Bicyclic [b]‐heteroannulated pyridazine derivatives. 9. cyclization reactions of 4,4‐dimethyl‐ and 4‐phenyltetrahydropyridazine‐3,6‐dione 3‐hydrazones with esters of keto dicarboxylic acids

Bis(ethoxycarbonyl)alkylidene derivatives 4 and 5 of the respective title hydrazones were obtained in the reactions with diethyl oxomalonate, diethyl oxosuccinate, diethyl 2‐oxoglutarate, and diethyl oxalo‐propionate as mixtures of geometric isomers with high predominance of one of them. On heating at 160‐200° without any solvent or on refluxing in ethanol 4 cyclized to yield the corresponding pyri‐dazino[6, 1‐c]triazines 6 , whereas heating of 5 gave, depending on the chain length, the corresponding pyra‐zolylpyridazines 8b and 8d or the pyridazinylpyridazine 8c . X‐ray analysis was used to determine the structures of 6 and 8 ; the unit cell of 6c was found to accommodate 16 molecules representing four conforma‐tional varieties. The different behavior of 4 and 5 in the cyclization reactions was interpreted in terms of the tautomeric equilibrium which was shifted towards the enamine form in 4 , and towards the imine form, in 5 . Transmission of a long‐range chirality effect in 4d and 5a‐d manifested itself in the ¹H nmr spectra as the magnetic non‐equivalence of the CH₂ protons in one or both ester ethyl groups.     

Analysis of exhaled breath from smokers,passive smokers and non‐smokers by solid‐phase microextraction gas chromatography/mass spectrometry

In this study, 38 samples of expired air were collected and analyzed from 20 non‐smoking volunteers, four passive smokers and 14 smokers (21 women and 17 men). Measurements were carried out using solid‐phase microextraction (SPME) as an isolation and preconcentration technique. The determination and identification were accomplished by gas chromatography coupled with mass spectrometry (GC/MS). Our data showed that ca 32% of all identified compounds in the breath of healthy non‐smokers were saturated hydrocarbons. In the breath of smoking and passive smoking volunteers hydrocarbons were predominant, but also present were more exogenous analytes such as furan, acetonitrile and benzene than in the breath of non‐smokers. Acetonitrile, furan, 3‐methylfuran, 2,5‐dimethylfuran, 2‐butanone, octane and decane were identified in breath of smoking and passive smoking persons. Copyright © 2008 John Wiley & Sons, Ltd.     

On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.     

Synthesis and structural characterization of novel 2-benzimidazolylthioureas: adducts of natural isothiocyanates and 2-amino-1-methylbenzimidazole

Adducts of natural allyl, phenethyl, and benzyl isothiocyanates and 2-amino-1-methylbenzimidazole were synthesized. After optimization of the reaction conditions, the target 2-benzimidazolylthioureas were obtained in reasonable yields. The detailed molecular and crystal structures of these compounds were characterized by spectroscopic and X-ray methods. Spectral analysis demonstrated that N-(1-methylbenzimidazolyl)-N′-allylthiourea, N-(1-methylbenzimidazolyl)-N′-benzylthiourea, and N-(1-methylbenzimidazolyl)-N′-phenethylthiourea exist in solution in an unprecedented three tautomeric forms, whose structures were corroborated unambiguously.     

Cocrystals of 2,3,5,6‐tetrafluorobenzene‐1,4‐diol with diaza aromatic compounds

2,3,5,6‐Tetrafluorobenzene‐1,4‐diol easily forms cocrystals with heteroaromatic bases containing the pyrazine unit. In the 1:1 complexes with pyrazine, C₆H₂F₄O₂·C₄H₄N₂, (I), and quinoxaline, C₆H₂F₄O₂·C₈H₆N₂, (II), the crystal components are linked via O—H...N hydrogen bonds into one‐dimensional chains. With the largest base, phenazine, the 1:2 benzenediol–phenazine complex, C₆H₂F₄O₂·2C₁₂H₈N₂, (III), was obtained, with the molecules linked via O—H...N interactions into a discrete heterotrimer. In all three cocrystals, the two types of molecules are organized into layers via softer C—H...O and C—H...F interactions and π–π stacking interactions, with stronger hydrogen bonds linking molecules of adjacent layers. In (II) and (III), molecules are arranged into heterostacks, whereas in (I) separate stacks are formed by the heterocyclic base and the benzenediol molecule.     

Transversality conditions for infinite horizon variational problems on time scales

We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler–Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.     

Empirical wavelet analysis of tail and memory properties of LARCH and FIGARCH models

Using computationally efficient wavelet methods, we study two nonlinear models of financial returns {r _t }: linear ARCH (LARCH) and fractionally integrated GARCH (FIGARCH). We estimate the tail index α and the long memory parameter d of the squared returns X_t = r_t²{X_t= r_t^2} of LARCH, and of the powers X _t = |r _t | ^p of FIGARCH. We find that the X _t have infinite variance and long memory, and show how the estimates of α and d depend on the model parameters. These relationships are determined empirically, as the setting is quite complex, and no suitable theory has been developed so far. In particular, we provide empirical relationships between the estimates [^(d)]{hat d} and the difference parameters in LARCH and FIGARCH. Our computational work uncovers tail and memory properties of LARCH and FIGARCH for practically relevant parameter ranges, and provides some guidance on modeling returns on speculative assets including FX rates, stocks and market indices.     

Edge-disjoint Open Trails in Complete Bipartite Multigraphs

Let ^r K _a,b be a complete bipartite multigraph. We show a necessary and sufficient condition for a multigraph ^r K _a,b to be arbitrarily decomposable into open trails. We extend the results obtained by Balister for complete graphs (Balister in Probab Comput 10:463–499, 2001). Moreover we show that a multigraph ^r K _a,b with even r and a ≥ 3 or b ≥ 3 is arbitrarily decomposable into open and closed trails.