Quasi-unitary algebras attached to temperature states in statistical mechanics. A comment on the work of Haag,Hugenholtz and Winnink

We show that the *-algebra of analytic elements with respect to time translations which plays a central role inHaag, Hugenholtz andWinnink's formulation of the Kubo-Martin-Schwinger boundary condition, is a quasi-unitary algebra in the sense ofDixmier. The commutant theorem proved byHaag, Hugenholtz andWinnink is thus reduced toDixmier's commutant theorem for quasi-unitary algebras.     

Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig–Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by intervals instead of by fixed values. The flexible cargo sizes have consequences for the times used in the ports because both the loading and unloading times depend on the cargo sizes. We found it computationally hard to find exact solutions to the subproblems, so our method does not guarantee to find the optimum over all solutions. To be able to say something about how good our solution is, we generate a bound on the difference between the true optimal objective and the objective in our solution. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that our Dantzig–Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimality.     

Unimodular functions and interpolating Blaschke products

The result by Bourgain that every unimodular function on the unit circle can be factored as with and Blaschke products can be improved. We show that the same result holds with and interpolating Blaschke products. This will at the same time be a refinement of Jones's result that every unimodular function can be approximated in the -norm by a ratio of interpolating Blaschke products.

     

Delocalized carotenoid cations in relation to the soliton model

A series of charge-delocalized carotenoid mono- and dications have been prepared by treatment of selected carotenoids with Br?nsted and Lewis acids. The detailed structures of the carbocations were established by NMR studies in the temperature range from -10 to -20 degrees C. The general strategy for structure elucidation by NMR of several cationic components in a mixture is outlined. Bond type and regions of bond inversion were established, as well as the charge distribution, which was determined from the difference in (13)C chemical shift at each carbon. This method gave a more accurate estimate for the partial charges than by using the Spiesecke-Schneider relationship. The resulting charge distribution was used as models for the structure of charged solitons. These carotenoid cations have the most delocalized charge so far determined, and the monocations represent the first experimental structure determination of positively charged solitons. The soliton width determined here is in good agreement with the results of previous AM1 calculations.     

Dynamic roughening and fluctuations of dipolar chains

Nonmagnetic particles in a carrier ferrofluid acquire an effective dipolar moment when placed in an external magnetic field. This fact leads them to form chains that will roughen due to Brownian motion when the magnetic field is decreased. We study this process through experiments, theory and simulations, three methods that agree on the scaling behavior over 5 orders of magnitude. The rms width goes initially as t(1/2), then as t(1/4) before it saturates. We show how these results complement existing results on polymer chains, and how the chain dynamics may be described by a recent non-Markovian formulation of anomalous diffusion.     

Effects of short-term irradiation on photoinhibition and accumulation of mycosporine-like amino acids in sun and shade species of the red algal genus Porphyra

The effect of irradiance (40 and 840 micromol photons m(-2) s(-1)) of short-term (48 h) irradiation on photosynthetic activity (estimated as oxygen evolution and as chlorophyll fluorescence), specific absorption and fluorescence excitation spectra, photosynthetic pigment accumulation (chlorophyll a and biliproteins) and UV-absorbing compounds (mycosporine-like amino acids, MAAs) was investigated in sun and shade species of the red algal genus Porphyra collected in Trondheimsfjord (Norway). In the sun type, high irradiance exposure (840 micromol photons m(-2) s(-1)) did not alter the Chl a concentration, however, exposure to a lower irradiance (40 micromol photons m(-2) s(-1)) for 48 h significantly increased the chlorophyll concentration. The content of MAAs was significantly higher in the suntype than in the shade type algae. Porphyra-334 is the main MAA in this species followed by shinorine. The total content of MAAs significantly (P<0.05) increased in the sun type after 48 h exposure to both high and low irradiances. However, in the shade type, porphyra-334 significantly decreased (P<0.05) after both high and low irradiance exposure. Photosynthetic activity (as oxygen evolution) and the optimal quantum yield (F(v)/F(m)), as an indicator of photoinhibition, decreased under low and high irradiance in the shade type algae and no full recovery was observed when the algae were transferred to very low irradiation.The sun type algae presented a higher capacity of acclimation to increased irradiance than the shade type algae. This high acclimation of sun type algae to short term high irradiance exposure (48 h) is explained by the higher thermal dissipation. This was estimated as the ratio of nonphotochemical quenching related to the light dose (q(N):dose) and by the accumulation of MAAs.     

Physical properties of aqueous solutions of a thermo-responsive neutral copolymer and an anionic surfactant: turbidity and small-angle neutron scattering studies

Aqueous mixtures of the anionic sodium dodecyl sulfate (SDS) surfactant and thermo-responsive poly(N-vinylcaprolactam) chains grafted with omega-methoxy poly(ethylene oxide) undecyl alpha-methacrylate (PVCL-g-C11EO42) have been characterized using turbidimetry and small-angle neutron scattering (SANS). Turbidity measurements show that the addition of SDS to a dilute aqueous copolymer solution (1.0 wt %) induces an increase of the cloud point (CP) value and a decrease of the turbidity at high temperatures. In parallel, SANS results show a decrease of both the average distance between chains and the global size of the objects in solution at high temperatures as the SDS concentration is increased. Combination of these findings reveals that the presence of SDS in the PVCL-g-C11EO42 solutions (1.0 wt %) promotes the formation of smaller aggregates and, consequently, leads to a more homogeneous distribution of the chains in solution upon heating of the mixtures. Moreover, the SANS data results show that the internal structure of the formed aggregates becomes more swollen as the SDS concentration increases. On the other hand, the addition of moderate amounts of SDS (up to 4 mm) to a semidilute copolymer solution (5.0 wt %) gives rise to a more pronounced aggregation as the temperature rises; turbidity and SANS studies reveal in this case a decrease of the CP value and an increase of the scattered intensity at low q. The overall picture that emerges from this study is that the degree of aggregation can be accurately tuned by varying parameters such as the temperature, level of surfactant addition, and polymer concentration.     

Longer polyenyl cations in relation to soliton theory

The carotene-like polyenes decapreno-beta-carotene (C50), C54-beta-carotene (C54, first synthesis) and dodecapreno-beta-carotene (C60) with 15, 17 and 19 conjugated double bonds, respectively, were synthesized by double Wittig reactions. Introduction of a leaving group in allylic position failed, and cations were obtained by hydride elimination effected by i) triphenylcarbenium tetrafluoroborate-d15, prepared by a new method, or ii) treatment with trifluoroacetic acid-d. Deuterated reagents were employed for product analysis by 1H NMR. Parallel experiments were performed with beta,beta-carotene (C40). NIR spectra at room temperature and at -15 degrees C were employed for characterisation and stability studies of the cationic products. In CH2Cl2lambdamax in the 900-1350 nm region was recorded. NMR data for the cationic product of beta,beta-carotene obtained by the two new preparation methods were consistent with the two monocations previously characterised. The cationic products of the longer polyenes provided downfield-shifted, broadened signals, compatible with C50-monocation, mixed C54-mono- and dication and C60-dication. Combined NIR and NMR data suggest that the extent of charge delocalisation is limited by the maximum soliton width for cations obtained from linear polyenes with more than ca. 20 sp2-hybridized carbon atoms.