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

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

A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, in the form of the mountain pass lemma, to the analysis of the Hamiltonian constraint equation, which has been previously studied by other methods.Comment: 15 page

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

Interactions of Catalytic Enzymes with n-Type Polymers for High-Performance Metabolite Sensors

The tight regulation of the glucose concentration in the body is crucial for balanced physiological function. We developed an electrochemical transistor comprising an n-type conjugated polymer film in contact with a catalytic enzyme for sensitive and selective glucose detection in bodily fluids. Despite the promise of these sensors, the property of the polymer that led to such high performance has remained unknown, with charge transport being the only characteristic under focus. Here, we studied the impact of the polymer chemical structure on film surface properties and enzyme adsorption behavior using a combination of physiochemical characterization methods and correlated our findings with the resulting sensor performance. We developed five n-type polymers bearing the same backbone with side chains differing in polarity and charge. We found that the nature of the side chains modulated the film surface properties, dictating the extent of interactions between the enzyme and the polymer film. Quartz crystal microbalance with dissipation monitoring studies showed that hydrophobic surfaces retained more enzymes in a densely packed arrangement, while hydrophilic surfaces captured fewer enzymes in a flattened conformation. X-ray photoelectron spectroscopy analysis of the surfaces revealed strong interactions of the enzyme with the glycolated side chains of the polymers, which improved for linear side chains compared to those for branched ones. We probed the alterations in the enzyme structure upon adsorption using circular dichroism, which suggested protein denaturation on hydrophobic surfaces. Our study concludes that a negatively charged, smooth, and hydrophilic film surface provides the best environment for enzyme adsorption with desired mass and conformation, maximizing the sensor performance. This knowledge will guide synthetic work aiming to establish close interactions between proteins and electronic materials, which is crucial for developing high-performance enzymatic metabolite biosensors and biocatalytic charge-conversion devices

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

Precision of genetic parameters and breeding values estimated in marker assisted BLUP genetic evaluation

In practical implementations of marker-assisted selection economic and logistic restrictions frequently lead to incomplete genotypic data for the animals of interest. This may result in bias and larger standard errors of the estimated parameters and, as a consequence, reduce the benefits of applying marker-assisted selection. Our study examines the impact of the following factors: phenotypic information, depth of pedigree, and missing genotypes in the application of marker-assisted selection. Stochastic simulations were conducted to generate a typical dairy cattle population. Genetic parameters and breeding values were estimated using a two-step approach. First, pre-corrected phenotypes (daughter yield deviations (DYD) for bulls, yield deviations (YD) for cows) were calculated in polygenic animal models for the entire population. These estimated phenotypes were then used in marker assisted BLUP (MA-BLUP) evaluations where only the genotyped animals and their close relatives were included

MAPPING THE SPAIN´S EXCLUSIVE ECONOMIC ZONE IN THE GALICIAN MARGIN

MAPPING THE SPAIN´S EXCLUSIVE ECONOMIC ZONE IN THE GALICIAN MARGIN Gómez Ballesteros, M.1(*), González-Aller, J-D. 2, Martín Dávila, J. 3, Carbó, A., 4, Somoza, L. 5, Druet, M. 1, Martínez-Espinosa, S. 2, Catalán, M. 3, Muñoz, A. 4, León, R 5 1 Instituto Español de Oceanografía / C/. Corazón de María, 8, 28020 Madrid 2 Instituto Hidrográfico de la Marina / Pl. San Severiano, 3, 11007 Cádiz 3 Real Observatorio de la Armada, C/. Cecilio Pujazón s/n 11100Cádiz 4 Universidad Complutense de Madrid / Av Séneca, 2, 28040 Madrid 5 Instituto Geológico y Minero de España, Calle de Ríos Rosas, 23, 28003 Madrid (*)Corresponding Author: [email protected] In the context of the Hydrographic and Oceanographic Research of the Spain´s Exclusive Economic program (ZEEE), operated jointly by Instituto Hidrográfico de la Marina (IHM) and Real Observatorio de la Armada (ROA) working in close collaboration with the Instituto Español de Oceanografía (IEO), Universidad Complutense de Madrid (UCM) and Instituto Geológico y Minero de España (IGME) have conducted seven oceanographic cruises in Galician waters (EEZ -01 -02 ZEE , ZEE -03, ZEE -06 -07 ZEE , ZEE- ZEE- 08 and 09). The main objective of the Spain´s Exclusive Economic Zone project is mapping the seafloor, carrying out a systematic bathymetric survey of the 200 miles that comprise this area. In addition, as secondary objectives were performed acquiring that complement other geophysical parameters characterizing the seafloor and seabed from the knowledge of other variables such as the Terrestrial Magnetic Field , Terrestrial Gravity field, sound velocity and seabed internal structure. For the acquisition of detailed and accurate information during these cruises, carried on board the BIO Hespérides, high-resolution geophysical techniques were used to compile the data and the bathymetry of the region was mapped using a multibeam system during which 100 per cent coverage was obtained. At the same time high-resolution parametric seismic reflection profiles, as well as gravity and magnetic, were also recorded in the survey areas. These systems provide data on bathymetry, quality seafloor, acoustics backscatter , gravimetry, magnetometry and subsurface structure and require the use of precise positioning techniques, so were used in conjunction with GPSD and inertial navigation systems. As a result of these oceanographic researches and post-processing, analysis and interpretation of the whole acquired data, a synthesis of 6 maps were published with 1:500.000 scale and corresponding to Bathymetric map, Geomorphology map, Geomagnetic Anomaly map, Bouguer and Free Air Anomaly maps and backscatter map. REFERENCIAS J. Martín Davila, M. Catalán, M. Larrán, Sección de Hidrografía del IHM, A. Carbó, A. Muñoz-Martín, JL Granja, P. Llanes, L. Somoza, R. León, F.J. Gonzalez, M. Gómez-Ballesteros, M. Druet, and J. Acosta, 2014: Zona Económica Exclusiva Española (ZEEE): Margen Continental Gallego. Mapas Generales de batimetría, de anomalías Geomagnéticas, Graviméwtricas de Aire Libre y Bpouguer, Geomorfológico y Mosaico de Imágenes de Reflectividad (E. 1:500.000). Ministerio de Defensa. Secretaria General Técnica, NIPO: 083-12-230-3, DL: M-39518-201