Two important but almost never related beliefs

Engelmann believes in two general strong beliefs. On one side, Engelmann believes in probabilistic skepticism. That the existence has its maximum probability or there is no existence at all is not possible. The other probabilities of existence are always possible. On the other hand, instead of elements that constitute a beginning arrived at by an unknown division, the Gestalt theory begins with wholes or Gestalten. These Gestalten can be divided in parts but each part can be only a part of his specific Gestalt. The majority of probabilistic skeptics and the majority of Gestalt theory followers do not believe they can be together accepted. On the contrary Engelmann is a member of a small group that both beliefs occur simultaneously. Bibace`s questions were each answered by Engelmann. In some questions Engelmann harmonize with Bibace, in others they disagree.

Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.

The chemiluminescent peroxyoxalate system: state of the art almost 50 years from its discovery

Almost fifty years after the discovery of the peroxyoxalate reaction by E. A. Chandross in the early nineteen sixties, this review article intends to give a general overview on mechanistic aspects of this system and to describe the principles of its analytical application. After a short general introduction on the principles of chemiluminescence and the history of peroxyoxalate discovery, mechanistic aspects of high-energy intermediate formation, its structure and its reaction with an activator in the peroxyoxalate system are discussed. Finally, analytical applications of peroxyoxalate chemiluminescence are exemplified using representative recent examples, including oxalic acid detection in biological samples.

Almost p-compact groups

We show that if p is a selective ultrafilter, then for each cardinal alpha <= omega(1), there exists a topological group G such that G(beta) is almost p-compact (in particular, countably compact), for beta < alpha, but G(alpha) is not countably compact. If in addition, we assume Martin's Axiom, then the result above holds for every alpha < c. (C) 2012 Elsevier By. All rights reserved.

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.