We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We concern only the quotient singularity of hypersurface type. The abelian group Ar (n) for A-type hypersurface quotient singularity of dimension n is introduced. For n = 4, the structure of Hilbert scheme of group orbits and crepant resolutions of Ar (4)-singularit...

We examine here the nature of the central singularity forming in the spherically symmetric collapse of a dust cloud and it is shown that this is always a strong curvature singularity where gravitational tidal forces diverge powerfully. An important consequence is that the nature of the naked singularity forming in the dust collapse turns out to be stable against the perturbations in the initial...

In this paper, an algorithm is proposed to avoid singularity associated with the most famous minimum element attitude parametrization, Euler angle set. The proposed algorithm makes use of the method of sequential rotation to avoid singularity associated with Euler angle set. Further, a switching algorithm is also proposed to switch between different Euler angle sets to avoid the singularity whi...

A class of simple statistical mechanical models for DNA melting, first proposed by Poland and Scheraga, have been demonstrated to exhibit first or second order thermodynamic singularity, notwithstanding the intrinsic one-dimensional nature of the problem. In the present paper we show that the inclusion of twist elastic energy in the Poland-Scheraga models either leads to suppression of the ther...

This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is widely used in rigid-body shape changing mechanisms. The general singularity equation is reduced to a condensed form, which allows geometric relationships to be readily detected. A method for formulating the singularity condition for...

One of the most significant current discussions in Utopian Studies and Science-Fiction Studies is the idea of Singularity, described by Vernor Vinge in the article “The Coming Technological Singularity: How To Survive in the Post-Human Era” (1993) as “the imminent creation by technology of entities with greater than human intelligence” (Vinge, 1993: 12). The concept of singularity is central to...

The analytic behavior of the heavy-light meson form factor is investigated using several relativistic examples including unconfined, weakly confined, and strongly confined mesons. It is observed that confinement erases the anomalous threshold singularity and also induces an essential singularity at the normal annihilation threshold. In the weak confinement limit, the would be anomalous threshol...

The asymptotics of the Schatten norms of finite Toeplitz matrices generated by functions with a Fisher-Hartwig singularity are described as the matrix dimension n goes to infinity. The message of the paper is to reveal some kind of a kink: the pth Schatten norm increases as n to the power 1/p before the singularity reaches a critical point and as n to an exponent depending on the singularity be...

We apply techniques recently introduced in quantum cosmology to the Schwarzschild metric inside the horizon and near the black hole singularity at r = 0. In particular, we use the quantization introduced by Husain and Winkler, which is suggested by Loop Quantum Gravity and is based on an alternative to the Schrödinger representation introduced by Halvorson. Using this quantization procedure, we...

We examine here the nature of the central singularity forming in the spherically symmetric collapse of a dust cloud and it is shown that this is always a strong curvature singularity where gravitational tidal forces diverge powerfully. An important consequence is that the nature of the naked singularity forming in the dust collapse turns out to be stable against the perturbations in the initial...