Gold(I) catalysts with bifunctional P, N ligands

A series of phosphanes with imidazolyl substituents were prepared as hemilabile PN ligands. The corresponding gold(I) complexes were tested as bifunctional catalysts in the Markovnikov hydration of 1-octyne, as well as in the synthesis of propargylamines by the three component coupling reaction of piperidine, benzaldehyde, and phenylacetylene. While the activity in the hydration of 1-octyne was low, the complexes are potent catalysts for the three component coupling reaction. In homogeneous solution the conversions to the respective propargylamine were considerably higher than under aqueous biphasic conditions. The connectivity of the imidazolyl substituents to the phosphorus atom, their substitution pattern, as well as the number of heteroaromatic substituents have pronounced effects on the catalytic activity of the corresponding gold(I) complexes. Furthermore, formation of polymetallic species with Au(2), Au(3), and Au(4) units has been observed and the solid-state structures of the compounds [(5)(2)Au(3)Cl(2)]Cl and [(3c)(2)Au(4)Cl(2)]Cl(2) (3c = tris(2-isopropylimidazol-4(5)-yl phosphane, 5 = 2-tert-butylimidazol-4(5)-yldiphenyl phosphane) were determined. The gold(I) complexes of imidazol-2-yl phosphane ligands proved to be a novel source for bis(NHC)gold(I) complexes (NHC = N-heterocyclic carbene).     

On the behavior of solutions of certain differential equations of the fourth order

Summary In this paper three new results are obtained for equations of the form (1.1). Conditions are established which guarantee asymptotic stability, ultimate boundedness, and convergence of solutions of (1.1). This work was supported by the National Science Foundation COSIP (GY 4754). Entrata in Redazione il 12 ottobre 1970.     

Conjugate processes and the silumation of ruin problems

A general methods is developed for giving simulation estimates of boundary crossing probabilities for processes related to random walks in discreate or continuous time. Particular attention is given to the probability ψ(u, T of ruin before time T in cpumpound Poisson risk processes. When the provbabi;ity law P governing the given process is imbedded in an exponentaial family (P_gq), one can write ψ (u, T) + _θR_gq for certain random variables R_gq given by Wald's fundamental identity. Using this to simulate from P_gq rather than P, it is possible not only to overcome the difficulties connected with the case T =∞, but also to obtain a considerable variance reduction.It is shown that the solution of the Lundberg equation determines the asymptotically optimal value of θ in heavy traffic when T = ∞, and some results guidelining the choice of θ when T > ∞ are also given. The potential of the method in different is illustrated by two examples.     

Extrem aufgeweitete Tetrathiafulvalene mit Polyen-Spacern. Carotinoide Tetrathiafulvalene. Polymethin-tetracyanotetrathiafulvalen-Radikalkationen,eine neue Klasse von Violenen

Extremely Expanded Tetrathiafulvalenes with Polyene Spacers. Carotinoid Tetrathiafulvalenes. Polymethin-Tetracyanotetrathiafulvalene Radical Cations, a New Class of Violenes The synthesis of extended tetrathiafulvalenes 11 with di-, tetra-, hexa-, octa-, deca- and dodecamethine spacers is described by a PPh₃-induced Wittig-reaction-like condensation of the corresponding polyenedials 10 with 2-thio-1,3-dithiole-4,5-dicarbonitrile ( 9 ). By the same procedure, the dimethyloctamethine- and the tetramethyl-hexadecamethine-tetrathiafulvalenes 14 and 15 , respectively, were obtained. The extended tetrathiafulvalenes represent multistep vinylogous redox systems of the ‘violene type’. They can be oxidized to give the cyanine-like radical cations, e.g. 11 _sem, 14 _sem, and 15 _sem, and the dications, e.g. 11 _ox, 14 _ox, and 15 _ox; their UV/VIS/NIR spectra are reported. The crystal and molecular structure of (all-E)-2,2′-(octa-2,4,6-trien-1,8-diylidene)bis[1,3-dithiole-4,5-dicarbonitrile] ( 11e ) was determined: it is a rod-like, planar molecule; in the crystal, it forms staples along the longest molecule axis. The CV measurements confirm that the redox potentials of 11, 14 , and 15 decrease asymptotically with the increasing length of the spacer. Because of the close relationship of the extended tetrathiafulvalenes (ETTF's) to the carotinoids, they are named ‘caroviologenes’; they formally belong to the class of molecular wires.     

Electrocatalytic Carbon Dioxide Reduction by Using Cationic Pentamethylcyclopentadienyl–Iridium Complexes with Unsymmetrically Substituted Bipyridine Ligands

Eight [Ir(bpy)Cp*Cl]⁺‐type complexes (bpy= bipyridine, Cp*=1,2,3,4,5‐pentamethylcyclopentadienyl) containing differently substituted bipyridine ligands were synthesized and characterized. Cyclic voltammetry (CV) of the complexes in Ar‐saturated acetonitrile solutions showed that the redox behavior of the complexes could be fine tuned by the electronic properties of the substituted bipyridine ligands. Further CV in CO₂‐saturated MeCN/H₂O (9:1, v/v) solutions showed catalytic currents for CO₂ reduction. In controlled potential electrolysis experiments (MeCN/MeOH (1:1, v/v), E_app=?1.80 V vs Ag/AgCl), all of the complexes showed moderate activity in the electrocatalytic reduction of CO₂ with good stability over at least 15 hours. This electrocatalytic process was selective toward formic acid, with only traces of dihydrogen or carbon monoxide and occasionally formaldehyde as byproducts. However, the turnover frequencies and current efficiencies were quite low. No direct correlation between the redox potentials of the complexes and their catalytic activity was observed.     

Extreme Value Theory for Queues Via Cycle Maxima

The present state of extreme value theory for queues is surveyed. The exposition focuses on the regenerative properties of queueing systems, which reduces the problem to the study of the tail of the maximum of the queueing process during a regenerative cycle . For simple queues, methods for obtaining the distribution of both explicitly and asymptotically are reviewed. In greater generality, the study leads into Wiener–Hopf problems. Extensions to queues in a Markov regime, for example governed by Markov-modulated Poisson arrivals, are also considered.