Abstract:
Based on an explicit verification of the coupling matrix elements between the 1p1h and 2p2h states we propose a new method of selecting the most important 2p2h states responsible for fragmentation effects. In this way the dimensionality of the problem is reduced, such that the computation becomes feasible and the spreading of the strength is realistic, as verified by some tests of convergence. Calculations in $^{208}$Pb show that due to sizable mixing effects only about 50% of the total isoscalar giant dipole resonance (ISGDR) $3\hbar\omega$ strength is located in the energy region between 20 and 25 MeV. This is the energy region which currently is available in experiment. Even above 30 MeV we find about 10% of the total strength. This indicates that the current experimantal evaluations of the ISGDR centroid energy may significantly underestimate its value.

Abstract:
We investigate the origin of order in the low-lying spectra of many-body systems with random two-body interactions. Contrary to the common belief our study based both on analytical as well as on numerical arguments shows that these are the higher $J$-sectors whose ground states are more orderly than the ones in the J=0-sector. A predominance of J=0 ground states turns out to be the result of putting on together states with different characteristic energy scales from different $J$-sectors.

Abstract:
We investigate the origin of order in the low-lying spectra of many-body systems with random two-body interactions. Our study based both on analytical as well as on numerical arguments shows that except for the most $J$-stretched states, the ground states in the higher $J$-sectors are more orderly and develop larger energy gaps than the ones in the J=0-sector. Due to different characteristic energy scales in different $J$-sectors the J=0 ground states may predominate only when all the states are taken together.

Abstract:
We construct an example of a real-valued continuous non-constant function $f$ defined on a connected complete metric space $X$ such that every point of $X$ is a point of local minimum or local maximum for $f$. The space $X$ is connected but fails to be separably connected.

Abstract:
In this paper, influence of crowding by inert particles on the geminate reaction kinetics is theoretically investigated. Time evolution equations for the survival probability of a geminate pair are derived from the master equation taking into account the correlation among all diffusing particles. The results interpolate between low and high concentrations of the inert particles. Excluded volume interactions by the inert particles hinder the diffusive motion of reactants. When the initial distribution of the inert particles is uniform, the excluded volume interactions slow the decay of the survival probability of a geminate pair in contrast to the acceleration of the decay found for the target problem under the presence of the excluded volume interactions among reactants. We also obtain the escape probability for a non-uniform initial distribution of the inert particles and show that reaction yield is increased when the reaction proceeds in the presence of a positive density gradient of the inert particles which inhibits the escape of reactants. The effect can be interpreted as a cage effect.

Abstract:
Results of d.c. electric conductivity and Seebeck coefficient measurements for PFN, PFN+Li ceramic samples and PFN single crystals are presented. Marked influence of doping with lithium on the value of electric conductivity, and on the type of electric conductance has been found.

Abstract:
A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump motion, interferes with the reaction at the encounter distance. Therefore, the reaction term has a memory effect. The derived equation is applied to the geminate recombination problem. The recombination is shown to depend on the intrinsic reaction rate, in contrast with the results of Sung et al. [J. Chem. Phys. {\bf 116}, 2338 (2002)], which were obtained from the fractional reaction-diffusion equation where the diffusion term has a memory effect but the reaction term does not. The reactivity dependence of the recombination probability is confirmed by numerical simulations.

Abstract:
The photoluminescence in amorphous semiconductors decays according to power law $t^{-delta}$ at long times. The photoluminescence is controlled by dispersive transport of electrons. The latter is usually characterized by the power $alpha$ of the transient current observed in the time-of-flight experiments. Geminate recombination occurs by radiative tunneling which has a distance dependence. In this paper, we formulate ways to calculate reaction rates and survival probabilities in the case carriers execute dispersive diffusion with long-range reactivity. The method is applied to obtain tunneling recombination rates under dispersive diffusion. The theoretical condition of observing the relation $delta = alpha/2 + 1$ is obtained and theoretical recombination rates are compared to the kinetics of observed photoluminescence decay in the whole time range measured.

Abstract:
Single crystals of KNbO3 and KNbO3 : Fe have been grown using the flux method at various technological conditions. The investigations of optical absorption of these crystals were carried out. Marked influence of technological conditions and doping with iron on optical absorption has been found. Observed changes of the absorption spectra are associated with lattice defects arising due to nonstoichiometry and/or doping.

Abstract:
The micronucleus assay is frequently used for purposes of biological dosimetry. Due to high interindividual variability in the spontaneous frequency of micronuclei, its sensitivity in the low dose region is poor. It has been suggested that this problem can be mitigated by selectively analyzing the frequency of those micronuclei which contain only acentric fragments. Using a pan-centromeric FISH probe we have studied the dose dependence of micronuclei with centromeres in peripheral lymphocytes of human donors. In contrast to previous publications, our approach is based on determining the relative frequency of micronuclei with and without centromeric signals. Our results confirm previous observations that in the low dose range of ionizing radiation, the micronucleus-centromere assay is more sensitive than the conventional micronucleus test.