On rational integrability of Euler equations on Lie algebra so(4, ℂ)

We consider the Euler equations on the Lie algebra so(4, ℂ) with a diagonal quadratic Hamiltonian. It is known that this system always admits three functionally independent polynomial first integrals. We prove that if the system has a rational first integral functionally independent of the known three ones so called fourth integral, then it has a polynomial first integral that is also functionally independent of them. This is a consequence of more general fact that for these systems the existence of Darboux polynomial with no vanishing cofactor implies the existence of polynomial fourth integral.     

Anion Coreceptor Molecules. Linear Molecular Recognition in the Selective Binding of Dicarboxylate Substrates by Ditopic Polyammonium Macrocycles

Three macrocyclic hexaamines 1 , 2 , and 4 , and the acyclic tetraamine 5 and hexaamine 6 have been synthesized. The hexaamines 1 , 2 , and 4 are ditopic coreceptor molecules containing two triamine subunits which may bind anionic substrates when protonated. The stability constants of the complexes between the protonated forms of the macrocyclic polyamines and terminal dicarboxylates ^?O₂C?(CH₂)_m- CO₂^? as well as amino-acid and dipeptide dicarboxylates have been determined by pH-metric measurements. Around neutral pH, 1 and 2 give mainly complexes of the fully protonated species 1 ·6H⁺ and 2 ·6H⁺, whereas 4 yields predominantly complexes of 4 ·5H⁺ and 4 ·4H⁺. The stability sequences of the complexes formed indicate preferential binding of the dianionic substrates whose length is compatible with the separation of the triammonium binding subunits in the protonated receptor molecules 1 , 2 , and 4 . This selectivity pattern corresponds to a process of linear molecular recognition based on ditopic binding between the two ammonium subunits of the coreceptor and the terminal carboxylates of the substrate of complementary length. The complexes of the acyclic ligands 5 and 6 are much weaker and much less selective, indicating a marked macrocyclic effect on both stability and selectivity of binding, i.e. on recognition.     

Preparation and reductive lithiation of 2-deoxy-D-glucopyranosyl phenylsulfones: A highly stereoselective route to C-glycosides

2-Deoxy-D-glucopyranosyl phenylsulfones 3a–c have been synthesized in 75–83% yield from commercial tri-O-acetyl-D-glucal 1. Their reductive desulfonylation by lithium naphthalenide and reaction of the intermediate glycosyl-lithium 5 with aldehydes leads to α-D-C-glucopyranosides with high stereoselectivity.     

Evidence for direct observation by Mössbauer spectroscopy of surface tin atoms in platinum–tin particles

The diamond-bearing gravels found along South Africa's West Coast are being beneficiated by means of dense medium separation (DMS) to reclaim the alluvial diamonds. Granular ferrosilicon (Fe–Si) is used as the DMS material and at the end of each operation the Fe–Si is reclaimed from the process stream using a magnetic separator and is then recycled but losses of Fe–Si due to attrition, adhesion to the separation products, density changes and changes to the magnetic properties can occur. The gravel obtained from the mining operation is washed and screened before heavy mineral separation. The concentrate, tailings and Fe–Si samples were investigated by means of SEM and Mössbauer spectroscopy to determine where changes to the Fe–Si, or contamination could occur. The composition of the Fe–Si was determined to be Fe (76.1 at.%), Si (20.3 at.%), Mn (1.5 at.%), Al (1.5 at.%) and Cr (0.6 at.%) resulting in a more or less ordered DO₃ phase with a calculated composition of Fe₃Si for this Fe–Si, consistent with the Mössbauer results where two sextets with hyperfine magnetic fields of 18.6 T and 28.4 T were observed. After DMS, magnetite and ilmenite, the minerals found in the gravel, were still present in the concentrate. In the tailings virtually no magnetite or ilmenite was found and only a doublet, identified as an oxihydroxide, due to the abrasion of the Fe–Si, was found. After magnetic separation, to wash and clean the Fe–Si for re-use, it was found that magnetite and ilmenite were still present in the Fe–Si, which results in a change in density of the Fe–Si, resulting in a higher density and loss of valuable diamonds.     

Photoactive Cryptands. Crystal Structure of the Sodium Cryptate of the Tris(phenanthroline) Macrobicyclic Ligand

The crystal structure of the complex [phen · phen · phen] · NaBr · 2 CHCl₃ of the macrobicyclic ligand 1 has been determined. The complex is of cryptate type, the Na⁺ cation being contained in the molecular cavity of 1 and coordinated to all eight N-atoms. The ligand has a propeller shape and interconverts in solution between the two enantiomeric helical forms.