This paper surveys, in the first place, some basic facts from the classification theory of normal complex singularities, including details for the low dimensions 2 and 3. Next, it describes how the toric singularities are located within the class of rational singularities, and recalls their main properties. Finally, it focuses, in particular, on a toric version of Reid’s desingularization strat...

In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [2]. This relation is finer than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci (or saddl...

An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial kinematic chains or its modification for closed-loop kinematic chains. The method developed is based upon analyt...

In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [3]. This relation is deeper than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci of diffe...

We study the question of existence of a Riemannian metric of positive scalar curvature metric on manifolds with the Sullivan-Baas singularities. The manifolds we consider are Spin and simply connected. We prove an analogue of the Gromov-Lawson Conjecture for such manifolds in the case particular type of singularities. We give an affirmative answer when such manifolds with singularities accept a...

It is well known that for a first order system of linear difference equationswith rational function coefficients, a solution that is holomorphic in some le‰ half plane can be analytically continued to a meromorphic solution in the whole complex plane. Œe poles stem from the singularities of the rational function coefficients of the system. Just as for differential equations, not all of these si...

We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also show that apparent singularities can be removed like in the univariate case by adding suitable additional solutions to the system at hand. Several algorithms a...

We use the identification between null singularities of correlators in the bulk with time singularities in the boundary correlators to study the analytic structure of time-dependent thermal Green functions using the eikonal approximation for classical solutions in the AdS black hole background. We show that the location of singularities in complex time can be understood in terms of null rays bo...

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled usi...

While adaptive optical systems are able to remove moderate wavefront distortions in scintillated optical beams, phase singularities that appear in strongly scintillated beams can severely degrade the performance of such an adaptive optical system. Therefore the detection of these phase singularities is an important aspect of strong-scintillation adaptive optics. We investigate the detection of ...