This paper reports the discovery of a new type of singularity that is as signijlcant as other singularities like kinematic singularity, algorithmic singularity, and semi-singularity. This singularity, named semi algorithmic singularity(SAS), occurs when a redundant manipulator, faced with inequality constraints arising from kinematic limits such as joint angle limits and obstacles, proceeds to ...

Singularity is an inherent characteristic of a closed-chain manipulator. This paper presents an approach to singularity analysis of the planar 3-RRR parallel manipulator. On the basis of screw theory, the motion/force transmission analysis of the manipulator is first achieved. The singularity is classified into three types: constraint singularity, input transmission singularity, and output tran...

The method of intersection spaces associates rational Poincaré complexes to singular stratified spaces. For a conifold transition, the resulting cohomology theory yields the correct count of all present massless 3-branes in type IIB string theory, while intersection cohomology yields the correct count of massless 2-branes in type IIA theory. For complex projective hypersurfaces with an isolated...

In this paper, we propose and analyze a spectral approximation for the numerical solutions of fractional integro-differential equations with weakly kernels. First, original are transformed into an equivalent singular Volterra integral equation, which possesses nonsmooth solutions. To eliminate singularity solution, introduce some suitable smoothing transformations, then use Jacobi collocation m...

Weighted degrees of quasihomogeneous Hamiltonian functions the Painlevé equations are investigated. A t-uple positive integers, called a regular weight, satisfying certain conditions related to singularity theory is classified. For each polynomial equation weight associated. Conversely, for 2 and 4-dim cases, it shown that there exists differential property associated with weight. Kovalevskaya ...

In this article, we examine the possibility that there exist special scalar-tensor theories of gravity with completely nonsingular FRW solutions. Our investigation in fact shows that while most probes living in such a Universe never see the singularity, gravity waves always do. This is because they couple to both the metric and the scalar field, in a way which effectively forces them to move al...

Basis and limitations of singularity theorems for Gravity are examined. As singularity is a critical situation in course of time, study of time paths, in full generality of Equivalence principle, provides two mechanisms to prevent singularity. Resolution of singular Time translation generators into space of its orbits, and essential higher dimensions for Relativistic particle interactions has f...

We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cos-mologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are asymptotically null with respect to each other, their respective Weyl parameters generally both tend to zero, constant, or infinity together. We examine three ...

The formal arc space L X of an algebraic variety X carries an important amount of information on singularities of X . Little is known about singularities of the formal arc scheme itself. According to Grinberg, Kazhdan [12] and Drinfeld [9] it is known, nevertheless, that the singularity of L X at a non-degenerate arc is finite dimensional i.e. for every non-degenerate arc x ∈L X , the formal co...

We discuss the evidence for and implications of a conjecture that the universal abelian cover of a Q-Gorenstein surface singularity with finite local homology (i.e., the singularity link is a Q-homology sphere) is a complete intersection singularity.