A New Algorithm for Solving the Word Problem in Braid Groups

One of the most interesting questions about a group is whether its word problem can be solved and how. The word problem in the braid group is of particular interest to topologists, algebraists, and geometers, and is the target of intensive current research. We look at the braid group from a topological point of view (rather than a geometric one). The braid group is defined by the action of diffeomorphisms on the fundamental group of a punctured disk. We exploit the topological definition in order to give a new approach for solving its word problem. Our algorithm, although not better in complexity, is faster in comparison with known algorithms for short braid words, and it is almost independent of the number of strings in the braids. Moreover, the algorithm is based on a new computer presentation of the elements of the fundamental group of a punctured disk. This presentation can be used also for other algorithms.     

μ+SR frequency shifts in the van‐Vleck paramagnet PrIn3

As part of an ongoing μ⁺SR study on cubic van‐Vleck paramagnets of the PrM₃ series ( M\ =\ In,Pb,Tl,Sn), in which the CEF level scheme varies systematically, we present preliminary static μ⁺SR results on a single crystal of PrIn₃. From the angular dependence and from the appearance of the μSR spectra, we could determine that stopped μ⁺ occupy octahedral sites of the (1/2, 0, 0) type, i.e. sites with 2 Pr and 4 In atoms as neighbors. The spectral frequency shifts can be accounted for by assigning to the Pr sites essentially unperturbed 4f dipole moment values, as derived from bulk magnetization measurements. The temperature dependence of the shifts scales to a good accuracy with the bulk susceptibility. It is concluded that unlike previous observations with PrNi₅, the local perturbations induced by an interstitial μ⁺ on the CEF levels of neighboring Pr in the PrIn₃ system are small compared with the unperturbed level splitting itself. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comparison of stabilization modes of a symmetrical third-order non-linear oscillatory unit

The possibility of constructing symmetrical stabilized oscillator models that operate in several phases instead of operating in two phases, as is more usual, is considered in the present paper. In particular, symmetrical oscillator models operating in three phases are discussed comprehensively. An interesting feature of their dynamic behaviour, e.g. the appearance of limit cycles which are regionally stable and not orbitally stable, as is the case in the two phase counterpart, is suggested and dealt with.     

Functionalization of Silk Fibroin with NeutrAvidin and Biotin

New methods are needed to modify silk biomaterials with bioactive molecules for tissue engineering and drug delivery. In the present study, silk fibroin in solution or in microsphere format was coupled with NeutrAvidin via carbodiimide chemistry. Silk fibroin retained its self‐assembly features after reaction. It was found that more than four NeutrAvidin molecules bound to one silk molecule. Non‐specific binding of biotin or NeutrAvidin to silk microspheres could be reduced by pre‐treatment of the microspheres with BSA or post‐treatment with detergent. The NeutrAvidin‐coupled silk microspheres were coupled with biotinylated anti‐CD3 antibody and the functionalized microspheres were able to specifically bind to the CD3 positive T‐lymphocytic cell line Jurkat.

     

Destillation

Ohne Zusammenfassung     

Equilibrium and pre-equilibrium emissions in proton-induced reactions on <Superscript>203,205</Superscript>Tl

In this study, the excitation functions for the reactions ²⁰³Tl(p, n)²⁰³Pb, ²⁰⁵Tl(p, 3n)²⁰³Pb, ²⁰³Tl(p, 2n)²⁰²Pb, ²⁰⁵Tl(p, 4n)²⁰²Pb, ²⁰³Tl(p, 3n)²⁰¹Pb, ²⁰⁵Tl(p, 5n)²⁰¹Pb, ²⁰³Tl(p, 4n)²⁰⁰Pb and ²⁰⁵Tl(p, 6n)²⁰⁰Pb have been calculated using pre-equilibrium and equilibrium reaction mechanisms. Calculated results based on hybrid model, geometry-dependent hybrid model and cascade-exciton model have been compared with the experimental data.      

Elaboration of hybrid nanocluster materials by solution chemistry

The [(M₆L₁₂ⁱ)L₆^a]ⁿ⁻ and [(M₆L₈ⁱ)L₆^a] units (a = apical, i = inner) constitute the basic building blocks in the octahedral cluster chemistry. Nano-sized metallic clusters are easily obtained by solid state synthesis with transition elements associated with halogen or chalcogen. The intrinsic properties of M₆ cluster units—one or two electron reversible redox process, magnetism and luminescence—depend on the nature of the metal and ligands. The solubilisation of M₆ solid state compounds provides [(M₆L₁₂ⁱ)L₆^a]ⁿ⁻ or [(M₆L₈ⁱ)L₆^a]ⁿ⁻ building blocks with individual properties that can be further used for the design of hybrid organic/inorganic materials. Several examples of solid state precursors are presented as well as substitution reactions of apical ligands in solution. Indeed, hexacyano M₆ clusters are obtained by direct reaction of solid state precursors in aqueous KCN solutions. Low dimensional frameworks are subsequently obtained by recrystallisation of hexacyano M₆ clusters with transition elements. The functionalisation of cluster proceeds in two steps. The first one consists in the replacement of apical halogens of cluster unit precursors by labile groups as CF₃SO₃ (triflate) or solvent molecules after solution reaction. The second one consists in the substitution of the labile groups by functionalised phenolate or pyridine ligands.