Nowhere zero 4‐flow in regular matroids

Jensen and Toft 8 conjectured that every 2‐edge‐connected graph without a K₅‐minor has a nowhere zero 4‐flow. Walton and Welsh 19 proved that if a coloopless regular matroid M does not have a minor in {M(K_3,3), M*(K₅)}, then M admits a nowhere zero 4‐flow. In this note, we prove that if a coloopless regular matroid M does not have a minor in {M(K₅), M*(K₅)}, then M admits a nowhere zero 4‐flow. Our result implies the Jensen and Toft conjecture. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Capture-ROMP-release: application to the synthesis of amines and alkyl hydrazines

Application of a capture-ROMP-release strategy for the chromatography-free purification of Mitsunobu reaction products is described. Norbornenyl-tagged reagents are utilized for standard solution phase Mitsunobu chemistry. Post-reaction phase-switching is accomplished via in situ ring-opening metathesis polymerization (ROMP) followed by precipitation of the polymer with methanol. Release of the product from the polymer affords amines and alkyl hydrazine derivatives with good yields and purities.     

Evolution of lowest singlet and triplet excited states with transition metals in group 10-12 metallaynes containing biphenyl spacer

A new series of thermally stable group 10 platinum(II) and group 12 mercury(II) poly-yne polymers containing biphenyl spacer trans-[-Pt(PBu₃)₂CC(p-C₆H₄)₂CC-]_n and [HgCC(p-C₆H₄)₂CC-]_n were prepared in good yields by Hagihara’s dehydrohalogenation reaction of the corresponding metal chloride precursors with 4,4′-diethynylbiphenyl HCC(p-C₆H₄)₂CCH at room temperature. We report the optical spectroscopy of these polymetallaynes and compare the results with their bimetallic model complexes trans-[Pt(Ph)(PEt₃)₂CC(p-C₆H₄)₂CCPt(Ph)(PEt₃)₂] and [MeHgCC(p-C₆H₄)₂CCHgMe] as well as the group 11 gold(I) counterpart [(PPh₃)AuCC(p-C₆H₄)₂CCAu(PPh₃)]. The structural properties of all model complexes have been studied by X-ray crystallography. The influence of the heavy metal atom in these metal alkynyl systems on the intersystem crossing rate and the spatial extent of lowest singlet and triplet excitons is systematically characterized. Our investigations indicate that the organic triplet emissions can be harvested by the heavy-atom effect of group 10-12 transition metals (viz., Pt, Au, and Hg) which enables efficient intersystem crossing from the S₁ singlet excited state to the T₁ triplet excited state.     

Shear zones and wall slip in the capillary flow of concentrated colloidal suspensions

We image the flow of a nearly random close packed, hard-sphere colloidal suspension (a "paste") in a square capillary using confocal microscopy. The flow consists of a "plug" in the center while shear occurs localized adjacent to the channel walls, reminiscent of yield-stress fluid behavior. However, the observed scaling of the velocity profiles with the flow rate strongly contrasts yield-stress fluid predictions. Instead, the velocity profiles can be captured by a theory of stress fluctuations originally developed for chute flow of dry granular media. We verified this both for smooth and rough walls.