Existence of a positive solution to a right focal boundary value problem

In this paper we apply the recent extension of the Leggett-Williams Fixed Point Theorem which requires neither of the functional boundaries to be invariant to the second order right focal boundary value problem. We demonstrate a technique that can be used to deal with a singularity and provide a non-trivial example

Minimal model for aeolian sand dunes

We present a minimal model for the formation and migration of aeolian sand dunes. It combines a perturbative description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The latter are shown to provide the characteristic length scale. The model can explain the origin of important features of dunes, such as the formation of a slip face, the broken scale invariance, and the existence of a minimum dune size. It also predicts the longitudinal shape and aspect ratio of dunes and heaps, their migration velocity and shape relaxation dynamics. Although the minimal model employs non-local expressions for the wind shear stress as well as for the sand flux, it is simple enough to serve as a very efficient tool for analytical and numerical investigations and to open up the way to simulations of large scale desert topographies.Comment: 19 pages, 22 figure

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic

Young and Intermediate-age Distance Indicators

Distance measurements beyond geometrical and semi-geometrical methods, rely mainly on standard candles. As the name suggests, these objects have known luminosities by virtue of their intrinsic proprieties and play a major role in our understanding of modern cosmology. The main caveats associated with standard candles are their absolute calibration, contamination of the sample from other sources and systematic uncertainties. The absolute calibration mainly depends on their chemical composition and age. To understand the impact of these effects on the distance scale, it is essential to develop methods based on different sample of standard candles. Here we review the fundamental properties of young and intermediate-age distance indicators such as Cepheids, Mira variables and Red Clump stars and the recent developments in their application as distance indicators.Comment: Review article, 63 pages (28 figures), Accepted for publication in Space Science Reviews (Chapter 3 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age

A look at the other 90 per cent: Investigating British Sign Language vocabulary knowledge in deaf children from different language learning backgrounds

In this study we present new data on deaf children's receptive and expressive vocabulary knowledge in British Sign Language (BSL) from a sample consisting of children with deaf parents, children with hearing parents, and children with additional needs. Their performance on three BSL vocabulary tasks was compared with (previously reported findings from) a sample of deaf fluent signers. We use these data to assess the effects of some key demographic/ child variables on deaf signing children's vocabulary and discuss findings in the relation to the meaning of 'normative' data and samples for this heterogeneous population. Findings show no effect of the presence of additional disabilities on participants' scores for any of the three tasks. As expected, chronological age is the most significant factor in performance on all vocabulary tasks while the number of deaf relatives only becomes statistically significant for the form recall task. This study contributes to the field of sign language assessment by seeking to identify key variables in heterogeneity and how these variables affect signed vocabulary acquisition with the long-term objective of informing intervention

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Aboveground biomass of a "campina" ecosystem in Roraima, Northern of Brazilian Amazonia

The aboveground biomass of a "campina" ecosystem was estimated in Roraima, in the northern portion of Brazilian Amazonia. The biomass was determined from a phytosociological inventory (1 ha) and distributed between two categories: (1) grassy-woody, composed of "herbs+lichens" (Poaceae, Cyperaceae, Eriocaulaceae, Cladonia spp), Bromeliaceae, seedlings, fine and coarse litter and, (2) woody, composed of trees and bushes. The grassy-woody category was estimated by the direct method (cutting and weighing) in 10 1-m² plots, taking advantage of transects of the inventory. The category woody was estimated by the indirect method cutting 98 individuals of different species and diameters. A model was generated to express the relationship among total dry above-ground biomass (kg), base circumference (cm) and total height (m) for the individuals in this category. The equation was applied to the 3,966 ind.ha-1 observed in the inventory. The total biomass was estimated at 15.91 t.ha-1, of which 2.20 ± 0.23 t.ha-1 (13.8%) was in the grassy-woody category and 13.70 ± 7.13 t.ha-1 (86.2%) in woody category. The tree species with the highest biomass was Humiria balsamifera (Aubl.) St. Hill. (8.43 t.ha-1), followed by Pagamea guianensis Aubl. (1.14 t.ha-1). These results are important for refining the calculations of greenhouse-gas emissions from burning and decomposition of above-ground biomass in "campina" ecosystems in the Amazon region.Foi estimada a biomassa (viva + morta) acima do solo de um ecossistema de "campina" localizado em Roraima, norte da Amazônia brasileira. A biomassa foi determinada a partir de um inventário fitossociológico (1 ha amostral) e distribuída em dois estratos(1) gramíneo-lenhoso, composto de "ervas + liquens" (Poaceae, Cyperaceae, Eriocaulaceae, Cladonia spp), Bromeliaceae, plântulas, "litter" fino e grosso e, (2) arbóreo-arbustivo, composto por árvores e arbustos. O estrato gramíneo-lenhoso foi estimado pelo método direto (corte e pesagem) através de 10 quadras de 1m², aproveitando os transectos do inventário. O estrato arbóreo-arbustivo foi estimado pelo método indireto com o corte de 98 indivíduos de diferentes espécies e diâmetros. Foi gerado um modelo para expressar a relação entre a biomassa seca total (kg), a circunferência de base (cm) e a altura total (m) para os indivíduos deste estrato. A equação foi aplicada nos 3.966 indivíduos.ha-1 observados no inventário. A biomassa total foi estimada em 15,91 t.ha-1, sendo 2,20 ± 0,23 t.ha-1 (13,8%) do estrato gramíneo-lenhoso e 13,70 ± 7,13 t.ha-1 (86,2%) do arbóreo-arbustivo. A espécie arbórea de maior biomassa foi Humiria balsamifera (Aubl.) St. Hill. (8,43 t.ha-1), seguida de Pagamea guianensis Aubl. (1,14 t.ha-1). Estes resultados são importantes para refinar os cálculos de emissão de gases do efeito estufa pela queima e decomposição da biomassa acima do solo em ecossistemas de campinas na Amazônia

Hermitian K-theory and 2-regularity for totally real number fields

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. We also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory. The result is then exactly periodic of period 8. In both the orthogonal and symplectic cases, we prove the 2-primary hermitian Quillen-Lichtenbaum conjecture.Comment: To appear in Mathematische Annale

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review