Singularity analysis, Hadamard products, and tree recurrences

We present a toolbox for extracting asymptotic information on the coefficients of combinatorial generating functions. This toolbox notably includes a treatment of the effect of Hadamard products on singularities in the context of the complex Tauberian technique known as singularity analysis. As a consequence, it becomes possible to unify the analysis of a number of divide-and-conquer algorithms, or equivalently random tree models, including several classical methods for sorting, searching, and dynamically managing equivalence relationsComment: 47 pages. Submitted for publicatio

SINGULAB - A Graphical user Interface for the Singularity Analysis of Parallel Robots based on Grassmann-Cayley Algebra

This paper presents SinguLab, a graphical user interface for the singularity analysis of parallel robots. The algorithm is based on Grassmann-Cayley algebra. The proposed tool is interactive and introduces the designer to the singularity analysis performed by this method, showing all the stages along the procedure and eventually showing the solution algebraically and graphically, allowing as well the singularity verification of different robot poses.Comment: Advances in Robot Kinematics, Batz sur Mer : France (2008

Singularity analysis of a spherical Kadomtsev-Petviashvili equation

The (2+1)-dimensional spherical Kadomtsev-Petviashvili (SKP) equation of J.-K. Xue [Phys. Lett. A 314:479-483 (2003)] fails the Painleve test for integrability at the highest resonance, where a nontrivial compatibility condition for recursion relations appears. This compatibility condition, however, is sufficiently weak and thus allows the SKP equation to possess an integrable (1+1)-dimensional reduction, which is detected by the Weiss method of truncated singular expansions.Comment: 7 page

Stress–singularity analysis in space junctions of thin plates

The stress singularity in space junctions of thin linearly elastic isotropic plate elements with zero bending rigidities is investigated. The problem for an intersection of infinite wedge-shaped elements is considered first and the solution for each element, being in the plane stress state, is represented in terms of holomorphic functions (Kolosov–Muskhelishvili complex potentials) in some weighted Hardy-type classes. After application of the Mellin transform with respect to radius, the problem is reduced to a system of linear algebraic equations. By use of the residue calculus during the inverse Mellin transform, the stress asymptotics at the wedge apex is obtained. Then the asymptotic representation is extended to intersections of finite plate elements. Some numerical results are presented for a dependence of stress singularity powers on the junction geometry and on membrane rigidities of plate elements