We construct a new class of plane-symmetric solutions possessing a curvature singularity which is null and weak, like the spacetime singularity at the Cauchy horizon of spinning (or charged) black holes. We then analyse the stability of this singularity using a rigorous non-perturbative method. We find that within the framework of (linearly-polarized) plane-symmetric spacetimes this type of nul...

Fixed a point O on a non-singular surface S and a complete mO-primary ideal I in OS,O , the curves on the surface X = BlI (S) obtained by blowing-up I are studied in terms of the base points of I. Criteria for the principality of these curves are obtained. New formulas for their multiplicity, intersection numbers and order of singularity at the singularities of X are given. The semigroup of bra...

We study the homogeneous Dirichlet problem for some elliptic equations with a first order term b(u,Du) which is quadratic in the gradient variable and singular in the u variable at a positive point. Moreover, the gradient term we consider, changes its sign at the singularity. Dealing with an appropriate concept of solution that gives sense to the equation at the singularity, we prove existence ...

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...

Algorithms aiming at solving dictionary learning problem usually involve iteratively performing two stage operations: sparse coding and dictionary update. In the dictionary update stage, codewords are updated based on a given sparsity pattern. In the ideal case where there is no noise and the true sparsity pattern is known a priori, dictionary update should produce a dictionary that precisely r...

Kernel discriminant analysis (KDA) is a widely used approach in feature extraction problems. However, for high-dimensional multi-class tasks, such as faces recognition, traditional KDA algorithms have a limitation that the Fisher criterion is non-optimal with respect to classification rate. Moreover, they suffer from the small sample size problem. This paper presents two variants of KDA called ...

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...