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

Four-body effects on 9Be + 208Pb scattering and fusion around the Coulomb barrier

We investigate the 9Be + 208Pb elastic scattering and fusion at energies around the Coulomb barrier. The $^9$Be nucleus is described in a \alpha + \alpha + n three-body model, using the hyperspherical coordinate method. The scattering with $^{208}$Pb is then studied with the Continuum Discretized Coupled Channel (CDCC) method, where the \alpha + \alpha + n continuum is approximated by a discrete number of pseudostates. Optical potentials for the $\alpha+^{208}$Pb and $n+^{208}$Pb systems are taken from the literature. We present elastic-scattering and fusion cross sections at different energies, and investigate the convergence with respect to the truncation of the \alpha + \alpha + n continuum. A good agreement with experiment is obtained, considering that there is no parameter fitting. We show that continuum effects increase at low energies.Comment: 6 pages, 4 figures. Submitted to the proceedings of the "NUBA Conference Series -1: Nuclear Physics and Astrophysics" Adrasan-Antalya, Turkey, September 15-21, 201

Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary conditions or for the singularly perturbed Klein Gordon Maxwell system with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that stable critical points of the mean curvature of the boundary generates solutions when the perturbation parameter is sufficiently small.Comment: arXiv admin note: text overlap with arXiv:1410.884

Accounting for heterogeneous variances in multitrait evaluation of Jersey type traits

peer reviewedThe multitrait genetic evaluation system for type traits was modified to estimate adjustments for heterogeneous variance (HV) simultaneously with estimated breeding values (EBV) for final score and 14 linear traits. Each variance within herd, year, and parity was regressed toward a predicted variance, which was determined by fitting a model with fixed effects of the mean final score for herd, size of the contemporary group, appraisal month, and year-season and a random effect for herd-appraisal date. Herd-appraisal date was included as a random effect to regress the observed heterogeneity for a given herd-appraisal date toward the fixed effects. Method R was used to estimate variances for the heterogeneity model in each EBV iteration. To evaluate the effect of the adjustment, parent averages were calculated from evaluations with recent appraisals removed. The adjustment slightly improved correlations within birth year between those parent averages and EBV from current data on bulls for most traits, but did not improve correlations for final score, strength, dairy form, teat length, or foot angle. Annual trends for EBV were lower with HV adjustment than for unadjusted EBV for all traits except final score and rump angle for cows and rump width for bulls, which were essentially unchanged. Standard deviations of Mendelian sampling (evaluation minus mean of parent evaluations) declined less over time for HV-adjusted than for unadjusted evaluations. The slope at year 2000 of Mendelian-sampling standard deviations from HV-adjusted evaluations ranged from 10.0% for udder depth to 42.7% for teat length compared with the slope for unadjusted evaluations. This HV adjustment, which was implemented for USDA evaluations in May 2001 for Jerseys and in 2002 for other breeds, improves the accuracy of evaluations, particularly comparisons over time, by accounting for the change in variation

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

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

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

Existence of solutions to a higher dimensional mean-field equation on manifolds

For $m\geq 1$ we prove an existence result for the equation $$(-\Delta_g)^m u+\lambda=\lambda\frac{e^{2mu}}{\int_M e^{2mu}d\mu_g}$$ on a closed Riemannian manifold $(M,g)$ of dimension $2m$ for certain values of $\lambda$.Comment: 15 Page

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

New Gravity Map of the Western Galicia Margin:The Spanish Exclusive Economic Zone Project

Since 1995, the most intensive mapping of the seafloor off the Spanish coast has been carried out in the framework of the Spanish Exclusive Economic Zone Project (ZEEE).The main objectives of this project are to obtain improved multibeam bathymetric cartography of the areas off Spanish coastlines, and to perform a geophysical survey,well-suited with a 10-knot navigation velocity (some techniques requires lower navigation velocity). The geophysical survey includes gravity, geomagnetism, and low-penetration seismic techniques in order to infer the geological structure of the seafloor. Other oceanographic variables such as current, surface salinity, and temperature profiles, can be recorded without compromising this systematic survey effort. The ZEEE Project has carried out its survey activities for one month every year.Data acquisition is achieved aboard the Spanish R/V Hesperides. Until 1997, surveying efforts concentrated on the Balearic Sea and Valencia Gulf, both in the western Mediterranean Sea. Between 1998 and 2000, the ZEEE Project investigations were conducted offshore the Canary Archipelago. Since 2001, the third phase of the program has been focused on the West Galicia Margin in the northeastern Atlantic Ocean. Survey results on the West Galicia Margin area are of interest for two key reasons. First, there is great scientific interest in the improvement of the knowledge of this non-volcanic rifting margin, since this margin offers good conditions for the study of the processes that take place in this type of geological context,because it is sediment-starved. Second, the obtained results also have major socioeconomic repercussions because they can prove significant to defining the expansion of the Spanish shelf,beyond Spain’s Economic Exclusive Zone distance of 200 nautical miles. All of the gravity data acquired to date on this area have been stored as a database, with the aim of preparing gravity anomaly maps on a scale 1:200,000.The database and gravity anomaly charts from the ZEEE Project will provide the most coherent and complete gravity perspective available for this area. This article describes the efforts and accomplishments of the project to date