Piecewise Deterministic Markov Control Processes with Feedback Controls and Unbounded Costs

The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover the discount rate may be zero. The value function is shown to be solution to the Bellman equation in a weak sense; however the solution concept is strong enough to generate optimal policies. Continuity and compactness conditions are given for the existence of nonrelaxed optimal feedback controls.     

Quantitative Depth Profiling of K-Doped Fullerene Films Using XPS and SIMS

 Phenomena accompanying electrochemical doping of solid fullerene films with potassium were studied by sputter ion depth profiling (XPS and SIMS). The potassium distribution was determined, and artifacts associated with possible damage of the layer composition caused by ion impact were investigated and discussed. To compare the charge transfer while reductive doping is taking place at fullerene/solution interface with doping from gas phase, model layers were prepared and doped by potassium under UHV conditions. It was found that sputtering by Ar⁺ primary ions yields both accurate information on the alkaline metal distribution and on its concentration. Sputtering by O⁺ ions led to an enrichment of potassium, apparently due to the reactivity of oxygen with the fullerene matrix. It is shown that the reductive doping starts at the fullerene/solution interface. The concentration of potassium in the doped films was found to be lower than expected from the charge transferred during the electrochemical reduction. Other phase transformations such as hydrogenation are discussed. Received March 4, 2002; accepted July 26, 2002     

Mild and efficient synthesis of propargylamines by copper-catalyzed Mannich reaction

Terminal alkynes undergo mild and efficient aminomethylation with aqueous formaldehyde and secondary amines under CuI catalysis. In most cases high to nearly quantitative yields of tertiary propargylamines are obtained in DMSO solution at room temperature. Aromatic, aliphatic and silylated acetylenes as well as alkynols can be used. Primary amines are less reactive and satisfactory yields of secondary propargylamines are obtained only with phenylacetylene.     

The asymptotic behaviour of certain entire functions of order zero

Summary A certain class of entire functionsF(s) of order zero which are asymptotically equal to the sum of just two neighbouring terms of their power series when |s| with |args| < – for any fixed > 0, is investigated. Which two terms one has to take, depends upons. It is shown that these functions have infinitely many negative zeros, and the asymptotic behaviour of the zeros is also determined.     

Photodynamic Therapy of 9L Gliosarcoma with Liposome-Delivered Photofrin

Abstract— The effect of Photofrin encapsulated in a liposome delivery vehicle for photodynamic therapy (PDT) of the 9L gliosarcoma and normal rat brain was tested. We hypothesized that the liposome vehicle enhances therapeutic efficacy, possibly by increasing tumor tissue concentration of Photofrin. Male Fisher rats bearing a 9L gliosarcoma were treated 16 days after intracerebral tumor implantation with either Photofrin in dextrose (n = 5) or Photofrin in liposome (n = 6). Nontumor-bearing animals were treated with Photofrin delivered either in dextrose (n = 4) or liposome (n = 4) vehicle. Tissue concentrations of Photofrin delivered either in dextrose (n = 4) or liposome (n = 4) vehicle were measured in tumor, brain adjacent to tumor and in normal brain tissue. Photofrin was administered (intraperitoneally) at a dose of 12.5 mg/kg and PDT (17 J/cm₂ of 632 nm light at 100 mW/cm₂) was performed 24 h after Photofrin administration. Brains were removed 24 h after PDT and stained with hematoxylin and eosin for analysis of cellular damage. The PDT using Photofrin in the liposome vehicle caused significantly more damage to the tumor ( P < 0.001) than did PDT with Photofrin in dextrose. The PDT of tumor with Photofrin delivered in liposomes caused a 22% volume of cellular necrosis, while PDT of tumor with Photofrin delivered in dextrose caused only scattered cellular damage. Photofrin concentration in tumors was significantly higher ( P = 0.021) using liposome (33.8 ± 18.9 μg/g) compared to dextrose delivery (5.5 ± 1.5 μg/g). Normal brain was affected similarly in both groups, with only scattered cellular necrosis. Our data suggest that the liposome vehicle enhances the therapeutic efficacy of PDT treatment of 9L tumors.