Synthesis of novel retinoid X receptor-selective retinoids

Retinoids 1-5 have been identified as potent RXR agonists for evaluation in the treatment of non-insulin-dependent (type II) diabetes mellitus (NIDDM). Highly convergent syntheses of 1-5 have been developed. The core tetrahydronaphthalene 7, employed in the synthesis of 1 and 2, was prepared in 98% yield using an AlCl(3)-catalyzed (0.03 equiv) Friedel-Crafts alkylation of toluene with 2,5-dichloro-2,5-dimethylhexane 6. A nitromethane-mediated Fridel-Crafts acylation of 7 with chloromethylnicotinate 9 was developed to prepare ketone 10 in 68% yield. Chelate-controlled addition of MeMgCl to 10 followed by dehydration afforded olefin 11 in 65% yield. Cyclopropanation of 11 with trimethylsulfoxonium ylide, followed by saponification, completed a five-step synthesis of 1 in 33% yield. FeCl(3)-catalyzed (0.05 equiv) Friedel-Crafts acylation of 7 with chloromethylterephthalate 14 afforded ketone 15 in 81% yield. Saponification of 15 and reaction with 50% aqueous NH(2)OH in AcOH afforded a 9:1 mixture of cis and trans oximes, from which the desired cis-oxime 2 was isolated in 43% yield. The core bromo-dihydronaphthalene 29 required for the synthesis of 3-5 was prepared by a Shapiro reaction. Transmetalation of 29 and reaction with Weinreb amides 30b or 36 afforded ketones 32 and 37, which were converted into 3-5 using chemistry comparable to the tetrahydronaphthylene series. Suzuki coupling of boronic acids 41 and 42 with vinyl triflate 43 provided an alternative approach to the synthesis of this class of compounds.     

Longitudinal dispersion in flows that are homogeneous in the streamwise direction

The longitudinal dispersion of a pulse of passive scalar contaminant within a flow that is unchanging in the downstream direction is established to be a function of the mean-velocity-history of molecules from a uniform distribution on the flow cross-section. The specific case of laminar flow between parallel plates is investigated in detail, wherein it is found that $$\frac{1}{2}\frac{{\overline {d\eta (t)^2 } }}{{dt}} = \frac{9}{{2\pi ^6 }}\frac{{\bar U^2 d^2 }}{k}\sum\limits_{n = 1}^\infty {\frac{1}{{n^6 }}} \left( {1 - \exp \left( {\frac{{ - (2n\pi )^2 tK}}{{d^2 }}} \right)} \right),$$ where η(t) is the displacement relative to an axis located byūt whenū is the discharge velocity,K is the molecular diffusivity andd is the plate separation. This flow is used to show that the molecule mean velocity-histories can be approximated by a function that does not directly depend on the release position of the molecule on the flow cross-section. The results of a numerical simulation of the dispersion in this flow are presented for comparison.     

The approach to normality of the distance-neighbour function when used to describe relative turbulent dispersion

Batchelor [1] suggested that the Distance-Neighbour Function when used to describe the relative turbulent dispersion of a cloud of marked fluid, whose diameter is well within the length scale range of the universal inertial sub-range of turbulence, would become of Gaussian form. This paper determines that a necessary condition for the Gaussian form to apply is that the non-dimensional time of (/v)^1/2 t 300, following the release of the marked fluid with an initial diameter <(v ³/t)^1/4, be attained.

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Zusammenfassung Batchelor [1] hat die Behauptung aufgestellt, dass die Abstands-Nachbar-Funktion (räumliche Korrelation) die Gauss'sche Form annimmt, wen man sie zur Beschreibung der relativen turbulenten Dispersion einer Wolke von markierter Flüssigkeit benützt, falls der Durchmesser der Wolke nicht über die Längenskala des universellen Inertial-Unterbereichs der Turbulenz hinausgeht. In dieser Arbeit wird gezeigt, dass eine notwendige Bedingung der Anwendbarkeit der Gauss'schen Form darin besteht, dass die dimensionsloze Zeit (/v)^1/2 t 300 nach dem Ablösen einer markierten Flüssigkeits-wolke mit dem Anfangsdurchmesser <(v ³/t)^1/4 erreicht wird.

     

Advances in positron and electron scattering*

The topical issue on Advances in Positron and Electron Scattering” combines contributionsfrom POSMOL 2015 together with others devoted to celebrate the unprecedented scientificcareers of our loyal colleagues and trusted friends Steve Buckman (Australian NationalUniversity, Australia) and Michael Allan (University of Fribourg, Switzerland) on theoccasion of their retirements. POSMOL 2015, the XVIII International Workshop on Low-EnergyPositron and Positronium Physics and the XIX International Symposium on Electron-MoleculeCollisions and Swarms, was held at Universidade NOVA de Lisboa, Lisboa, Portugal, from17–20 July 2015. The international workshop and symposium allowed to achieve a veryprivileged forum of sharing and developing our scientific expertise on current aspects ofpositron, positronium and antiproton interactions with electrons, atoms, molecules andsolid surfaces, and related topics, as well as electron interactions with molecules inboth gaseous and condensed phases. Particular topics include studies of electroninteractions with biomolecules, electron induced surface chemistry and the study of plasmaprocesses. Recent developments in the study of swarms are also fully addressed.     

Saturation of Berge hypergraphs

Given a graph $F$, a hypergraph is a Berge- $F$ if it can be obtained by expanding each edge in $F$ to a hyperedge containing it. A hypergraph $H$ is Berge-$F$-saturated if $H$ does not contain a subhypergraph that is a Berge-$F$, but for any edge $e\in E\left(\overline{H}\right)$, $H+e$ does. The $k$-uniform saturation number of Berge-$F$ is the minimum number of edges in a $k$-uniform Berge-$F$-saturated hypergraph on $n$ vertices. For $k=2$ this definition coincides with the classical definition of saturation for graphs. In this paper we study the saturation numbers for Berge triangles, paths, cycles, stars and matchings in $k$-uniform hypergraphs.