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The room temperature oxidation of betulin by Cr(VI) compounds in aqueous acetone on solid supports such as alumina, zeolites and silica gel has been studied. The oxidation on alumina support leaded to a single product--betulonic acid--in quantitative yield. One hundred percent selective oxidation during 30 min of betulin up to betulonic aldehyde was… (More)

We study the structure of the solution set of a class of infinite-horizon dynamic programming problems with one-dimensional state spaces, as well as their bifurcations as problem parameters are varied. The solutions are represented as the integral curves of a multi-valued 'optimal' vector field on state space. Generically, there are three types of integral… (More)

We develop a method of obtaining an asymptotic series of the value function of a stochas-tic optimal control problem over an unbounded domain with a finite number of irregularity points. These are points of non-differentiability of the value function of the corresponding deterministic problem. We apply singular perturbation methods to obtain the solution… (More)

A new method for evaluating disorders in the sense of color has been developed and offered for practice. A total of 340 patients with diseases of the retina and optic nerve and 80 normal subjects were examined. The results indicate that different conditions of examination, selection of combination by the color, brightness, and deepness of the stimulus and… (More)

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