Lifting classes for the fixed point theory of nn-valued maps

The theory of lifting classes and the Reidemeister number of single-valued maps of a finite polyhedron $X$ is extended to $n$-valued maps by replacing liftings to universal covering spaces by liftings with codomain an orbit configuration space, a structure recently introduced by Xicot\'encatl. The liftings of an $n$-valued map $f$ split into self-maps of the universal covering space of $X$ that we call lift-factors. An equivalence relation is defined on the lift-factors of $f$ and the number of equivalence classes is the Reidemeister number of $f$. The fixed point classes of $f$ are the projections of the fixed point sets of the lift-factors and are the same as those of Schirmer. An equivalence relation is defined on the fundamental group of $X$ such that the number of equivalence classes equals the Reidemeister number. We prove that if $X$ is a manifold of dimension at least three, then algebraically the orbit configuration space approach is the same as one utilizing the universal covering space. The Jiang subgroup is extended to $n$-valued maps as a subgroup of the group of covering transformations of the orbit configuration space and used to find conditions under which the Nielsen number of an $n$-valued map equals its Reidemeister number. If an $n$-valued map splits into $n$ single-valued maps, then its $n$-valued Reidemeister number is the sum of their Reidemeister numbers.Comment: near complete rewrite from previous versio

Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schrodinger equation

The two-dimensional cubic nonlinear Schrodinger equation admits a large family of one-dimensional bounded traveling-wave solutions. All such solutions may be written in terms of an amplitude and a phase. Solutions with piecewise constant phase have been well studied previously. Some of these solutions were found to be stable with respect to one-dimensional perturbations. No such solutions are stable with respect to two-dimensional perturbations. Here we consider stability of the larger class of solutions whose phase is dependent on the spatial dimension of the one-dimensional wave form. We study the spectral stability of such nontrivial-phase solutions numerically, using Hill's method. We present evidence which suggests that all such nontrivial-phase solutions are unstable with respect to both one- and two-dimensional perturbations. Instability occurs in all cases: for both the elliptic and hyperbolic nonlinear Schrodinger equations, and in the focusing and defocusing case.Comment: Submitted: 13 pages, 3 figure

The factor structure of executive function in childhood and adolescence

Executive functioning (EF) plays a major role in many domains of human behaviour, including self-regulation, academic achievement, and even sports expertise. While a significant proportion of cross-sectional research has focused on the developmental pathways of EF, the existing literature is fractionated due to a wide range of methodologies applied to narrow age ranges, impeding comparison across a broad range of age groups. The current study used a cross-sectional design to investigate the factor structure of EF within late childhood and adolescence. A total of 2166 Flemish children and adolescents completed seven tasks of the Cambridge Brain Sciences test battery. Based on the existing literature, a Confirmatory Factor Analysis was performed, which indicated that a unitary factor model provides the best fit for the youngest age group (7–12 years). For the adolescents (12–18 years), the factor structure consists of four different components, including working memory, shifting, inhibition and planning. With regard to differences between early (12–15 years) and late (15–18 years) adolescents, working memory, inhibition and planning show higher scores for the late adolescents, while there was no difference on shifting. The current study is one of the first to administer the same seven EF tests in a considerably large sample of children and adolescents, and as such contributes to the understanding of the developmental trends in EF. Future studies, especially with longitudinal designs, are encouraged to further increase the knowledge concerning the factor structure of EF, and the development of the different EF components

Surface finish control by electrochemical polishing in stainless steel 316 pipes

Electrochemical machining (ECM) is a non-conventional machining process which is based on the localised anodic dissolution of any conductive material. One of the main applications of ECM is the polishing of materials with enhanced characteristics, such as high strength, heat-resistance or corrosion-resistance, i.e. electrochemical polishing. The present work presents an evaluation of the parameters involved in the ECM of Stainless Steel 316 (SS316) with the objective of predicting the resulting surface finish on the sample. The interest of studying ECM on SS316 resides on the fact that a repeatable surface finish is not easily achieved. ECM experimental tests on SS316 pipes of 1.5" (0.0381 m) diameter were conducted by varying machining parameters such as voltage, interelectrode gap, electrolyte inlet temperature, and electrolyte flow rate. The surface finish of the samples was then evaluated in order to find the significance of each of these parameters on the surface quality of the end product. Results showed that overvoltage, which is dependent on the interelectrode gap and the electrolyte temperature, is one of the main parameters affecting the surface finish; additionally there is a strong relationship between the resulting surface finish and the electrolyte flow. The interelectrode gap and inlet electrolyte temperature also affect the resulting surface finish but their influence was not so evident in this work. Finally, the variation of the electrolyte temperature during the process was found to have a great impact on the uniformity of the surface finish along the sample. We believe that this contribution enables the tailoring of the surface finish to specific applications while reducing manufacturing costs and duration of the ECM process

Pole dynamics for the Flierl-Petviashvili equation and zonal flow

We use a systematic method which allows us to identify a class of exact solutions of the Flierl-Petvishvili equation. The solutions are periodic and have one dimensional geometry. We examine the physical properties and find that these structures can have a significant effect on the zonal flow generation.Comment: Latex 40 pages, seven figures eps included. Effect of variation of g_3 is studied. New references adde

Relative age, biological maturation and anaerobic characteristics in elite youth soccer players

Being relatively older and having an advanced biological maturation status have been associated with increased likelihood of selection in young elite soccer players. The aims of the study were to investigate the presence of a relative age effect (RAE) and the influence of birth quarter on anthropometry, biological maturity and anaerobic parameters in 374 elite Belgian youth soccer players. The sample was divided into 3 age groups, each subdivided into 4 birth quarters (BQ). Players had their APHV estimated and height, weight, SBJ, CMJ, sprint 5 and 30 m were assessed. Overall, more players were born in BQ1 (42.3%) compared with players born in BQ4 (13.7%). Further, MANCOVA revealed no differences in all parameters between the 4 BQ's, controlled for age and APHV. These results suggest that relatively youngest players can offset the RAE if they enter puberty earlier. Furthermore, the results demonstrated possible differences between BQ1 and BQ4, suggesting that caution is necessary when estimating differences between players because of large discrepancies between statistical and practical significance. These findings also show that coaches should develop realistic expectations of the physical abilities of younger players and these expectations should be made in the context of biological characteristics rather than chronological age-based standards. © Georg Thieme Verlag KG Stuttgart. New York

Exact Floquet states of a driven condensate and their stabilities

We investigate the Gross-Pitaevskii equation for a classically chaotic system, which describes an atomic Bose-Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded in chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states could be prepared from the uniformly initial states by slow growth of the external potential.Comment: 14 pages, 3 eps figures, final version accepted for publication in J. Phys.

Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential

We present a new family of stationary solutions to the cubic nonlinear Schroedinger equation with a Jacobian elliptic function potential. In the limit of a sinusoidal potential our solutions model a dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided the ratio of the height of the variations of the condensate to its DC offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Numerical simulations suggest such stationary states are experimentally observable.Comment: 4 pages, 4 figure

Analysis of new control applications

This document reports the results of the activities performed during the first year of the CRUTIAL project, within the Work Package 1 "Identification and description of Control System Scenarios". It represents the outcome of the analysis of new control applications in the Power System and the identification of critical control system scenarios to be explored by the CRUTIAL project