Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

Multiplicity of non-acyclic SL⁡2\operatorname{SL}_2-representations and L-functions of twisted Whitehead links

We consider a natural divisor on $\operatorname{SL}_2(\mathbb C)$-character varieties of knots and links, given by the so-called acyclic Reidemeister torsion. We provide a geometric interpretation of this divisor. We focus on the particular family of odd twisted Whitehead links, where we show that this divisor has multiplicity two. Moreover, we apply these results to the study of the $L$-functions of the universal deformations of representations over finite fields of twisted Whitehead links.Comment: Comments welcom

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471

Juice constituents and skin pigments in Vitis coignetiae Pulliat grapevines

Research Note

Potential Role of Protein Kinase B in Insulin-induced Glucose Transport, Glycogen Synthesis, and Protein Synthesis

Various biological responses stimulated by insulin have been thought to be regulated by phosphatidylinosi-tol 3-kinase, including glucose transport, glycogen syn-thesis, and protein synthesis. However, the molecular link between phosphatidylinositol 3-kinase and these biological responses has been poorly understood. Re-cently, it has been shown that protein kinase B (PKB/c-Akt/ Rac) lies immediately downstream from phosphati-dylinositol 3-kinase. Here, we show that expression of a constitutively active form of PKB induced glucose up-take, glycogen synthesis, and protein synthesis in L6 myotubes downstream of phosphatidylinositol 3-kinase and independent of Ras and mitogen-activated protein kinase activation. Introduction of constitutively active PKB induced glucose uptake and protein synthesis but not glycogen synthesis in 3T3L-1 adipocytes, which lack expression of glycogen synthase kinase 3 different from L6 myotubes. Furthermore, we show that deactivation of glycogen synthase kinase 3 and activation of rapamy-cin- sensitive serine/threonine kinase by PKB in L6 myo-tubes might be involved in the enhancement of glycogen synthesis and protein synthesis, respectively. These re-sults suggest that PKB acts as a key enzyme linking phosphatidylinositol 3-kinase activation to multiple bi-ological functions of insulin through regulation of downstream kinases in skeletal muscle, a major target tissue of insulin