Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

Synthesis and Conformational Switching of Partially and Differentially Bridged Resorcin[4]arenes Bearing Fluorescent Dye Labels. Preliminary Communication

We report the synthesis of modified Cram‐type cavitands bearing one or two fluorescent labels for single‐molecule spectroscopic studies of vase? kite conformational switching (Scheme 3). Syntheses were performed by stepwise bridging of the four couples of neighboring H‐bonded OH groups of resorcin[4]arene bowls (Schemes 2 and 3). The new substitution patterns enable the construction of a large variety of future functional architectures. ¹H‐NMR Investigations showed that the new partially and differentially bridged cavitands feature temperature‐ and pH‐triggered vase? kite conformational isomerism similar to symmetrical cavitands with four identical quinoxaline bridges (Table). It was discovered that vase? kite switching of cavitands is strongly solvent‐dependent.     

Origin of enantioselection in chiral alcohol oxidation catalyzed by Pd[(-)-sparteine]Cl2

A kinetic investigation into the origin of enantioselectivity for the Pd[(-)-sparteine]Cl(2)-catalyzed aerobic oxidative kinetic resolution (OKR) is reported. A mechanism to account for a newly discovered chloride dissociation from Pd[(-)-sparteine]Cl(2) prior to alcohol binding is proposed. The mechanism includes (1) chloride dissociation from Pd[(-)-sparteine]Cl(2) to form cationic Pd(-)-sparteine]Cl, (2) alcohol binding, (3) deprotonation of Pd-bound alcohol to form a Pd-alkoxide, and (4) beta-hydride elimination of Pd-alkoxide to form ketone product and a Pd-hydride. Utilizing the addition of (-)-sparteine HCl to control the [Cl(-)] and [H(+)] and the resulting derived rate law, the key microscopic kinetic and thermodynamic constants were extracted for each enantiomer of sec-phenethyl alcohol. These constants allow for the successful simulation of the oxidation rate in the presence of exogenous (-)-sparteine HCl. A rate law for oxidation of the racemic alcohol was derived that allows for the successful prediction of the experimentally measured k(rel) values when using the extracted constants. Besides a factor of 10 difference between the relative rates of beta-hydride elimination for the enantiomers, the main enhancement in enantiodetermination results from a concentration effect of (-)-sparteine HCl and the relative rates of reprotonation of the diastereomeric Pd-alkoxides.     

Annulated pyranosides—V : An wenantiospecific route to (+) and (-) chrysanthemum dicarboxylic acids

-Methyl 2,3-anhydro-4,6-O-benzylidene-α-D-allopyranoside undergoes the Wadsworth- Emmons cyclopropanation with phosphonopropionate to give a cyclopropyl carboxylate which is processed to give the gem-dimethylcyclopropano pyranoside. The glycosylic acetal of this substance is readily hydrolyzed by boiling water, and the resulting cis-cyclopropane carboxaldehyde may be epimerized quantitatively to the trans-analog by treatment with sodium methoxide. These aldehydes are now converted into the (+)- and (-)-chrysanthemum dicarboxylic acids, respectively, by the same sequence of reactions involving (a) olefination with methyl 2-(triphenylphosphoranylidene)propionate, (b) hydro- lysis of the benzylidine ring and cleavage of the resulting triol with sodium metaperiodate, and (c) oxidation of the resulting aldehyde with silver I oxide. In the case of the (+)-enantiomer the last reaction is proceeded by epimerization. The overall yields from the D-allopyranoside are respectively 27%, in 10 steps for the (+)-enantiomer, and 24%, in 10 steps for the (-)-enantiomer, from the known epoxide 7.     

Single-site heterogeneous Cr-based catalyst for the selective trimerisation of ethylene

TAC-Cr3+/SiO2 complexes are highly active and selective ethylene trimerisation catalysts and possess single-site catalytic behaviour, an unusual property for heterogeneous catalysts.