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.     

Photofragmentation of Dibenzyl Ketone in the Presence of Tetramethylpiperidine Derivatives. Studies on light stabilizer mechanisms [1]

The interaction of selected tetramethylpiperidine derivatives with radicals arising from the Norrish-type I cleavage of dibenzyl ketone under oxygen was studied. Product analyses and kinetic studies showed that the investigated sterically hindered piperidine derivatives have a pronounced effect on both the nature and distribution of the products of photolysis of dibenzyl ketone in the presence of oxygen. Observations indicated that the phenylperacetoxyl radical is formed as an intermediate during irradiation and that it interacts with the additives used. Possible mechanisms of the reactions studied are discussed. The observation that oxidation of an isolated double bond by the radicals formed in dibenzyl ketone photolysis under oxygen is strongly inhibited in the presence of the studied sterically hindered amines is discussed in the light of the results presented. The findings are considered in relation to the problem of polymer stabilization.     

Influenza epidemic spread simulation for Poland — a large scale, individual based model study

In this work a construction of an agent based model for studying the effects of influenza epidemic in large scale (38 million individuals) stochastic simulations, together with the resulting various scenarios of disease spread in Poland are reported. Simple transportation rules were employed to mimic individuals’ travels in dynamic route-changing schemes, allowing for the infection spread during a journey. Parameter space was checked for stable behaviour, especially towards the effective infection transmission rate variability. Although the model reported here is based on quite simple assumptions, it allowed to observe two different types of epidemic scenarios: characteristic for urban and rural areas. This differentiates it from the results obtained in the analogous studies for the UK or US, where settlement and daily commuting patterns are both substantially different and more diverse. The resulting epidemic scenarios from these ABM simulations were compared with simple, differential equations based, SIR models — both types of the results displaying strong similarities. The pDYN software platform developed here is currently used in the next stage of the project employed to study various epidemic mitigation strategies.     

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.     

Syntheses of potassium 1,1‐dioxopyrido[4,3‐e]‐1,4,2‐dithiazine‐3‐thiolate and its application to the synthesis of novel sulfonamides with potential biological activity

Potassium 1,1‐dioxopyrido[4,3‐e]‐1,4,2‐dithiazine‐3‐thiolate 2 has been synthesized and applied to the syntheses of 7H‐1,1‐dioxopyrido[4,3‐e]‐1,4,2‐dithiazolium‐3‐thiolate 3 and 3‐methylthiopyrido[4,3‐e]‐1,4,2‐dithiazine 1,1‐dioxide 4 which provided easy access to a variety of its 3‐amino derivatives 5‐10 . Hydrazinolysis of 7, 8 and 10 afforded the corresponding 3‐amino‐2‐(1,4‐dihydro‐4‐thioxopyrid‐3‐ylsulfonyl)guanidines 11‐13 . Subsequent reaction of 12 with 4‐chlorobenzaldehyde gave condensation product 14 . 1,4‐Dihydro‐2‐thioxopyridine‐3‐sulfonamide 15 was also prepared from the potassium salt 2 upon alkaline hydrolysis, whereas alkylation of 15 gave the appropriate S‐substituted derivatives 16‐19 or S,N‐disubstituted compounds 20‐21 .     

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.     

Synthesis of a new scaffold: the 7H,8H-pyrimido[1,6-b]pyridazin-6,8-dione nucleus

This paper describes a modified method of preparation of a number of alpha-aryl-alpha-(pyridazin-3-yl)-acetonitriles via the C-arylation reaction of the corresponding carbanionsof phenylacetonitriles using 3-chloropyridazine derivatives. KOH and DMSO were used inthe deprotonation process, which made the reaction very simple and safe to perform.Nitriles were obtained in the hydrolysis reaction to the corresponding alpha-aryl-alpha-(pyridazin-3-yl)-acetamide derivatives, which were next subjected to cyclization to afford the finalproducts. A number of new derivatives of 7H,8H-pyrimido[1,6-b]pyridazin-6,8-dione weresynthesized in the cyclocondensation reaction of respective alpha-aryl-alpha-(pyridazin-3-yl)-acetamides with diethyl carbonate in the presence of EtONa. The structure andcomposition of the new compounds were confirmed by IR, (1)H- and (13)C- NMR analysesand by elemental C, H and N analysis.     

Quantitative EPR study on free radicals in the natural polyphenols interacting with metal ions and other environmental pollutants

Quantitative electron paramagnetic resonance (EPR) method was applied to characterise radicals stabilised in polyphenolic matrices of various biogenic materials: lichens, mosses, composts, soils, peats, brown coals and sewage sludge sediments. The investigations were carried out on raw materials and extracted fractions of humic acids (HA). General trends of g value and spin concentration changes were found. These parameters in lichens strongly depend on lichen species and air pollution. Determination of the g value and semiquinone spin concentration allows to assess degree of transformation of organic matter in compost, soil, peat and lignite. Application of gaseous ammonia as a base penetrating the organic matrices extends the possibilities and usefulness of the method. Interaction of metal ions with humic materials is illustrated by interaction of VO2+ ion with peat and lignite HA as well as demineralised (raw and carbonised) brown coal. Our investigations demonstrate that quantitative EPR is a rapid and effective monitoring method to study the influence of various environmental factors on substances containing polyphenolic matrices.     

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.