Supercritical Spatially Homogeneous Branching in Admits no Equilibria

At the beginning of investigations in spatially homogeneous branching processes in Euclidean space (Liemant [1]) it seemed to be obvious that the existence of equilibria implies criticality of branching. This prejudice was disproved by the example [2] of a subcritical homogeneous branching equilibrium in dimension one. We prove that supercritical homogeneous branching processes in Euclidean space and, more general, in a broad class of topological groups have no (non – void, homogeneous) equilibria.     

Effect of the External Mirror Feedback Strength in the Dynamics and Spectrum of the Injected Semiconductor Lasers

We analytically investigate the effect of an external mirror on the stability of an injected semiconductor laser, the latter treated as injected damped oscillators. In the studied configuration, the injected semiconductor laser with an external mirror is under the influence of a chaotic oscillating optical signal that is generated by a similar semiconductor master laser. We derive our results in terms of the damping rate and resonance frequency. We show that the external mirror can eliminate the unstable modes of the injected laser at low frequencies. Furthermore, the mirror can enhance the damping of the oscillation modes of the injected semiconductor laser; consequently, the driven response of the injected laser may have a broad spectrum, even wider than that of the chaotic driving signal. We also show results for the bandwidths of the injection amplitude and phase increment as functions of the injection rate and feedback strength of the external mirror. In addition, we use bifurcation and time-series curves to describe the dynamical behavior of the injected laser. We identify the feedback strength of injected laser, relative to that of the master laser, which induces synchronization between the injected-laser oscillation modes and the master laser.     

Photo-triggered pulsed cavity compressor for bright electron bunches in ultrafast electron diffraction

Temporally resolved observation of microscopic structural dynamics of solids with ultrafast electron diffraction (UED) requires extremely short pulsed, highly charged, monoenergetic electron beams with sufficient transverse coherence length of several unit cells of the investigated samples. However, Coulomb repulsion defeats these parameters in free propagation of an electron pulse initially bright on the photo cathode. We demonstrate a new electron pulse compressor design based on a simple and compact RF structure incorporating a pair of gallium arsenide photoconductive semiconductor switches that are triggered by femtosecond laser pulses, thereby providing a longitudinal voltage gradient of up to 20?V/ps. Our proof of principle experiment achieved compression of bunches containing 26,000 electrons to a duration of below 750?fs and a beam diameter of 300???m in the temporal and spatial focus of the device while maintaining the good beam collimation required for time resolved electron diffraction experiments. The simplicity of the compressor provides a strong incentive for its further development toward practical implementation in sub-relativistic UED experiments requiring the highest possible source brightness.     

Quantification of the electrophilicities of dithiocarbenium ions

The reactions of the dithio substituted carbenium ions 2a-c with allylsilanes, allylstannanes (3), and silylated enol ethers (4) which yield dithioacetal protected β, ψ-unsaturated carbonyl compounds (7) and selectively protected 1,3-dicarbonyl compounds (8), have been studied kinetically. The second-order rate constants have been used to determine the electrophilicity parameters for the [1,3]dithiolan-2-ylium ion 2a (E=?6.25) and the [1,3]dithian-2-ylium ions 2b (E=?6.82) and 2c (E=?2.17). It is shown how these parameters can be used to predict the electrophilic potential of 2a-c.     

Brownian approximations to first passage probabilities

Summary By direct probabilistic argument one term of an Edgeworth type asymptotic expansion is obtained for certain first passage distributions for random walks. These results provide partial justification for and extensions of approximations suggested earlier as a heuristic consequence of Laplace transform calculations.Research supported by ONR Contract N00014-77-C-0306, NSF Grant MCS77-16974, and by the Humboldt Stiftung     

An efficient one-pot construction of substituted pyrimidinones

A concise, scaleable synthesis of building block 10 for p38 kinase inhibitor B is described. The key step is the one-pot construction of 5-aryl-3-methyl-2-methylsulfanyl-6-pyridin-4-yl-3H-pyrimidin-4-one 4 from arylacetic acid ethyl ester 1. Subsequent hydrolysis of the thiomethyl group to the hydroxy group and chlorination provided the key intermediate, 2-chloro-3-methyl-6-pyridin-4-yl-5-aryl-3H-pyrimidin-4-one 10. This class of reactive building blocks enabled the rapid evaluation of a variety of side chains at the 2-position of the pyrimidinone in SAR studies of inhibitors of p38 MAP kinase.     

Synthesis and Electrochemical Investigation of Phosphine Substituted Diiron Phosphadithiolate Complexes

This work reports on ligand exchange reactions between a [FeFe] hydrogenase model containing the higher homologue ( PhosDT ) and phosphines selected to cover a variety of electronic properties and possible coordination modes. Additionally, the amount of the phosphines and the reaction temperature were varied to study the formation of complexes with multiple phosphines or altered binding modes. Due to steric effects caused by the position of the bridgehead, the phosphines bind preferentially at the more accessible iron centre on the phosphinate averted side. While all ligand exchanges resulted in a ligand-specific main product at room temperature, reflux conditions induced decomposition in case of PhosDT-(κ²-dppe) and PhosDT-(κ²-dppv) and a change in the binding mode for the dppm containing complex. Moreover, we highlight two novel iron complexes obtained as side products of the reactions with dppe and dppv, while in case of dppm an additional model with two bridging phosphine ligands was generated. Finally, the six novel phosphine substituted PhosDT models were electrochemically investigated, revealing a cathodic shift compared to the starting material due to the increased electron density at the iron atoms. Moreover, the models with monodentate ligands exhibit a different CV pattern for the Fe^IFe^I/Fe^IFe⁰ process than complexes with bidentate phosphines.