Existence and concentration of ground state solutions for a critical nonlocal Schr\"odinger equation in R2\R^2

We study the following singularly perturbed nonlocal Schr\"{o}dinger equation -\vr^2\Delta u +V(x)u =\vr^{\mu-2}\Big[\frac{1}{|x|^{\mu}}\ast F(u)\Big]f(u) \quad \mbox{in} \quad \R^2, where $V(x)$ is a continuous real function on $\R^2$, $F(s)$ is the primitive of $f(s)$, $0<\mu<2$ and \vr is a positive parameter. Assuming that the nonlinearity $f(s)$ has critical exponential growth in the sense of Trudinger-Moser, we establish the existence and concentration of solutions by variational methods.Comment: 3

Jet-induced gauge field instabilities in the quark-gluon plasma: A kinetic theory approach

We discuss the properties of the collective modes of a system composed by a thermalized quark-gluon plasma traversed by a relativistic jet of partons. The transport equations obeyed by the components of the plasma and of the jet are studied in the Vlasov approximation. Assuming that the partons in the jet can be described with a tsunami-like distribution function we derive the expressions of the dispersion law of the collective modes. Then the behavior of the unstable gauge modes of the system is analyzed for various values of the velocity of the jet, of the momentum of the collective modes and of the angle between these two quantities. We find that the most unstable modes are those with momentum orthogonal to the velocity of the jet and that these instabilities appear when the velocity of the jet is higher than a threshold value, which depends on the plasma and jet frequencies. The results obtained within the Vlasov approximation are compared with the corresponding results obtained using a chromohydrodynamical approach.The effect we discuss here suggests a possible collective mechanism for the description of the jet quenching phenomena in heavy ion collisions.Comment: 13 pages, 6 figure

Fat residue and use-wear found on Acheulian biface and scraper associated with butchered elephant remains at the site of Revadim, Israel

The archaeological record indicates that elephants must have played a significant role in early human diet and culture during Palaeolithic times in the Old World. However, the nature of interactions between early humans and elephants is still under discussion. Elephant remains are found in Palaeolithic sites, both open-air and cave sites, in Europe, Asia, the Levant, and Africa. In some cases elephant and mammoth remains indicate evidence for butchering and marrow extraction performed by humans. Revadim Quarry (Israel) is a Late Acheulian site where elephant remains were found in association with characteristic Lower Palaeolithic flint tools. In this paper we present results regarding the use of Palaeolithic tools in processing animal carcasses and rare identification of fat residue preserved on Lower Palaeolithic tools. Our results shed new light on the use of Palaeolithic stone tools and provide, for the first time, direct evidence (residue) of animal exploitation through the use of an Acheulian biface and a scraper. The association of an elephant rib bearing cut marks with these tools may reinforce the view suggesting the use of Palaeolithic stone tools in the consumption of large game

Elliptic equations with compactly supported solutions

For any p in (1,2) and arbitrary f in L^p(R^2) with compact support, it is proved that there exists a pair (L, u), with L second order uniformly elliptic operator and u in W^{2,p}_0(R^2) such that L u = f a.e. in R^2

Travel of studies: cities of João Pessoa, Maceio, Natal and Recife: a look on the urban space and brazilian architectural production

Ponencia presentada a Session 8: Dimensiones psicosociales de la arquitectura y el urbanismo / Psycological dimensions of architecture and planningThis article aims to present the methodology and the final results of the elective course “Travel of Studies” which belongs to the new pedagogical project from the Architecture and Urbanism course at the University Federal of Pernambuco. It was offered for the first time in 2013.The discipline was organized to occur in four long weekends through visits of four capitals of the Northeast of Brazil: Recife, João Pessoa, Natal and Maceió. The purpose was to allow the students to apprehend the cities through four axis: intervention in historical center (axis 1), production of urban space (axis 2), production of coastline space (axis 3) and contemporary architecture (axis 4). After the four visits were complete, we prepared a poster with the comparison of the cities based on the identification of the similarities and differences of each axis we have studied

A formula for polynomials with Hermitian matrix argument

AbstractWe construct and study orthogonal bases of generalized polynomials on the space of Hermitian matrices. They are obtained by the Gram–Schmidt orthogonalization process from the Schur polynomials. A Berezin–Karpelevich type formula is given for these multivariate polynomials. The normalization of the orthogonal polynomials of Hermitian matrix argument and expansions in such polynomials are investigated

Absolute Density Measures Estimation Functions with Very High Resolution Satellite Images

Assessment and monitoring of forest structure is frequently done with absolute density measures with field forest inventory data and expansion methods. The development of basal area and the number of trees estimation functions with data derived from very high spatial resolution satellite images enable their short-term and cost-effective evaluation, allowing also the estimation for the area not requiring extrapolation methods. The functions of basal area and the number of trees per hectare are based on crown cover obtained with very high spatial resolution satellite images for two evergreen oaks and umbrella pine. The three tree species are especially important in the agroforestry systems of the Mediterranean region. The linear functions fitted for pure stands of the three species and mixed stands of cork and holm oak and of cork oak and umbrella pine showed a better performance for basal area than for the number of trees per hectare. The inclusion of dummy variables for species composition improved the accuracy of the functions