Volume of a doubly truncated hyperbolic tetrahedron

Volume of a doubly truncated hyperbolic tetrahedron

The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the previous results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to expressing the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.

A Truncated [Mn12] Tetrahedron from Oxime-based [Mn3O] Building Blocks

Acute Triangulations of Archimedean Surfaces . The Truncated Tetrahedron

In this paper we prove that the surface of the regular truncated tetrahedron can be triangulated into 10 non-obtuse geodesic triangles, and also into 12 acute geodesic triangles. Furthermore, we show that both triangulations have minimal size.

Nonparametric analysis of doubly truncated data

One of the principal goals of the quasar investigations is to study luminosity evolution. A convenient one-parameter model for luminosity says that the expected log luminosity, T ∗, increases linearly as θ0 · log(1+ Z∗), and T ∗(θ0) = T ∗ − θ0 · log(1 + Z∗) is independent of Z∗, where Z∗ is the redshift of a quasar and θ0 is the true value of evolution parameter. Due to experimental constraints...

Truncated microsupport and hyperbolic inequalities

We prove that the k-truncated microsupport of the specialization of a complex of sheaves F along a submanifold is contained in the normal cone to the conormal bundle along the k-truncated microsupport of F . In the complex case, applying our estimates to F = RHomD(M,O), where M is a coherent D-module, we obtain new estimates for the truncated microsupport of real analytic solutions. When M is r...