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.

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.

The legs: a key to bird evolutionary success

Birds are the most diverse and largest group of extant tetrapods. They show marked variability, yet much of this variation is superficial and due to feather and bill color and shape. Under the feathers, the skeleto-muscular system is rather constant throughout the bird group. The adaptation to flight is the explanation for this uniformity. The more obvious morphological adaptations for flight are the wings, but the trunk is always rigid, the tail is short and the neck is flexible, since all these features are correlated with flying behaviour. Unrelated to the exigencies of flight, the legs always have three long bones, and all the birds walk on their toes. This leg structure is a striking plesiomorphic feature that was already present in related dinosaurs. The multi-purpose potential of the legs is the result of the skeletal architecture of a body with three segmented flexed legs. This configuration provides mechanical properties that allow the use of the legs as propulsive, paddling, foraging or grooming tools. It is the association of diverse modes of locomotion-walking, running, hopping, flying and swimming-that have enabled the birds to colonize almost all the environments on Earth.

ON THE RADICAL OF A FREE MALCEV ALGEBRA

We prove that the prime radical rad M of the free Malcev algebra M of rank more than two over a field of characteristic not equal 2 coincides with the set of all universally Engelian elements of M. Moreover, let T(M) be the ideal of M consisting of all stable identities of the split simple 7-dimensional Malcev algebra M over F. It is proved that rad M = J(M) boolean AND T(M), where J(M) is the Jacobian ideal of M. Similar results were proved by I. Shestakov and E. Zelmanov for free alternative and free Jordan algebras.

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.