Value distribution of the hyperbolic Gauss maps for flat fronts in hyperbolic three-space

We give an effective estimate for the totally ramified value number of the hyperbolic Gauss maps of complete flat fronts in the hyperbolic three-space. As a corollary, we give the upper bound of the number of exceptional values of them for some topological cases. Moreover, we obtain some new examples for this class.Comment: 14 pages, to appear in Houston Journal of Mathematic

Majorana bound state in rotating superfluid 3He-A between parallel plates

A concrete and experimentally feasible example for testing the putative Majorana zero energy state bound in a vortex is theoretically proposed for a parallel plate geometry of superfluid $^3$He-A phase. We examine the experimental setup in connection with ongoing rotating cryostat experiments. The theoretical analysis is based on the well-established Ginzburg--Landau functional, supplemented by microscopic calculations of the Bogoliubov--de Gennes equation, both of which allow the precise location of the parameter regions of the Majorana state to be found in realistic situations.Comment: 5 pages, 4 figure

Stability of half quantum vortex in rotating superfluid 3He-A between parallel plates

We have found the precise stability region of the half quantum vortex (HQV) for superfluid $^3$He A phase confined in parallel plates with a narrow gap under rotation. Standard Ginzburg-Landau free energy, which is well established, is solved to locate the stability region spanned by temperature $T$ and rotation speed ($/Omega$). This $/Omega$-$T$ stability region is wide enough to check it experimentally in available experimental setup. The detailed order parameter structure of HQV characterized by A$_1$ core is given to facilitate the physical reasons of its stability over other vortices or textures.Comment: 5 pages, 4 figure

Vertical and meridional distributions of the atmospheric CO2 mixing ratio between northern midlatitudes and southern subtropics

The atmospheric CO2 mixing ratio was measured using a continuous measurement system onboard a Gulfstream-II aircraft between the northern midlatitudes and the southern subtropics during the Biomass Burning and Lightning Experiment Phase A (BIBLE A) campaign in September-October 1998. The vertical distribution Of CO2 over tropical regions was almost constant from the surface to an altitude of 13 km. CO2 enhancements from biomass burning and oceanic release were observed in the tropical boundary layer. Measurements in the upper troposphere indicate interhemispheric exchange was effectively suppressed between 2°N-7°N. Interhemispheric transport of air in the upper troposphere was suppressed effectively in this region. The CO2 mixing ratios in the Northern and Southern Hemispheres were almost constant, with an average value of about 365 parts per million (ppm) and 366 ppm, respectively. The correlation between the CO2 and NOy mixing ratios observed north of 7°N was apparently different from that obtained south of 2°N. This fact strongly supports the result that the north-south boundary in the upper troposphere during BIBLE A was located around 2°N-7°N as the boundary is not necessary a permanent feature