Robustness of exponential dichotomy in a class of generalised almost periodic linear differential equations in infinite dimensional Banach spaces

In this paper we study the robustness of the exponential dichotomy in nonautonomous linear ordinary differential equations under integrally small perturbations in infinite dimensional Banach spaces. Some applications are ob- tained to the case of rapidly oscillating perturbations, with arbitrarily small periods, showing that even in this case the stability is robust. These results extend to infinite dimensions some results given in Coppel [2]. Based in Ro- drigues [6] and in Kloeden & Rodrigues [5,7] we use the class of functions that we call Generalized Almost Periodic Functions that extend the usual class of almost periodic functions and are suitable to model these oscillating per- turbations. We also present an infinite dimensional example of the previous results

Propriétés physiques et petrographiques de quelques varietes de 'Pierre Bateig'

Bateig stone is an allochemical calcareous rock (mainly biosparite - biomicrite) worked in Novelda, named Novelda stone too (Alicante province, Spain) that belongs to a transgressive unit of Middle - Late Miocene age. This stone is a highly workable material that often was used in monumental Spanish architecture. Using criterium publising by the M.I.T., Bateig stone may be classified as a Medium to Low Limestone. Data from Mercury Porosimeter has been used to stimate a DDS (Durability Dimensional Stimation). The DDS equation is supported on the calculus of the pressure of salt crystallization in porous mediums. The DDS values obtained, for different varieties of Bateig stone let us establish that the microporosity, size pores less than 0,1 μm, is the main factor responsible for durability of materials.La "Pierre Bateig" est une roche carbonatee a allochemes (biosparite-biomicrite) extraite en Novelda, elle est appellee aussi "Pierre de Novelda" (Province de Alicante, Espagne); elle appartient a une unite transgresive du Miocene Moyen- Superieur. Cette roche est tres facile a travailler et souvent a ete utilisee dans la architecture monumentale espagnole. En utilisant le criterium publie par le M.I.T. la "Pierre Bateig" peut etre classifiee comme "Moyen a Low Limestone". Les donnees du Porosimetre de Mercure ont ete utilisees a la fin d'etablir une DDS (Durability Dimensional Stimation). L'equation de la DDS est basee dans le calcule de la pression de cristallisation des sels dans un moyen poreux. Les valeurs obtenues pour les differentes varietes de la Pierre Bateig permettent d'etablir que la microporosite, pores plus petits de 0, 1 μm, est le principal facteur responsable de la durabilite des materiaux.Depto. de Mineralogía y PetrologíaFac. de Ciencias GeológicasTRUEpu

The configuration of the seismic zone and the downgoing slab in southern Peru

Using data from temporary networks of portable seismographs in southern Peru, we located 888 shallow and intermediate depth events near a proposed discontinuity in the seismic zone there. These events reveal a prominent contortion, instead of a discontinuity, that trends approximately N80°E, parallel to the direction of relative plate motion. North of about 15°S, the seismic zone beneath Peru is nearly horizontal, but south of about 15.5°S, it dips at about 25°. Volcanoes lie above the more steeply dipping zone where earthquakes occur between 120 and 140 km, and the volcanic line in southern Peru stops abruptly at the contortion

A blind hierarchical coherent search for gravitational-wave signals from coalescing compact binaries in a network of interferometric detectors

We describe a hierarchical data analysis pipeline for coherently searching for gravitational wave (GW) signals from non-spinning compact binary coalescences (CBCs) in the data of multiple earth-based detectors. It assumes no prior information on the sky position of the source or the time of occurrence of its transient signals and, hence, is termed "blind". The pipeline computes the coherent network search statistic that is optimal in stationary, Gaussian noise, and allows for the computation of a suite of alternative statistics and signal-based discriminators that can improve its performance in real data. Unlike the coincident multi-detector search statistics employed so far, the coherent statistics are different in the sense that they check for the consistency of the signal amplitudes and phases in the different detectors with their different orientations and with the signal arrival times in them. The first stage of the hierarchical pipeline constructs coincidences of triggers from the multiple interferometers, by requiring their proximity in time and component masses. The second stage follows up on these coincident triggers by computing the coherent statistics. The performance of the hierarchical coherent pipeline on Gaussian data is shown to be better than the pipeline with just the first (coincidence) stage.Comment: 12 pages, 3 figures, accepted for publication in Classical and Quantum Gravit

Muon-spin rotation and magnetization studies of chemical and hydrostatic pressure effects in EuFe_{2}(As_{1-x}P_{x})_{2}

The magnetic phase diagram of EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ was investigated by means of magnetization and muon-spin rotation studies as a function of chemical (isovalent substitution of As by P) and hydrostatic pressure. The magnetic phase diagrams of the magnetic ordering of the Eu and Fe spins with respect to P content and hydrostatic pressure are determined and discussed. The present investigations reveal that the magnetic coupling between the Eu and the Fe sublattices strongly depends on chemical and hydrostatic pressure. It is found that chemical and hydrostatic pressure have a similar effect on the Eu and Fe magnetic order.Comment: 11 pages, 10 figure

Adaptive number knowledge and its relation to arithmetic and pre-algebra knowledge

Traditionally measured skills with arithmetic are not related to later algebra success at levels that would be expected given the close conceptual relation between arithmetic and algebra. However, adaptivity with arithmetic may be one aspect of arithmetic competences that can account for additional variation in algebra attainment. With this in mind, the present study aims to present evidence for the existence and relevance of a newly acknowledged component of adaptivity with arithmetic, namely, adaptive number knowledge. In particular, we aim to examine whether there are substantial individual differences in adaptive number knowledge and to what extent these differences are related to arithmetic and pre-algebra skills and knowledge. Adaptive number knowledge is defined as the well-connected knowledge of numerical characteristics and relations. A large sample of 1065 Finnish late primary school students completed measures of adaptive number knowledge, arithmetic conceptual knowledge, and arithmetic fluency. Three months later they completed a measure of pre-algebra skills. Substantial individual differences in adaptive number knowledge were identified using latent profile analysis. The identified profiles were related to concurrent arithmetic skills and knowledge. As well, adaptive number knowledge was found to predict later pre-algebra skills, even after taking into account arithmetic conceptual knowledge and arithmetic fluency. These results suggest that adaptive number knowledge is a relevant component of mathematical development, and may help account for disparities in algebra development.</p