Analysis of Phosphorescence Decay in Heterogeneous Systems: Consequences of Finite Excitation Flash Duration

Analysis of phosphorescence lifetimes using the Stern-Volmer equation is a reliable means of determining quencher concentration for a uniform sample. Methods of analysis for heterogeneous systems are based on the assumption that the excitation is produced by a momentary flash. This condition is an idealization because a real flash has a finite duration and a complex time profile. In the case of a heterogeneous quencher concentration, an excitation flash produces different initial intensities and different times of peak intensity from compartments having different concentrations of quencher. We formulated a model to explore the effects of flash duration on the shape of the emission curve obtained from systems in which the heterogeneity is continuous. We developed mathematical models that can be used to recover fitting parameters of continuous distributions of reciprocal lifetimes approximated as rectangular or Gaussian distributions, or an arbitrary histogram. We also formulated a procedure to convert the distribution of reciprocal lifetimes into a volume distribution of quencher concentration. We found that (1) the Stern-Volmer ratio of phosphorescence intensities cannot be employed for interpretation of pulse phosphorometric data in terms of a volume distribution of quencher; (2) shortening the flash duration decreases the difference of initial intensities between compartments having high and low quencher concentration; (3) the parameters of the volume distribution of quencher concentration can be recovered correctly only after taking account of the difference in initial intensities; and (4) calibration of the initial intensities for a given fitting delay and flash function is necessary.     

On spherical expansions of zonal functions on Euclidean spheres

This paper describes a new approach to the problem of computing spherical expansions of zonal functions on Euclidean spheres. We derive an explicit formula for the coefficients of the expansion expressing them in terms of the Taylor coefficients of the profile function rather than (as done usually) in terms of its integrals against Gegenbauer polynomials. Our proof of this result is based on a polynomial identity equivalent to the canonical decomposition of homogeneous polynomials and uses only basic properties of this decomposition together with simple facts concerning zonal harmonic polynomials. As corollaries, we obtain direct and apparently new derivations of the so-called plane wave expansion and of the expansion of the Poisson kernel for the unit ball. Received: 26 January 2007     

Reaction of 2-trifluoroacetyl-1,8-Bis(dimethylamino)naphthalene with strong organic bases: Deprotonation of 1-NMe2 group resulting in the formation of Benzo[g]indole derivatives versus nucleophilic addition to CO group

A novel approach to pyrrole ring closure in 2-trifluoroacetyl- and 2-ethoxycarbonyl-1,8-bis(dimethylamino)naphthalenes via treatment with 2-lithium-1,8-bis(dimethylamino)naphthalene producing the corresponding benzo[g]indole derivatives, was examined with different alkyl- and aryllithium compounds as well as with LDA. It was found that the highest yields of benzo[g]indoles (up to 70%) are obtained with aryllithium reagents when they contain NMe₂ group in ortho-position to the carbanionic centre. In all other cases the formation of acyclic alcohol arising from ordinary intermolecular addition of the carbanion to the CO group strongly prevails. The dramatic facilitation of deprotonation of the N-Me group in substrate followed by pyrrolic cyclization in the case of 2-lithium-N,N-dimethylanilines was explained through a specific structure of the reaction transition state.     

Synthesis and properties of epoxy-anhydride polymers modified with polyfluorolakyl-substituted oxiranes in the course of curing

Epoxy-anhydride polymers based on N,N,O-triglycidyl-p-aminophenol and isomethyltetrahydrophthalic anhydride were synthesized in the presence of new active modifiers, polyfluoroalkyl glycidyl ethers. The kinetics of the reactions of the modifiers with the anhydride were studied by differential scanning calorimetry and IR spectroscopy. The physicomechanical characteristics, glass transition points, and water absorption of the polymers were determined.     

Curing of epoxy-anhydride formulations in the presence of imidazoles

Differential scanning calorimetry was used to study the reaction of isomethyltetrahydrophthalic anhydride with phenyl glycidyl ether and the curing kinetics of diglycidyl ether of diphenylolpropane in the presence of imidazoles. The deformation-strength characteristics of cured epoxy polymers were determined.     

Ergodic properties of anomalous diffusion processes

In this paper we study ergodic properties of some classes of anomalous diffusion processes. Using the recently developed measure of dependence called the Correlation Cascade, we derive a generalization of the classical Khinchin theorem. This result allows us to determine ergodic properties of Lévy-driven stochastic processes. Moreover, we analyze the asymptotic behavior of two different fractional Ornstein–Uhlenbeck processes, both originating from subdiffusive dynamics. We show that only one of them is ergodic.     

The formation of oxide nanoparticles on the surface of natural clinoptilolite

Nanoparticles of NiO, ZnO and Cu₂O crystallize when the Ni-, Zn- and Cu-exchanged natural clinoptilolite, respectively, are dehydrated by heating in air at 550 °C. The dehydration of Mn-exchanged clinoptilolite does not lead to the crystallization of manganese oxide but affects the crystallinity of the host clinoptilolite lattice, which becomes amorphous. The NiO, ZnO and Cu₂O nanoparticles are found to be randomly dispersed in the clinoptilolite matrix. The particle size varies from 2 to 5 nm and exceeds the aperture of the clinoptilolite channel (approximately 0.4 nm), suggesting that the crystallization of the oxide phases takes place on the surfaces of clinoptilolite microcrystals.     

Periodic solutions of nonlinear hyperbolic evolution systems

We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation operator associated with the nonlinear evolution system, expressed in terms of the topological degree. The abstract results shall be applied to the damped hyperbolic partial differential equation.