Stability properties and the KMS condition

First we derive stability properties of KMS states and subsequently we derive the KMS condition from stability properties. New results include a convergent perturbation expansion for perturbed KMS states in terms of appropriate truncated functions and stability properties of ground states. Finally we extend the results of Haag, Kastler, Trych-Pohlmeyer by proving that stable states ofL ¹-asymptotically abelian systems which satisfy a weak three point cluster property are automatically KMS states. This last theorem gives an almost complete characterization of KMS states, ofL ¹-asymptotic abelian systems, by stability and cluster properties (a slight discrepancy can occur for infinite temperature states).Supported during this research by the Norwegian Research Council for Science and Humanities     

Daily duration of vitamin D synthesis in human skin with relation to latitude, total ozone, altitude, ground cover, aerosols and cloud thickness

Vitamin D production in human skin occurs only when incident UV radiation exceeds a certain threshold. From simulations of UV irradiances worldwide and throughout the year, we have studied the dependency of the extent and duration of cutaneous vitamin D production in terms of latitude, time, total ozone, clouds, aerosols, surface reflectivity and altitude. For clear atmospheric conditions, no cutaneous vitamin D production occurs at 51 degrees latitude and higher during some periods of the year. At 70 degrees latitude, vitamin D synthesis can be absent for 5 months. Clouds, aerosols and thick ozone events reduce the duration of vitamin D synthesis considerably, and can suppress vitamin D synthesis completely even at the equator. A web page allowing the computation of the duration of cutaneous vitamin D production worldwide throughout the year, for various atmospheric and surface conditions, is available on the Internet at http://zardoz.nilu.no/~olaeng/fastrt/VitD.html and http://zardoz.nilu.no/~olaeng/fastrt/VitD-ez.html. The computational methodology is outlined here.     

Relaxing the clustering condition in the derivation of the KMS property

We consider as in [1] an infinite dynamical system idealized as aC*-algebra acted upon by time-translation automorphisms. We show that a stationary state of such a system which is stable for local perturbations of the dynamics and is clustering in time, either gives rise to a one-sided energy spectrum or is a KMS state. The clustering property assumed here is weaker than the one assumed in [1]. The new proof makes explicit use of spectral properties of clustering states.Supported by the Norwegian Research Council for Science and Humanities.     

The absorption spectrum of localized electrons in crystalline 1,8-octanediol, γ-irradiated at 4.2 K

Crystalline 1.8-octanediol has been γ-irradiated and its optical absorption spectrum has been measured at 4.2 K. The spectrum consists of three partially resolved peaks with maxima at 740, 590, and 490 nm. The peaks cannot be separated by photobleaching or annealing. It is suggested that they arise from transitions inherent in each localized electron.     

Constant factor approximation for ATSP with two edge weights

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was given recently by Svensson. This was accomplished by introducing an easier problem called Local-Connectivity ATSP and showing that a good solution to this problem can be used to obtain a constant factor approximation for ATSP. In this paper, we solve Local-Connectivity ATSP for two different edge weights. The solution is based on a flow decomposition theorem for solutions of the Held–Karp relaxation, which may be of independent interest.     

Universal inequalities for the eigenvalues of a power of the Laplace operator

In this paper, we obtain a new abstract formula relating eigenvalues of a self-adjoint operator to two families of symmetric and skew-symmetric operators and their commutators. This formula generalizes earlier ones obtained by Harrell, Stubbe, Hook, Ashbaugh, Hermi, Levitin and Parnovski. We also show how one can use this abstract formulation both for giving different and simpler proofs for all the known results obtained for the eigenvalues of a power of the Laplace operator (i.e. the Dirichlet Laplacian, the clamped plate problem for the bilaplacian and more generally for the polyharmonic problem on a bounded Euclidean domain) and to obtain new ones. In a last paragraph, we derive new bounds for eigenvalues of any power of the Kohn Laplacian on the Heisenberg group.     

Incorporation of nanogels within calcite single crystals for the storage,protection and controlled release of active compounds

Nanocarriers have tremendous potential for the encapsulation, storage and delivery of active compounds. However, current formulations often employ open structures that achieve efficient loading of active agents, but that suffer undesired leakage and instability of the payloads over time. Here, a straightforward strategy that overcomes these issues is presented, in which protein nanogels are encapsulated within single crystals of calcite (CaCO₃). Demonstrating our approach with bovine serum albumin (BSA) nanogels loaded with (bio)active compounds, including doxorubicin (a chemotherapeutic drug) and lysozyme (an antibacterial enzyme), we show that these nanogels can be occluded within calcite host crystals at levels of up to 45 vol%. Encapsulated within the dense mineral, the active compounds are stable against harsh conditions such as high temperature and pH, and controlled release can be triggered by a simple reduction of the pH. Comparisons with analogous systems – amorphous calcium carbonate, mesoporous vaterite (CaCO₃) polycrystals, and calcite crystals containing polymer vesicles – demonstrate the superior encapsulation performance of the nanogel/calcite system. This opens the door to encapsulating a broad range of existing nanocarrier systems within single crystal hosts for the efficient storage, transport and controlled release of various active guest species.

Nanocarriers have tremendous potential for the encapsulation, storage and delivery of active compounds.     

Removal of Water-Soluble Extractives Improves the Enzymatic Digestibility of Steam-Pretreated Softwood Barks

Softwood bark contains a large amounts of extractives—i.e., soluble lipophilic (such as resin acids) and hydrophilic components (phenolic compounds, stilbenes). The effects of the partial removal of water-soluble extractives before acid-catalyzed steam pretreatment on enzymatic digestibility were assessed for two softwood barks—Norway spruce and Scots pine. A simple hot water extraction step removed more than half of the water-soluble extractives from the barks, which improved the enzymatic digestibility of both steam-pretreated materials. This effect was more pronounced for the spruce than the pine bark, as evidenced by the 30 and 11% glucose yield improvement, respectively, in the enzymatic digestibility. Furthermore, analysis of the chemical composition showed that the acid-insoluble lignin content of the pretreated materials decreased when water-soluble extractives were removed prior to steam pretreatment. This can be explained by a decreased formation of water-insoluble “pseudo-lignin” from water-soluble bark phenolics during the acid-catalyzed pretreatment, which otherwise results in distorted lignin analysis and may also contribute to the impaired enzymatic digestibility of the barks. Thus, this study advocates the removal of extractives as the first step in the processing of bark or bark-rich materials in a sugar platform biorefinery.