Helium cosmic ray flux measurements at Mars

The helium energy spectrum in Martian orbit has been observed by the MARIE charged particle spectrometer aboard the 2001 Mars Odyssey spacecraft. The orbital data were taken from March 13, 2002 to October 28, 2003, at which time a very intense Solar Particle Event caused a loss of communication between the instrument and the spacecraft. The silicon detector stack in MARIE is optimized for the detection of protons and helium in the energy range below , which typically includes almost all of the flux during SPEs. This also makes MARIE an efficient detector for GCR helium in the energy range of 50–. We will present the first fully normalized flux results from MARIE, using helium ions in this energy range.     

The generalized Füredi conjecture holds for finite linear lattices

We say that a rank-unimodal poset P has rapidly decreasing rank numbers, or the RDR property, if above (resp. below) the largest ranks of P, the size of each level is at most half of the previous (resp. next) one. We show that a finite rank-unimodal, rank-symmetric, normalized matching, RDR poset of width w has a partition into w chains such that the sizes of the chains are one of two consecutive integers. In particular, there exists a partition of the linear lattices L_n(q) (subspaces of an n-dimensional vector space over a finite field, ordered by inclusion) into chains such that the number of chains is the width of L_n(q) and the sizes of the chains are one of two consecutive integers.     

Detection of discontinuities in scattered data approximation

A Detection Algorithm for the localisation of unknown fault lines of a surface from scattered data is given. The method is based on a local approximation scheme using thin plate splines, and we show that this yields approximation of second order accuracy instead of first order as in the global case. Furthermore, the Detection Algorithm works with triangulation methods, and we show their utility for the approximation of the fault lines. The output of our method provides polygonal curves which can be used for the purpose of constrained surface approximation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Photo‐Induced Electron Transfer Between Photosystem 2 via Cross‐linked Redox Hydrogels

Photosystem 2 (PS2) that catalyses light driven water splitting in photosynthesis was ‘wired’ to electrode surfaces via osmium‐containing redox polymers based on poly(vinyl)imidazol. The redox polymer hydrogel worked as both immobilization matrix and electron acceptor for the enzyme. Upon illumination, the enzymatic reaction could be switched on and a catalytic current was observed at the electrode. The catalytic current is directly dependent on the intensity of light used for the excitation of PS2. A typical current density of 45 μA cm^?2 at a light intensity of 2.65 mW cm^?2 could be demonstrated with a significantly improved operational stability.     

Position dependent and stochastic thinning of point processes

A short probabilistic proof of Kallenberg's theorem [2] on thinning of point processes is given. It is extended to the case where the probability of deletion of a point depends on the position of the point and is itself random. The proof also leads easily to a statement about the rate of convergence in Renyi's theorem on thinning a renewal process.     

Restricted rotation about the BN bond in aminoboranes: the determination of activation parameters using 13C NMR

In suitable cases, VT ¹³C NMR can provide a rapid and reliable method for obtaining activation parameters ΔH^★ and ΔS^★ for restricted rotation about the B  N bond in aminoboranes.     

Generalized Drinfel'd-Sokolov hierarchies

A general approach is adopted to the construction of integrable hierarchies of partial differential equations. A series of hierarchies associated to untwisted Kac-Moody algebras, and conjugacy classes of the Weyl group of the underlying finite Lie algebra, is obtained. The generalized KdV hierarchies of V.G. Drinfel'd and V.V. Sokolov are obtained as the special case for the Coxeter element. Various examples of the general formalism are treated in some detail; including the fractional KdV hierarchies.