Erratum for “Unsymmetrically Loaded Hyperboloids of Revolution”

Multi-factorial Analysis on Vault Stability of an Unsymmetrically Loaded Tunnel Using Response Surface Method

This study investigated the vault settlement characteristics of an unsymmetrically loaded tunnel which was excavated by annular excavation via core rock support method. Response surface methodology (RSM) was employed to design the experiments, evaluate the results with the purpose of optimizing the value of design parameters for reducing the vault settlement. The parameters such as horizontal d...

Lattice points on hyperboloids of one sheet

The problem of counting lattice points on a hyperboloid of two sheets is Gauss’ circle problem in hyperbolic geometry. The problem of counting lattice points on a hyperboloid of one sheet does not have the same geometric interpretation, and in general, the solution(s) to Gauss’ circle problem gives a lower bound, but not an upper bound. In this paper, we describe an exception. Given an ample he...

Diluting Gravity with Compact Hyperboloids

I give a brief informal introduction to the idea and tests of large extra dimensions, focusing on the case in which the space-time manifold has a direct product structure. I then describe some attractive implementations in which the internal space comprises a compact hyperbolic manifold. This construction yields an exponential hierarchy between the usual Planck scale and the true fundamental sc...

Erratum

Wigner functions for curved spaces I: On hyperboloids

We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature —in this paper on hyperboloids—, which returns the correct marginals and has the covariance of the Shapiro functions under SO(D, 1) transformations. To the free systems obeying the Laplace-Beltrami equation on the hyperboloid, we add a conic-oscillator potential in the hyperbolic c...