Synthesis of MnP nanocrystals by treatment of metal carbonyl complexes with phosphines: a new, versatile route to nanoscale transition metal phosphides

The reaction of Mn2(CO)10 with P(SiMe3)3 in coordinating solvents at T >/= 220 degrees C yields low polydispersity, highly crystalline MnP nanoparticles for the first time. The effect of dimensional limiting has resulted in the stabilization of a ferromagnetic ground state at low temperatures, rather than the metamagnetic state observed in bulk (microcrystalline) MnP. The synthetic methodology reported here is demonstrated to be general for a number of different metals and phosphine sources.     

Reflecting the pascal matrix about its main antidiagonal

Let B denote either of two varieties of order n Pascal matrix, i.e., one whose entries are the binomial coefficients. Let B_R denote the reflection of B about its main antidiagonal. The matrix B is always invertible modulo n; our main result asserts that B^-1 ≡ B^R mod n if and only if n is prime. In the course of motivating this result we encounter and highlight some of the difficulties with the matrix exponential under modular arithmetic. We then use our main result to extend the "Fibonacci diagonal" property of Pascal matrices.     

Control of Stereoselectivity in Diverse Hapalindole Metabolites is Mediated by Cofactor‐Induced Combinatorial Pairing of Stig Cyclases

Stereospecific polycyclic core formation of hapalindoles and fischerindoles is controlled by Stig cyclases through a three‐step cascade involving Cope rearrangement, 6‐exo‐trig cyclization, and a final electrophilic aromatic substitution. Reported here is a comprehensive study of all currently annotated Stig cyclases, revealing that these proteins can assemble into heteromeric complexes, induced by Ca²⁺, to cooperatively control the stereochemistry of hapalindole natural products.     

Control of Stereoselectivity in Diverse Hapalindole Metabolites is Mediated by Cofactor-Induced Combinatorial Pairing of Stig Cyclases

Stereospecific polycyclic core formation of hapalindoles and fischerindoles is controlled by Stig cyclases through a three-step cascade involving Cope rearrangement, 6-exo-trig cyclization, and a final electrophilic aromatic substitution. Reported here is a comprehensive study of all currently annotated Stig cyclases, revealing that these proteins can assemble into heteromeric complexes, induced by Ca²⁺, to cooperatively control the stereochemistry of hapalindole natural products.     

The quantum euler class and the quantum cohomology of the Grassmannians

The Poincaré duality of classical cohomology and the extension of this duality to quantum cohomology endows these rings with the structure of a Frobenius algebra. Any such algebra possesses a canonical “characteristic element;” in the classical case this is the Euler class, and in the quantum case this is a deformation of the classical Euler class which we call the “quantum Euler class.” We prove that the characteristic element of a Frobenius algebraA is a unit if and only ifA is semisimple, and then apply this result to the cases of the quantum cohomology of the finite complex Grassmannians, and to the quantum cohomology of hypersurfaces. In addition we show that, in the case of the Grassmannians, the [quantum] Euler class equals, as [quantum] cohomology element and up to sign, the determinant of the Hessian of the [quantum] Landau-Ginzbug potential.     

Random packing by ρ-connected ρ-regular graphs

A graph G is packable by the graph F if its edges can be partitioned into copies of F. If deleting the edges of any F-packable subgraph from G leaves an F-packable graph, then G is randomly F-packable. If G is F-packable but not randomly F-packable then G is F-forbidden. The minimal F-forbidden graphs provide a characterization of randomly F-packable graphs. We show that for each ρ-connected ρ-regular graph F with ρ > 1, there is a set (F) of minimal F-forbidden graphs of a simple form, such that any other minimal F-forbidden graph can be obtained from a graph in (F) by a process of identifying vertices and removing copies of F. When F is a connected strongly edge-transitive graph having more than one edge (such as a cycle or hypercube), there is only one graph in (F).     

Syntheses of differentially protected isocoumarins

Syntheses of an isocoumarin subunit suitable for the completion of purpuromycin are outlined. Specifically, work targeting an orthogonally protected isocoumarin (eventually 12% yield over 12 steps) and an improved synthesis of a symmetrically protected isocoumarin (18% over 10 steps) are described. A new modification for selective catechol protection as mediated by potassium bicarbonate is also presented along with insights into oxidative and reductive functionalization of isocoumarins.     

Variance‐reduced Monte Carlo solutions of the Boltzmann equation for low‐speed gas flows: A discontinuous Galerkin formulation

We present and discuss an efficient, high‐order numerical solution method for solving the Boltzmann equation for low‐speed dilute gas flows. The method's major ingredient is a new Monte Carlo technique for evaluating the weak form of the collision integral necessary for the discontinuous Galerkin formulation used here. The Monte Carlo technique extends the variance reduction ideas first presented in Baker and Hadjiconstantinou (Phys. Fluids 2005; 17 , art. no. 051703) and makes evaluation of the weak form of the collision integral not only tractable but also very efficient. The variance reduction, achieved by evaluating only the deviation from equilibrium, results in very low statistical uncertainty and the ability to capture arbitrarily small deviations from equilibrium (e.g. low‐flow speed) at a computational cost that is independent of the magnitude of this deviation. As a result, for low‐signal flows the proposed method holds a significant computational advantage compared with traditional particle methods such as direct simulation Monte Carlo (DSMC). Copyright © 2008 John Wiley & Sons, Ltd.