Nonradiative excitation energy transport in one-component disordered systems

High-accuracy Monte Carlo simulations of the time-dependent excitation probabilityG ^s (t) and steady-state emission anisotropyr _M /r _0M for one-component three-dimensional systems were performed. It was found that the values ofr _M /r _0M obtained for the averaged orientation factor only slightly overrate those obtained for the real values of the orientation factor _ik ² . This result is essentially different from that previously reported. Simulation results were compared with the probability coursesG ^s (t) andR(t) obtained within the frameworks of diagrammatic and two-particle Huber models, respectively. The results turned out to be in good agreement withR(t) but deviated visibly fromG ^s (t) at long times and/or high concentrations. Emission anisotropy measurements on glycerolic solutions of Na-fluorescein and rhodamine 6G were carried out at different excitation wavelengths. Very good agreement between the experimental data and the theory was found, with _ex0-0 for concentrations not exceeding 3.5·10^–2 and 7.5·10^–3 M in the case of Na-fluorescein and rhodamine 6G, respectively. Up to these concentrations, the solutions investigated can be treated as one-component systems. The discrepancies observed at higher concentrations are caused by the presence of dimers. It was found that for _ex <_0-0 (Stokes excitation) the experimental emission anisotropies are lower than predicted by the theory. However, upon anti-Stokes excitation (_ex>_0-0), they lie higher than the respective theoretical values. Such a dispersive character of the energy migration can be explained qualitatively by the presence of fluorescent centers with 0-0 transitions differing from the mean at _0-0.     

On (strong) α-favorability of the Wijsman hyperspace

The Banach-Mazur game as well as the strong Choquet game are investigated on the Wijsman hyperspace from the nonempty player's (i.e. α's) perspective. For the strong Choquet game we show that if X is a locally separable metrizable space, then α has a (stationary) winning strategy on X iff it has a (stationary) winning strategy on the Wijsman hyperspace for each compatible metric on X. The analogous result for the Banach-Mazur game does not hold, not even if X is separable, as we show that α may have a (stationary) winning strategy on the Wijsman hyperspace for each compatible metric on X, and not have one on X. We also show that there exists a separable 1st category metric space such that α has a (stationary) winning strategy on its Wijsman hyperspace. This answers a question of Cao and Junnila (2010) [6].     

On (strong) α-favorability of the Vietoris hyperspace

For a normal space X, α (i.e. the nonempty player) having a winning strategy (resp. winning tactic) in the strong Choquet game Ch(X) played on X is equivalent to α having a winning strategy (resp. winning tactic) in the strong Choquet game played on the hyperspace CL(X) of nonempty closed subsets endowed with the Vietoris topology τ _V . It is shown that for a non-normal X where α has a winning strategy (resp. winning tactic) in Ch(X), α may or may not have a winning strategy (resp. winning tactic) in the strong Choquet game played on the Vietoris hyperspace. If X is quasi-regular, then having a winning strategy (resp. winning tactic) for α in the Banach-Mazur game BM(X) played on X is sufficient for α having a winning strategy (resp. winning tactic) in BM(CL(X), τ _V ), but not necessary, not even for a separable metric X. In the absence of quasi-regularity of a space X where α has a winning strategy in BM(X), α may or may not have a winning strategy in the Banach-Mazur game played on the Vietoris hyperspace.     

Existence and multiplicity of solutions for semilinear hemivariational inequalities at resonance

In this paper we study semilinear hemivariational inequalities at resonance. Assuming a partially anticoercive nonsmooth potential we prove an existence and a multiplicity theorem. The method of the proof is variational and in the multiplicity result, we employ the nonsmooth local linking theorem.     

Bound for resolvent of second order elliptic operator in low spectral stripe

Mourre method of commutators is used to get low energy resolvent bound for an abstract operatorin a Hilbert space and for a second order variable coefficient elliptic operator in R^d, d?3. Copyright © 2002 John Wiley & Sons, Ltd.     

Diporphyrinyl derivatives of 1,10-phenanthroline and 2,2′-bipyridyl

The title derivatives were synthesized containing two meso-tri-p-tolylpheneleneporphyrin units attached via amide bridges to 4, 7- and 4,4′ positions of the respective heteroaromatic spacers.     

Simultaneous scission and crosslinking of polystyrene chains on irradiation by ultraviolet light in CCl4 and CHCl3 solutions

This work is the continuation of the investigations of changes in the structure of polystyrene initiated by radiation of wavelengths λ ≥ 270 nm in oxygen-free solutions in CCl₄ and CHCl₃. Coupled integral and quasielastic light scattering techniques have been applied, enabling observations of changes in the molecular weight distribution function w(M). On the basis of the experimental data and application of Saito and Inokuti's theoretical results, it is shown that in the irradiated solutions polystyrene undergoes simultaneous chain scission and crosslinking. The average number of scissions and crosslinks per macromolecule as a function of irradiation time is calculated. The effect of macromolecular mobility on both photochemical processes is also discussed.     

A mortar element method for some discretizations of a plate problem

Summary. In this paper mortar element methods for the clamped plate problem are discussed. Locally, we use conforming Hsieh-Clough-Tocher (HCT) and reduced HCT macro elements and a nonconforming Morley element. We establish error bounds for these methods. Received December 1, 2000 / Revised version received December 3, 2001 / Published online April 17, 2002 This work was partially supported by Polish Scientific Grant 237/PO3/99/16     

Interplay between acetate ions, peripheral groups, and reactivity of the core nitrogens in transmetalation of tetrapyrroles

The mechanism of acetate-assisted transmetalation of tetrapyrroles was investigated in a model system consisting of chlorophyll a and copper(II) acetate in organic solvents by using a spectroscopic and kinetic approach. Surprisingly, acetate ions bind to the central Mg in chlorophyll much more strongly than do acetonitrile, methanol and even pyridine, one of the best ligands in chlorophyllic systems. This exceptionally strong non-symmetrical axial ligation of the central Mg by acetate causes its out-of-plane displacement and deformation of the tetrapyrrole ring, thus facilitating the interaction with an incoming CuII complex. This mechanism is controlled by a keto-enol tautomerism of the chlorophyll isocyclic ring. Additionally, depending on solvent, acetate activates the incoming metal ions. These new insights allow to suggest a mechanism for the acetate method of metal exchange in tetrapyrrolic macrocycles, which resembles biological insertion of metal ions into porphyrins. It also provides a guideline for the design of more efficient methods for the metalation of porphyrins and related macrocycles.