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.     

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.     

Synthese und Kristallstruktur von Blei(II)‐oxidhalogenid‐Alkoholaten mit unterschiedlichen Verknüpfungsvarianten von Pb4O4‐Heterokubaneinheiten

Synthesis and Crystal Structure Determination of Lead(II) Oxide Halide Alcoholates with Different Connectivity of Pb₄O₄ Heterocubane‐like Subunits The reaction of red lead(II) oxide (Litharge) and lead(II) halide (Cl^? and Br^?) with diethylene glycole at a temperature of 180 °C leads to the isotypic compounds [Pb₆(C₄H₈O₃)O₂Cl₆] (1) and [Pb₆(C₄H₈O₃)O₂Br₆] (2) . In a similar synthesis with PbI₂ as educt at temperature of 160 °C the two modifications β‐[Pb₆(C₄H₈O₃)O₂I₆] (3) and α‐[Pb₆(C₄H₈O₃)O₂I₆] (4) were found, whereas at a reaction temperature of 180 °C [Pb₉(C₂H₄O₂)(C₄H₈O₃)O₃I₈] (5) was surprisingly obtained as product. The X‐ray diffraction data show that at a temperature of 180 °C a splitting of the ether took place. The cited compounds show cubane like subunits built by lead and oxygen atoms. These fragments are connected by alkoholate molecules. In 5 additionally an I₆ octahedra centered by lead is observed.