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.     

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.     

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.     

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.     

Synthesis,Structure and Cytotoxicity Testing of Novel 7-(4,5-Dihydro-1H-imidazol-2-yl)-2-aryl-6,7-dihydro-2H-imidazo[2,1-c][1,2,4]triazol-3(5H)-Imine Derivatives

The appropriate 1-arylhydrazinecarbonitriles 1a–c are subjected to the reaction with 2-chloro-4,5-dihydro-1H-imidazole (2), yielding 7-(4,5-dihydro-1H-imidazol-2-yl)-2-aryl-6,7-dihydro-2H-imidazo[2,1-c][1,2,4]triazol-3(5H)-imines 3a–c, which are subsequently converted into the corresponding amides 4a–e, 8a–c, sulfonamides 5a–n, 9, ureas 6a–I, and thioureas 7a–d. The structures of the newly prepared derivatives 3a–c, 4a–e, 5a–n, 6a–i, 7a–d, 8a–c, and 9 are confirmed by IR, NMR spectroscopic data, as well as single-crystal X-ray analyses of 5e and 8c. The in vitro cytotoxic potency of these compounds is determined on a panel of human cancer cell lines, and the relationships between structure and antitumor activity are discussed. The most active 4-chloro-N-(2-(4-chlorophenyl)-7-(4,5-dihydro-1H-imidazol-2-yl)-6,7-dihydro-2H-imidazo[2,1-c][1,2,4]triazol-3(5H)-ylidene)benzamide (4e) and N-(7-(4,5-dihydro-1H-imidazol-2-yl)-2-(p-tolyl)-6,7-dihydro-2H-imidazo[2,1-c][1,2,4]triazol-3(5H)-ylidene)-[1,1′-biphenyl]-4-sulfonamide (5l) inhibits the growth of the cervical cancer SISO and bladder cancer RT-112 cell lines with IC₅₀ values in the range of 2.38–3.77 μM. Moreover, N-(7-(4,5-dihydro-1H-imidazol-2-yl)-2-phenyl-6,7-dihydro-2H-imidazo[2,1-c][1,2,4]triazol-3(5H)-ylidene)-4-phenoxybenzenesulfonamide (5m) has the best selectivity towards the SISO cell line and induces apoptosis in this cell line.     

Routine analysis of iron ores by X-ray spectrometry

A number of iron ores from all parts of the world were analysed with a powder sample preparation technique. Calibration curves were plotted for Fe, Ca, Si, Al and Mg in wide concentration ranges using 32 international and a few local standards. All iron ores were divided into 5 groups related to mineralogical differences; however, the calibration curve for Ca is common for all samples. For hematites and magnetites the relationship FeO + Fe₂O₃ = f(Fe) was experimentally established. The total time for sample preparation and analysis is about 5 min. A good correlation of chemical and X-ray results was obtained in this routine work.     

A characterization of the Hamiltonian

The classical Hamiltonian ) of the very classical quantum harmonic oscillator, which is regarded as a germ of the most of what comes about in quantum mechanics, can be sublimed to an abstract operator in a separable Hilbert space. Having this done one may ask for a condition which would allow it to be identified among operators of a suitable class. This class is that corresponding to three diagonal matrices and the property which makes the action successful is a kind of diagonal invariance (up to change of basis) within the class in question.     

Detecting Mass Points of Representing Measures

We discuss a possibility of deciding whether measures representing a moment sequence or realizing orthogonality of polynomials have atoms. This is done on the real line and in several variables.