a non-trivial convergent sequence. (C) 2011 Elsevier B.V. All rights reserved.