On the hydrodynamic limit of a Ginzburg-Landau lattice model

Summary A lattice system of interacting diffusion processes is investigated. The evolution is attractive and time reversible, the spin satisfies a conservation law. It is shown that the rescaled spin field converges in probability to the corresponding solution to a nonlinear diffusion equation.Supported in part by the Hungarian National Foundation for Scientific Research, grant No. 819/1, and by the Mathematical Department of Rutgers University, N.S.F. grant DMR 8612369     

An explicit characterization of Calogero-Moser systems

Combining theorems of Halphen, Floquet, and Picard and a Frobenius type analysis, we characterize rational, meromorphic simply periodic, and elliptic KdV potentials. In particular, we explicitly describe the proper extension of the Airault-McKean-Moser locus associated with these three classes of algebro-geometric solutions of the KdV hierarchy with special emphasis on the case of multiple collisions between the poles of solutions. This solves a problem left open since the mid-1970s.

     

Infinite time optimal control and periodicity

For smooth nonlinear systems

Synthesis and molecular structure of [Al(CH3)2]2[C10H22N4] [Al(CH3)3]2: Condensation product of trimethylaluminum and a multidentate open-chain amine

The crystalline condensation product [Al(CH₃)₂]₂[C₁₀H₂₂N₄][Al(CH₃)₃]₂ is prepared from reaction of the multidentate open-chain amine 1,4-bis(3-aminopropyl)piperazine with trimethylaluminum in methylene chloride. The compound crystallized in the monoclinic space groupC2/c with unit cell parametersa=25.166(12),b=7.268(4),c=17.316(4) Å,=115.3(4)°, andD _c =1.06 g cm^–3 forZ=4. Least-squares refinement based on 1054 observed reflections with intensitiesI 3(I) in the range 2<2<45° led to a finalR factor of 0.053 (R _w =0.064). The title compound resides on a crystallographic center of symmetry with independent Al-N distances of 1.889(5), 2.058(5), and 2.030(5) Å.     

On the tensor product of supersingleton representations ofosp(1, 2n)

The tensor product of two supersingleton representations _n of the Lie superalgebraosp (1, 2n) is studied forn2. The main results are as follows: (a) anticommutators and commutators of the odd generators in _{n n} form a skew-symmetric representation of the Lie algebrau(n, n); (b) simple explicit form of all irreducible components of _{n n}, which are labelled by a single parameterJ=0, 1, ..., has been found. Each of them is a^*-representation ofosp (1, 2n) for which assertion (a) is valid. The dimension of its vacuum subspace equals , i.e., the nondegenerate vacuum occurs for J=0 only. Basic property of this family of irreducible^*-representations of osp(1, 2n) are analogous to those of massless representations of osp(1, 4).Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

Miniaturized solid-phase extraction with resin disks

The properties and advantages of membrane disks for solid-phase extraction (SPE) are described. Miniaturization is a trend in SPE, as well as chemical analysis in general. A semimicro method is reviewed in which an extraction disk 4 mm in diameter is used for SPE. Even smaller scale separations are possible with a device in which a membrane 0.7 mm in diameter was incorporated into the needle of a 50-micro syringe. Aqueous samples containing 10 ppb of eight substituted benzenes were passed through the miniaturized-SPE syringe automatically using a single-syringe infusion pump. Elution volumes of 5 microl provided 500-fold concentrations and delivered average recoveries greater than 90% and an average relative standard deviation (RSD) of 4.6% for the analytes. Direct injection of the 5 microl eluate from the miniaturized-SPE syringe into a gas chromatograph also produced average recoveries greater than 90% and an average RSD of 6.2%.     

Intramolecular meerwein reactions of the anthraquinone system. Synthesis,X-ray structural analysis and spectroscopic properties of anthra[9,1-bc:10,5-b'c']tetrahydrodipyran derivatives

Meerwein reactions of 1,5-anthraquinone bis(diazonium hydrogen sulfate) with sufficiently activated olefins, such as acrylonitrile, acrylic esters, methacrylonitrile and its esters, styrene and α-methylstyrene yielded derivatives of the new heterocyclic system anthra[9,1-bc:10,5-b'c']-2,3,7,8-tetrahydrodipyran. Isolation of derivatives was realized and yields enhanced by using dimethyl methylphosphonate as reaction medium. Compounds 5–18 were isolated as mixtures of diastereomers, some of which were separated by crystallization. Proof of structure and stereochemistry was obtained for some of the compounds by X-ray crystallographic analysis. The ¹H- and ¹³C-nmr data provided further support. Surprisingly large chemical shift differences between some of the proton signals of isomers were observed although the two asymmetric centers are far apart through bonds and through space. The mechanism of formation is explained on the basis of redox modulation of a charge transfer complex in which the aliphatic radical attacks the oxygen atom of the anthraquinone. It is proposed to classify this new type of reaction as an intramolecular Meerwein reaction.