Krzysztof Wojciechowski

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Stochastic Completeness of Graphs We analyze the stochastic completeness of the heat kernel on infinite, locally finite, connected graphs. For general graphs, a sufficient condition for stochastic completeness is given in terms of the maximum valence on spheres about a fixed vertex. That this result is optimal follows by studying a specific family of trees.(More)
Carbanions of phenylacetonitriles, benzyl sulfones, and dialkyl benzylphosphonates add nitroarenes at the ortho-position to the nitro group to form $$\sigma ^\mathrm{H}$$ σ H -adducts that, upon treatment with trialkylchlorosilane and additional base (t-BuOK or DBU), transform into 3-aryl-2,1-benzisoxazoles in moderate-to-good yields.
Alkylation of 5-nitroindol-4-ylacetonitriles with ethyl chloroacetate, α-halomethyl ketones, and chloroacetonitrile followed by a treatment of the products with chlorotrimethylsilane in the presence of DBU gives 1-cyanopyrrolo[3,2-e]indoles substituted in position 2 with electron-withdrawing groups.
Anilines react with 5-nitroindoles in the presence of t-BuOK in N,N-dimethylformamide (DMF) to form 5-nitroso-4-arylaminoindoles that in turn when treated with N,O-bis(trimethylsilyl)acetamide cyclize to pyrrolo[3,2-a]phenazines. In an alternative approach pyr-rolo[3,2-a]phenazines are formed from aminoindoles and nitroarenes.