Sistemas L de rayos y sumabilidad

The work under consideration fits into the following general circle of problems: Given a Banach space B which possesses a distinguished basis (ei) i∈N and a bounded linear operator A:B→C, to what extent does the sequence (Aei) constitute some sort of basis (ai) on C, where ai=Aei? It turns out to be more suitable to work with systems of rays (ri)i∈N (that is, one-dimensional subspaces) such that ai∈ri. Compact operators A are excluded for what turn out to be obvious reasons, and the operators A are required to be injective. This leads at various points to a consideration of cases: the range R(A) of A is a closed subspace; and R(A) is dense in C but not equal to C. The paper is devoted principally to the case B=C=l2 with the distinguished basis (ei) being a complete orthonormal set (c.o.s.). There are also results applying to lp, p≠2. A sequence (ai) is said to be doubly bounded (d.b.) provided that 00 for some particular c.o.s. (e′i) contained in a previously fixed linear subspace dense in l 2. Henceforth A represents a noncompact injective operator with R(A)≠R(A) ¯ ¯ ¯ . It is proved that there exists a c.o.s. (e′i) such that the L-system (Ae′i) is d.b., complete in R(A) ¯ ¯ ¯ and heterogonal in blocks. Furthermore, it is shown that for a noncompact A, the following are equivalent: (i) N(A)=0. (ii) There exists a c.o.s. (ei) such that (Aei) is a strong M base which is d.b. in R(A) ¯ ¯ ¯ . Definition: A sequence (ai) is minimal if ai is not in the closed linear subspace spanned by the aj, j≠i. An M-base is a complete minimal sequence (ai) such that ⋂ ∞ i=1 [a i ,a i+1 ,⋯]=0 where [a i ,a i+1 ⋯] represents the closed linear subspace spanned by ai, a i+1,⋯. A further theorem states that given a sequence of rays (ri) the following are equivalent: (I) (ri) is an SLR; (II) for (ai∈ri∖{0}) one has ∑ ∞ i=1||ai||22 and (xn) is a d.b. sequence in lp then the following are equivalent: (1) (xn) is weakly p-summable; (2) ∑ ∞ 1 ξ n x n converges unconditionally if and only if ∑ ∞ 1 |ξ n | p′ <∞, where 1/p+1/p′ =1. For p<2, there are no d.b. weakly summable sequences in lp

A genetic algorithm for robust berth allocation and quay crane assignment

Scheduling problems usually obtain the optimal solutions assuming that the environment is deterministic. However, actually the environment is dynamic and uncertain. Thus, the initial data could change and the initial schedule obtained might be unfeasible. To overcome this issue, a proactive approach is presented for scheduling problems without any previous knowledge about the incidences that can occur. In this paper, we consider the berth allocation problem and the quay crane assignment problem as a representative example of scheduling problems where a typical objective is to minimize the service time. The robustness is introduced within this problem by means of buffer times that should be maximized to absorb possible incidences or breakdowns. Therefore, this problem becomes a multi-objective optimization problem with two opposite objectives: minimizing the total service time and maximizing the robustness or buffer time

Mechanical Bonds and Topological Effects in Radical Dimer Stabilization

While mechanical bonding stabilizes tetrathiafulvalene (TTF) radical dimers, the question arises: what role does topology play in catenanes containing TTF units? Here, we report how topology, together with mechanical bonding, in isomeric [3]- and doubly interlocked [2]catenanes controls the formation of TTF radical dimers within their structural frameworks, including a ring-in-ring complex (formed between an organoplatinum square and a {2+2} macrocyclic polyether containing two 1,5-dioxynaphthalene (DNP) and two TTF units) that is topologically isomeric with the doubly interlocked [2]catenane. The separate TTF units in the two {1+1} macrocycles (each containing also one DNP unit) of the isomeric [3]catenane exhibit slightly different redox properties compared with those in the {2+2} macrocycle present in the [2]catenane, while comparison with its topological isomer reveals substantially different redox behavior. Although the stabilities of the mixed-valence (TTF2)^(•+) dimers are similar in the two catenanes, the radical cationic (TTF^(•+))_2 dimer in the [2]catenane occurs only fleetingly compared with its prominent existence in the [3]catenane, while both dimers are absent altogether in the ring-in-ring complex. The electrochemical behavior of these three radically configurable isomers demonstrates that a fundamental relationship exists between topology and redox properties

Pla funcional del Programa d’incorporació de fisioterapeutes a l’atenció primària i comunitària: programa d’incorporació de fisioterapeutes per a la promoció del funcionament i la prevenció de la discapacitat a l’atenció primària i comunitària

Fisioterapeutes; Atenció primària; IncorporacióFisioterapeutas; Atención primaria; IncorporaciónPhysiotherapists; Primary care; IncorporationEl present pla funcional és una eina de suport per a l’acollida i la incorporació dels nous fisioterapeutes1 d’atenció primària i comunitària (FisioAPiC) als equips d’atenció primària (EAP) d’arreu de Catalunya. Aquest és un document dinàmic que requerirà les aportacions dels professionals dels EAP que han incorporat aquest nou rol per tal de fer-lo evolucionar i enriquir-lo en les versions següents

La interdisciplinariedad y el itinerario curricular elegido por el estudiante, ejes fundamentales para desarrollar competencias curriculares en Química

Póster presentado en: V Jornadas de Innovación Docente de la UBU, Burgos, 21-22 de octubre de 2010, organizadas por el Instituto de Formación e Innovación Educativa-IFIE de la Universidad de Burgo

Sequence-selective assembly of tweezer-molecules on linear templates enables frameshift-reading of sequence information

Monomer-sequence information in synthetic copolyimides can be recognised by tweezer-type molecules binding to adjacent triplet-sequences on the polymer chains. In the present paper different tweezer-molecules are found to have different sequence-selectivities, as demonstrated in solution by 1H NMR spectroscopy and in the solid state by single crystal X-ray analyses of tweezer-complexes with linear and macrocyclic oligo-imides. This work provides clear-cut confirmation of polyimide chain-folding and adjacent-tweezer-binding. It also reveals a new and entirely unexpected mechanism for sequence-recognition which, by analogy with a related process in biomolecular information processing, may be termed "frameshift-reading". The ability of one particular tweezer-molecule to detect, with exceptionally high sensitivity, long-range sequence-information in chain-folding aromatic copolyimides, is readily explained by this novel process

Geometric aspects of Banach spaces: essays in honour of Antonio Plans

This volume concentrates on some important and contemporary themes in Banach space theory

Compatible locally convex topologies for normed spaces: cardinality aspects

DOI: 10.1017/S000497271700009