Gerald Teschl

Jacobi operators and completely integrable nonlinear lattices

Jacobi operators: Jacobi operators Foundations of spectral theory for Jacobi operators Qualitative theory of spectra Oscillation theory Random Jacobi operators Trace formulas Jacobi operators with periodic coefficients Reflectionless Jacobi operators Quasi-periodic Jacobi operators and Riemann theta functions Scattering theory Spectral deformations-Commutation methods Completely integrable nonlinear lattices: The Toda system The initial value problem for the Toda system The Kac-van Moerbeke system Notes on literature Compact Riemann surfaces-A review Hergoltz functions Jacobi difference equations with MathematicaR Bibliography Glossary of notations Index.

Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. This new edition has additions and improvements throughout the book to make the presentation more student friendly.

Isoprene and acetone concentration profiles during exercise on an ergometer

A real-time recording setup combining exhaled breath volatile organic compound (VOC) measurements by proton transfer reaction-mass spectrometry (PTR-MS) with hemodynamic and respiratory data is presented. Continuous automatic sampling of exhaled breath is implemented on the basis of measured respiratory flow: a flow-controlled shutter mechanism guarantees that only end-tidal exhalation segments are drawn into the mass spectrometer for analysis. Exhaled breath concentration profiles of two prototypic compounds, isoprene and acetone, during several exercise regimes were acquired, reaffirming and complementing earlier experimental findings regarding the dynamic response of these compounds reported by Senthilmohan et al (2000 Redox Rep. 5 151-3) and Karl et al (2001 J. Appl. Physiol. 91 762-70). While isoprene tends to react very sensitively to changes in pulmonary ventilation and perfusion due to its lipophilic behavior and low Henry constant, hydrophilic acetone shows a rather stable behavior. Characteristic (median) values for breath isoprene concentration and molar flow, i.e., the amount of isoprene exhaled per minute are 100 ppb and 29 nmol min(-1), respectively, with some intra-individual day-to-day variation. At the onset of exercise breath isoprene concentration increases drastically, usually by a factor of ∼3-4 within about 1 min. Due to a simultaneous increase in ventilation, the associated rise in molar flow is even more pronounced, leading to a ratio between peak molar flow and molar flow at rest of ∼11. Our setup holds great potential in capturing continuous dynamics of non-polar, low-soluble VOCs over a wide measurement range with simultaneous appraisal of decisive physiological factors affecting exhalation kinetics. In particular, data appear to favor the hypothesis that short-term effects visible in breath isoprene levels are mainly caused by changes in pulmonary gas exchange patterns rather than fluctuations in endogenous synthesis.

Physiological modeling of isoprene dynamics in exhaled breath.

Human breath contains a myriad of endogenous volatile organic compounds (VOCs) which are reflective of ongoing metabolic or physiological processes. While research into the diagnostic potential and general medical relevance of these trace gases is conducted on a considerable scale, little focus has been given so far to a sound analysis of the quantitative relationships between breath levels and the underlying systemic concentrations. This paper is devoted to a thorough modeling study of the end-tidal breath dynamics associated with isoprene, which serves as a paradigmatic example for the class of low-soluble, blood-borne VOCs. Real-time measurements of exhaled breath under an ergometer challenge reveal characteristic changes of isoprene output in response to variations in ventilation and perfusion. Here, a valid compartmental description of these profiles is developed. By comparison with experimental data it is inferred that the major part of breath isoprene variability during exercise conditions can be attributed to an increased fractional perfusion of potential storage and production sites, leading to higher levels of mixed venous blood concentrations at the onset of physical activity. In this context, various lines of supportive evidence for an extrahepatic tissue source of isoprene are presented. Our model is a first step towards new guidelines for the breath gas analysis of isoprene and is expected to aid further investigations regarding the exhalation, storage, transport and biotransformation processes associated with this important compound.

A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone

Recommended standardized procedures for determining exhaled lower respiratory nitric oxide and nasal nitric oxide (NO) have been developed by task forces of the European Respiratory Society and the American Thoracic Society. These recommendations have paved the way for the measurement of nitric oxide to become a diagnostic tool for specific clinical applications. It would be desirable to develop similar guidelines for the sampling of other trace gases in exhaled breath, especially volatile organic compounds (VOCs) which may reflect ongoing metabolism. The concentrations of water-soluble, blood-borne substances in exhaled breath are influenced by: (i) breathing patterns affecting gas exchange in the conducting airways, (ii) the concentrations in the tracheo-bronchial lining fluid, (iii) the alveolar and systemic concentrations of the compound. The classical Farhi equation takes only the alveolar concentrations into account. Real-time measurements of acetone in end-tidal breath under an ergometer challenge show characteristics which cannot be explained within the Farhi setting. Here we develop a compartment model that reliably captures these profiles and is capable of relating breath to the systemic concentrations of acetone. By comparison with experimental data it is inferred that the major part of variability in breath acetone concentrations (e.g., in response to moderate exercise or altered breathing patterns) can be attributed to airway gas exchange, with minimal changes of the underlying blood and tissue concentrations. Moreover, the model illuminates the discrepancies between observed and theoretically predicted blood-breath ratios of acetone during resting conditions, i.e., in steady state. Particularly, the current formulation includes the classical Farhi and the Scheid series inhomogeneity model as special limiting cases and thus is expected to have general relevance for a wider range of blood-borne inert gases. The chief intention of the present modeling study is to provide mechanistic relationships for further investigating the exhalation kinetics of acetone and other water-soluble species. This quantitative approach is a first step towards new guidelines for breath gas analyses of volatile organic compounds, similar to those for nitric oxide.

Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies

Introduction The Toda hierarchy, recursion relations, and hyperelliptic curves The stationary Baker-Akhiezer function Spectral theory for finite-gap Jacobi operators Quasi-periodic finite-gap solutions of the stationary Toda hierarchy Quasi-periodic finite-gap solutions of the Toda hierarchy and the time-dependent Baker-Akhiezer function The Kac-van Moerbeke hierarchy and its relation to the Toda hierarchy Spectral theory for finite-gap Dirac-type difference operators Quasi-periodic finite-gap solutions of the Kac-van Moerbeke hierarchy Hyperelliptic curves of the Toda-type and theta functions Periodic Jacobi operators Examples,

Measurement of endogenous acetone and isoprene in exhaled breath during sleep

g-0,1

LONG-TIME ASYMPTOTICS FOR THE CAMASSA-HOLM EQUATION

Acknowledgments Bibliography.

Weyl–Titchmarsh Theory for Schrödinger Operators with Strongly Singular Potentials

This explorative study aims at characterizing the breath behavior of two prototypic volatile organic compounds, acetone and isoprene, during normal human sleep and to possibly relate changes in the respective concentration time courses to the underlying sleep architecture. For this purpose, six normal healthy volunteers (two females, four males, age 20-29 years) were monitored over two consecutive nights (the first one being an adaption night) by combining real-time proton-transfer-reaction mass spectrometry measurements from end-tidal exhalation segments with laboratory-based polysomnographic data. Breath acetone concentrations increased overnight in all measurements, with an average relative change by a factor of up to 4 (median 2.5). Nighttime concentration maxima were usually recorded 2-3 h before lights on. For breath isoprene, a nocturnal increase in baseline concentrations of about 74% was observed, with individual changes ranging from 36-110%. Isoprene profiles exhibited pronounced concentration peaks, which were highly specific for leg movements as scored by tibial electromyography. Furthermore, relative to a linear trend, baseline isoprene concentrations decreased during the transition from the NREM to the REM phase of a complete sleep cycle.

A modeling-based evaluation of isothermal rebreathing for breath gas analyses of highly soluble volatile organic compounds.

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa–Holm equation for decaying initial data, completing previous results by Boutet de Monvel and Shepelsky.