Stitching pairs of Lévy processes into harnesses

We consider natural exponential families of Lévy processes with randomized parameter. Such processes are Markov, and under suitable assumptions, pairs of such processes with shared randomization can be “stitched together” into a single harness. The stitching consists of deterministic reparametrization of the time for both processes, so that they run on adjacent time intervals, and of the choice of the appropriate law at the boundary.     

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.     

Synthesis of polyetherols with isocyanuric ring: Kinetics and mechanisms of reactions in the presence of DABCO as catalyst

To establish the mechanism of reaction of formation of oligoetherols with perhydro‐1,3,5‐triazine ring, the kinetics of reaction of isocyanuric acid and 1,3,5‐tris(2‐hydroxyetyl) isocyanurate with ethylene carbonate resulting in formation of polyetherols in the presence of diazabicyclo[2.2.2]octane as a catalyst has been investigated. The kinetic and mechanistic studies revealed that the initial step of reaction is zero order related to ethylene carbonate and the reaction is inhibited by imide groups of isocyanuric acid. The mechanism of reaction was confirmed by spectroscopic and electrochemical methods. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 550–561, 2010     

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 betulin derivatives and the determination of their relative lipophilicities using reversed‐phase thin‐layer chromatography

A series of superlipophilic or highly lipophilic semisynthetic betulin derivatives was prepared and their relative lipophilicity was measured by reversed‐phase thin‐layer chromatography (RP‐TLC) at different pH values using 1,4‐dioxane–acetate buffer mixtures as mobile phases. Cholesterol, 17β‐estradiol and pure betulin were used as the reference compounds. Linear relationships were found between R_M values and 1,4‐dioxane concentrations in the mobile phases. LogP values were also calculated with computer programs ACD/LogP (ChemSketch 11.0, Advanced Chemistry Development Inc.) and ClogP (Daylight Chemical Information Systems Inc.). The empirical and theoretical data were compared, and the R_M0 values correlated well with logP. Two of the synthesized betulin derivatives are reported for the first time. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Analysis of NH3-TPD Profiles for CuSSZ-13 SCR Catalyst of Controlled Al Distribution – Complexity Resolved by First Principles Thermodynamics of NH3 Desorption,IR and EPR Insight into Cu Speciation**

NH₃ temperature-programmed desorption (NH₃-TPD) is frequently used for probing the nature of the active sites in CuSSZ-13 zeolite for selective catalytic reduction (SCR) of NO_x. Herein, we propose an interpretation of NH₃-TPD results, which takes into account the temperature-induced dynamics of NH₃ interaction with the active centers. It is based on a comprehensive DFT/GGA+D and first-principles thermodynamic (FPT) modeling of NH₃ adsorption on single Cu²⁺, Cu⁺, [CuOH]⁺ centers, dimeric [Cu-O-Cu]²⁺, [Cu-O₂²⁻-Cu]² species, segregated CuO nanocrystals and Brønsted acid sites (BAS). Theoretical TPD profiles are compared with the experimental data measured for samples of various Si/Al ratios and distribution of Al within the zeolite framework. Copper reduction, its relocation, followed by the intrazeolite olation/oxolation processes, which are concomitant with NH₃ desorption, were revealed by electron paramagnetic resonance (EPR) and IR. DFT/FPT results show that the peaks in the desorption profiles cannot be assigned univocally to the particular Cu and BAS centers, since the observed low-, medium- and high-temperature desorption bands have contributions coming from several species, which dynamically change their speciation and redox states during NH₃-TPD experiment. Thus, a rigorous interpretation of the NH₃-TPD profiles of CuSSZ-13 in terms of the strength and concentration of the active centers of a particular type is problematic. Nonetheless, useful connections for molecular interpretation of TPD profiles can be established between the individual component peaks and the corresponding ensembles of the adsorption centers.     

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.     

Analytic structure of dynamical systems

The study of the analytic structure of nonlinear ordinary and partial differential equations is shown to provide a unified approach to determining their properties and finding their solutions. A course of lectures delivered at the School on Chaos and Nonlinear Dynamics held at the Indian Institute of Science, Bangalore, India (June 24th–July 18th 1987)