This is the third in a series of papers aimed at generalizing Siebenmann’s famous PhD thesis [13] so that the results apply to manifolds with nonstable fundamental groups at infinity. Siebenmann’s work provides necessary and sufficient conditions for an open manifold of dimension ≥ 6 to contain an open collar neighborhood of infinity, ie, a manifold neighborhood of infinity N such that N ≈ ∂N ×...

This article is a further contribution to our research [1] into a class of infinite-dimensional Lie algebras L∞(N+, N−) generalizing the standardW∞ algebra, viewed as a tensor operator algebra of SU(1, 1) in a group-theoretic framework. Here we interpret L∞(N+, N−) either as infinite continuations of pseudo-unitary symmetries or as “higher-U(N+, N−)spin extensions” of the diffeomorphism algebra...

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open n–manifold (n ≥ 7). This paper may be viewed as a generalization of Siebenmann’s famous collaring theorem to open manifolds with non-stable fundamental group syst...

The Miller-Rabin pseudo primality test is widely used in cryptographic libraries, because of its apparent simplicity. But the test is not always correctly implemented. For example the pseudo primality test in GNU Crypto 1.1.0 uses a fixed set of bases. This paper shows how this flaw can be exploited to break the SRP implementation in GNU Crypto. The attack is demonstrated by explicitly construc...

We will study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. A special attention will be paid to the lexicographic product of the group of the integers with an arbitrary po-group. Then we apply these results to the study of n-perfect pseudo effect algebras. We show that the category of strong n-perfect pseudo-e...

BACKGROUND Acute appendicitis is a surgical emergency in which the appendix is surgically removed to prevent peritonitis due to perforation of the appendix. Depending on age and gender, up to 17% of removed appendices do not show the histopathological changes pathognomonic for acute appendicitis and are called 'pseudo-appendicitis'. Intestinal spirochaetes have been reported in up to 12.3% of t...