Finite horizon optimal stopping of time-discontinuous functionals with applications to impulse control with delay

We study finite horizon optimal stopping problems for continuous-time Feller–Markov processes. The functional depends on time, state, and external parameters and may exhibit discontinuities with respect to the time variable. Both left- and right-hand discontinuities are considered. We investigate the dependence of the value function on the parameters, on the initial state of the process, and on the stopping horizon. We construct $\varepsilon$-optimal stopping times and provide conditions under which an optimal stopping time exists. We demonstrate how to approximate this optimal stopping time by solutions to discrete-time problems. Our results are applied to the study of impulse control problems with finite time horizon, decision lag, and execution delay

Soluble chlorofullerenes C60CI2,4,6,8,10. synthesis, purification, compositional analysis, stability, and experimental/theoretical structure elucidation, including the x-ray structure of C-1-C60Cl10

The efficacy of various analytical techniques for the characterization of products of C-60 chlorination reactions were evaluated by (i) using samples of C60Cl6 of known purity and (ii) repeating a number of literature syntheses reported to yield pure C60Cln compounds. The techniques were NMR, UV vis, IR, and Raman spectroscopy, FAB, MALDI, LDI, ESI, and APCI mass spectrometry, HPLC, TGA, elemental analysis, and single-crystal X-ray diffraction. Most of these techniques are shown to give ambiguous or erroneous results, calling into question the composition and/or purity of nearly all C60Cln compounds reported to date. The optimum analytical method for chlorofullerenes was found to be a combination of HPLC and either MALDI or APCI mass spectrometry. For the first time, the chlorination of C-60 by ICl, ICl3, and Cl-2 was studied in detail using dynamic HPLC analysis and APCI mass spectrometry. Suitable conditions were found for the preparation of the new chlorofullerenes 1,7-C60Cl2, 1,9-C60Cl2, 1,6,9,18-C60Cl4, and 1,2,7,10,14,24,25,28,29,31-C60Cl10. The latter compound was also studied by C-13 NMR spectroscopy and X-ray diffraction, which led to the unambiguous determination of its asymmetric addition pattern. The unusual structure of C60Cl10 was compared with other possible isomers using DFT-predicted relative energies. These results, along with additional experimental data and an analysis of the DFT-predicted frontier orbitals of likely intermediates, were used to rationalize the formation of the new compound C60Cl10 from C60Cl6 and excess ICl without the rearrangement of any C-Cl bonds. For the first time, the stability of C60Cln compounds under a variety of conditions was studied in detail, leading to the discovery that they are, in general, very light-sensitive in solution. The X-ray structure of C60Cl6 was also redetermined with higher precision