Semi-Markov failure rates processes

Usually, a reliability function is defined by a failure rate which is a real function taking the non-negative real values. In this paper the failure rate is assumed to be a stochastic process with non-negative and right continuous trajectories. The reliability function is defined as an expectation of a function of that random process. Particularly, the failure rate defined by the semi-Markov processes is considered here. The theorems dealing with the renewal equations for the conditional reliability functions with a semi-Markov process as a failure rate are presented in this paper. A system of that kind of equations for the discrete state space semi-Markov process is applied for calculating the reliability function for the 3-states semi-Markov random walk. Using the introduced system of renewal equations for the countable state space, the reliability function for the Furry-Yule failure rate process is obtained.     

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.     

Quiet imaging with interleaved spiral read-out

The acoustic noise generated during an MRI sequence can be effectively reduced with the help of soft gradient pulses using sinusoidal ramps. The long slope duration, however, leads to long acquisition times. The use of interleaved spiral trajectories, calculated with long gradient slopes, is proposed to reduce the acquisition time while maintaining low acoustic noise levels. The practibility of this approach is demonstrated on phantom and volunteer images.     

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.     

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, 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.     

Crystal and molecular structure of 3-(4-chlorobenzoylimino)-5,6-dihydro-3H-imidazo[2,1-c]-1,2,4-dithiazole

Crystal structure of the title compound belonging to the group of-acylimino derivatives of sulfur(II) compounds has been determined by X-ray structure analysis. The crystals are monoclinic, P2₁/c,a=11.210(2),b=8.197(1),c=13.659(2) Å,=102.36(2)°,V=1226.0(3) ų,Z=4,D _x =1.61 g cm^–3, (MoK)=0.71069 Å,=6.3 cm^–1. The structure has been refined to a finalR value of 0.035 for 1401 observed reflexions.The molecule is nearly planar with symmetrym. The title compound contains a very short intramolecular C=OS contact of 2.328(3) Å, suggesting a bond-non-bond resonance interaction.     

Three paths toward the quantum angle operator

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight” functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.