Total synthesis of (±)-desepoxy-4,5-didehybromethylenomycin A

The total synthesis of (±)-desepoxy-4,5-didehydromethylenomycin A employing a retrolactonization strategy has been achieved.     

Synthesis of (±)-averufanin,1noraverufanin and bis-deoxyaverufanin

Alkylation of xanthopurpurin (8) by 2-hydroxy-6-methyltetrahydropyran (6a and 6b) produced bis-deoxyaverufanin (9). This reaction was first carried out in aqueous sodium bicarbonate solution. Use of (S)-(?)-proline in dimethylformamide gave a quantitative yield of 9. With this method, 1,3,6,8-tetrahydroxyanthraquinone (4) was alkylated by 2-hydroxytetrahydropyran (15). Chromatography of the reaction mixture produced noraverufanin (17) along with a dialkytation product 18. Synthesis of (±)-averufanin (12) with 42% yield was achieved.     

A COMPARISON OF DECAY KINETICS OF PHOTO-PRODUCED ABSORBANCE,EPR, AND LUMINESCENCE CHANGES IN CHROMATOPHORES OF RHODOSPIRRILLUM RUBRUM*

–Quantitative comparison of the decay rate for absorbance photochanges in chromatophores of R. rubrum at the major wavelengths of peaks and troughs (280, 365, 385, 433, 605, 763, 790, 810, 850, 865, 890 nm) reveal no major differences under a variety of sample conditions. In addition, the decay kinetics of EPR phtochange at the two environmental potentials used in this study are identical with the absorbance ph;otochange decay. Decay curves for fresh chromatophores, aged chromatophores, and fresh chromatophores at high ionic strength display a variety of half times and curve shapes. All of these data however, may be fit (within 10 per cent) by the equation x=αe^8.2t+βe^0.18t by merely varying the values of α and β. This is interpreted as meaning that any single trapping site may exist in one of two major forms each of which decays following a first order or pseudo-first order reaction. Although the change in decay pattern upon aging is not reversible, that due to high ionic strength is. The time dependencies for two light emission phenomena have been measured as well as their response to the oxidation state of molecules at the trapping site. A major component of long-lived luminescence follows pseudo-second order kinetics with a half time of 38 msec. A very long lived luminescence shows an increse with time which is nearly proportional to the decay of absorbance photochanges.     

Metal-ammonia reduction: the ring reduction of aromatic carboxylic esters

Aryl benzoates are reduced to 1,4-dihydroaromatics with Na/NH₃ in the presence of water.     

Numerical solution of an inverse initial boundary-value problem for the full time-dependent Maxwell's equations in the presence of imperfections of small volume

We consider the numerical solution, in a three-dimensional bounded domain, of the inverse problem for identifying the location of small electromagnetic imperfections in a medium with homogeneous background. Our numerical algorithm is based on the coupling of a discontinuous Galerkin method for the time-dependent Maxwell's equations, on the exact controllability method and on a Fourier inversion. Several numerical results are given with one and two imperfections and the robustness and accuracy of the numerical method used for the dynamic detection problem are shown.     

Bounded-degree polyhedronization of point sets

In 1994 Grünbaum showed that, given a point set S in ${\mathbb{R}}^3$, it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. extended this work in 2008 by showing that there always exists a polyhedronization that can be decomposed into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present a randomized algorithm running in $O(n{\log }^{6}n)$ expected time which constructs a serpentine polyhedronization that has vertices with degree at most 7, answering an open question by Agarwal et al.     

Conformational Analysis of (S)-4,5,6,7-Tetrahydro-5-Methylimidazo [4,5,1-jk][1,4]-Benzodiazepin-2(1H)-one (R78362)

The solution and solid state conformation of (S)-4,5,6,7-tetrahydro-5-methylimidazo [4,5,1-jk][1,4]-benzodiazepin-2(1H)-one (R78362) have been investigated by low temperature NMR and x-ray diffraction studies. The ¹H NMR spectrum of R78362 shows no evidence of the presence of multiple conformers in the temperature range 340K - 177K. Molecular mechanisms and semiempirical molecular orbital calculations suggest that the nitrogen and ring inversion barriers of R78362 are small and thus a time-averaged ¹H NMR spectrum is probably occurring at 298K. The x-ray diffraction data indicated that there were two independent molecules in the asymmetric unit of the crystal. The two molecules had similar conformations with the benzoimidazole ring being planar and the diazepine ring in a “half-chair” conformation.     

Disjoint Compatible Geometric Matchings

We prove that for every set of n pairwise disjoint line segments in the plane in general position, where n is even, there is another set of n segments such that the 2n segments form pairwise disjoint simple polygons in the plane. This settles in the affirmative the Disjoint Compatible Matching Conjecture by Aichholzer et al. (Comput. Geom. 42:617–626, 2009). The key tool in our proof is a novel subdivision of the free space around n disjoint line segments into at most n+1 convex cells such that the dual graph of the subdivision contains two edge-disjoint spanning trees.