A convergent star product for linear Poisson structures

An explicit star product ⋆ _α ^Γ on the dual of a general Lie algebra equipped with the linear Poisson bracket is constructed. An equivalence operator between this star product and the Kontsevich star product in [K₁] is given and diverse properties of the star product ⋆ _α ^Γ are studied. It is also proved that the star product ⋆ _α ^Γ provides a convergent deformation quantization in the sense of Rieffel [R₁].     

Microporated PEG Spheres for Fluorescent Analyte Detection

Poly(ethylene glycol) (PEG) hydrogels have been used to encapsulate fluorescently labeled molecules in order to detect a variety of analytes. The hydrogels are designed with a mesh size that will retain the sensing elements while allowing for efficient diffusion of small analytes. Some sensing assays, however, require a conformational change or binding of large macromolecules, which may be sterically prohibited in a dense polymer matrix. A process of hydrogel microporation has been developed to create cavities within PEG microspheres to contain the assay components in solution. This arrangement provides improved motility for large sensing elements, while limiting leaching and increasing sensor lifetime. Three hydrogel compositions, 100% PEG, 50% PEG, and microporated 100% PEG, were used to create pH-sensitive microspheres that were tested for response time and stability. In order to assess motility, a second, more complex sensor, namely a FITC-dextran/TRITC-Con A glucose-specific assay was encapsulated within the microspheres.     

Evidence for a wide extra-astrocytic distribution of S100B in human brain

Background  

S100B is considered an astrocytic in-situ marker and protein levels in cerebrospinal fluid (CSF) or serum are often used as biomarker for astrocytic damage or dysfunction. However, studies on S100B in the human brain are rare. Thus, the distribution of S100B was studied by immunohistochemistry in adult human brains to evaluate its cell-type specificity.     

10-GHz Optical Comb in L-Band Region With Brillouin/Erbium-Doped Fibre Laser

A multiwavelength Brillouin/erbium fibre laser (BEFL) which operates in the long wavelength (L-band) region is demonstrated for potential applications in an L-band wavelength division multiplexing (WDM) communication system. The laser configuration consists of a long erbium-doped fibre to enable L-band amplification where two 3-dB couplers take a portion of the generated BEFL signal and re-inject it into the single mode fibre to seed a cascaded BEFL line in the same direction as the first BEFL line. A stable and strong laser comb of up to five lines with 10-GHz spacing has been obtained with a Brillouin pump (BP) of 9.2 mW and a 980 nm pump of 92 mW. The BEFL has shown a broad tuning range with a tuning characteristic for line #1 which is flat over a range greater than 9.9 nm.     

Improved search for $B_{s}^{0} - \overline{B}_{s}^{0}$ oscillations

An improved search for B _s ⁰ oscillations is performed in the ALEPH data sample collected during the first phase of LEP, and reprocessed in 1998. Three analyses based on complementary event selections are presented. First, decays of B _s ⁰ mesons into hadronic flavour eigenstates are fully reconstructed. This selection yields a small sample of candidates with excellent decay length and momentum resolution and hi gh average B _s ⁰ purity. Semileptonic decays with a reconstructed D _s ^- meson provide a second sample with larger statistics, high average B _s ⁰ purity, but a poorer momentum and decay length resolution due to the partial decay reconstruction. Finally, semileptonic b-hadron decays are inclusively selected and yield the data sample with the highest sensitivity to B _s ⁰ oscillations, as the much higher statistics compensate for the low average B _s ⁰ purity and poorer time resolution. A lower limit is set atps^-1 at 95% C.L., significantly lower than the expected limit of 15.2 ps^-1. Received: 21 February 2003 / Published online: 11 June 2003     

Light Scattering Changes in Isolated Brain Mitochondria during Anoxia - Magnesium Effect on Morphological Changes and Respiration -

Under pathological conditions, morphological changes of the cells and tissues may differ from those of normal conditions, which can be reflected by changes in light scattering (LS). Consequently, LS has been recognized as a potential non-invasive tool for optical diagnosis of living tissue. This paper aimed to identify the basic properties of LS of isolated brain mitochondria in vitro under normoxic and anoxic conditions in the presence and absence of Mg²⁺. An increase in LS was observed during anoxia in both the presence and absence of Mg²⁺. In both cases, the changes in LS initiated by anoxia and reoxygenation started concomitantly with the reduction of heme aa₃. The rates of LS changes were slower than those of heme aa₃, particularly in the presence of Mg²⁺. Mg²⁺ inhibited the morphological responses of mitochondria caused by the addition of ADP and ATP, and significantly reduced the oxygen consumption rate in state 4. These results are due to modulation of the K⁺/H⁺ antiporter affected by Mg²⁺. In addition, the mitochondria were well coupled, although the basal level of LS fell after addition of Mg²⁺. Therefore, the observed responses of mitochondria at anoxia were physiological and independent of the presence or absence of Mg²⁺. The relationship between LS and redox state of cytochrome c oxidase, an anoxic indicator, provides a basis to assess the tissue conditions in vivo.     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

Hermitian quark matrices

Assuming a relation between the quark mass matrices of the two sectors a unique solution can be obtained for the CKM flavor mixing matrix. A numerical example is worked out which is in excellent agreement with experimental data.     

Connections on Naturally Reductive Spaces,Their Dirac Operator and Homogeneous Models in String Theory

 Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections ∇ ^t joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D ^t corresponding to t=1/3 is the so-called ``cubic' Dirac operator recently introduced by B. Kostant, and derive the formula for its square for any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new G-invariant first order differential operator on spinors and an eigenvalue estimate for the first eigenvalue of D <sup>1/3</sup>. This geometric situation can be used for constructing Riemannian manifolds which are Ricci flat and admit a parallel spinor with respect to some metric connection ∇ whose torsion T≠ 0 is a 3-form, the geometric model for the common sector of string theories. We present some results about solutions to the string equations and a detailed discussion of a 5-dimensional example. Received: 19 February 2002 / Accepted: 26 August 2002 Published online: 22 November 2002 RID="*" ID="*" This work was supported by the SFB 288 ``Differential geometry and quantum physics' of the Deutsche Forschungsgemeinschaft and the Max-Planck Society.     

Some analytical aspects in field theories with dynamical mass generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looked for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand in hand with the nontrivial solution for mass function. The consequences are discussed.