q-positive definiteness and related operators

We are in progress of extending the family of ‘q-deformed operators’ considered in the previous papers by joining to them q-subnormal as well as q-formally subnormal ones. It turns out that q-positive definiteness, a notion generalizing Halmos' standard positive definiteness of bounded subnormal operators, is likewise central for our new scheme.     

Optimization of scrapping decisions: Theory and applications

Contrary to the variety of models and procedures for optimizing the ordering decision in inventory control theory, no comparable tools exist for the scrapping decision. Thus, the current paper constitutes a step in this direction. Using a simple deterministic model, the basic economics and structure of the problem are introduced first. Then we determine explicitly scrap-optimal turn-around-times as well as the corresponding scrap- and rest-quantities. Accounting for the stochastic nature of demand, the model is generalized and algorithms for determination of optimal scrapping decision are discussed. Finally we compare the results and discuss practical applications.     

Organic matter transformation in the environment investigated by quantitative electron paramagnetic resonance (EPR) spectroscopy: studies on lignins

The lignins separated from angiosperm and gymnosperm trees, peat and xylitic brown coal were investigated by quantitative EPR. Observed free radicals in lignins are sensitive to alkaline environment. Gaseous ammonia interacting with solid lignins in resonance cavity shifts quinone-hydroquinone equilibria towards formation of semiquinone anions. Complexation of copper(II) by lignins causes drastic decrease of the semiquinones in the matrices. Formation of lignin-Pb(II) complexes yielded radicals characterised by unusually low g-value (1.9999-2.0003). Monomeric structural units of the investigated lignins were recognised by pyrolysis with in situ methylation by tetramethylammonium hydroxide. Although for the natural lignins the mixture of normal semiquinone signals at g about 2.0034 and signals at g 1.9999 were observed, some monomeric components of lignins (e.g., caffeic acid, pyrogallol) gave pure lines at g = 1.9999. The bacterial oxidative biodegradation of lignin monomeric components and their Pb(II) complexes resulted in increase of the radical signals.     

Quecksilber(II)-Titrationen mit Variaminblau als Redoxindicator

Zusammenfassung Es wird eine volumetrische Methode zur Bestimmung von Cyanid- und Quecksilber(II)-ionen mit titrierter Quecksilber(II)-nitratlösung gegen Variaminblau als Indicator beschrieben. Das Verfahren liefert genaue, wenig streuende Werte.Vorgetragen auf der III. Arbeitstagung für analytische Chemie in Prag am 1. September 1959.     

2‐Chloro‐4,5‐dihydroimidazole,Part X. Revisiting route to N‐heteroarylimidazolidin‐2‐ones

The ureidation reactions of 2‐ and 4‐picoline N‐oxides with 2‐chloro‐4,5‐dihydroimidazole are described. A mechanism of novel thioureidation reaction of 4‐picoline N‐oxide with 2‐(4,5‐dihydro‐1H‐imidazol‐2‐ylthioxy)‐4,5‐dihydro‐1H‐imidazole is proposed. Structural assignment is confirmed by ¹H and ¹³C nmr as well as by X‐ray crystallography.     

Kinetics and mechanism of the intra-cage oxidation of nitrite sodalite

The kinetics and mechanism of formation of sodium nitrate within a sodalite matrix by intracage oxidation of hydrothermally grown nitrite sodalite has been studied. The increase of the cell volume as well as the weight uptake during heating and the evaluation of the nitrate band in the IR spectra have been discussed to describe this reaction inside the aluminosilicate sodalite framework.

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Synthesis, molecular structure and reactivity of 5-methylidene-1,2,3,5-tetrahydroimidazo[2,1-b]quinazolines

Synthesis of novel 5-methylidene-1,2,3,5-tetrahydro[2,1-b]-quinazoline derivatives 2-4 with potential biological activities mediated by alpha-adrenergic and/or imidazoline receptors was performed by reacting 2-chloro-4,5-dihydroimidazole (1) with the corresponding 2-aminoacetophenones. Compound 2, which incorporates an enamine moiety, underwent a 1,3-dipolar cycloaddition reaction with the appropriate nitrones 5-9 to give 1,2,3,5-tetrahydro-imidazo[2,1-b]quinazolin-5,5'-spiro-2',3'-diphenylisoxazol-idines 10-14. Reactions of the title compounds 2 and 4 with dimethyl acetylene-dicarboxylate (DMAD) afforded dimethyl 2-(2,3-dihydroimidazo[2,1-b]quinazolin-5(1H)-ylidenemethyl)but-2-enedioates 15, 16. Imidazo[2,1-b]quinazoline 2 was further treated with acetyl chloride, benzoyl chloride and mesyl chloride to give the 1-substituted derivatives 17, 18 and 19, respectively. The structures of all new compounds obtained were confirmed by elemental analysis and spectral data (IR, (1)H- and (13)C-NMR) as well asX-ray crystallographic analysis of 3 and 18.     

Anion-pi interactions in cyanuric acids: a combined crystallographic and computational study

Several structures of pi complexes of isocyanuric acid and of several thio derivatives with anions have been computed by using high level ab initio calculations. The nature of the complexes has been studied by means of the method of molecular interaction potential with polarization (MIPp) and Bader's theory of atoms-in-molecules. These molecules form favorable complexes with anions and can be used as binding units for building receptors for the molecular recognition of anions. In several cases, the anion-pi interaction has been demonstrated experimentally by means of X-ray crystallography.     

Globally enumerating unstable periodic orbits for observed data using symbolic dynamics

The unstable periodic orbits of a chaotic system provide an important skeleton of the dynamics in a chaotic system, but they can be difficult to find from an observed time series. We present a global method for finding periodic orbits based on their symbolic dynamics, which is made possible by several recent methods to find good partitions for symbolic dynamics from observed time series. The symbolic dynamics are approximated by a Markov chain estimated from the sequence using information-theoretical concepts. The chain has a probabilistic graph representation, and the cycles of the graph may be exhaustively enumerated with a classical deterministic algorithm, providing a global, comprehensive list of symbolic names for its periodic orbits. Once the symbolic codes of the periodic orbits are found, the partition is used to localize the orbits back in the original state space. Using the periodic orbits found, we can estimate several quantities of the attractor such as the Lyapunov exponent and topological entropy.