Some remarks on the Hook formula

Summary Without the Frame-Robinson-Thral hook formula we establish some divisibility properties of degrees of irreducible representations of the symmetric group.

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Riassunto Senza utilizzare una nota formula di Frame-Robinson-Thrall stabiliamo alcune proprietà di divisibilità di gradi di rappresentazioni irriducibili del grupposimmetrico.

     

Über ein topologisches Theorem

Ohne Zusammenfassung     

Synthesis and structural characterization of novel 2-benzimidazolylthioureas: adducts of natural isothiocyanates and 2-amino-1-methylbenzimidazole

Adducts of natural allyl, phenethyl, and benzyl isothiocyanates and 2-amino-1-methylbenzimidazole were synthesized. After optimization of the reaction conditions, the target 2-benzimidazolylthioureas were obtained in reasonable yields. The detailed molecular and crystal structures of these compounds were characterized by spectroscopic and X-ray methods. Spectral analysis demonstrated that N-(1-methylbenzimidazolyl)-N′-allylthiourea, N-(1-methylbenzimidazolyl)-N′-benzylthiourea, and N-(1-methylbenzimidazolyl)-N′-phenethylthiourea exist in solution in an unprecedented three tautomeric forms, whose structures were corroborated unambiguously.     

Spin-label saturation-recovery EPR at W-band: applications to eye lens lipid membranes

Saturation-recovery (SR) EPR at W-band (94 GHz) to obtain profiles of the membrane fluidity and profiles of the oxygen transport parameter is demonstrated for lens lipid membranes using phosphatidylcholine (n-PC), stearic acid (n-SASL), and cholesterol analog (ASL and CSL) spin labels, and compared with results obtained in parallel experiments at X-band (9.4 GHz). Membranes were derived from the total lipids extracted from 2-year-old porcine lens cortex and nucleus. Two findings are especially significant. First, measurements of the spin-lattice relaxation times T1 for n-PCs allowed T1 profiles across the membrane to be obtained. These profiles reflect local membrane properties differently than profiles of the order parameter. Profiles obtained at W-band are, however, shifted to longer T1 values compared to those obtained at X-band. Second, using cholesterol analog spin labels and relaxation agents (hydrophobic oxygen and water-soluble NiEDDA), the cholesterol bilayer domain was discriminated in membranes made from lipids of the lens nucleus. However, membranes made from cortical lipids show a single homogeneous environment. Profiles of the oxygen transport parameter obtained from W-band measurements are practically identical to those obtained from X-band measurements, and are very similar to those obtained earlier at X-band for membranes made of 2-year-old bovine cortical and nuclear lens lipids (M. Raguz, J. Widomska, J. Dillon, E.R. Gaillard, W.K. Subczynski, Biochim. Biophys. Acta 1788 (2009) 2380-2388). Results demonstrate that SR EPR at W-band has the potential to be a powerful tool for studying samples of small volume, ～30 nL, compared with the sample volume of ～3 μL at X-band.     

On Mincʼs sheltered middle path

This paper shows that a construction, which was introduced by Piotr Minc in connection with a problem that came from Helly type theorems and that allows to replace three PL-arcs with a “sheltered middle path”, can in the case of general (non-PL) paths result in the topologist?s sine curve.     

Apoptosis-accommodating Effect of Nitric Oxide in Photodynamically Stressed Tumor Cells

Using a 5-aminolevulinic acid (ALA)-photodynamic therapy model, we have discovered a new effect of nitric oxide (NO)—the ability to accommodate apoptosis. When sensitized by disseminated ALA-generated protoporphyrin IX, COH-BR1 tumor cells in glucose-containing medium died mainly by necrosis with a low level of apoptosis. Introduced before light at a nontoxic concentration, the NO donor SPNO inhibited necrosis, but supported apoptosis such that the latter became predominant in the remaining cell death. Accompanying this was a large increase in caspase-3/7 activation. SPNO-supported apoptosis was more pronounced when glucose-deprived cells were compared with glucose-replenished, SPNO-treated counterparts. SPNO plus glucose also suppressed plasma membrane-damaging lipid peroxidation and loss of cellular ATP under photostress. The NO effect is attributed to membrane protection with maintenance of sufficient glycolytic ATP to sustain apoptosis.