General Formulation of Quantum Analysis

A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the G\^ateaux derivative or commutators. This yields a unified formulation of quantum analysis, namely the invariance of quantum derivatives, which are expressed by multiple integrals of ordinary higher derivatives with hyperoperator variables. Multivariate quantum analysis is also formulated in the present unified scheme by introducing a partial inner derivation and a rearrangement formula. Operator Taylor expansion formulas are also given by introducing the two hyperoperators $\delta_{A \to B} \equiv -\delta_A^{-1} \delta_B$ and $d_{A \to B} \equiv \delta_{(-\delta_A^{-1}B) ; A}$ with the inner derivation $\delta_A : Q \mapsto [A,Q] \equiv AQ-QA$. Physically the present noncommutative derivatives express quantum fluctuations and responses.Comment: Latex file, 29 pages, no figur

Orbits of parabolic subgroups on metabelian ideals

We consider the action of a parabolic subgroup of the General Linear Group on a metabelian ideal. For those actions, we classify actions with finitely many orbits using methods from representation theory.Comment: 10 pages, 6 eps figure

Entropic transport - A test bed for the Fick-Jacobs approximation

Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity of the higher dimensional diffusive dynamics is reduced by means of the so-called Fick-Jacobs approximation, yielding an effective one-dimensional stochastic dynamics. Accordingly, the elimination of transverse, equilibrated degrees of freedom stemming from geometrical confinements and/or bottlenecks cause entropic potential barriers which the particles have to overcome when moving forward noisily. The applicability and the validity of the reduced kinetic description is tested by comparing the approximation with Brownian dynamics simulations in full configuration space. This non-equilibrium transport in such quasi-one-dimensional irregular structures implies for moderate-to-strong bias a characteristic violation of the Sutherland-Einstein fluctuation-dissipation relation.Comment: 15 pages, 6 figures ; Phil. Trans. R. Soc. A (2009), in pres

Cellular distribution of the prion protein in palatine tonsils of mule deer (Odocoileus hemionus) and Rocky Mountain elk (Cervus elaphus nelsoni)

Chronic wasting disease (CWD) is a transmissible spongiform encephalopathy (TSE) that affects members of the Cervidae family, including deer (Odocoileus spp.), elk (Cervus Canadensis spp.), and moose (Alces alces spp.). While CWD is a neurodegenerative disease, lymphoid accumulation of the abnormal isoform of the prion protein (PrPSc) is detectable early in the course of infection. It has been shown that a large portion of the PrPSc lymphoid accumulation in infected mule deer takes place on the surface of follicular dendritic cells (FDCs). In mice, FDC expression of PrPC has been shown to be essential for PrPSc accumulation. FDCs have been shown to normally express high levels of PrPC in mice and humans but this has not been examined in natural hosts for CWD. We used double immunofluorescent labeling and confocal microscopy to determine the PrPC expression characteristics of B and T lymphocytes as well as FDCs in palatine tonsils of CWD-negative mule deer and elk. We detected substantial PrPC colocalization with all cellular phenotypic markers used in this study, not just with FDC phenotypic markers

Modelling with measures: Approximation of a mass-emitting object by a point source

We consider a linear diffusion equation on $\Omega:=\mathbb{R}^2\setminus\bar{\Omega_\mathcal{O}}$, where $\Omega_\mathcal{O}$ is a bounded domain. The time-dependent flux on the boundary $\Gamma:=\partial\Omega_\mathcal{O}$ is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of $\mathbb{R}^2$ with a measure-valued point source in the origin and provide estimates for the quality of approximation. For all time $t$, we derive an $L^2([0,t];L^2(\Gamma))$-bound on the difference in flux on the boundary. Moreover, we derive for all $t>0$ an $L^2(\Omega)$-bound and an $L^2([0,t];H^1(\Omega))$-bound for the difference of the solutions to the two models

Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux

We study the dynamics of a quantum particle moving in a plane under the influence of a constant magnetic field and driven by a slowly time-dependent singular flux tube through a puncture. The known adiabatic results do not cover these models as the Hamiltonian has time dependent domain. We give a meaning to the propagator and prove an adiabatic theorem. To this end we introduce and develop the new notion of a propagator weakly associated to a time-dependent Hamiltonian.Comment: Title and Abstract changed, will appear in Journal of Mathematical Physic

Searching the ideal inhaled vasodilator: From nitric oxide to prostacyclin

Today, the technique to directly administer vasodilators via the airway to treat pulmonary hypertension and to improve pulmonary gas exchange is widely accepted among clinicians. The flood of scientific work focussing on this new therapeutic concept had been initiated by a fundamental new observation by Pepke-Zaba {[}1] and Frostell in 1991 {[}2]: Both scientists reported, that inhalation of exogenous nitric oxide (NO) gas selectively dilates pulmonary vessels without a concomittant systemic vasodilation. No more than another decade ago NO was identified as an important endogenous vasodilator {[}3] while having merely been regarded an environmental pollutant before that time. Although inhaled NO proved to be efficacious, alternatives were sought-after due to NO's potential side-effects. In search for the ideal inhaled vasodilator another group of endogenous mediators - the prostanoids - came into the focus of interest. The evidence for safety and efficacy of inhaled prostanoids is - among a lot of other valuable work - based on a series of experimental and clinical investigations that have been performed or designed at the Institute for Surgical Research under the guidance and mentorship of Prof. Dr. med. Dr. h.c. mult. K. Messmer {[}4-19]. In the following, the current and newly emerging clinical applications of inhaled prostanoids and the experimental data which they are based on, will be reviewed. Copyright (C) 2002 S. Karger AG, Basel