Surface tensor estimation from linear sections

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n‐dimensional Euclidean space. The estimators are based on one‐dimensional linear sections. In a design based setting we suggest three types of estimators. These are based on isotropic uniform random lines, vertical sections, and non‐isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting.     

Diagonal-preserving ring ⁎-isomorphisms of Leavitt path algebras

The graph groupoids of directed graphs E and F are topologically isomorphic if and only if there is a diagonal-preserving ring ?-isomorphism between the Leavitt path algebras of E and F.     

Projektive Punktskalen und Summationsformeln für Tschebyscheff-Polynome

Zusammenfassung. Mit Hilfe der projektiven Geometrie werden neuartige Summationsformeln hergeleitet, die die Tschebyscheff-Polynome und modifizierte Polynome enthalten; z. B. gilt für alle : Daraus ergeben sich wiederum interessante Summationsformeln für die Hyperbelfunktionen; es gilt z. B. für positive reelle Zahlen t: Eingegangen am 28.02.96, revidierte Fassung am 25.08.97 / Angenommen am 09.10.97     

Modelling subsurface coupled chemical reactions and fluid flow over long time periods

Simulation of coupled chemical reactions and fluid flow in porous sedimentary basins over long time periods is a numerical challenge. Most models representing such a physical problem are solved as PDEs where efficient timestepping with controlled error is difficult. We use the differential algebraic equation system approach where robust adaptive timestepping algorithms are available in the solvers, e.g., RADAU5 and DASSL. Mathematical and numerical models for coupled chemical reactions and fluid flow are derived. The models have several interesting properties, e.g., strong nonlinearities and stiffness, which are discussed. We test the performance of our code. This revised version was published online in June 2006 with corrections to the Cover Date.     

Orthocomplemented complete lattices and graphs

The problem I consider originates from Dörfler, who found a construction to assign an Orthocomplemented latticeH(G) to a graphG. By Dörfler it is known that for every finite Orthocomplemented latticeL there exists a graphG such thatH(G)=L. Unfortunately, we can find more than one graphG with this property, i.e., orthocomplemented lattices which belong to different graphs can be isomorphic. I show some conditions under which two graphs have the same orthocomplemented lattice.     

Atome im Doppeltopf-Potential gefangen. Interferenz zwischen zwei Bose-Einstein-Kondensaten

Die Nachricht von den ersten Realisierungen von Bose-Einstein-Kondensaten aus schwach wechselwirkenden Atomen im Sommer 1995 [1,2] (siehe auch Physik in unserer Zeit, 27, 200 (5/1996)) zog eine Welle neuer Forschungsaktivitäten nach sich. Wolfgang Ketterle vom Massachusetts Institute of Technology, MIT, und Kollegen gelang es kürzlich, zwei Bose-Einstein-Kondensate zur Interferenz zu bringen [3].     

Moenomycin a: New chemistry that allows to attach the antibiotic to reporter groups, solid supports, and proteins

Moenomycin A (18) on reaction with the diazonium salt derived from bifunctional (protected) 15 yields the coupling product 19 which on reduction is converted into the moenomycin thiol derivative 21. Thiol 21 has been used to prepare selectively moenomycin dansyl and biotin adducts 26 and 28, respectively. This work was performed with the aim to use moenomycin as a tool for studies of the transglycosylation step in peptidoglycan biosynthesis.     

Ion-pair mediated transport of angiotensin, neurotensin, and their metabolites in liquid phase microextraction under acidic conditions

This paper discusses the behaviour of angiotensin 1 and neurotensin together with their metabolites in a three-phase liquid phase microextraction under acidic conditions. Variations in donor phase, organic phase, and acceptor phase are studied with extraction recovery as response variable. It is proved that for all peptides the transport across the organic phase is mediated by heptane-1-sulphonic acid. n-Octanol gave overall best results as organic phase. A donor phase volume of 1.0 mL was chosen as a compromise between optimal recovery and robustness of the LPME device. The optimal pH of the donor phase (using acceptor phase of pH 2) was found to be different for the peptides, which opens opportunities for selective sample preparation. Decreasing the acceptor phase pH to 1.0 resulted in increased extraction recoveries. On using 1.0 mL of donor phase containing 50 mM heptane-1-sulphonic acid pH 3, n-octanol as organic phase immobilized in the pores of the fibre, and 20 microL of acceptor phase containing 0.1 mol/L HCl, extraction recoveries up to 82% (enrichment factor = 41) were achieved. To our knowledge this is the first report on liquid phase microextraction of angiotensins and neurotensins.     

Excited state dynamics in solid and monomeric tetracene: The roles of superradiance and exciton fission

The excited state dynamics in polycrystalline thin films of tetracene are studied using both picosecond fluorescence and femtosecond transient absorption. The solid-state results are compared with those obtained for monomeric tetracene in dilute solution. The room temperature solid-state fluorescence decays are consistent with earlier models that take into account exciton-exciton annihilation and exciton fission but with a reduced delayed fluorescence lifetime, ranging from 20-100 ns as opposed to 2?μs or longer in single crystals. Femtosecond transient absorption measurements on the monomer in solution reveal several excited state absorption features that overlap the ground state bleach and stimulated emission signals. On longer timescales, the initially excited singlet state completely decays due to intersystem crossing, and the triplet state absorption superimposed on the bleach is observed, consistent with earlier flash photolysis experiments. In the solid-state, the transient absorption dynamics are dominated by a negative stimulated emission signal, decaying with a 9.2 ps time constant. The enhanced bleach and stimulated emission signals in the solid are attributed to a superradiant, delocalized S(1) state that rapidly fissions into triplets and can also generate a second superradiant state, most likely a crystal defect, that dominates the picosecond luminescence signal. The enhanced absorption strength of the S(0)→S(1) transition, along with the partially oriented nature of our polycrystalline films, obscures the weaker T(1)→T(N) absorption features. To confirm that triplets are the major species produced by relaxation of the initially excited state, the delayed fluorescence and ground state bleach recovery are compared. Their identical decays are consistent with triplet diffusion and recombination at trapping or defect sites. The results show that complications like exciton delocalization, the presence of luminescent defect sites, and crystallite orientation must be taken into account to fully describe the photophysical behavior of tetracene thin films. The experimental results are consistent with the traditional picture that tetracene's photodynamics are dominated by exciton fission and triplet recombination, but suggest that fission occurs within 10 ps, much more rapidly than previously believed.