Spectral decomposition of an elementary 3-fermion 2-body operator

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P²_g∧I¹A³∑_{1≤i≤j≤3}P²_g(i, j)A³ acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here P_g² denotes the projection operator onto a 2-particle antisymmetric function g², while A³ denotes the 3-particle antisymmetrizing operator.     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Model for describing the production of Centauro events and strangelets in heavy-ion collisions

A phenomenological model for describing the production of Centauro events in relativistic heavy-ion collisions is discussed. The model provides quantitative predictions for kinematical variables, for the baryon number, and for the masses of a Centauro fireball and of its decay products. A Centauro fireball decays predominantly into nucleons, strange hyperons, and possibly strangelets. Centauro events in Pb + Pb collisions at the LHC energy are simulated for the CASTOR detector. The signatures of these events are discussed in detail.     

Analysis of Glycosides and Aglycones of Flavonoid Compounds by Double-Development Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - Flavonoid glycosides are much more polar than their aglycones and the two groups of compounds are difficult to separate by planar...     

The capacity of parabolic julia sets

Supported by SFB 170 “Geometrie und Analysis” at the University of G?ttingen     

The complete grapht-packings andt-coverings

The aim of this paper is to introduce the notions of floor and ceiling functions related to graph edge-decompositions intot mutually isomorphic parts. It is shown that, given any natural numbert, uniform and extremal t-packing andt-covering exist for each complete graph and each complete bipartite graph. Extremal in this context means that both a remainder and a surplus are absolutely minimum. In proofs, decompositions of multigraphs into matchings are involved. Open problems and conjectures are stated.     

Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.     

On the existence and the stability of solutions for higher-order semilinear Dirichlet problems

We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.     

Influence of organic modifiers on morphology and crystallization of poly(ϵ‐caprolactone)/synthetic clay intercalated nanocomposites

ε‐caprolactone was polymerized in the presence of neat montmorillonite or organomontmorillonites to obtain a variety of poly(ε‐caprolactone) (PCL)‐based systems loaded with 10 wt % of the silicates. The materials were thoroughly investigated by different X‐ray scattering techniques to determine factors affecting structure of the systems. For one of the nanocomposites it was found that varying the temperature in the range corresponding to crystallization of PCL causes reversible changes in the interlayer distance of the organoclay. Extensive experimental and literature studies on this phenomenon provided clues indicating that this effect might be a result of two‐dimensional ordering of PCL chains inside the galleries of the silicate. Small angle X‐ray scattering and wide angle X‐ray scattering investigation of filaments oriented above melting point of PCL revealed that polymer lamellae were oriented perpendicularly to particles of unmodified silicate, while in PCL/organoclay systems they were found parallel to clay tactoids. Calorimetric and microscopic studies shown that clay particles are effective nucleating agents. In the nanocomposites, PCL crystallized 20‐fold faster than in the neat polymer. The crystallization rate in nanocomposites was also significantly higher than in microcomposite. Further research provided an insight how the presence of the filler affects crystalline fraction and spherulitic structure of the polymer matrix in the investigated systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2350–2367, 2007     

About Rotational Transitions and Muon Transfer in Muonic Hydrogen–Helium Systems

Hyperfine Interactions - Rotational J=1→J=0 transitions in muonic molecule, (3Heμd) J ++, in [(3Heμd)++,2e]–D and [(3Heμd)++,e]+–D collisions are considered. The...