Weakly symmetric spaces in dimension five

We prove that every five-dimensional simply connected naturally reductive space is weakly symmetric in the sense of A.Selberg [11]. (For dimension less than five it was shown in [1] by a different method). We also show that the converse holds for all dimensions not greater than five.Supported by the grant GACR 201/93/0469Supported by a National Research Project of the M. U. R. S. T (Italy).     

Randomization helps to perform independent tasks reliably

This paper is about algorithms that schedule tasks to be performed in a distributed failure‐prone environment, when processors communicate by message‐passing, and when tasks are independent and of unit length. The processors work under synchrony and may fail by crashing. Failure patterns are imposed by adversaries. Linearly‐bounded adversaries may fail up to a constant fraction of the processors. Weakly‐adaptive adversaries have to select, prior to the start of an execution, a subset of processors to be failure‐prone, and then may fail only the selected processors, at arbitrary steps, in the course of the execution. Strongly adaptive adversaries have a total number of failures as the only restriction on failure patterns. The measures of complexity are work, measured as the available processor steps, and communication, measured as the number of point‐to‐point messages. A randomized algorithm is developed, that attains both ??(n log*n) expected work and ??(n log*n) expected communication, against weakly‐adaptive linearly‐bounded adversaries, in the case when the numbers of tasks and processors are both equal to n. This is in contrast with performance of algorithms against strongly‐adaptive linearly‐bounded adversaries, which has to be Ω(n log n/log log n) in terms of work. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

TLC and HPLC Analysis of the Phenolic Acids in Silphium perfoliatum L. Leaves,Inflorescences and Rhizomes

JPC – Journal of Planar Chromatography – Modern TLC - TLC and HPLC have been used for preliminary evaluation of the phenolic acids occurring in the leaves, inflorescences, and rhizomes...     

Reactions of lithiated 2,5-dimethylazaferrocene with selected electrophiles

Lithiation of 2,5-dimethylazaferrocene 1 with sec-BuLi/TMEDA in THF at −78 °C proceeds (as shown by quenching with D₂O) to comparable extent on the methyl groups and the Cp ring. However, the outcome of the reaction of the lithiated 1 with an electrophile depends on the nature of this electrophile. In the reaction with 4-methoxybenzaldehyde only the product originated from the lateral lithiation is formed, whereas the reaction with 4-methoxyacetophenone and 4,4′-dimethoxybenzophenone afforded mixtures of the products resulting from lateral and ring-lithiation. Similar results were also obtained in the reaction of lithiated 1 with chlorodiphenylphosphine and diphenyl diselenide. On the other hand, the exclusive formation of the Cp-substituted product was observed in the reaction of lithiated 1 with N,N-dimethylformamide. The structures of selected products (oily compounds were transformed into the corresponding crystalline W(CO)₅-complexes) were confirmed by X-ray diffraction. The presented reactions open a novel entry to specifically substituted azaferrocenes (especially those containing heteroatom substituents) with potential applications as ligands for the homogenous catalysis.