Excitation energy transfer in isolated chlorosomes from Chlorobaculum tepidum and Prosthecochloris aestuarii

Excitation energy transfer in chlorosomes from photosynthetic green sulfur bacteria, Chlorobaculum (Cba.) tepidum and Prosthecochloris (Pst.) aestuarii, have been studied at room temperature by time-resolved femtosecond transient absorption spectroscopy. Bleach rise times from 117 to 270 fs resolved for both chlorosomes reflect extremely efficient intrachlorosomal energy transfer. Bleach relaxation times, from 1 to 3 ps and 25 to 35 ps, probed at 758 nm were tentatively assigned to intrachlorosomal energy transfer based on amplitude changes of the global fits and model calculations. The anisotropy decay constant of about 1 ps resolved at 807 nm probe wavelength for the chlorosomes from Chloroflexus aurantiacus, Pst. aestuarii and Cba. tepidum was related to energy transfer between bacteriochlorophyll a molecules of the baseplate and partly to intrachlorosomal energy transfer. The longer anisotropy components 6.6, 8.8 and 12.1 ps resolved for the three chlorosomes, respectively, were assigned to chlorosome to baseplate energy transfer. Global fits of magic-angle data also revealed longer chlorosome to baseplate energy transfer components from 95 to 135 ps, in accord with results from simulations.     

The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

For a wide class of radial weights we calculate the essential norm of a weighted composition operator uC_j{uC_\varphi} on the weighted Banach spaces of analytic functions in terms of the analytic function u \colon \mathbb D ? \mathbb C{u \colon \mathbb D \to \mathbb C} and the nth power of the analytic selfmap j{\varphi} of the open unit disc \mathbb D{\mathbb D} . We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.     

Vague objects and phenomenal wholes

We consider the so-called problem of the many, formulated by Peter Unger. It arises because ordinary material things do not have precise boundaries: it is always possible to find borderline parts of which it is not true to say either that they are parts or that they are not. Unger’s conclusion is that there are no ordinary things at all. We describe the solutions of Peter van Inwagen and David Lewis, and make some critical comments upon them. After that we present our own suggestion which is based on ideas developed by Leibniz in connection with problems of unity and plurality. We suggest that what the problem of the many teaches us is that in order to understand what ordinary things are, we have to take seriously the Leibnizian-Kantian distinction between phenomena and things-in-themselves.     

Tabu Search heuristics for the Vehicle Routing Problem with Time Windows

This paper surveys the research on the Tabu Search heuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes for a fleet of vehicles from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. In addition to describing basic features of each method, experimental results for Solomon’s benchmark test problems are presented and analyzed. This work was partially supported by the Emil Aaltonen Foundation, Liikesivistysrahasto Foundation, the Canadian Natural Science and Engineering Research Council and the TOP program funded by the Research Council of Norway. This support is gratefully acknowledged.     

Pentacarbonylmetallderivatevon phosphinidenen und diphosphenen

Reaction of Na₂[M₂CO₁₀] (M = Cr, Mo, W) with RPCl₂ (R = mesityl, CH(SiMe₃)₂) yields, depending on the reaction conditions as well as on the steric demand of R, phosphinidene compounds [(CO)₅M]₂PR and diphosphene species [(CO)₅M]_nRPPR (n = 1, 2). With especially bulky substituents mono-nuclear diphosphene derivatives are the preferred reaction products. For dinuclear diphosphene compounds the Z-configuration is induced when R = mesityl while in other cases the E-configuration is the more stable form.The structures of the new compounds are documented by X-ray analyses of three examples. The accumulated material allows for a comparative discussion of the ³¹P NMR spectra, which often show unconventional low-field shifts (up to 1216 ppm), as well as of the characteristic UV/VIS spectra. For all compounds IR, ¹H NMR and mass spectra as well as correct analyses are presented.     

Homeomorphisms of the Heisenberg group preserving BMO

We provide a new geometric proof of Reimann’s theorem characterizing quasiconformal mappings as the ones preserving functions of bounded mean oscillation. While our proof is new already in the Euclidean spaces, it is applicable in Heisenberg groups as well as in more general stratified nilpotent Carnot groups.     

Blow up of balls and coverings in metric spaces

We obtain some refinements and extensions of the Basic Covering Theorem in a metric space (X, ρ). The properties of the metric ρ are used to define an inclusion coefficient k in this theorem, and this is related to the supremum of numbers t such that ρ ^t is a metric in X. The inclusion coefficient k characterizes ultrametric spaces.     

Capacity and Potential Estimates for Quasiminimizers

We obtain estimates for quasiminimizing potentials and their level sets. A new method, based on one dimensional quasiminimizers, is used. The connection of these estimates and the maximum principle is studied.