This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...

In 1985 Goode and Wainwright devised the concept of an isotropic singularity. Since that time, numerous authors have explored the interesting consequences, in mathematical cosmology, of assuming the existence of this type of singularity. In this paper, we collate all examples of cosmological models which are known to admit an isotropic singularity, and make a number of observations regarding th...

The signal in the nature ofsingularity is always caused by mechanical fault of CNC machine tool. It is important to recognize the singularity correctly for mechanical fault diagnosis. This paper deals with the wavelet t ransform and the relation between the modulus maxima and the singularity detection, and based on the excellent property of the Hermitian wavelet, poses the conception that appli...

The monopole singularity string, infinite direct line in the rest reference frame, is considered as a rigid physical line, and behavior of its geometrical form under the Lorentz transformations is studied. The method to test the form of any rigid line or surface in relativistical terms is based on the use of light signals emitted from the origin of the reference frame. Influence of the motion o...

This article addresses an efficient and novel method for singularity-free path planning and obstacle avoidance of parallel manipulator based on neural networks. A modified 4-5-6-7 interpolating polynomial is used to plan a trajectory for a spherical parallel manipulator. The polynomial function which is smooth and continuous in displacement, velocity, acceleration and jerk is used to find a pat...

In this paper, we rst study an optimal boundary control problem governed by the Stokes system with point pressure observations on the boundary. A constrained LQR approach with some hydrostatic potential theory, boundary integral equations and a variational inequality in a Banach space setting is applied to establish a state feedback characterization of the optimal control. Since a hyper-singula...

We present a new shape descriptor that are robust to deformation and capture part details. In our framework, the shape descriptor is generated by 1) using running angle to transforming a shape into a 2-D description image in the position and scale space. 2) performing circular wavelet-like sub-band decomposition of this 2-D description image based on its periodic convolution with orthogonal ker...

We examine the growth of the Weyl curvature in two examples of naked singularity formation in spherical gravitational collapse dust and the Vaidya spacetime. We find that the Weyl scalar diverges along outgoing radial null geodesics as they meet the naked singularity in the past. The implications of this result for the Weyl curvature hypothesis are discussed. We mention the possibility that alt...