Beyond the chiral pool: a general approach to β-amino-α-keto amides

A simple route was developed for the synthesis of optically enriched β-amino-α-keto amides. The highly diastereoselective addition of alkyl dithiolanecarboxylates to optically enriched sulfinimines affords the corresponding β-amino-α-keto esters in which the ketone carbonyl group is protected as a dithiolane. Amidation of the ester functionality with a primary amine proceeds readily at room temperature. Treatment with HCl cleaves the N-S bond of the sulfinyl group to provide a free amine functionality, which can then be incorporated into a peptide. Removal of the dithiolane protecting group under oxidative conditions proceeds without epimerization as exemplified by a model dipeptide.     

Skew Schubert polynomials

We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schubert polynomials with nonnegative integer coefficients that are precisely the structure constants of the cohomology of the complex flag variety with respect to its basis of Schubert classes. We rederive the construction of Bergeron and Sottile in a purely combinatorial way, relating it to the construction of Schubert polynomials in terms of rc-graphs.

     

Gas permeability and selectivity of hexafluoroisopropylidene aromatic isophthalic copolyamides

The synthesis, thermal, and gas transport properties of poly(hexafluoroisopropylidene isophthalamide), HFA/ISO homopolymer, and HFA/TERT‐co‐HFA/ISO copolyamides with different poly(hexafluoroisopropilydene‐5‐t‐butylisophthalamide), HFA/TERT, ratios are reported. The results indicate that the glass transition temperatures of the copolyamides increase as the concentration of HFA/TERT in the polyamide increases. The gas permeability coefficients in the polyamides and copolyamides are independent of pressure or decrease slightly particularly with CO₂, N₂, and CH₄. It was seen that HFA/TERT is 2–6 times more permeable than HFA/ISO, depending on the gas being considered. This was assigned to the presence of the bulky lateral substituent, t‐butyl group in HFA/TERT and HFA/TERT‐co‐HFA/ISO copolyamides. This substituent increases fractional free‐volume, as expected. Therefore, the gas permeability and diffusion coefficients generally increase with increasing fractional free‐volume. The experimental results for the gas permeability and permselectivity for the copolyamides was well represented by a logarithmic mixing rule of the homopolyamides permeability coefficients and their volume fraction. The selectivity of gas pairs, such as O₂/N₂, CO₂/CH₄, and N₂/CH₄ decreased slightly with the addition of HFA/TERT. The temperature dependence of permeability for homopolyamides and copolyamides can be described by an Arrhenius type equation. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2625–2638, 2005     

Renormalization group method applied to the primitive equations

In this article we study the limit, as the Rossby number ε goes to zero, of the primitive equations of the atmosphere and the ocean. From the mathematical viewpoint we study the averaging of a penalization problem displaying oscillations generated by an antisymmetric operator and by the presence of two time scales.     

The Synthesis of Some Fused Pyrazolo‐1,4‐Naphthoquinones

New fused pyrazolo‐1,4‐naphthoquinones were prepared from the reaction of hydrazines with 6‐(4‐methyl‐3‐pentenyl)‐1,4‐naphthoquinone. The reaction was extended to hydroxylamine to afford the corresponding isoxazolo‐1,4‐napthoquinone compound.     

Hydrogen confinement in carbon nanopores: extreme densification at ambient temperature

In-situ small-angle neutron scattering studies of H(2) confined in small pores of polyfurfuryl alcohol-derived activated carbon at room temperature have provided for the first time its phase behavior in equilibrium with external H(2) at pressures up to 200 bar. The data were used to evaluate the density of the adsorbed fluid, which appears to be a function of both pore size and pressure and is comparable to the density of liquid H(2) in narrow nanopores at ～200 bar. The surface-molecule interactions responsible for densification of H(2) within the pores create internal pressures that exceed the external gas pressure by a factor of up to ～50, confirming the benefits of adsorptive storage over compressive storage. These results can be used to guide the development of new carbon adsorbents tailored for maximum H(2) storage capacities at near-ambient temperatures.     

Organomercury(II) and tellurium(II) compounds with the "pincer" ligand 2,6-[O(CH2CH2)2NCH2]2C6H3--stabilization of an unusual organotellurium(II) cationic species

The reaction of RH (1) with Hg(OAc)(2), in EtOH, gave the acetate RHgOAc (2) [R = 2,6-[O(CH(2)CH(2))(2)NCH(2)](2)C(6)H(3)]. The corresponding RHgCl (3) was obtained from 2 and LiCl. The reaction of 3 with TeCl(4) (1:1 molar ratio), in anhydrous 1,4-dioxane, resulted in the transfer of the organic ligand from mercury to tellurium and the isolation of the unexpected ionic compounds [RTe](2)[Hg(2)Cl(6)] (4) and [RH(3)][HgCl(4)] (5). The molecular structures of 1-4 and 5·H(2)O were established by single-crystal X-ray diffraction. The acetate 2 and the chloride 3 are monomeric in solid state. In both mercury and tellurium organometallic compounds the organic group acts as an (N,C,N) "pincer" ligand. This coordination pattern provided stability for the rare [RTe](+) cation. Weak cation-anion interactions [Te···Cl 3.869(3) ?] are present between [RTe](+) and the dinuclear anion [Hg(2)Cl(6)](2-) in the crystal of 4. Theoretical calculations with DFT methods were performed for models of 3 and 4. The results show that in the cation of 4 the coordination of the nitrogen atoms play an important role for the stabilization of the structure found in the crystal whereas in 3 the coordination of the nitrogen atoms to the metal centre stabilizes to a less extent the structure found in solid state.     

A comparison of lower bounds for the symmetric circulant traveling salesman problem

When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on the optimal value that may be computed in polynomial time. We derive a new linear programming (LP) relaxation of the SCTSP from the semidefinite programming (SDP) relaxation in [E. de Klerk, D.V. Pasechnik, R. Sotirov, On semidefinite programming relaxation of the traveling salesman problem, SIAM Journal of Optimization 19 (4) (2008) 1559-1573]. Further, we discuss theoretical and empirical comparisons between this new bound and three well-known bounds from the literature, namely the Held-Karp bound [M. Held, R.M. Karp, The traveling salesman problem and minimum spanning trees, Operations Research 18 (1970) 1138-1162], the 1-tree bound, and the closed-form bound for SCTSP proposed in [J.A.A. van der Veen, Solvable cases of TSP with various objective functions, Ph.D. Thesis, Groningen University, The Netherlands, 1992].