Catalytic conjugate additions of carbonyl anions under neutral aqueous conditions

The conjugate addition of carbonyl anions catalyzed by thiazolium salts that is fully operative under neutral aqueous conditions has been accomplished. The combination of alpha-keto carboxylates and thiazolium-derived zwitterions produces reactive carbonyl anions in a buffered protic environment that readily undergo conjugate additions to substituted alpha,beta-unsaturated 2-acyl imidazoles. The scope of the reaction has been examined and found to accommodate various alpha-keto carboxylates and beta-aryl substituted unsaturated 2-acyl imidazoles. The optimal precatalyst for this process is the commercially available thiazolium salt 5, a simple analogue of thiamin diphosphate. In this process, no benzoin products from carbonyl anion dimerization are observed. The corresponding 1,4-dicarbonyl compounds can be efficiently converted into esters and amides by way of activation of the N-methylimidazole ring via alkylation.     

Stability of Optically Injected Two‐State Quantum‐Dot Lasers

Simultaneous two‐state lasing is a unique property of semiconductor quantum‐dot (QD) lasers. This not only changes steady‐state characteristics of the laser device but also its dynamic response to perturbations. In this paper we investigate the dynamic stability of QD lasers in an external optical injection setup. Compared to conventional single‐state laser devices, we find a strong suppression of dynamical instabilities in two‐state lasers. Furthermore, depending on the frequency and intensity of the injected light, pronounced areas of bistability between both lasing frequencies appear, which can be employed for fast optical switching in all‐optical photonic computing applications. These results emphasize the suitability of QD semiconductor lasers in future integrated optoelectronic systems where a high level of stability is required.     

Bulk universality for Wigner matrices

We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e^?U(x). We prove that the eigenvalue statistics in the bulk are given by the Dyson sine kernel provided that U ∈ C⁶( input amssym $Bbb R$ ) with at most polynomially growing derivatives and ν(x) ≥ Ce^?C|x| for x large. The proof is based upon an approximate time reversal of the Dyson Brownian motion combined with the convergence of the eigenvalue density to the Wigner semicircle law on short scales. © 2010 Wiley Periodicals, Inc.     

Optimization of Fishing Strategies in Space and Time as a Non-convex Optimal Control Problem

The behavior of a fishing fleet and its impact onto the biomass of fish can be described by a nonlinear parabolic diffusion–reaction equation. Looking for an optimal fishing strategy leads to a non-convex optimal control problem with a bilinear control action. In this work, we present such an optimal control formulation, prove its well-posedness and derive first- and second-order optimality conditions. These results provide a basis for tailored finite element discretization as well as for Newton type optimization algorithms. First numerical test problems show typical features as so-called No-Take-Zones and maximal fishing quota (total allowable catches) as parts of an optimal fishing strategy.     

Generalized bases of finite groups

Archiv der Mathematik - Motivated by recent results on the minimal base of a permutation group, we introduce a new local invariant attached to arbitrary finite groups. More precisely, a subset...     

Perfect matchings and Hamiltonian cycles in the preferential attachment model

In this paper, we study the existence of perfect matchings and Hamiltonian cycles in the preferential attachment model. In this model, vertices are added to the graph one by one, and each time a new vertex is created it establishes a connection with m random vertices selected with probabilities proportional to their current degrees. (Constant m is the only parameter of the model.) We prove that if , then asymptotically almost surely there exists a perfect matching. Moreover, we show that there exists a Hamiltonian cycle asymptotically almost surely, provided that . One difficulty in the analysis comes from the fact that vertices establish connections only with vertices that are “older” (ie, are created earlier in the process). However, the main obstacle arises from the fact that edges in the preferential attachment model are not generated independently. In view of that, we also consider a simpler setting—sometimes called uniform attachment—in which vertices are added one by one and each vertex connects to m older vertices selected uniformly at random and independently of all other choices. We first investigate the existence of perfect matchings and Hamiltonian cycles in the uniform attachment model, and then extend the argument to the preferential attachment version.