Essential norm of the difference of weighted composition operators

We study differences of weighted composition operators between weighted Banach spaces H _ν ^∞ of analytic functions with weighted sup-norms and give an expression for the essential norm of these differences. We apply our result to estimate the essential norm of differences of composition operators acting on Bloch-type spaces. Authors’ addresses: Mikael Lindstr?m, Department of Mathematics, Abo Akademi University, FIN 20500 Abo, Finland; Elke Wolf, Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany     

The density condition and distinguishedness for weighted Fréchet spaces of holomorphic functions

We consider weighted Fréchet spaces of holomorphic functions which are defined as countable intersections of weighted Banach spaces of type H^∞. We study when these spaces have Stefan Heinrich's density condition and when they are distinguished.     

Why contextualists cannot know they are right: Self-refuting implications of contextualism

Conversational contextualism in epistemology is characterized by four main theses: 1. the indexicality of knowledge claims thesis; 2. the attributor contextualism thesis; 3. the conversational contextualism thesis, and 4. the main thesis of contextualism according to which a knowledge claim can be true in one context and false in another context in which more stringent standards for knowledge are operant. It is argued that these theses taken together generate problems for contextualism. In particular, it is shown that there is no context in which the contextualist can truthfully claim to know her theory is true. Since these results were obtained only with principles the contextualist cannot give up—like the principle of epistemic closure and the principle that knowledge implies truth—it seems that contextualism is in need of a thoroughgoing revision if it is to become a successful epistemic theory.     

A relativistic coupled-cluster interaction potential and rovibrational constants for the xenon dimer

An accurate potential energy curve has been derived for the xenon dimer using state-of-the-art relativistic coupled-cluster theory up to quadruple excitations accounting for both basis set superposition and incompleteness errors. The data obtained is fitted to a computationally efficient extended Lennard-Jones potential form and to a modified Tang–Toennies potential function treating the short- and long-range part separately. The vibrational spectrum of Xe₂ obtained from a numerical solution of the rovibrational Schrödinger equation and subsequently derived spectroscopic constants are in excellent agreement with experimental values. We further present solid-state calculations for xenon using a static many-body expansion up to fourth-order in the xenon interaction potential including dynamic effects within the Einstein approximation. Again we find very good agreement with the experimental (face-centred cubic) lattice constant and cohesive energy.     

Feminine after cricothyroid approximation?

A number of studies have evaluated the effectiveness of a cricothyroid approximation (CA) in creating a more female voice in male-to-female transsexuals (MFTs) from an acoustic perspective. An increase in pitch is of little value, however, unless it accurately indicates listeners' perceptions of gender. The purpose of this study was to further investigate the effectiveness of a CA in feminizing the voice from a perceptual perspective. Video recordings of nine MFTs, nine nontranssexual males (NTMs), and nine nontranssexual females (NTFs) were presented twice to the panel of judges in a randomized order: first auditory only (only hearing a subject's speech) and subsequently audiovisual (hearing and seeing a subject's speech). The panel of judges, 42 students (21 female, 21 male) from different disciplines, rated the participants' voices on a 100-mm visual analog scale with "very male" and "very female" as left and right extremes, respectively. The group of MFT obtained scores that were situated in between those of the NTM and the NTF, both for the auditory only and the audiovisual mode of presentation. Perception of femaleness significantly correlated with average fundamental frequency for both modes of presentation. It can be concluded that a CA approximation is a viable option to raise the voice pitch in MFTs but that this surgery alone may not be sufficient to create a voice that is perceived as a totally female.     

Efficient and sample-specific interpretation of ToF-SIMS data by additional postprocessing of principal component analysis results

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) is a powerful tool for surface analysis, but fragmentation of molecular species during the SIMS process may lead to complex mass spectra. While the fragmentation pattern is typically characteristic for each compound, industrial samples are engineered materials, and, thus, may contain a mixture of many compounds, which may result in a variety of overlapping peak patterns in ToF-SIMS spectra. Consequently, the process of data evaluation is challenging and time-consuming. Principal component analysis (PCA) can be used to simplify data analysis for complex sample systems. Especially, correlation loadings were observed as an ideal tool to identify relevant signals in PCA results, which induce the separation of different sample groups. This is because correlation loadings show the relevance of signals independent from their intensity in the raw data. In correlation loadings, however, fragmentation patterns are no longer observed and the identification of peaks' sum formulas is challenging. In this study, a new approach is presented, which simplifies peak identification and assignment in ToF-SIMS spectra after PCA is performed. The approach uses a mathematical transformation that projects PCA results, in particular loadings and correlation loadings, in the direction of specific sample groups. The approach does not change PCA results but rather presents them in a new way. This method allows to visualize characteristic spectra for specific sample groups that contain only relevant signals and, additionally, visualize fragmentation patterns. Data analysis is simplified and helps the user to focus on data interpretation rather than processing.     

Dichotomy of 1,3‐dipolar cycloreversions in a tetrasubstituted 2,5‐dihydro‐1,3,4‐thiadiazole

The cycloaddition of diphenyldiazomethane ( 8 ) to 16 thioketones at 40°C which furnishes tetrasubstituted 2,5‐dihydro‐1,3,4‐thiadiazoles, is followed by rapid N₂ loss (see the preceding paper), with one exception: For the dihydrothiadiazole 10 , the N₂ extrusion is slower by a factor of 4900 than its formation from 8 and 2,2,6,6‐tetramethycyclohexanethione ( 7 ). This elimination of N₂ is a 1,3‐dipolar cycloreversion which affords a thiocarbonyl ylide + N₂ As a consequence of steric hindrance in the example of 10 , a concomitant second cycloreversion furnishes thiobenzophenone ( 12 ) and the diazocyclohexane derivative 13 in an equilibrium. The complex kinetic system of Scheme 2 is confirmed by the irreversible interception of 13 with thioketone 14 . The structural conditions for retarded N₂ extrusions from dihydrothiadiazoles are discussed. © 2006 Wiley Periodicals, Inc. Heteroatom Chem 17:443–448, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20263     

Results from two interlaboratory comparison tests organized in Germany and at the EU level for analysis of acrylamide in food

After the publication of high levels of acrylamide (AA) in food, many research activities started all over the world in order to determine the occurrence and the concentration of this substance in various types of food. As no validated methods were available at that time, interlaboratory studies on the determination of AA in food were of the highest priority. Under the boundary conditions of applying well-established evaluation schemes, the results of 2 studies conducted by the Federal Institute for Risk Assessment (BfR) in Germany and by the European Commission's Directorate General Joint Research Center (JRC) exhibited an overall acceptable performance of the participants in these studies. Nevertheless, many laboratories showed problems in determining AA in food with a complex matrix such as cocoa. The results of analysis also showed a broader variation of AA for samples with low AA concentrations and indicated a bias of the results obtained by gas chromatography-mass spectrometry without derivatization. Improvements of the performance of some laboratories appeared to be necessary.