We study two types of axially symmetric, stationary and asymptotically flat spacetimes using highly accurate numerical methods. One type contains a black hole surrounded by a perfect fluid ring and the other a rigidly rotating disc of dust surrounded by such a ring. Both types of spacetime are regular everywhere (outside of the horizon in the case of the black hole) and fulfil the requirements ...

In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...

We present a formal method for the veriication of regular VLSI archi-tectures. In our method, the behavioral speciication of the chip and its implementation are rst expressed in Alpha, a functional language for the design of regular synchronous architectures. The behavioral speciication is reened down to an abstract architecture description, while the implementation is simpliied by induction te...

We adapt techniques employed in the design of parallel sorting algorithms to propose new sequential and multi-core sorting operations. The proposed approach is used to develop asymptotically efficient deterministic and randomized sorting operations whose practical sequential and multi-core performance, as witnessed by an experimental study, matches or surpasses existing optimized sorting algori...

Extending an old conjecture of Tutte, Jaeger conjectured in 1988 that for any fixed integer p ≥ 1, the edges of any 4p-edge connected graph can be oriented so that the difference between the outdegree and the indegree of each vertex is divisible by 2p+1. It is known that it suffices to prove this conjecture for (4p + 1)-regular, 4p-edge connected graphs. Here we show that there exists a finite ...

We enumerate all possible types of spacetime causal structures that can appear in static, spherically symmetric configurations of a self-gravitating, real, nonlinear, minimally coupled scalar field φ in general relativity, with an arbitrary potential V (φ) , not necessarily positive-definite. It is shown that a variable scalar field adds nothing to the list of possible structures with a constan...

It is a fact simple to establish that the mixing time of random walk on d-regular graph $G_n$ with n vertices asymptotically bounded from below by $d/ ((d-2)\log (d-1))\log n$. Such bound obtained comparing infinite $d$-regular tree. If one can map another transitive onto $G_n$, then we improve strategy using comparison this (instead regular tree), and obtain lower form $1/h \log n$, where $h$ ...

We present a formal method for the veriication of regular VLSI architectures. In our method, the behavioral speciication of the chip and its implementation are rst expressed in Alpha, a language for the design of regular synchronous architectures. The behavioral spec-iication is reened down to an abstract architecture description, while the implementation is simpliied by induction techniques up...

We construct a family of time and angular dependent, regular S-brane solutions which corresponds to a simple analytical continuation of the Zipoy-Voorhees 4-dimensional vacuum spacetime. The solutions are asymptotically flat and turn out to be free of singularities without requiring a twist in space. They can be considered as the simplest non-singular generalization of the singular S0-brane sol...

This paper clarifies learning efficiency of a non-regular parametric model such as a neural network whose true parameter set is an analytic variety with singular points. By using Sato’s b-function we rigorously prove that the free energy or the Bayesian stochastic complexity is asymptotically equal to λ1 log n− (m1 − 1) log log n+constant, where λ1 is a rational number, m1 is a natural number, ...