Toric Surface Patches

We define a toric surface patch associated with a convex polygon, which has vertices with integer coordinates. This rational surface patch naturally generalizes classical Bézier surfaces. Several features of toric patches are considered: affine invariance, convex hull property, boundary curves, implicit degree and singular points. The method of subdivision into tensor product surfaces is introduced. Fundamentals of a multidimensional variant of this theory are also developed.     

PICOSECOND ABSORPTION STUDIES OF Zn-OCTAETHYLPORPHIN π-MONOANIONS

Abstract— Using the example of Zn-octaethylporphin π-monoanion solution in tetrahydrofuran, we studied the dynamics of ultrafast photoprocesses in porphyrin π-anions using a tunable picosecond absorption spectrometer. The deactivation kinetics of the lowest excited electronic (doublet) state of Zn-octaethylporphin iT-monoanion has been determined and was found to be followed by a single exponential function with the characteristic time 135 ps. It is shown that upon picosecond excitation to the long wavelength absorption band (λ_max= 830 nm) the process of two-quantum photoionization of the involved monoanion is easily realized, with the results that the observable kinetics of spectral changes exhibit a strong dependence on the excitation intensity.     

Absorption and fluorescent properties of pyrylium compounds: II. Spectra and cross sections for absorption from the ground and excited states of the structurally rearranged form

The nonstationary absorption of solutions of 2,4,6-substituted pyrylium salt is studied by the pump-probe method. The solutions in methylene chloride are studied upon picosecond pumping and probing with different time delays. The solutions in methyl ethyl ketone are studied upon pumping and synchronous probing by nanosecond pulses. It is shown that excitation of the initially nonplanar molecule causes its structural rearrangement. As a result, substituent 2 enters into the pyrylium ring plane and two nonstationary conformers are formed that differ in the position of substituent 6. The motion upon structural rearrangement has a small amplitude, and localization of molecular orbitals changes only slightly. The temperature dependence of the nonstationary absorption is studied in the range from 293 to 223 K. The spectra and cross sections are measured for transitions from the S₀ and S₁ states. In addition, the activation energies and kinetic parameters of the rearrangement in the ground and excited states are determined. Experimental data are compared with theoretical calculations of the transitions from the S₁ state. It is shown that a partial flattening of conformer molecules results in the long-wavelength shift of the bands and an increase in the cross sections for transitions localized on a flat part of the molecule and does not change parameters of the band localized on the molecular part that did not change upon the rearrangement but remained nonplanar.