Measurement of heterogeneous reaction rates: three strategies for controlling mass transport and their application to indium-mediated allylations

We describe three new strategies for determining heterogeneous reaction rates using photomicroscopy to measure the rate of retreat of metal surfaces: (i) spheres in a stirred solution, (ii) microscopic powder in an unstirred solution, and (iii) spheres on a rotating shaft. The strategies are applied to indium-mediated allylation (IMA), which is a powerful tool for synthetic chemists because of its stereoselectivity, broad applicability, and high yields. The rate-limiting step of IMA, reaction of allyl halides at indium metal surfaces, is shown to be fast, with a minimum value of the heterogeneous rate constant of 1 × 10(-2) cm/s, an order of magnitude faster than the previously determined minimum value. The strategies described here can be applied to any reaction in which the surface is retreating or advancing, thereby broadening the applicability of photomicroscopy to measuring heterogeneous reaction kinetics.     

Spaces of matrices without non-zero eigenvalues in their field of definition, and a question of Szechtman

Let V be a vector space of dimension n over any field F. Extreme values for the possible dimension of a linear subspace of End_F(V) with a particular property are considered in two specific cases. It is shown that if E₁ is a subspace of End_F(V) and there exists an endomorphism g of V, not in E₁, such that for every hyperplane H of V some element of E₁ agrees with g on H, then E₁ has dimension at least . This answers a question that was posed by Szechtman in 2003. It is also shown that a linear subspace of M_n(F) in which no element possesses a non-zero eigenvalue in F may have dimension at most . The connection between these two properties, which arises from duality considerations, is discussed.     

Compact Differences of Composition Operators in Several Variables

When φ and ψ are linear–fractional self-maps of the unit ball B _N in \mathbb C^N,N 3 1{{\mathbb C}^N,N\geq 1}, we show that the difference C_j-C_y{C_{\varphi}-C_{\psi}} cannot be non-trivially compact on either the Hardy space H ²(B _N ) or any weighted Bergman space A²_a(B_N){A^2_{\alpha}(B_N)}. Our arguments emphasize geometrical properties of the inducing maps φ and ψ.     

Hydride as a leaving group in the reaction of pinacolborane with halides under ambient Grignard and Barbier conditions. One-pot synthesis of alkyl, aryl, heteroaryl, vinyl, and allyl pinacolboronic esters

Grignard reagents (aliphatic, aromatic, heteroaromatic, vinyl, or allylic) react with 1 equiv of 4,4,5,5-tetramethyl-1,3,2-dioxaborolane (pinacolborane, PinBH) at ambient temperature in tetrahydrofuran (THF) to afford the corresponding pinacolboronates. The initially formed dialkoxy alkylborohydride intermediate quickly eliminates hydridomagnesium bromide (HMgBr) and affords the product boronic ester in very good yield. Hydridomagnesium bromide (HMgBr) in turn disproportionates to a 1:1 mixture of magnesium hydride (MgH(2)) and magnesium bromide (MgBr(2)) on addition of pentane to the reaction mixture. DFT calculations (Gaussian09) at the B3LYP/6-31G(d) level of theory show that disproportionation of HMgBr to MgH(2) and MgBr(2) is viable in the coordinating ethereal solvents. This reaction also can be carried out under Barbier conditions, where the neat PinBH is added to the flask prior to the in situ formation of Grignard reagent from the corresponding organic halide and magnesium metal. Pinacolboronic ester synthesis under Barbier conditions does not give Wurtz coupling side products from reactive halides, such as benzylic and allylic halides. The reaction between PinBH and various Grignard reagents is an efficient, mild, and general method for the synthesis of pinacolboronates.     

Investigating the arenyl-diene double [3 + 2] photocycloaddition reaction

The double [3 + 2] photocycloaddition reaction involving arenyl-dienes has been used to assemble seven separate [5.5.5.5] fenestrane structures that include ether and aza variants. The primary photolysis step was a meta photocycloaddition reaction, while a secondary photocycloaddition step formed the fenestrane structure. Investigations involving the insertion of an additional methylene group into the basic arenyl-diene skeleton failed to afford the desired [5.5.5.6] fenestrane structure. The presence of an oxime moiety in the aromatic photosubstrate allowed the primary photolysis step to take place; however, an attempted secondary photocycloaddition reaction involving the oxime did not provide the intended polyheterocyclic fenestrane. An alternative strategy to form various "criss-cross" double meta photocycloadducts was investigated and led to the discovery of a Paterno-Büchi cycloaddition reaction between acetone and an angular meta photocycloadduct. Other novel thermally and photochemically mediated skeletal rearrangement reactions were also recorded.     

Synthesis of a benzotriazole azo dye phosphoramidite for labelling of oligonucleotides

The synthesis of a benzotriazole azo dye phosphoramidite and the subsequent use in solid phase synthesis of oligonucleotides is reported. The azo dye is shown as a surface enhanced resonance Raman label for oligonucleotides that is capable of immobilisation of the oligonucleotide on metal surfaces such as silver nanoparticles.     

Synthesis and biological evaluation of (-)-dictyostatin and stereoisomers

Total syntheses of (−)-dictyostatin, 6,16-bis-epi-dictyostatin, 6,14,19-tris-epi-dictyostatin, and a number of other isomers and analogs are reported. Three main fragments—top, middle, and bottom—were first assembled and then joined by olefination or anionic addition reactions. After appending the two dienes at either end of the molecule, macrolactonization and deprotection completed the syntheses. The work proves both the relative and absolute configurations of (−)-dictyostatin. The compounds were evaluated by cell-based measurements of increased microtubule mass and antiproliferative activity, and in vitro tubulin polymerization assays as well as competitive assays with paclitaxel for its binding site on microtubules. These assays showed dictyostatin to be the most potent of the agents and further showed that the structural alterations caused from 20- to >1000-fold decreases in activity.     

Government-provided annuities under insolvency risk

This paper seeks to determine whether governments should intervene in the private annuity market by directly providing public insurance in the form of annuities when both the government and the insurance companies could default. It is found that, although the government could default, intervening by means of an annuity can improve social welfare if the insurance companies could default and the expected return on the public annuity is greater than the rate of return on a risk-free bond. We also find that, under actuarially fair pricing, the government should provide more in terms of a public annuity than the optimal amount of the annuity that the individual purchases in the private market if the government is less likely to default on the public annuity than an insurance company would in the case of a private annuity.