Characterizations of locally testable events

Let Σ be a finite alphabet, Σ^* the free monoid generated by Σ and χ the length of χ ∈ Σ^*. For any integer k0, f_k(χ) (t_k(χ)) is χ if χ < k + 1, and it is the prefix (suffix) of χ of length k, othewise. Also let m_k+1(χ) = {νχ = uνw and ν = k+1}. For χ, y ε Σ^* define χ ～ _k+1y iff f_k(χ) = f_k(y), t_k(χ) = t_k(y) and m_k+1(χ) = m_k+1(y). The relation ～_k+1 is a congruence of finite index over Σ^*. An event E ? Σ^* is (k+1)-testable iff it is a union of congruence classes of ～_k+1. E is locally testable (LT) if it is k+1-testable for some k. (This definition differs from that of [6] but is equivalent.)We show that the family of LT events is a proper sub-family of star-free events of dot-depth 1. LT events and k-testable events are characterized in terms of (a) restricted star-free expressions based on finite and cofinite events; (b) finite automata accepting these events; (c) semigroups; and (d) structural decomposition of such automata. Algorithms are given for deciding whether a regular event is (a) LT and (b) k+1-testable. Generalized definite events are also characterized.     

Nachweis und volumetrische Bestimmung von Nitrosoderivaten im Mikromaßstab

Zusammenfassung Nitrosoverbindungen lassen sich in Gegenwart von Rhodanidionen durch Eisen(II)-sulfat quantitativ reduzieren. Auf dieser Reaktion beruht ein neuer Nachweis der Nitrosogruppe auf Grund der Farbe des Eisen(III)-rhodanidkomplexes, sowie ihre Bestimmung durch Titration des Eisen(III) mit Quecksilber(I)-nitrat-Maßlösung. Diese Methode ermöglicht die Analyse auch in Gegenwart von Nitroverbindungen.

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Detection and volumetric microdetermination of nitroso compounds

Summary Nitroso compounds can be quantitatively reduced by iron(II) sulphate in the presence of thiocyanate ions. The reaction provides a new method for the detection of the nitroso group, based on the colour developed by the iron(III) thiocyanate complex. The determination of nitroso group can also be carried out by titrating the iron(III) with mercury(I) nitrate, even if nitro compounds are present.

     

Non-empirical LCAO-MO-SCF-CI calculations on organic molecules with gaussian type functions

This part of the series presents the results obtained by open shell SCF computations on the G, N, O, and F Atoms.

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Zusammenfassung Dieser Teil der Reihe gibt die Ergebnisse von SCF-Rechnungen für offene Schalen am C, N, O und F an.

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Résumé Cette partie de la suite d'articles présente les résultats obtenus par des calculs SCF à couches ouvertes sur les atomet C, N, O et F.

     

Quantum chemical study of the geometries and stabilities of the two valence-tautomers of C2H2F+

Non-empirical SCF-MO molecular wavefunctions were computed for the two limiting structures of C₂H₂F⁺ with full geometry optimization using double-zeta quality atomic orbital basis sets. The bridged structure (fluorenium ion) was found to be an energy maximum (transition state) about 31 kcal/mole higher than the open structure (fluoro-vinyl cation). The latter, contrary to the unsubstituted vinyl cation, is slightly (4.5 °) bent away from fluorine at the electron deficient centre.     

Mathematical characterization and shape analysis of localized,fractal, and complex distributions in extended systems

The availability of recent supercomputers and massively parallel computing facilities makes possible the calculation of the electronic structure of highly extended (mesoscopic) molecular networks. Disorder, which is practically always present in these systems, causes an extreme complexity of the wave function that typically shows multifractal behavior in the intermediate length scale. Multifractal analysis, however, is possible only on systems that cover several orders of length scales. Though such calculation can be carried out on model systems, it is beyond the bounds of present ab initio or semiempirical treatments. In this contribution, a shape-analysis method of the wave function is given that is applicable both for localized and multifractal one-particle states even in moderately large networks without a regular geometrical structure. No boxing of the distributions is necessary through several orders of magnitude of scaling distances. Multifractal behavior and different regularly decaying localization shape functions can be distinguished. Finite-size multifractal distributions are also discussed. The described method is intended to serve as an easily applicable and efficient tool for bridging over the gap between the wave-function analysis of systems containing macroscopic and moderately large number of particles. © 1994 John Wiley & Sons, Inc.     

Metal ion selectivity of oligopeptides

Metal binding affinity and selectivity of peptides are reviewed with a special emphasis on the high structural variety of peptide complexes. The most common structural type of these complexes is built up by the deprotonation and metal ion coordination of subsequent amide groups in the form of fused five-membered chelate rings. The metal ion selectivity of this process and the role of various anchoring groups are discussed in detail. The highest metal binding affinity of peptides is connected to the presence of two anchoring groups in appropriate location (the "double anchor"): e.g. the NH2-Xaa-Xaa-His/Cys/Asp/Met-Xaa sequence. Among the side chain donor functions, the imidazole of histidyl and thiolate of cysteinyl residues are the most effective ligating groups and their involvement in metal binding results in a great variety of different macrochelate or loop structures and/or formation of various polynuclear complexes. Examples of these structural motifs and their possible applications have been thoroughly discussed.     

Optical, structural and adsorption properties of zinc peroxide/hydrogel nanohybrid films

Hybrid nanofilms from zinc-peroxide/poly(acrylamide) (ZnO₂/PAAm) and zinc-peroxide/poly(N-isopropyl-acrylamide) (ZnO₂/PNIPAAm) were prepared using the photopolymerization procedure. The thin layers were prepared by the combination of the Layer-by-Layer (LbL) self-assembly method and photopolymerization using UV light in every step of the procedure. The hybrid multilayer films consisting of layers of zinc peroxide nanoparticles and hydrogel alternating in a sandwich-like fashion with thicknesses of 65-246 nm. The chemical structures of the hybrid films were investigated by FTIR spectroscopy, their morphology was studied by atomic force microscopy (AFM). The build up of the films was studied by measuring the optical reflection spectrum, and we have calculated the refractive index and layer thickness of the hybrid layers using simulating software. The adsorption properties of the ZnO₂/hydrogel nanohybrid composite networks were investigated by measuring water and ethanol vapour adsorption by a quartz crystal microbalance (QCM). It was established that on partially hydrophobic ZnO₂/PNIPAAm hybrids the adsorbed amounts were lower, against the hydrophilic ZnO₂/PAAm film the vapour amount was higher. These results correspond to those of the bulk gel swelling results.     

Vibrational Spectroscopic and Theoretical Studies of Urea Derivatives with Biochemical Interest: N,N′-Dimethylurea,N,N,N′,N′-Tetramethylurea,and N,N′-Dimethylpropyleneurea

Abstract

Mid-infrared, far-infrared, and Raman vibrational spectroscopic studies were combined with density functional theory (DFT) calculations and normal coordinate force field analyses for N,N′-dimethylurea (DMU), N,N,N′,N′-tetramethylurea (TMU), and N,N′-dimethylpropyleneurea (DMPU: IUPAC name 1,3-dimethyltetrahydropyrimidin-2(1H)-one). The equilibrium molecular geometry of DMU (all three conformers), TMU, and DMPU and the frequencies, intensities, and depolarization ratios of their fundamental infrared (IR) and Raman vibrational transitions were obtained by DFT calculations. The vibrational spectra were fully analyzed by normal coordinate methods as well. A starting force field for DMPU was obtained by adapting corresponding force constants for DMU and TMU, resulting after refinements in the stretching force constants C=O (7.69, 7.30, 7.68 N·cm^?1), C–N (5.16, 5.55, 5.05 N·cm^?1), and C-Me (5.93, 4.00, 4.22 N·cm^?1) for DMU, TMU, and DMPU, respectively. The dominating conformer of liquid DMU was identified as trans-trans, strong intermolecular hydrogen bonding was verified in solid DMU, and weak dipole–dipole association was found in liquid TMU and in DMPU. Special attention was paid to analyzing the methyl group frequencies, which revealed deviations from local C_3v symmetry. A linear correlation was found between the CH stretching force constants and the inverse of the CH bond lengths (1/r ²). The averaged NH stretching frequencies of gaseous, dissolved, and solid urea and of DMU, with variations for hydrogen bonding of different strength, are linearly correlated to the NH stretching force constants. Characteristic skeletal vibrations were assigned for a broad variety of urea derivatives and also for pyrimidine derivatives, which all contain the N₂C=O entity. The very strong IR bands of C=O stretching (1,676 ± 40 cm^?1) and asymmetric CN₂ stretching (1,478 ± 60 cm^?1), and the very intense Raman feature of symmetric CN₂ stretching or ring breathing (757 ± 80 cm^?1), can be recognized as fingerprint bands also for the pyrimidine derivatives cytosine, thymine, and uracil, which all are nucleobases in DNA and RNA nucleotides.     

Case studies in dynamic modelling of large-scale wastewater treatment plants

Several large-scale wastewater treatment plants have been modelled successfully using an extensive modelling library in the General Purpose Simulator, GPS-X. The mathematical models included all important processes on the selected wastewater treatment plants, i.e. primary sedimentation, activated sludge biokinetics and final clarification.The models have been used in different areas, such as: a)analysis of operational scenarios; b) determenation of sustained and peak capacity of plants(rated plant capacity) and c) investigation of plant expansion scenarios. Out of more than twenty documented cases four, involving simulation studies on large-scale wastewater plants are discussed.