Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

A fourth‐order compact finite difference scheme for the steady stream function–vorticity formulation of the Navier–Stokes/Boussinesq equations

A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

Template synthesis in the nickel(II)–thiocarbohydrazide–propanone triple system

The complexing process proceeding in the Ni^II–thiocarbohydrazide (H₂N–H–NC(=S)–NH–NH₂)–propanone triple system in EtOH solution and nickel(II)hexacyanoferrate(II) gelatin-immobilized matrix has been studied. It has been found that in the first case, template synthesis leading, as a minimum, to formation of three coordination compounds of Ni^II with (N,N,S,S)-donor tetradentate ligands having NiL¹, NiL² and NiL³compositions where L¹ is 4,6,6-trimethyl-2,3,7,8-tetraazanonen-3-di(thiohydrazide)-1,9, L² is 4,6,6,12-tetrametyl-1,9-dithio-2,3,7,8,10,11-hexaazatridekadien-3,11-hydrazide-1 and L³ is 2,8,10,10,16-pentamethyl-5,13-dithio-3,4,6,7,11,12,14,15-octaazaheptadekatrien-2,7,15 is observed, whereas in the gelatin-immobilized matrix, a complexing process in the system considered does not occur.     

Molecular structure and pseudopolymorphism of squamtin A from Annona squamosa

The cyclopeptide, squamtin A (1, formula: C₃₉H₆₀O₁₁N₈S), was found to crystallized in two pseudopolymorphisms, i.e. 1·(H₂O)_3.5 and 1·(H₂O)_3.9. The composition of the amino acids and their linkage sequences are the same. The main differences between the two kinds of crystals lie in the positions and occupancies of the water molecules, the positions of the sulfur atoms and the conformation of the side chains. The absolute configuration of 1 is established by X-ray analysis in combination with the Marfey's analysis of its hydrolysates.     

Chemische Vitamin D<Subscript>3</Subscript>-Bestimmung in Lebertran

The different aspects of Vitamin D₃ determination and the data reported in the literature are discussed. The spectrophotometric determination of Vitamin D₃ in cod-liver oil is carried out after the alkaline saponification, extraction of unsaponified parts, precipitation of accompanying sterols and the column- and thin-layer chromatographic purification and separation of vitamin D₃ on 40 cm plates from other vitamins. The dyestuff α-naphtholbenzein is suited well as standard substance for the better location and identification of vitamin D₃ zone on the thin-layer plate. The results obtained from the chemical method were checked through the simultaneous biological determination.     

Analysis of bufadienolides in the Chinese drug ChanSu by high-performance liquid chromatography with atmospheric pressure chemical ionization tandem mass spectrometry

The qualitative analysis of bufadienolides in the Chinese drug ChanSu was performed using high-performance liquid chromatography with atmospheric pressure chemical ionization tandem mass spectrometry (APCI-MS/MS). Bufadienolides are the major bioactive constituents of ChanSu, which is used to treat heart failure and cancer in traditional Chinese medicine. The APCI-MS fragmentation behavior of bufadienolides was studied. For bufadienolides with only hydroxyl substituents, the fragmentation was characterized by successive eliminations of H(2)O and CO molecules, and the profile of MS/MS product ions was correlated with the number of hydroxyl groups. If a C-16 acetoxyl group was present, the fragmentation of [M+H](+) ions was triggered by initial loss of 60 Da (HOAc). The elimination of CO was significant for bufadienolides with a 19-formyl group, and the 19-hydroxyl group could be characterized by the loss of 30 Da (HCHO). These fragmentation rules were applied to the identification of bufadienolides in a methanolic extract of ChanSu, which was separated on a C(18) column with gradient elution. A total of 35 bufadienolides were identified, including four new constituents. The method established here facilitated the convenient and rapid quality control of ChanSu crude drug and its pharmaceutical preparations.