The Kinetic Theory of Simple Reacting Spheres: I. Global Existence Result in a Dilute-Gas Case

Existence of global-in-time, spatially inhomogeneous, and L ¹-renormalized solutions is proven for the model of simple reacting spheres under the assumptions that initially the system has a finite total mass, energy, and entropy.     

Attenuation of high energy multi-hadron systems leptoproduced in nuclear matter

Attenuation of groups of high energy particles leptoproduced in nuclear matter is calculated in terms of parameters describing strongly interacting systems at the early stages of particle production: formation time of hadrons and cross-section for the intermediate state to interact inside the nucleus. It is argued that measurements of attenuation of multihadron systems can remove some ambiguities in determining these parameters.     

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.     

Synthesis of organofunctional silanes with sterically hindered substituents at silicon atoms

Organofunctional silanes with more sterically hindered substituents at the silicon atom than the typical methoxy (ethoxy) group have lately been frequently used as silane coupling agents, in polymer coupling systems, sol‐gel processes and also as interpenetrating polymer network substrates. New and very efficient synthetic ways leading to organofunctional silanes of the above type with methacryl, amine, chloro and isocyanato functional groups are proposed here. Catalytic transesterification and/or alcoholysis of chloropropyltrialkoxysilanes followed by­nucleophilic substitution has been employed. Copyright © 2001 John Wiley & Sons, Ltd.     

Low-loss geodesic lens: Meridional profile and fabrication tolerances

The most recent formulation of the perfect geodesic lens problem is utilized to evaluate a novel solution. This solution describes a smooth geodesic depression profile with a finite value of its local curvature radius at the edge of the lens. This feature should minimize radiation and scattering losses by the guided modes that take place mainly at the lens boundary. The external rounded section of the proposed lens is described by a simple, explicit expression that considerably eases designing procedure. The presented lens is capable of perfect focusing once the theoretically prescribed ideal depression profile is accurately fabricated. For straightforward examination of the influence of technological grinding errors on the lens focal characteristics, a simple analytical method is proposed and investigated.     

The equipotential surfaces of cubic lattices

The areas of zero electrostatic potential within an array of electric charges in an ionic crystal can be represented as a zero equipotential surface (ZEPS), which separates space into domains of positive and negative potential. ZEPS are conventionally expressed in terms of nodal surfaces. We express the coordinates and charge distribution of several ZEPS in terms of the Jacobi theta functions, and provide their graphical visualisation.     

Preparation and characterization of 1,2,3‐triazole‐cured polymers from endcapped azides and alkynes

Fourteen commercial polyols have been characterized by GPC, NMR spectroscopy, and elemental analysis. From these, eight corresponding tosylates, six nitrate esters, seven mesylates, 13 alkynes, and 14 azides have been prepared and all these derivatives have been fully characterized. Five alkyne monomers and eight azide monomers were also prepared. Twelve alkynes and 13 azides (functionality 2–4) were combined in 1,3‐dipolar cycloaddition reactions under neat conditions to prepare triazole‐cured polymers, avoiding any heavy metal catalyst. Characterization by NMR spectroscopy, elemental analysis, and gel permeation chromatography indicated triazole polymers 14 , 22 , 23 , 28 , and 30 with degrees of polymerization of 17–28 to be the best candidates for future work. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 238–256, 2008     

Syntheses and reactions of terpene β-hydroxyselenides and β-hydroxydiselenides

A convenient method for the synthesis of optically active trans-hydroxyselenides and trans-hydroxydiselenides from the bicyclic terpene group based on the reactions of sodium selenide or sodium diselenide with cis- and trans-(+)-3-carane, trans-(+)-2-carane and (?)-β-pinane epoxides is described. The corresponding cis-hydroxy and cis-methoxydiselenides were obtained in the reaction of sodium diselenide with β-hydroxy- and β-methoxytosylates. The influence of a hydroxy group at the β-position on the diastereomeric ratio of the products of the asymmetric methoxyselenenylation of styrene has been established by composition of the products, crystal structure analyses, and theoretical calculations using a DFT method on the B3LYP level (6-311G(d)).     

Simultaneous confidence bands for the integrated hazard function

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Four methods of construction of such confidence bands are proposed. The weird and conditional bootstrap methods are used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal-tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present application of our confidence bands to the data regarding survival after heart transplant. This research was partly supported by AGH grant No. 10.420.03.