We study a simple system of two hyperbolic semi-linear equations, inspired by the Einstein equations. The system, which was introduced in [1], is a model for singularity formation inside black holes. We show for a particular case of the equations that the system demonstrates a finite time blowup. The singularity that is formed is a null singularity. Then we show that in this particular case the...

We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both in light-cone gauge and covariantly. We also compute some tree and one loop amplitudes which exhibit interesting behavior near the singularity. Our results a...

This paper presents the Eclipse-II, a new six degree-offreedom parallel mechanism, which can be used as a basis for general motion simulators. The Eclipse-II is capable of x, y and z-axis translations and a, b and c-axis rotations. In particular, it has the advantage of enabling continuous 360-degree spinning of the platform. The computational procedures for forward and inverse kinematics of th...

A black hole is considered a gravitational one-dimensional point of singularity containing an infinite mass within an infinitely small space, and spacetime curves infinitely. Within this singularity all the laws of physics are no longer valid. The physical domains of the large macroscopic scale are described by general relativity and on the small microscopic scale by quantum effects. It is prop...

This paper presents the Eclipse-11, a new six degree-offreedom parallel mechanism, which can be used as a basis for general motion simulators. The Eclipse-I1 is capable of x, y and z-axis translations and a, b and c-axis rotations. In particular, it has the advantage of enabling continuous 360-degree spinning of the platform. The computational procedures for forward and inverse kinematics of th...

We study analytically the spacelike singularity inside a spherically-symmetric, charged black hole coupled to a self-gravitating spherical massless scalar field. We assume spatial homogeneity, and find a generic solution in terms of a formal series expansion. This solution is tested against fullynonlinear and inhomogeneous numerical simulations. We find full compliance between our analytical so...

A generalised Thurston-Bennequin invariant for a Q-singularity of a real algebraic variety is defined as a linking form on the homologies of the real link of the singularity. The main goal of this paper is to present a method to calculate the linking form in terms of the very good resolution graph of a real normal unibranch singularity of a real algebraic surface. For such singularities, the va...

In a recent paper [3], Y. Cao and Y. Xu established the Galerkin method for weakly singular Fredholm integral equations that preserves the singularity of the solution. Their Galerkin method provides a numerical solution that is a linear combination of a certain class of basis functions which includes elements that reflect the singularity of the solution. The purpose of this paper is to extend t...

In this paper we address the problem of identifying the property of the singularity loci of a class of 6/6-Gough–Stewart manipulators in which the moving and base platforms are two similar semiregular hexagons. After constructing the Jacobian matrix of this class of 6/6-Gough–Stewart manipulators according to the theory of statical equilibrium, we derive a cubic polynomial expression in the mov...

This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model through a quantum spin chain. In particular, finite-size scaling measurements on the quantum spin chain are used to determine the low-lying excitation spectrum and central charge at the Yang-Lee edge singularity. The measured values are consistent with predictions for the (A4, A1) minimal conformal field theory. ...