Spectral Properties of Thioflavin T and Its Complexes with Amyloid Fibrils

Comparative analysis of the absorption and fluorescence spectra and fluorescence excitation spectra of thioflavin T (ThT) in various solvents and in the composition of amyloid fibrils has shown that ThT, when excited in the region of the long-wavelength absorption band, fluoresces in the spectral region with a maximum at 478–484 nm. The appearance in aqueous and alcohol solutions of a fluorescence band with a maximum near 440 nm has been attributed to the presence in the composition of the ThT preparations of an impurity with an absorption band in the 340–350-nm range. The literature data showing that in glycerol ThT has a wide fluorescence spectrum with two maxima are due to the artifact connected with the use of a high concentration of the dye. It has been suggested that the cause of the low quantum yield of ThT aqueous and alcohol solutions is the breakage of the system of conjugated bonds due to the reorientation of the benzothiozole and benzaminic rings of ThT in the excited state with respect to one another. The main factor determining the high quantum yield of fluorescence of ThT incorporated in fibrils is the steric restriction of the rotation of the rings about one another under these conditions. The suggestions made have been verified by the quantum-chemical calculation of the ThT molecule geometry in the ground and excited states.     

Calculation of the infrared spectrum and density of the vibrational states of an SiO2 melt by molecular dynamics

The density of the vibrational states of an SiO₂ melt under various PT conditions, the distributions of the Si-O-Si and O-Si-O angles in it, and its IR absorption spectra have been calculated by molecular dynamics with the use of a pairwise additive Born-Mayer potential. A comparison with the experimental data reveals that the ionic approximation selected is capable of basically reproducing the structural and spectroscopic properties of the melt, but the distributions of the bond angles are considerably broader than the experimentally determined distributions, and the absorption band caused by the stretching vibrations is not displayed in the calculated spectrum. The disparities indicated are apparently due to the isotropic nature of the potential of the interparticle interactions.V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 467–470, July–August, 1991. Original article submitted October 12, 1990.     

Polarization dynamics of longitudinally monomode bipolarized microchip solid-state lasers

This paper is devoted to the polarization dynamics of a longitudinally monomode bipolarized Nd:YAG laser: the low-frequency polarization dynamics of a microchip laser is studied experimentally and theoretically. The intensities and the relaxation oscillation spectrum of orthogonally polarized modes versus the direction of pump polarization is observed. A phase-sensitive model of a longitudinally monomode bipolarized solid-state laser with linear polarized diode laser pump is developed to account for the experimental observations.     

Class of singular integral operators

A class of singular integral operators is studied from the point of view of the boundedness of their action from some symmetric spaces into other spaces.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 105–110, January, 1991.     

Contractive multifunctions, fixed point inclusions and iterated multifunction systems

We study the properties of multifunction operators that are contractive in the Covitz-Nadler sense. In this situation, such operators T possess fixed points satisfying the relation x∈Tx. We introduce an iterative method involving projections that guarantees convergence from any starting point x₀∈X to a point x∈XT, the set of all fixed points of a multifunction operator T. We also prove a continuity result for fixed point sets XT as well as a “generalized collage theorem” for contractive multifunctions. These results can then be used to solve inverse problems involving contractive multifunctions. Two applications of contractive multifunctions are introduced: (i) integral inclusions and (ii) iterated multifunction systems.     

On the theory of isentropic solutions of quasilinear conservation laws

This paper studies isentropic solutions of quasilinear first-order equations with two independent variables and a flux function that is only continuous. The isentropic solutions are characterized by the requirement that the S. N. Kruzhkov entropy conditions hold for these solution with the equality sign. It turns out that the existence of a nonconstant isentropic solution imposes rather strong restrictions on the nonlinearity. In particular, it is shown that on the minimal interval containing the essential image of the isentropic solution, the flux function satisfies the local Lipschitz condition, and its generalized derivative is a function of locally bounded variation. Also, it is proved that when the flux function is nonlinear, any isentropic solution is continuous on nondegenerate intervals. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.