We study the singularities of the Higgs branch of supersymmetric U (1) r gauge theories with eight supercharges. We derive new solutions for the mod-uli space of vacua preserving manifestly the eight supercharges by using a geometric realization of the SU (2) R symmetry and a separation procedure of the gauge and SU (2) R charges, which allow us to put the hypermultiplet vacua in a form dependi...

This paper presents a general methodology for the offline planning of trajectory of a six axis serial robot along a specified path. The objective of trajectory planning is to minimise a cost function when subjected to joint angles, joint velocities, acceleration, jerks, torques and gripping force constraints by considering dynamic of the robot. A trigonometric spline is used to represent the tr...

We construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the values taken by the process. The result relies on fine properties of the distribution of Poisson point processes and on ubiquity theorems.

Let π : X → S be a holomorphic map from a compact Kähler manifold (X, gX) to a compact Riemann surface S. Let Σπ be the critical locus of π and let ∆ = π(Σπ) be the discriminant locus. Let (ξ, hξ) be a holomorphic Hermitian vector bundle on X. We determine the singularity of the Quillen metric on detRπ∗ξ near ∆ with respect to gX |TX/S and hξ.

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...

In this article we give first results on Stewart Gough Platforms with planar base and platform, whose singularity set for any orientation of the platform is a cylindrical surface with rulings parallel to a given fixed direction p in the space of translations. In this case the singularity set can easily be visualized as curve by choosing p as projection direction. Moreover the computation of sin...

This paper is concerned with the analysis of a singularity that can occur in threedimensional discontinuous feedback control systems. The singularity is the two-fold – a tangency of orbits to both sides of a switching manifold. Particular attention is placed on the Teixeira singularity, which previous literature suggests as a mechanism for dynamical transitions in this class of systems. We show...

0 Introduction We consider algebraic surfaces Y ⊂ IP3(C). A cusp (=singularity A2) on Y is a singularity near which the surface is given in local (analytic) coordinates x, y and z, centered at the singularity, by an equation xy − z = 0. This is an isolated quotient singularity C2/ZZ3. A set P1, ..., Pn of cusps on Y is called 3-divisible, if there is a cyclic global triple cover of Y branched p...

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic...

The Cosmic Censorship Conjecture (CCC)[1,2] states that the space-time singularity produced by gravitational collapse must be covered by the horizon. The CCC is yet one of the unresolved problem in General Relativity. In fact the conjecture has not yet any precise mathematical proof. However the singularity theorems as such do not state anything about the visibility of the singularity to an out...