Reduction zweier Covarianten binärer Formen

Ohne Zusammenfassung     

Retention-index based vapor pressure estimation for polychlorobiphenyl (PCB) by gas chromatography

Summary Vapor pressures for 133 individual polychlorobiphenyl congeners as subcooled liquids were determined by two different approaches on the basis of gas-chromatographic retention indices obtained with two different non-polar stationary phases. The approach which is based on the retention indices obtained on a methyl-50% octyl polysiloxane phase (SB Octyl 50) and on reference vapor pressures of PCB congeners, and thus contains less approximations, should yield more accurate results than the method which uses retention indices obtained on a methyl polysiloxane phase (OV 101) and reference vapor pressure data taken from the n-alkanes of the retention index system. A systematic deviation is observed between the values obtained by the two different methods. The first method gives constantly slightly higher values for the vapor pressure. This will be caused by the different separation characteristics of the two non-polar stationary phases used, as well as by uncertainties in the reference data for the vapor pressure calculations.     

Fibonacci Numbers and an Area Puzzle: Connecting Geometry and Algebra in the Mathematics Classroom

A mathematical puzzle that asks about “missing” area leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. This article discusses the inquiry, the concepts, the solution, and an extension that deepens all students’ understanding of connections between algebra and geometry.     

Synthesis of Novel Ethyl (substituted)phenyl‐4‐oxothiazolidin‐3‐yl)‐1‐ethyl‐4‐oxo‐1,4‐dihydroquinoline‐3‐Carboxylates as Potential Anticancer Agents

A series of ethyl (substituted)phenyl‐4‐oxothiazolidin‐3‐yl)‐1‐ethyl‐4‐oxo‐1,4‐dihydroquinoline‐3‐carboxylates ( 7a , 7b , 7c , 7d , 7e , 7f , 7g ) has been prepared from reactions between aminoquinolones 6 with arenealdehydes and mercaptoacetic acid. The critical intermediates, 6 a and 6b , were obtained from appropriate amines by a sequence of steps involving (i) reaction with diethylethoxymethylenemalonate, (ii) thermal cyclization in diphenyl ether, (iii) ethylation and (iv) Pd/C catalyzed reduction. New compounds 7a , 7b , 7c , 7d , 7e , 7f , 7g were fully identified and characterized by NMR (¹H and ¹³C) and specifically for 7d by X‐ray crystallography. Compounds 7b , 7c , 7d , 7e , 7f were found not to exhibit activity at 10 uM concentrations against gastric ascitis (AGP‐01), gastric adenocarcinoma kind intestinal (ACP‐02), colon (HCT‐116) and murine melanome (B16F10) cancer cells. However, none exhibited cytotoxicity against normal cells human fibroblast (MRC‐5), murine fibroblast (NIH3T3) and normal human melanocyte (Melan‐A).