El número exacto de primos menores que x

En este trabajo vamos a estudiar la distribución de los números primos. En primer lugar, vamos a centrarnos en los métodos que proporcionan la cantidad exacta de primos menores x, denotado como pi(x), desde los griegos hasta el comienzo del siglo XX. La búsqueda de éstos métodos comienza con Eratóstenes, (276 A.C.-197 A.C.), es desarrollada por Legendre en 1830, simplificada por Meissel en 1870 y mejorada por Lehmer en 1959. Además, implementamos un algoritmo para cada método con el que obtenemos la cantidad exacta de primos menores que x. Al mismo tiempo, históricamente, el comportamiento asintótico de pi(x) ha sido de gran interés. En particular vamos a estudiar el conocido resultado de Chebyshev, a partir de sus funciones y métodos, así como el postulado de Bertrand. <br /

Crystal structure and local ordering in epitaxial Fe100−x_{100-x}Gax_x/MgO(001) films

In this work we present a study of the structural properties of Fe$_{100-x}$ Ga$_x$ grown by Molecular Beam Epitaxy on Mg0(100). We combine long range and local/chemically selective X-ray probes (X-ray Diffraction and X-ray absorption spectroscopy) together with real space imaging by means of Transmission Electron Microscopy and surface sensitive $in situ$ Reflected High Energy Electron Diffraction. For substrate temperature $T_s$ below 400 $^o$C we obtain $bcc$ films while, for $x \approx$ 24 and $T_s \geq$ 400$^o$C the nucleation of the $fcc$ phase is observed. For both systems a Ga anticlustering or local range ordering phenomenon appears. The Ga/Fe composition in the first and second coordination shells of the $bcc$ films is different from that expected for a random Ga distribution and is close to a D0$_3$-like ordered phase, leading to a minimization of the number of Ga-Ga pairs. On the other side, a true long-range D0$_3$ phase is not observed indicating that atomic ordering only occurs at a local scale. Overall, the epitaxial growth procedure presented in this work, first, avoids the formation of a long range ordered D0$_3$ phase, which is known to be detrimental magnetostrictive properties, and second, demonstrates the possibility of growing $fcc$ films at temperatures much smaller than those required to obtain bulk $fcc$ samples.Comment: 21 pages, 7 figure

Equilibrium properties of a Josephson junction ladder with screening effects

In this paper we calculate the ground state phase diagram of a Josephson Junction ladder when screening field effects are taken into account. We study the ground state configuration as a function of the external field, the penetration depth and the anisotropy of the ladder, using different approximations to the calculation of the induced fields. A series of tongues, characterized by the vortex density $\omega$, is obtained. The vortex density of the ground state, as a function of the external field, is a Devil's staircase, with a plateau for every rational value of $\omega$. The width of each of these steps depends strongly on the approximation made when calculating the inductance effect: if the self-inductance matrix is considered, the $\omega=0$ phase tends to occupy all the diagram as the penetration depth decreases. If, instead, the whole inductance matrix is considered, the width of any step tends to a non-zero value in the limit of very low penetration depth. We have also analyzed the stability of some simple metastable phases: screening fields are shown to enlarge their stability range.Comment: 16 pp, RevTex. Figures available upon request at [email protected] To be published in Physical Review B (01-Dec-96

Sun exposure and knowledge about skin care of physical educators

El propósito del estudio fue identificar los hábitos de exposición solar y conocimientos del cuidado de la piel de profesionales de la educación física en México. Fue un estudio descriptivo transversal probabilístico por selección al azar con un margen de error del 7%, con una muestra de 131 docentes (98 hombres y 33 mujeres). El instrumento para el levantamiento de datos fue un cuestionario autogestivo validado dividido en tres categorías: sociodemográficas, hábitos de exposición solar y conocimientos del cuidado de la piel. Entre los principales hallazgos se constata los deficientes hábitos de cuidado de la piel de los educadores físicos, aun conociendo el riesgo y los peligros de la exposición, no utilizan la indumentaria básica y las cremas de protección solar recomendada por los organismos internacionales. Se concluye considerar a este grupo profesional en alta vulnerabilidad por su contante exposición al sol, así como, promover campañas de información integrales que fomenten la revisión médica constante de la piel, el uso adecuado de la ropa y las cremas de protección solar.The study aimed to identify the sun exposure habits and knowledge of Physical Education professionals in Mexico. A cross-sectional descriptive study by random selection with a margin of error of 7%, was designed on a sample of 131 teachers (98 men and 33 women). Participants answered a validated self-completed questionnaire divided into sociodemographic categories, sun exposure habits, and skin care knowledge. The findings suggest the poor skin care habits of physical education professionals even knowing the risk and dangers of exposure. They not using the essential clothing recommended by international organizations, using very few and misapply it sunscreen creams. It is concluded to this professional group is considered highly vulnerable and promote comprehensive information campaigns that encourage constant medical review of the skin and proper use of clothing and sun protection creams

Impact of long-term viral suppression in CD4+ recovery of HIV-children on Highly Active Antiretroviral Therapy

BACKGROUND: The effects of HAART may differ between children and adults because children have a developing immune system, and the long-term immunological outcome in HIV-infected children on HAART is not well-known. A major aim of our study was to determine CD4+ evolution associated with long-term VL control during 4 years of observation on HAART. METHODS: We carried out a retrospective study on a cohort of 160 vertically HIV-infected children. It was carried out from 1996 to 2004 in six large Spanish pediatric referral hospitals. We compared 33 children who had long-term VL suppression (VL ≤400 copies/ml) in the first 12 months of follow-up and maintained that level throughout follow-up (Responders-group), and 127 children with persistently detectable VL in spite of ART switches (Non-Responders-group). RESULTS: We observed a quick initial and significant increase in CD4(+ )counts from the baseline to 12 months on HAART in both groups (p < 0.01). The Non-Responders group sustained CD4+ increases and most of these children maintained high CD4(+ )level counts (≥25%). The Non-Responders group reached a plateau between 26% and 27% CD4(+ )at the first 12 months of follow-up that remained stable during the following 3 years. However, the Responders group reached a plateau between 30% and 32% CD4(+ )at 24, 36 and 48 months of follow-up. We found that the Responders group had higher CD4(+ )count values and higher percentages of children with CD4(+ )≥25% than the Non-Responders group (p < 0.05) after month 12. CONCLUSION: Long-term VL suppression in turn induces large beneficial effects in immunological responses. However, it is not indispensable to recover CD4(+ )levels

Manifold domain structure of double films with perpendicular magnetic anisotropy

We present epitaxial structures made of twin nickel blocks with perpendicular magnetic anisotropy separated by a copper layer which, for some values of this interleaving layer, show domain structures with four levels of contrast in magnetic force microscopy images. This manifold domain structure implies that the magnetization in the Ni blocks, in addition to the parallel orientation, undergoes a non-collinear configuration with respect to each other. To explain this result we consider a magnetoelastic domain structure with M in the plane that can elude the clamping done by the substrate with an average strain of -42 × 10-6 (≈70% of the bulk value). Thus, the out-of-plane anisotropy is balanced and a biquadratic exchange coupling can stabilize the non-collinear domain configurations between the Ni blocks. © 2011 IOP Publishing Ltd.This work has been supported by the Spanish MICINN (Grant NosMAT2006-07094 andMAT2009-10040) and DGA (Grants E81 and PI049/08) and Fondo Social Europeo.Peer Reviewe

Transverse magnetization in Cu/Ni/Cu epitaxial nanorings

The micromagnetic structure in epitaxial (001)-oriented Cu/Ni(14 nm)/Cu rings fabricated by electron beam and focused ion beam lithographies with external diameter of 3 μm and linewidths between 100 and 500 nm is presented. We found that a state with radial orientation of the magnetization prevails at remanence. The evaluation of the magnetoelastic, magnetocrystalline and magnetostatic energies shows that a value as low as 1.5 × 10-3 for the anisotropic relaxation of the in-plane strain components is enough to induce an effective radial easy magnetization direction.This work has been supported by Spanish MICINN (Grant No. MAT2009-10040) and Gobierno de Aragón (Grants E81 and PI049/08) and Fondo Social Europeo.Peer Reviewe

Magnetic properties of Ni/Cu/Ni epitaxial films with perpendicular anisotropy

The effective magnetic anisotropy Keff has been studied at room temperature in Cu/Ni/Cu/Ni/Cu(001) epitaxial films with perpendicular magnetization as a function of the interleaving Cu block thickness tCu ranging from 0 nm to 6 nm and being the Ni blocks 3 nm thick. We have found that the value of Keff decreases when comparing the structures with tCu = 0 and 0.2 nm, although the strain increases. For larger values of tCu, Keff increases, although above tCu = 1.8 nm, Keff is nearly independent of tcu. These results can be explained using the measured in-plane strain and a surface anisotropy constant, Ks = −0.4 mJ/m2.This work has been supported by Spanish MICINN (Grants No. MAT2006-07094, and NAN2004-09183-C10-10) and DGA (Grants E81 and PI049/08).Peer Reviewe

Strain-induced spin reorientation of bcc-like iron films grown on Cu(001)

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).The in-plane orientation of the magnetization vector M in bcc-like Fe(110) films grown on Cu(001) is determined by means of scanning electron microscopy with polarization analysis. For thicknesses of 2 nm, slightly above the fcc/bcc phase transition, it is found that M is oriented along the directions of the Cu(001) substrate. Following the Pitsch orientational relationship these correspond to magnetically hard and axes of bulk iron. This finding is in strong contrast to the behavior reported for thicker films (above 3 nm) of bcc Fe/Cu(001), where the directions of the substrate are preferred. The role of strain in the iron film is discussed, inferring that the presence of a shear strain is mandatory to explain the spin reorientation via the magnetoelastic contribution to the magnetic anisotropy energy.This work has been supported by Spanish MICINN (Grants No. MAT2009-10040 and No. MAT2012-31309) and Gobierno de Aragón (Grants No. E81) and Fondo Social Europeo, as well as by the Deutsche Forschungsgemeinschaft within SFB 668. E.C.C. acknowledges the financial support from Ministerio de Educación, through program Campus de Excelencia Internacional Iberus.Peer Reviewe

Strain-induced magnetization reorientation in epitaxial Cu/Ni/Cu rings

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).-- Trabajo presentado como al Joint European Magnetic Symposia (JEMS2012).The role of the strain state in epitaxial (001)-oriented Cu/Ni(14 nm)/Cu rings is investigated using a combination of magnetic force microscopy and finite-element calculations. Rings with an external diameter of 3 and 2 ¿m and linewidth W larger than 400 nm show two different structures: domains with magnetization oriented in the radial direction exist at the inner and outer radius, separated by an area in the interior of the ring consisting of stripe domains with perpendicular magnetization. The former is the sole magnetic structure observed for W<400 nm. Micromagnetic calculations on narrow-linewidth structures indicate that the radial domain-wall structure consists of elliptical Bloch lines with a shorter and longer length along the tangential and radial directions, respectively. Finite-element calculations show that the anisotropic relaxation of the in-plane strain is larger at the ring inner and outer edges than in the interior part of the ring and accounts for the reorientation of the magnetization direction.This work has been supported by Spanish MICINN (Grants No. MAT2009-10040) and Gobierno de Aragón (Grants No. E81 and PI049/08) and Fondo Social Europeo, the Singapore-MIT Alliance and National Science Foundation.Peer Reviewe