A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space–times to some properties of the orbits near the Cauchy surface. In particular it is shown that all Killing orbits are complete in maximal developements of asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact manifold.

Given a globally hyperbolic spacetime, the existence of a (smooth) spacelike Cauchy hypersurface S has been proven recently. Here, we prove that any acausal spacelike compact submanifold with boundary can be smoothly extended to a spacelike Cauchy hypersurface. Apart from the interest as a purely geometric question (applicable to the Cauchy problem in General Relativity), the result is motivate...

Intuitionistic set theory without choice axioms does not prove that every Cauchy sequence of rationals has a modulus of convergence, or that the set of Cauchy sequences of rationals is Cauchy complete. Several other related non-provability results are also shown.

In this paper, the existence and uniqueness theorems for a solution to an uncertain characteristic Cauchy reaction-diffusion problem is studied by Adomian decomposition method. Sufficient conditions are presented for uniform convergence of the proposed method. Also, some illustrative examples are given for solving the problem. Key WordsUncertain characteristic Cauchy problem, System of characte...

The usual domains for Cauchy distributions have been straight lines and unit circles. These domains are closed under arbitrary changes in location and scale, whether done sequentially or simultaneously. Such closure properties have been extended to spherical Cauchy distributions. Higher dimensional Cauchy based domains are created herein for unit hyperspheres and sets of straight lines of arbit...

For an o-minimal expansion R of a real closed eld and a set V of Th(R)-convex valuation rings, we construct a \pseudo completion" with respect to V. This is an elementary extension S of R generated by all completions of all the residue elds of the V 2 V , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings up to ...

The standard choice for mutating an individual of an evolutionary algorithm with con tinuous variables is the normal distribution however other distributions especially some versions of the multivariate Cauchy distribution have recently gained increased popularity in practical applications Here the extent to which Cauchy mutation distributions may a ect the local convergence behavior of evoluti...

In this contribution we deal with the development, theoretical examination and numerical examples of a method of lines approximation for the Cauchy problem for elliptic partial differential equations. We restrict ourselves to the Laplace equation. A more general elliptic equation containing a diffusion coefficient will be considered in a forthcoming paper. Our main results are the regularizatio...

An MV-convergence is a convergence on an MV-algebra which renders the operations continuous. We show that such convergences on a given MV-algebra A are exactly the restrictions of the bounded `-convergences on the abelian `-group in which A appears as the unit interval. Thus the theory of `-convergence and Cauchy structures transfers to MV-algebras. We outline the general theory, and then apply...

|x−y|≤ǫ |x−y| |V (y)|dy = 0) compared to the classical Cauchy-Lipshitz condition for vector fields. On the other hand, tremendous progress have been done in the last 25 years concerning the theory of ODEs using PDE’s methods: extension of the Cauchy-Lipshitz condition to Sobolev ones (DiPerna-Lions 1989) and BV vector fields (Bouchut for the Hamiltonian case 2001 and Ambrosio for the general ca...