After a brief introduction to the Painlevé property for ordinary differential equations, we present a concise review of the various methods of singularity analysis which are commonly referred to as Painlevé tests. The tests are applied to several different examples, and we discuss the connection between singularity structure and integrability for ordinary and partial differential equations.

I first recount Raychaudhuri’s deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity. PACS numbers: 04.20.Jb, 04.2.Cv, 98.80 Dr 1 Singularity and AKR ...

This paper shows how the computation of the singularity locus of a 3R robot can be reduced to the analysis of the relative position of two coplanar ellipses. Since the relative position of two conics is a projective invariant, and the basic projective geometric invariants are determinants, it is not surprising that, using Distance Geometry, the computation of the singularity locus of a 3R robot...

Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with the local analysis of singularities. In this paper, the relationship between these two notions i...

We investigate the free-edge stresses in anisotropic bimaterials through the use of the free-edge stress intensity factor, Kf . This requires a determination of the singularity order at the free-surface as well as a calculation of the near-field stresses. We determine the order of the singularity for arbitrary free-surface orientation of the upper material using an eigenvalue analysis for aniso...

This paper presents a new generalized approach to the singularity analysis of a general mechanism (arbitrary kinematic chain), considered as a non-redundant inputoutput device with equal number of inputs and outputs. The instantaneous kinematics of a mechanism is described by means of a velocity equation, explicitly including not only the input and output velocities but also the passive-joint v...

This paper introduces a new approach to identify singularities of planar parallel manipulators (PPMs). This method is based on Maxwell’s reciprocal figure theory which establishes a duality between self-stress frameworks and reciprocal figures. We use line geometry tools to introduce a new graphical construction called the Mechanism’s Line of action Graph (MLG). The MLG is introduced in order t...

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

INTRODUCTION Quantitative analysis of complex self-excitatory wave patterns, such as cardiac fibrillation and other high-order reentry, requires the development of new tools for identifying and tracking the most important features of the activation, such as phase singularities. METHODS AND RESULTS Image processing operations can be used to detect the phase singularity at the tip of a spiral w...

We give a precise average-case analysis of a complete polynomial factorization chain over nite elds by methods based on generating functions and singularity analysis. Polyn^ omes al eatoires et factorisation de polyn^ omes R esum e Nous donnons une analyse en moyenne pr ecise d'une cha^ ne compl ete de factorisation de polyn^ omes sur les corps nis par des m ethodes fond ees sur les fonctions g...