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We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.
Denkmalentdeckungen
(2007)
»Wenn du reisen willst, mußt du die Geschichte dieses Landes kennen und lieben. Das ist ganz unerläßlich. [...] Wag’ es getrost und du wirst es nicht bereuen. Eigentümliche Freuden und Genüsse werden dich begleiten. Du wirst Entdeckungen machen, denn überall wohin du kommst, wirst du, vom Touristenstandpunkt aus, eintreten wie in ›jungfräuliches Land‹. Du wirst Klosterruinen begegnen, von deren Existenz höchstens die nächste Stadt eine leise Kenntnis hatte; du wirst inmitten alter Dorfkirchen, deren zerbröckelter Schindelturm nur auf Elend deutete, große Wandbilder oder in den treppenlosen Grüften reiche Kupfersärge mit Kruzifix und vergoldeten Wappenschildern finden; du wirst Schlachtfelder überschreiten, Wendenkirchhöfe, Heidengräber, von denen die Menschen nichts mehr wissen.«
Die in diesem Bildband gesammelten »Denkmalentdeckungen« verstehen sich als Einladung zu einer Reise durch das Land Brandenburg. Theodor Fontane hatte für ein solches Unternehmen genau den richtigen Blick, als er in seinen »Wanderungen durch die Mark Brandenburg« 1864 diese Sätze schrieb. Auch heute noch sollten wir seiner Anregung zu Begegnungen mit der Geschichte und der Kunstgeschichte des Landes folgen, die uns im Dialog der Kulturen und der Zeiten eine Standortbestimmung in der Gegenwart und eine Orientierung für die Zukunft zugleich bietet.
While ubiquitous, the making and breaking of hydrogen bonds in solution is notoriously difficult to study due to the associated complex changes of nuclear and electronic structures. With the aim to reduce the according uncertainty in correlating experimental observables and hydrogen-bond configurations, we combine the information from proximate methods to study the N-H center dot center dot center dot O hydrogen bond in solution. We investigate hydrogen-bonding of the N-H group of N-methylaniline with oxygen from liquid DMSO and acetone with infrared spectra in the N-H stretching region and X-ray absorption spectra at the N K-edge. We experimentally observe blue shifts of the infrared stretching band and an X-ray absorption pre-edge peak when going from DMSO to acetone. With ab initio molecular dynamics simulations and calculated spectra, we qualitatively reproduce the experimental observables but we do not reach quantitative agreement with experiment. The infrared spectra support the notion of weakening the N-H center dot center dot center dot O hydrogen bond from DMSO to acetone. However, we fail to theoretically reproduce the measured shift of the X-ray absorption pre-edge peak. We discuss possible shortcomings of the simulation models and spectrum calculations. Common features and distinct differences with the O-H center dot center dot center dot O hydrogen bond are highlighted, and the implications for monitoring hydrogen-bond breaking in solution are discussed.
Acoustic emission signals generated during high speed cutting of steel are investigated. The data are represen ted in time-folded form. Several methods from linear and nonlinear data analysis based on time- and frequency- domain are applied to the data and reveal signatures of the observed acoustic emission signal. These investiga tions are necessary for modeling the cutting process by means of differential equations.
We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.