How large can the first eigenvalue be on a surface of genus two?

Sharp upper bounds for the first eigenvalue of the Laplacian on a surface of a fixed area are known only in genera zero and one. We investigate the genus two case and conjecture that the first eigenvalue is maximized on a singular surface which is realized as a double branched covering over a sphere. The six ramification points are chosen in such a way that this surface has a complex structure of the Bolza surface. We prove that our conjecture follows from a lower bound on the first eigenvalue of a certain mixed Dirichlet-Neumann boundary value problem on a half-disk. The latter can be studied numerically, and we present conclusive evidence supporting the conjecture.Comment: 20 pages; 4 figure

Effect of Y substitution on the structural and magnetic properties of Dy1-xYxCo5 compounds

Structural and magnetization studies were carried out on Dy1-xYxCo5 [x = 0, 0.2, 0.4, 0.6, 0.8, 1] compounds which crystallize in the hexagonal CaCu5-type structure. Lattice parameters and unit-cell volume increase with Y concentration. Large thermomagnetic irreversibility between the field-cooled and the zero-field cooled magnetization data has been observed in all the compounds, which has been attributed to the domain wall pinning effect. Temperature dependence of magnetization data shows that except DyCo5 and YCo5, all the compounds show spin reorientation transitions in the range of 5-300 K. The spin reorientation temperature decreases from 266 K for x=0.2 to 100 K for x=0.8. Powder x-ray diffractograms of the magnetically aligned samples show that DyCo5 has planar anisotropy at room temperature whereas all the other compounds possess axial anisotropy. The spin reorientation transition has been attributed to a change in the easy magnetization direction from the ab-plane to the c-axis, as the temperature is increased. The anisotropy field and the first order anisotropy constant are found to be quite high in all the compounds except DyCo5. The magnetic properties have been explained by taking into account the variations in contributions arising from the rare earth and transition metal sublattices.Comment: 12 pages, 7 figure

Role of Ni-Mn hybridization in magnetism of martensitic state of Ni-Mn-In shape memory alloys

Extended X-ray Absorption Fine Structure (EXAFS) studies on Ni$_{50}$Mn$_{25+x}$In$_{25-x}$ have been carried out at Ni and Mn K edge as a function of temperature. Thermal evolution of nearest neighbor Ni-Mn and Mn-Mn bond distances in the martensitic phase give a clear evidence of a close relation between structural and magnetic degrees of freedom in these alloys. In particular, the study highlights the role of Ni 3d - Mn 3d hybridization in the magnetism of martensitic phase of these alloys.Comment: Accepted for publication in EP

Monitoring of ambient air quality in relation to traffic density in Bareilly City (U.P.), India

An ambient air quality study was undertaken in Bareilly city, U.P., India during the year 2010 and 2011. The seasonal air quality data was obtained from ten monitoring sites across the city considering sampling site of Cantt as control site. The maximum (713.06±55.64 µg/m3) suspended particulate matter (SPM), sulphur dioxide (SO2) (80.08±4.77 µg/m3) and nitrogen oxides (NOx) (64.98±3.53 µg/m3) level was found at Choupla during the winter 2011. Among the annual mean values of air pollutants were analyzed, SPM level was found to be above the National Ambient Air Quality Standards (NAAQS) (200 µg/m3) at all the polluted sites. SO2 and NOx levels were below the threshold limits (80 µg/m3) as per NAAQS. The ambient air quality was correlated with the traffic density in the city. The pollution level was observed to be positively correlated with traffic density which is the major source of air pollution in the city. The ambient air quality at different monitoring sites was categorized into different pollution level on the basis of Oak ridge air quality index (ORAQI). Light to moderate air pollution conditions were present at different sites. Sampling site of Choupla (SVII) observe maximum ORAQI of 64.48 and 70.81 and falls under category of moderate pollution

Kinematical Analogy for Marginal Dyon Decay

We describe a kinematical analogy for the marginal decay of 1/4-BPS dyons in 4-dimensional N=4 string compactifications. In this analogy, the electric and magnetic charges play the role of spatial momenta, the BPS mass plays the role of energy, and 1/2-BPS dyons correspond to massless particles. Using SO(12,1) "Lorentz" invariance and standard kinematical formulae in particle physics, we provide simple derivations of the curves of marginal stability. We also show how these curves map into the momentum ellipsoid, and propose some applications of this analogy.Comment: 10 pages, minor revision