Equiaffine immersions of general codimension and its transversal volume element map

With an equiaffine immersion of codimension 1 into the affine space with the natural equiaffine structure, the conormal map is associated. In this paper, for an equiaffine immersion of general codimension into the space, we shall define the map corresponding to the conormal map, which is called the transversal volume element map. And we shall investigate if, an equiaffine immersion of general codimension into the space is determined by its affine fundamental form and its transversal volume element map.     

An extension of the Uchiyama theorem and its application to composition operators which preserve BMO

Uchiyama constructed certain extremal BMO functions on Euclidean spaces which show that the John-Nirenberg estimate is in some sense remarkably precise. We extend his result to the case of general subdomains of Euclidean spaces. Also, as an application, we characterize Lebesgue measurable maps between general subdomains of Euclidean spaces which preserve BMO. To the memory of Professor Nobuyuki Suita     

Construction of CM Picard curves

In this article we generalize the CM method for elliptic and hyperelliptic curves to Picard curves. We describe the algorithm in detail and discuss the results of our implementation.

     

A generating function for sums of multiple zeta values and its applications

A generating function for specified sums of multiple zeta values is defined and a differential equation that characterizes this function is given. As applications, some relations for multiple zeta values over the field of rational numbers are discussed.

     

Optically driven actuators using poly(vinylidene difluoride)

Optically driven actuators have a feature of a non-contact method supplied by light energy. A new method is proposed with three poly(vinylidene difluoride) (PVDF) cantilevers as the legs and a polymer film as the body. The PVDF cantilevers are coated with silver on one surface. When one side of the cantilever is irradiated by a laser beam, an electric field is produced along a cross-section of the cantilever by the pyroelectric effect and a mechanical displacement occurs by the piezoelectric effect. Its response time and its generated force are measured experimentally. Two types of optically driven actuators using PVDF film are proposed to move using different characteristics.     

Pulsed laser deposition of pure fluoroapatite film without OH groups

The relation between O₂ pressure and composition in the pulsed‐laser deposition of fluoroapatite was investigated using both on‐axis and off‐axis methods to determine the optimal conditions for obtaining a pure fluoroapatite film without OH groups. Through this, it was found that an O₂ pressure of 10 Pa, combined with an off‐axis method, results in P/Ca and F/Ca values (0.6 and 0.2, respectively) that match closely with a stoichiometric composition of Ca₁₀(PO₄)₆F₂. Fourier transform infrared spectroscopy analysis confirmed that this optimized film was almost pure fluoroapatite, with no evidence of any OH groups originating from hydroxyapatite. X‐ray diffraction also revealed that this fluoroapatite film crystallizes with a c‐axis orientation perpendicular to its surface.