Geometry of minimal networks and the one-dimensional Plateau problem

Abstract

Spherical Si solar cells were fabricated based on polycrystalline Si spheres with a diameter of 1 mm produced by a dropping method. To decrease the cooling rates of Si spheres by decreasing the convection heat transfer to ambient, the Si spheres were dropped in a free-fall tower at a pressure of 0.2 atm. The conversion efficiency of low-pressure spherical Si solar cells was higher than that of normal-pressure spherical Si solar cells. Both Si spheres were polycrystals that consisting of crystal grains of about 200 mm. The distribution between electric active defects and the crystal quality were characterized by electron beam induced current (EBIC) measurements and transmission electron microscopy (TEM). By EBIC measurements, the lowpressure spherical Si solar cells were clearly observed to have the lower recombination sinks than the normal-pressure spherical Si solar cells. By TEM, the dislocation density in the low-pressure spherical Si solar cells was observed to be more reduced than that in the normal-pressure spherical Si solar cells. The dislocation density in the low-pressure Si spheres decreased because the reduction in the stress generated in the crystal grain.

Steiner Ratio for Hadamard Surfaces of Curvature at Most k < 0

“…Vertices of regular polygons were considered as terminal sets that approach the Steiner ratio to 1/2. It was shown, in particular, that all Steiner points of a regular n-gon are contained in a certain neighborhood of the polygon center, independently of how far the vertices are located from the center; the radius of the neighborhood depends only on n. It is known [10] that Steiner trees on Riemannian manifolds have the following structure:…”

Minimal binary trees with a regular boundary: The case of skeletons with five endpoints

“…The papers [1,[8][9][10][11] describe all skeletons of the triangulations T that admit a convex minimal realization (they turned out to have a rather simple structure), as well as all the possible ways of attaching growths to them such that the emerging triangulations have convex minimal realizations again. The papers [1,[8][9][10][11] describe all skeletons of the triangulations T that admit a convex minimal realization (they turned out to have a rather simple structure), as well as all the possible ways of attaching growths to them such that the emerging triangulations have convex minimal realizations again.…”

“…In their previous articles [1,2,[8][9][10][11], A. O. Ivanov and A. A. Tuzhihn gave a complete description of locally minimal binary trees with convex boundaries and applied the theory thus created to the case where the boundary is the set of vertices of a regular polygon (called a regular boundary in what follows).…”

A plasticity principle of some generalized Gauss trees

“…Concerning various computational aspects of the Steiner tree problem in ℝ 3 , we refer to the classical works given in [4,[6][7][8].…”

“…2,8,4, 0 ὔ . The weight ( ) corresponds to the vertex that lies in the ray 0 regarding the tetrahedron for , , by ( ) 35607 the weight which corresponds to the vertex that lies on the ray 0 ὔ for = 1, 2, 8, 4, 0 ὔ .…”