Chruściel and Galloway constructed a Cauchy horizon that is nondifferentiable on a dense set. We prove that in a certain class of Cauchy horizons densely nondifferentiable Cauchy horizons are generic. We show that our class of densely nondifferentiable Cauchy horizons implies the existence of densely nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also the existence o...

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

We work throughout in a finite relational language L. Our aim is to analyze in as purely a model-theoretic context as possible some recent results of Shelah et al in which 0 − 1-laws for random structures of various types are proved by a specific kind of quantifier elimination: near model completeness. In Section 2 we describe the major results of these methods ([12], [11] etc.) and some of the...

Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers.

The eeect of query order on NP-completeness is investigated. A sequence ~ D = (D 1 ; : : : ; D k) of decision problems is deened to be sequentially complete for NP if each D i 2 NP and every problem in NP can be decided in polynomial time with one query to each of D 1 ; : : : ; D k in this order. It is shown that, if NP contains a language that is p-generic in the sense of Ambos-Spies, Fleischh...

Evolution strategies are a class of general optimisation algorithms which are applicable to functions that are multimodal, non-diierentiable, or even discontinuous. Although recombination operators have been introduced into evolution strategies, their primary search operator is still mutation. Classical evolution strategies rely on Gaussian mutations. A new mutation operator based on the Cauchy...

We express the generalized Cauchy-Stieltjes transforms of some particular Beta distributions depending on a positive parameter λ as λ-powered Cauchy-Stieltjes transforms of some probability measures. The Cauchy-Stieltjes transforms of the latter measures are shown to be the geometric mean of the Cauchy-Stieltjes transform of the Wigner law together with another one. Moreover, they are absolutel...

We show that several weakenings of the Cauchy condition are all equivalent under the assumption of countable choice, and investigate to what extent choice is necessary. We also show that the syntactically reminiscent notion of metastability allows similar variations, but in terms of its computational content is an empty notion. §1. Almost Cauchyness. Apart from the last section, we work in Bish...