Umbilicity and characterization of Pansu spheres in the Heisenberg group

For $n\geq 2$ we define a notion of umbilicity for hypersurfaces in the Heisenberg group $H_{n}$. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant $p$(or horizontal)-mean curvature in $H_{n}$ up to Heisenberg translations.Comment: 32 pages, 2 figures; in Crelle's journal, 201

Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

We study immersed, connected, umbilic hypersurfaces in the Heisenberg group $H_{n}$ with $n$ $\geq$ $2.$ We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.Comment: 28 pages, 6 figure

Stacking-enriched magneto-transport properties of few-layer graphenes

The quantum Hall effects in the sliding bilayer graphene and AAB-stacked trilayer system are investigated by the Kubo formula and the generalized tight-binding model. The various stacking configurations can greatly diversify the magnetic quantization and thus create the rich and unique transport properties. The quantum conductivities are very sensitive to the Fermi energy and magnetic-field strength. The diverse features cover the specific non-integer conductivities, the integer conductivities with the distinct steps, the splitting-created reduction and complexity of quantum conductivity, a vanishing or non-zero conductivity at the neutral point, and the well-like, staircase, composite, and abnormal plateau structures in the field-dependencies. Such stacking-dependent characteristics mainly originate from the crossing, anticrossing and splitting Landau-level energy spectra and three kinds of quantized modes.Comment: 33 pages, 10 figure

Computational Simulation and Comparison of the Effect of Different Surroundings on Wind Loads on Domed Structures

[[abstract]]Mean surface pressures and overall wind loads on domes immersed in a boundary layer were obtained by computational fluid dynamics simulation. The effects of alternative turbulence models, upwind area roughness were examined and compared with wind tunnel studies. Surface pressures on dome structures were calculated in two cases by numerical simulation. One is with surrounding structures to calculate the wind comes from east and west direction, another one is no surrounding structure existing. The results will be evaluated the accuracy of numerical simulation with different roughness types of upwind area and effect of surroundings. Calculated values were compared to wind-tunnel measurements made in equivalent flow conditions.[[notice]]補正完畢[[incitationindex]]EI[[booktype]]紙