Aziridine-mediated ligation and site-specific modification of unprotected peptides

A synthesis of aziridine-containing peptides via the Cu(II)-promoted coupling of unprotected peptide thioacids and N-H aziridine-2-carbonyl peptides is reported. The unique reactivity of the resulting N-acylated aziridine-2-carbonyl peptides facilitates their subsequent regioselective and stereoselective nucleophilic ring-opening to give unprotected peptides that are specifically modified at the ligation site. The aziridine-mediated peptide ligation concept is exemplified using H(2)O as the nucleophile, producing a Xaa-Thr linkage (where Xaa can be an epimerizable and hindered amino acid). The overall process is compatible with a variety of unprotected amino acid functionality, most notably the N-terminal and Lys side chain amines.     

Photocatalytic Water Oxidation by a Pyrochlore Oxide upon Irradiation with Visible Light: Rhodium Substitution Into Yttrium Titanate

A stable visible‐light‐driven photocatalyst (λ≥450 nm) for water oxidation is reported. Rhodium substitution into the pyrochlore Y₂Ti₂O₇ is demonstrated by monitoring Vegard′s law evolution of the unit‐cell parameters with changing rhodium content, to a maximum content of 3 % dopant. Substitution renders the solid solutions visible‐light active. The overall rate of oxygen evolution is comparable to WO₃ but with superior light‐harvesting and surface‐area‐normalized turnover rates, making Y₂Ti_1.94Rh_0.06O₇ an excellent candidate for use in a Z‐scheme water‐splitting system.     

Bridging M?Cl Bonds with Ambiphilic Phosphine–Borane Ligands

Bridging or pendant? Palladium and rhodium complexes deriving from an ambiphilic phosphine–borane ligand are shown to adopt a bridging P→M? Cl→B coordination mode in the solid state. DFT calculations provide more insight into the Cl→B interaction and suggest the possible interconversion of the bridging and B‐pendant forms in solution.

     

Development of a Synthetic Route to Unsymmetrical Triphosphine Ligands and an Investigation of Their Coordination Chemistry with Nickel and Palladium

Chiral tridentate phosphines, R(2)P(CH(2))(3)PPh(CH(2))(2)PPh(2) where R = C(6)H(5), p-ClC(6)H(4), and p-FC(6)H(4), can be prepared from simple starting materials, (R(3)P, I(CH(2))(3)I, and Ph(2)P(CH(2))(2)PPh(2)), in a few stages involving phosphonium salts and phosphine oxides as intermediates. Crystalline diamagnetic complexes of nickel(II) and palladium(II) have been isolated. In solution these show first-order 12 line (31)P NMR spectra consistent with three nonequivalent phosphorus nuclei coupled to one another in a square planar geometry. A single X-ray crystallographic study of NiI(2){P(CH(2))(3)PPh(CH(2))(2)PPh(2)} showed that this was square pyramidal in the solid state with a weakly held apical iodo ligand.     

Path coupling using stopping times and counting independent sets and colorings in hypergraphs

We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q‐colorings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Embeddings of root systems I: Root systems over commutative rings

This paper gives examples of embeddings of root systems of Coxeter groups, including sporadic embeddings of standard real root systems in other standard real root systems, and, for a general Coxeter group, an embedding of its universal symmetric root system over commutative rings into the standard real root system of a simply laced Coxeter group.     

Volatility estimation for stochastic project value models

One of the key parameters in modeling capital budgeting decisions for investments with embedded options is the project volatility. Most often, however, there is no market or historical data available to provide an accurate estimate for this parameter. A common approach to estimating the project volatility in such instances is to use a Monte Carlo simulation where one or more sources of uncertainty are consolidated into a single stochastic process for the project cash flows, from which the volatility parameter can be determined. Nonetheless, the simulation estimation method originally suggested for this purpose systematically overstates the project volatility, which can result in incorrect option values and non-optimal investment decisions. Examples that illustrate this issue numerically have appeared in several recent papers, along with revised estimation methods that address this problem. In this article, we extend that work by showing analytically the source of the overestimation bias and the adjustment necessary to remove it. We then generalize this development for the cases of levered cash flows and non-constant volatility. In each case, we use an example problem to show how a revised estimation methodology can be applied.