Blow-up solutions for linear perturbations of the Yamabe equation

For a smooth, compact Riemannian manifold (M,g) of dimension N \geg 3, we are interested in the critical equation $$\Delta_g u+(N-2/4(N-1) S_g+\epsilon h)u=u^{N+2/N-2} in M, u>0 in M,$$ where \Delta_g is the Laplace--Beltrami operator, S_g is the Scalar curvature of (M,g), $h\in C^{0,\alpha}(M)$, and $\epsilon$ is a small parameter

Numerical analysis of the influence of dynamic properties of a vertically stratified basin upon the phytoplankton concentration in the sea

The paper presents the assumptions of a one-dimensional mathematical model of turbulent diffusion of marine suspensions, as well as the results of numerical investigations on the influence of dynamic conditions in a defined basin on the chlorophyll-a concentration. The influence of the duration and disappearance time of a disturbance, and the thickness of the layer disturbing uniform media of varying degrees of turbulence on the vertical distribution of the chlorophyll-a concentration is analysed

Quantization for an elliptic equation of order 2m with critical exponential non-linearity

On a smoothly bounded domain $\Omega\subset\R{2m}$ we consider a sequence of positive solutions $u_k\stackrel{w}{\rightharpoondown} 0$ in $H^m(\Omega)$ to the equation $(-\Delta)^m u_k=\lambda_k u_k e^{mu_k^2}$ subject to Dirichlet boundary conditions, where $0<\lambda_k\to 0$. Assuming that $$\Lambda:=\lim_{k\to\infty}\int_\Omega u_k(-\Delta)^m u_k dx<\infty,$$ we prove that $\Lambda$ is an integer multiple of \Lambda_1:=(2m-1)!\vol(S^{2m}), the total $Q$-curvature of the standard $2m$-dimensional sphere.Comment: 33 page

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

Sharp constants in weighted trace inequalities on Riemannian manifolds

We establish some sharp weighted trace inequalities W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M) on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page

Use of partial least squares regression to impute SNP genotypes in Italian Cattle breeds

Background The objective of the present study was to test the ability of the partial least squares regression technique to impute genotypes from low density single nucleotide polymorphisms (SNP) panels i.e. 3K or 7K to a high density panel with 50K SNP. No pedigree information was used. Methods Data consisted of 2093 Holstein, 749 Brown Swiss and 479 Simmental bulls genotyped with the Illumina 50K Beadchip. First, a single-breed approach was applied by using only data from Holstein animals. Then, to enlarge the training population, data from the three breeds were combined and a multi-breed analysis was performed. Accuracies of genotypes imputed using the partial least squares regression method were compared with those obtained by using the Beagle software. The impact of genotype imputation on breeding value prediction was evaluated for milk yield, fat content and protein content. Results In the single-breed approach, the accuracy of imputation using partial least squares regression was around 90 and 94% for the 3K and 7K platforms, respectively; corresponding accuracies obtained with Beagle were around 85% and 90%. Moreover, computing time required by the partial least squares regression method was on average around 10 times lower than computing time required by Beagle. Using the partial least squares regression method in the multi-breed resulted in lower imputation accuracies than using single-breed data. The impact of the SNP-genotype imputation on the accuracy of direct genomic breeding values was small. The correlation between estimates of genetic merit obtained by using imputed versus actual genotypes was around 0.96 for the 7K chip. Conclusions Results of the present work suggested that the partial least squares regression imputation method could be useful to impute SNP genotypes when pedigree information is not available

A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page

Study of the eastern margin of the Antarctic Peninsula based on gravimetric and magnetic data

La península Antártica, constituida fundamentalmente por rocas ígneas y metamórficas, forma parte del cinturón orogénico andino de edad mesozoico-cenozoica, y fue separada de Sudamérica tras la apertura del paso de Drake desde el Oligoceno. La península está formada por procesos relacionados con la subducción de la corteza oceánica del Pacífico en su margen occidental, que aún hoy es activa al NE de la zona de fractura Hero, dando lugar a la formación de la cuenca de trasarco de Bransfield. El margen oriental es el menos conocido por su inaccesibilidad, es de tipo pasivo y se caracteriza por una plataforma continental extensa con un tránsito gradual hacia el dominio oceánico del mar de Weddell. La modelización de 2 perfiles magnéticos y gravimétricos indica [1] que la estructura cortical presenta un adelgazamiento progresivo de la corteza hacia el SE, [2] una gran variación del espesor de sedimentos y [3] la existencia de una zona de diques basálticos asociada al borde occidental del mar de WeddellThe Antarctic Peninsula, mainly composed of igneous and metamorphic rocks, was separated from South America during the opening of the Drake Passage from the Oligocene, as part of the Mesozoic-Cenozoic Andean orogenic belt. It was formed by processes related to the subduction of Pacific Ocean floor at its western margin, still active northwards of the Hero fracture zone, where the Bransfield backarc basin was developed. The eastern margin is less known due to its inaccessibility and is described as a continental passive margin gradually in transition to the Weddell Sea ocean floor. The modelling of 2 magnetic and gravimetric profiles shows [1] that the eastern margin of the Antarctic Peninsula depicts a progressively thinning of the upper crust towards the SE, [2] a remarkable sediment thickness changes, and [3] basaltic dikes related to the western edge of the Weddell Se

Cold-water corals research in the lab and in the field: (1) growth rates of four CWC species maintained in aquaria, (2) new research areas: the Galicia Bank and the Avilés canyon (Atlantic and Cantabrian Sea), a scientific and methodological approach

Growth rates of 4 Cold-water Coral (CWC) species (Madrepora occulata, Lophe/ia pertusa, Desmophyllum cristagalli and Dendrophyllia cornigera) from the Mediterranean Sea have been measured under the same and controlled laboratory conditions over a nine months period. Results showed that M. occulata grew faster than the other three species, which presented similar growth rates. These results are discussed and also compared with the growth of tropical coral species maintained in aquaria, but in different light and temperature conditions, which corresponded to the usual culture conditions of these corals. It appeared that the zooxanthellate tropical coral Galaxea fascicularis exhibited similar growth rates than the CWC M. oculata. Further we present new research areas on the Atlantic and Cantabrian continental margin, the Galicia Bank and the Aviles canyon, which are part of the zones studied in the Spanish LIFE project INDEMARES, as well as possible targets as Marine Protected Areas (MPAs) for the NATURA 2000 network. Both areas are studied considering an ecosystem approach, aboarding an integrated study of the physical scenario (hydrography, geomorphology), all ecosystem compartments (fish, endo-, epi-, and suprabenthic and benthopelagic fauna) and the trophic relationships between them. All this information, together with the study of the impact of the fisheries working in the areas, will be integrated in a trophodynamic mass-balance model and will be used to identify vulnerable ecosystems (VE) (as the CWC habitats are) and essential fish habitats (EFH). This methodological approach offers a holistic view of these deep-sea ecosystems and can be used to design more effective and successful management strategies for MPA