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     

Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution

Summary. We introduce linear semi-implicit complementary volume numerical scheme for solving level set like nonlinear degenerate diffusion equations arising in image processing and curve evolution problems. We study discretization of image selective smoothing equation of mean curvature flow type given by Alvarez, Lions and Morel ([3]). Solution of the level set equation of Osher and Sethian ([26], \[30]) is also included in the study. We prove and estimates for the proposed scheme and give existence of its (generalized) solution in every discrete time-scale step. Efficiency of the scheme is given by its linearity and stability. Preconditioned iterative solvers are used for computing arising linear systems. We present computational results related to image processing and plane curve evolution. Received April 25, 2000 / Revised version received June 11, 2001 / Published online November 15, 2001     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

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...     

Determination of the Lipophilicity of Xanthines by Reversed-Phase Liquid Chromatography

JPC – Journal of Planar Chromatography – Modern TLC -     

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.     

31P and 1h NMR as probes of domain alignment in a rigid crystalline surfactant mesophase

A viscous reverse hexagonal surfactant mesophase containing bis(2-ethylhexyl) sodium sulfosuccinate (AOT) and alpha-phosphatidylcholine (lecithin), with comparable volume fractions of isooctane and water, was characterized by Fourier transform (31)P and (1)H NMR spectroscopy. Shear alignment was reflected through both (31)P NMR and (1)H NMR spectra. A complicated (31)P spectrum was observed as a result of superposition of chemical shifts according to the distribution of crystalline domains prior to shear. The initially disordered samples with polydomain structures become macroscopically aligned after Couette shear. (31)P NMR chemical shift anisotropy characteristics are used to elucidate orientation of the hexagonal phase. Interestingly, (1)H NMR spectra exhibit spectral changes upon shear alignment closely corresponding with that of (31)P NMR spectra. These observations complement the findings of mesophase alignment obtained using SANS and imply that (31)P and (1)H NMR spectroscopy can be used as probes to define microstructure and monitor orientation changes in this binary surfactant system. This is especially beneficial if these mesophases are used as templates for materials synthesis.     

The synthesis and characterisation of 1′-ethynyl-2,5-dimethylazaferrocene and derivatives

The synthesis of 1′-ethynyl-2,5-dimethylazaferrocene is reported along with its cyclic voltammetry measurements and the X-ray structure determination of its W(CO)₅-complex. Basic coordination and organic chemistry of 1′-ethynyl-2,5-dimethylazaferrocene is also presented via derivatives incorporating cis-Pt(dppe) and Si(Et)₃ units.