The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace of the mobile platform. Singularity analysis become important in design, motion planning, and control of parallel robots. Focusing on the instantaneous velocities of passive joints, a new formulation approach is proposed for the instantaneous kinematics and singularity analysis of a class o...

The author is supported by the Danish Science Research Council. We describe a computer program, based on Maple, that decides whether or not a polynomial function has a simple or unimodal singularity at the origin, and determines theK-class of this singularity. The program applies the splitting lemma to the function, in an attempt to reduce the number of variables. Then, in the more interesting ...

We study the prototype of fractional D3 branes at non-isolated singularities in gauge/gravity duality at the nonperturbative level. We embed the quantum moduli space of N = 2 pure SYM, the gauge theory on fractional D3 branes at the A1 singularity, into that of the cascading quiver gauge theory on regular and fractional D3 branes at the same singularity, for which a gravity dual description exi...

The null-brane space-time provides a simple model of a big crunch/big bang singularity. A non-perturbative definition of M-theory on this space-time was recently provided using matrix theory. We derive the fermion couplings for this matrix model and study the leading quantum effects. These effects include particle production and a time-dependent potential. Our results suggest that as the null-b...

In this talk we discuss the cosmic singularity. We motivate the need to correct general relativity in the study of singularities, and mention the kind of corrections provided by string theory. We review how string theory resolves time-like singularities with two examples. Then, a simple toy model with lightlike singularities is presented, and studied in classical string theory. It turns out tha...

The evolution of a small but nite three-dimensional disturbance on a at uniform vortex sheet is studied numerically on the basis of a Lagrangian representation of the motion. The numerical simulations connrm the asymptotic analysis by Ishihara and Kaneda (1995; J. Fluid Mech., 300, 339-366) for the spontaneous singularity formation in the shape of the vortex sheet. They also suggest that the si...

Many types of point singularity have a topological index, or ‘charge’, associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero, enabling the zeros to be assigned charges of ±1. In random fields we can define a correlation function for the charge-weighted density of singularities....

Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number t...

We consider the notion of a connection on a module over a commutative ring, and recall the obstruction calculus for such connections. This obstruction calculus is defined using Hochschild cohomology. However, in order to compute with Gröbner bases, we need the conversion to a description using free resolutions. We describe our implementation in Singular 3.0, available as the library conn.lib. F...