The first Chern class and conformal area for a twistor holomorphic immersion

We obtain an inequality involving the first Chern class of the normal bundle and the conformal area for a twistor holomorphic surface. Using this inequality, we can improve an inequality obtained by T. Friedrich for the Euler class of the normal bundle of a twistor holomorphic surface in the four-dimensional space form. Moreover, as a corollary, we see that the area of a superminimal surface in the unit sphere is an integer multiple of $2 \pi $ , which is essentially proved by E. Calabi.     

Crosstalk Suppression in Header Recognition Unit Using Time-Space Conversion

We demonstrate a suppression effect of a crosstalk among a target and similar header signals using the header recognition filter designed by a design technique of the multiple-object discriminant filter.     

Closed Curves in E 2 and S 2 Whose Total Squared Curvatures and Almost Minimal

The total squared curvature of a closed plane curve is minimized by a covering of a circle, if the rotation number of the curve is not zero. We measure the closeness of a closed plane curve to a circle by the difference of its total squared curvature from the minimum. A similar result is obtained for a simple closed curve in the 2-sphere.     

Nonlinear Sigma Models in (1+2) Dimensions and an Infinite Number of Conserved Currents

In this Letter, we treat nonlinear sigma models such as the C P¹-model, Q P¹-model, etc. in 1+2 dimensions. For submodels of such models, we definitely construct an infinite number of nontrivial conserved currents. Our result is a generalization of Alvarez, Ferreira and Guillen.     

Electronic structures of the highest occupied molecular orbital bands of a pentacene ultrathin film

We report the energy dispersions of the highest occupied molecular orbitals (HOMO)-derived bands of a pentacene (Pn) thin film, whose in-plane structure resembles closely that of the ab plane of a low-density bulk Pn phase. Our present photoemission result indicates that the overlap of the pi-orbitals of adjacent Pn molecules is larger than what was expected from theoretical calculations. Further, of the two HOMO-derived bands, the large dispersion width of the band with higher binding energy suggests that this one mainly contributes to the bandlike charge transport in a Pn crystal.     

The Critical Effect of Niobium Doping on the Formation of Mesostructured TiO2: Single‐Crystalline Ordered Mesoporous Nb‐TiO2 and Plate‐like Nb‐TiO2 with Ordered Mesoscale Dimples

Highly ordered mesoporous niobium‐doped TiO₂ with a single‐crystalline framework was prepared by using silica colloidal crystals with ca. 30 nm in diameter as templates. The preparation of colloidal crystals composed of uniform silica nanoparticles is a key to obtain highly ordered mesoporous Nb‐doped TiO₂. The XPS measurements of Nb‐doped TiO₂ showed the presence of Nb⁵⁺ and correspondingly Ti³⁺. With the increase in the amount of doped Nb, the crystalline phase of the product was converted from rutile into anatase, and the lattice spacings of both rutile and anatase phases increased. Surprisingly, the increase in the amount of Nb led to the formation of plate‐like TiO₂ with dimpled surfaces on one side, which was directly replicated from the surfaces of the colloidal silica crystals.