Ein etwas modificirtes Calcimeter

Ohne Zusammenfassung     

Separation and Determination of Chloroplast Pigments from Spinach by Thin-Layer Chromatography: a Student Laboratory Experiment

JPC – Journal of Planar Chromatography – Modern TLC -     

RSOS Models and Jantzen–Seitz Representations of Hecke Algebras at Roots of Unity

A special family of partitions occurs in two apparently unrelated contexts: the evaluation of one-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras H_m. We provide an explanation of this coincidence by showing how the irreducible H_m-modules which remain irreducible under restriction to H_{m_1} (Jantzen–Seitz modules) can be determined from the decomposition of a tensor product of representations sl_n.     

A power-law distribution for tenure lengths of sports managers

We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.     

The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Synthesis and mesomorphic behaviour of comb-like polymers based on lipopeptides with two hydrophobic chains

Polymerizable lipopeptides with two hydrophobic chains were synthesized and transformed into comb-like polymers by radical polymerization. The structure of dry polymerizable lipopeptides and comb-like polymers and of their aqueous solutions was determined by X-ray diffraction. Comb-like polymers exhibit both thermotropic and lyotropic properties. Three types of mesomorphic structure were resolved: smectic B, smectic A and cylindrical hexagonal. The domains of stability of the mesophases and the values of their structural parameters were established.     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

Straightforward conversion of alcohols into dibenzenesulfonimides

The reaction of various alcohols with N-fluorodibenzenesulfonimide and triphenylphosphine leads to the corresponding dibenzenesulfonylated amines in high yields.     

Multiple recurrence and nilsequences

Aiming at a simultaneous extension of Khintchine(X,X,m,T)(X,\mathcal{X},\mu,T) and a set A ? XA\in\mathcal{X} of positive measure, the set of integers n such that A T^2nA T^knA)(A)^k+1-\mu(A{\cap} T^{n}A{\cap} T^{2n}A{\cap} \ldots{\cap} T^{kn}A)>\mu(A)^{k+1}-\epsilon is syndetic. The size of this set, surprisingly enough, depends on the length (k+1) of the arithmetic progression under consideration. In an ergodic system, for k=2 and k=3, this set is syndetic, while for kòf(x)f(Tⁿx)f(T²ⁿx)? f(T^knx)  dm(x)\int{f(x)f(T^{n}x)f(T^{2n}x){\ldots} f(T^{kn}x) \,d\mu(x)} , where k and n are positive integers and f is a bounded measurable function. We also derive combinatorial consequences of these results, for example showing that for a set of integers E with upper Banach density d^*(E)>0 and for all {n ? \mathbbZ\colon d^*(E?(E+n)?(E+2n)?(E+3n)) > d^*(E)⁴-e}\big\{n\in\mathbb{Z}{\colon} d^*\big(E\cap(E+n)\cap(E+2n)\cap(E+3n)\big) > d^*(E)^4-\epsilon\big\}     

Inverse gas chromatography of lignocellulosic fibers coated with a thermosetting polymer: Use of peak maximum and conder and young methods

The Conder and Young (CY) and the peak maximum (PM) methods were used to estimate the retention time of n-alkane probes on chemithermomechanical pulp (CTMP) wood fibers treated with a low molecular weight grade phenol-formaldehyde resin (PFR). Thermodynamic functions (ΔH_a^o, ΔG_a^o, and ΔS_a^o) and the London dispersive component of the surface energy were derived from these retention times. Treated wood fibers show a high energy surface due to the presence of the thermoset resin on their surface. Values of ΔH_a^o obtained from the CY method were higher than those obtained with the PM method at relatively high temperatures and with relatively low molecular weight alkanes. The results from the two methods were identical at low temperature (293 K) and with the relatively high molecular weight alkane n-undecane.