We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singul...

Fundamental theories of quantum gravity such as supergravity include a four form field strength which contributes to the cosmological constant. The inclusion of such a field into our theory of open inflation [1] solves the problem of the most likely universe being too empty. It also allows an anthropic solution to the cosmological constant problem in which cosmological constant gives a small bu...

This paper addresses the problem of identifying the property of the singularity loci of a class of 3/6‐ Gough‐Stewart manipulators for general orientations in which the moving platform is an equilateral triangle and the base is a semiregular hexagon. After constructing the Jacobian matrix of this class of 3/6‐Gough‐Stewart manipulators according to the screw theory, a...

Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing...

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...

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...