Edge scaling limits for a family of non-Hermitian random matrix ensembles

A family of random matrix ensembles interpolating between the Ginibre ensemble of n × n matrices with iid centered complex Gaussian entries and the Gaussian unitary ensemble (GUE) is considered. The asymptotic spectral distribution in these models is uniform in an ellipse in the complex plane, which collapses to an interval of the real line as the degree of non-Hermiticity diminishes. Scaling limit theorems are proven for the eigenvalue point process at the rightmost edge of the spectrum, and it is shown that a non-trivial transition occurs between Poisson and Airy point process statistics when the ratio of the axes of the supporting ellipse is of order n ^?1/3. In this regime, the family of limiting probability distributions of the maximum of the real parts of the eigenvalues interpolates between the Gumbel and Tracy–Widom distributions.     

Importance Sampling for Backward SDEs

In this article, we explain how the importance sampling technique can be generalized from simulating expectations to computing the initial value of backward stochastic differential equations (SDEs) with Lipschitz continuous driver. By means of a measure transformation we introduce a variance reduced version of the forward approximation scheme by Bender and Denk [4 Bender , C. , and Denk , R. 2007 . A forward scheme for backward SDEs . Stochastic Processes and their Applications 117 ( 12 ): 1793 – 1812 . [Google Scholar]] for simulating backward SDEs. A fully implementable algorithm using the least-squares Monte Carlo approach is developed and its convergence is proved. The success of the generalized importance sampling is illustrated by numerical examples in the context of Asian option pricing under different interest rates for borrowing and lending.     

Gold(I)-catalyzed intramolecular hydroamination of unactivated C==C bonds with alkyl ammonium salts

A mixture of (5)AuCl [ = PCy2[2-(2,6-C6H3(OMe)2)C6H4]] and AgOTf catalyzes the intramolecular hydroamination of unactivated C==C bonds with primary and secondary ammonium salts.     

One‐ or Two‐Electron Transfer? The Ambiguous Nature of the Discharge Products in Sodium–Oxygen Batteries

Rechargeable lithium–oxygen and sodium–oxygen cells have been considered as challenging concepts for next‐generation batteries, both scientifically and technologically. Whereas in the case of non‐aqueous Li/O₂ batteries, the occurring cell reaction has been unequivocally determined (Li₂O₂ formation), the situation is much less clear in the case of non‐aqueous Na/O₂ cells. Two discharge products, with almost equal free enthalpies of formation but different numbers of transferred electrons and completely different kinetics, appear to compete, namely NaO₂ and Na₂O₂. Cells forming either the superoxide or the peroxide have been reported, but it is unclear how the cell reaction can be influenced for selective one‐ or two‐electron transfer to occur. In this Minireview, we summarize available data, discuss important control parameters, and offer perspectives for further research. Water and proton sources appear to play major roles.     

Synthesis of the antifungal beta-1,3-glucan synthase inhibitor CANCIDAS (caspofungin acetate) from pneumocandin B0

A novel three-step synthesis of the highly functionalized antifungal agent CANCIDAS (caspofungin acetate, 2) is described, starting from the natural product pneumocandin B0 (1). The highlights of the synthesis include a stereoselective formation of a phenylthioaminal, a remarkable chemoselective, high-yielding, one-step borane reduction of a primary amide, and a stereoselective substitution of the phenylthioaminal with ethylenediamine producing 2 in a 45% overall yield.     

Consequences of the center–of–mass correction in nuclear mean–field models

We study the influence of the scheme for the correction for spurious center–of–mass motion on the fit of effective interactions for self–consistent nuclear mean–field calculations. We find that interactions with very simple center–of–mass correction have significantly larger surface coefficients than interactions for which the center–of–mass correction was calculated for the actual many–body state during the fit. The reason for that is that the effective interaction has to counteract the wrong trends with nucleon number of all simplified schemes for center–of–mass correction which puts a wrong trend with mass number into the effective interaction itself. The effect becomes clearly visible when looking at the deformation energy of largely deformed systems, e.g. superdeformed states or fission barriers of heavy nuclei. Received: 6 September 1999