Enantioselective parallel synthesis using polymer-supported chiral Co(salen) complexes

[formula: see text] The kinetic resolution of epoxides with phenols catalyzed by a polymer-supported Co(salen) complex is applied to the first enantioselective catalytic synthesis of parallel libraries. The corresponding 1-aryloxy-2-alcohols are obtained in high yield, purity, and enantiomeric excess. Further elaboration with diversity elements provides highly efficient access to important classes of pharmacologically active compounds.     

Semi-Balanced Colorings of Graphs: Generalized 2-Colorings Based on a Relaxed Discrepancy Condition

We generalize the concept of a 2-coloring of a graph to what we call a semi-balanced coloring by relaxing a certain discrepancy condition on the shortest-paths hypergraph of the graph. Let G be an undirected, unweighted, connected graph with n vertices and m edges. We prove that the number of different semi-balanced colorings of G is: (1) at most n+1 if G is bipartite; (2) at most m if G is non-bipartite and triangle-free; and (3) at most m+1 if G is non-bipartite. Based on the above combinatorial investigation, we design an algorithm to enumerate all semi-balanced colorings of G in O(nm²) time.Acknowledgments The authors thank Tetsuo Asano, Naoki Katoh, Kunihiko Sadakane, and Hisao Tamaki for helpful discussions and comments.Supported in part by Sweden-Japan FoundationFinal version received: November 17, 2003     

A staggered six-vertex model with non-compact continuum limit

The antiferromagnetic critical point of the Potts model on the square lattice was identified by Baxter [R.J. Baxter, Proc. R. Soc. London A 383 (1982) 43] as a staggered integrable six-vertex model. In this work, we investigate the integrable structure of this model. It enables us to derive some new properties, such as the Hamiltonian limit of the model, an equivalent vertex model, and the structure resulting from the Z₂$Z_2$ symmetry. Using this material, we discuss the low-energy spectrum, and relate it to geometrical excitations. We also compute the critical exponents by solving the Bethe equations for a large lattice width N  . The results confirm that the low-energy spectrum is a collection of continua with typical exponent gaps of order (logN)⁻²${(\log N)}^{\mathrm{-2}}$.     

Improved Measurement of the Cabibbo-Kobayashi-Maskawa angle alpha using B0(B) --> rho+rho- decays

We present results from an analysis of B(0)B(0)--> rho(+)rho(-) using 232 x 10(6) Gamma (4S) --> BB decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC. We measure the longitudinal polarization fraction f(L) = 0.978 +/- 0.014(stat) + 0.021 / -0.029(syst) and the CP-violating parameters S(L)= -0.33 +/- 0.24(stat) + 0.08 / -0.14(syst) and C(L)= -0.03 +/- 0.18(stat) +/- 0.09(syst). Using an isospin analysis of B --> rhorho decays, we determine the unitarity triangle parameter alpha. The solution compatible with the standard model is alpha = (100 +/- 13) degrees.     

Fundamental limitations to gain enhancement in periodic media and waveguides

A common strategy to compensate for losses in optical nanostructures is to add gain material in the system. By exploiting slow-light effects it is expected that the gain may be enhanced beyond its bulk value. Here we show that this route cannot be followed uncritically: inclusion of gain inevitably modifies the underlying dispersion law, and thereby may degrade the slow-light properties underlying the device operation and the anticipated gain enhancement itself. This degradation is generic; we demonstrate it for three different systems of current interest (coupled-resonator optical waveguides, Bragg stacks, and photonic crystal waveguides). Nevertheless, a small amount of added gain may be beneficial.