Particle Size Distribution and Aspect Ratio of Organic Pigments

Particle size and aspect ratio are amongst the most important parameters which determine the application properties of pigments, fillers and powders for ceramics. A statistical characterization of the samples is therefore needed. In this paper we discuss the measurement of bivariate size distributions of organic pigments and describe a correction procedure for particles with interchanged crystallographic axes. During the crystallization of a pigment, the larger aspect ratios usually result from faster growth rates.     

Stationary Fokker-Planck equation applied to fission dynamics

By use of both analytical and numerical techniques, we study the relaxation of time-dependent solutions of the Fokker-Planck equation for an inverted oscillator to Kramers' stationary solution. This is done by integrating over all time the time-dependent solutions for given initial conditions at the saddle point to obtain stationary solutions, whose densities and higher velocity moments are compared as functions of the coordinate with the corresponding quantities calculated from Kramers' stationary solution. For large values of the coordinate an a symptotic expansion of the density is obtained, but for general values of the coordinate and for higher velocity moments the time integration must be done numerically. With increasing dissipation the relaxation to Kramers' stationary solution occurs at successively smaller values of the coordinate. By use of Kramers' stationary solution, we derive analytical expressions as functions of nuclear temperature and dissipation strength for several quantities of interest in fission dynamics, including the mean time from the saddle point to scission, the mean fission-fragment kinetic energy at the scission point and the contribution to the variance in the fission-fragment kinetic energy resulting from fluctuations in the fission degree of freedom. We apply these results to some examples that have been studied experimentally, including the mean saddle-to-scission time for the heavy-ion-induced fission of the compound nucleus ¹⁶⁸Yb and the mean fission-fragment kinetic energy at scission and the contribution to its variance for the α-particle-induced fission of the compound nucleus ²¹³At.     

Novel Zwitterionic Sulfides,Selenides and Tellurides

The zwitterionic compounds Im‐E‐Mel [ 9 , E = S ( a ), Se ( b ), Te ( c ), Im = 2‐{1, 3‐diisopropyl‐4, 5‐dimethylimidazolium}, Mel = 5‐{2, 2‐dimethyl‐4, 6‐dioxo‐1, 3‐dioxan‐5‐ylide}] are obtained from the corresponding 2‐chalcogeno‐1, 3‐diisopropyl‐4, 5‐dimethylimidazolines 8 and 5‐bromo‐2, 2‐dimethyl‐4, 6‐dioxo‐1, 3‐dioxan ( 7 ) in the presence of triethylamine in excellent yields. The crystal structures of the thermally stable compounds reveal most effective charge separations from which the compounds 9 resemble closely to diaryl chalkogenides. 9b and 9c are the first selenocarbonyl and tellurocarbonyl ylides reported, to our knowledge.     

Robust Adaptive Fuzzy Identification of Time-Varying Processes with Uncertain Data. Handling Uncertainties in the Physical Fitness Fuzzy Approximation with Real World Medical Data: An Application

This study considers the problem of Robust Fuzzy approximation of a time-varying nonlinear process in the presence of uncertainties in the identification data using a Sugeno Fuzzy System while maintaining the interpretability of the fuzzy model during identification. A recursive procedure for the estimation of fuzzy parameters is proposed based on solving local optimization problem that attempt to minimize the worst-case effect of data uncertainties on approximation performance. To illustrate the approach, several simulation studies on numerical examples are provided. The developed scheme was applied to handle the vagueness, ambiguity and uncertainty inherently present in the general notion of a Medical Expert about Physical Fitness based on a set of various Physiological parameters measurements.     

Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane

An isomorphism between the Lobachevsky and de Sitter’s world geometries with the symplectic geometry and the Lie algebra of binary quadratic forms is used to derive the altitudes concurrence for the Lobachevsky and de Sitter triangles.     

On the finite element method for elliptic problems with degenerate and singular coefficients

We consider Dirichlet boundary value problems for second order elliptic equations over polygonal domains. The coefficients of the equations under consideration degenerate at an inner point of the domain, or behave singularly in the neighborhood of that point. This behavior may cause singularities in the solution. The solvability of the problems is proved in weighted Sobolev spaces, and their approximation by finite elements is studied. This study includes regularity results, graded meshes, and inverse estimates. Applications of the theory to some problems appearing in quantum mechanics are given. Numerical results are provided which illustrate the theory and confirm the predicted rates of convergence of the finite element approximations for quasi-uniform meshes.

     

Differentiation of commercial tobacco blends by pyrolysis field ionization mass spectrometry and pattern recognition

Summary For the first time operational fingerprinting techniques have been applied to pyrolysis field ionization mass spectra of nine commercial tobacco blends. After thermal decomposition in high vacuum and soft ionization of the pyrolysis products, the mass spectral pattern of tobacco between m/z 50 and m/z 500 was reduced to the 29 most characteristic signals by the calculation of the Fisher ratios. Using the autoscaled signals with the highest discriminant power, it is possible to distinguish two major groups of tobacco blends. However, differentiation is clearly improved by principal component score plots. In a novel methodological step, results of other analytical methods have been added as external parameters to the reduced data set resulting in even better differentiation and classification. Actually five groups of tobacco blends which yield very different smoke properties could be classified.Pyrolysis field ionization mass patterns of tobacco are well suited for the distinction of commercial tobacco blends and are assumed to allow a prediction of external parameters such as condensate and nicotine concentrations in smoke. Pyrolysis field ionization mass spectrometry in combination with operational fingerprinting techniques and multivariate statistical methods appears to be a fast and reliable tool for future assessments of tobacco properties.

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Unterscheidung von handelsüblichen Tabakmischungen durch Pyrolyse-Feldionisation-Massenspektrometrie und Mustererkennung

Zusammenfassung Zum ersten Mal wurden operationale Techniken der Mustererkennung auf Massenspektren der Pyrolyse-Feldionisation von neun handelsüblichen Tabakmischungen angewendet. Nach dem thermischen Abbau im Hochvakuum und schonender Ionisierung der Pyrolyseprodukte wurde das massenspektrometrische Muster von Tabak im Bereich von m/z 50 bis m/z 500 durch die Berechnung der Fisher-Quotienten auf die 29 charakteristischsten Massensignale reduziert. Unter Verwendung dieser standardisierten Massensignale mit der stärksten trennenden Wirkung ist es möglich, zunächst zwei Hauptgruppen von Tabakmischungen zu unterscheiden. Diese Unterscheidung wird jedoch durch die Hauptkomponentenanlyse deutlich verbessert. Als neuer methodischer Schritt wurden chemische Daten von anderen analytischen Methoden als externe Parameter zu dem reduzierten Datensatz hinzugefügt, um eine noch bessere Differenzierung und Klassifizierung zu erreichen. Tatsächlich konnten fünf Gruppen von Tabakmischungen (Endprodukten) ermittelt werden, die sich durch sehr unterschiedliche Raucheigenschaften auszeichnen.Die Signalmuster von Massenspektren der Pyrolyse-Feldionisation von Tabak sind gut geeignet für eine Unterscheidung von handelsüblichen Tabakmischungen und man kann annehmen, daß sie auch eine Vorhersage von externen Parametern wie Kondensat- und Nikotinkonzentration erlauben. Reproduzierbarer thermischer Abbau mit nachfolgender schonender Ionisierung der Pyrolysate durch Feldionisation ergibt Massenspektren, die in Kombination mit operationalen Mustererkennungstechniken und multivariaten statistischen Methoden ein schnelles und zuverlässiges Verfahren für die zukünftige Beurteilung von Tabakeigenschaften ergeben.

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Dedicated to Prof. Dr. H. D. Beckey on occasion of his 65th birthday     

Analysis of a Stokes interface problem

We consider a stationary Stokes problem with a piecewise constant viscosity coefficient. For the variational formulation of this problem we prove a well-posedness result in which the constants are uniform with respect to the jump in the viscosity coefficient. We apply a standard discretization with a pair of LBB stable finite element spaces. The main result of the paper is an infsup result for the discrete problem that is uniform with respect to the jump in the viscosity coefficient. From this we derive a robust estimate for the discretization error. We prove that the mass matrix with respect to some suitable scalar product yields a robust preconditioner for the Schur complement. Results of numerical experiments are presented that illustrate this robustness property. This author was supported by the German Research Foundation through the guest program of SFB 540