Palladium-catalyzed α-arylation of ketones on solid support: scope and limitations

The palladium-catalyzed α-arylation of ketones on solid support is described. Using modified Buchwald-Hartwig reaction conditions, the coupling of immobilized 4-bromobenzamide with various aromatic, heteroaromatic, and aliphatic ketones was investigated. Subsequent cleavage from the resin provided the desired α-aryl ketones almost in moderate to high yields and good to excellent purities. The scope and limitations of this protocol will be discussed.     

New Combinatorial Descriptions of the Triangulations of Cyclic Polytopes and the Second Higher Stasheff–Tamari Posets

This paper is concerned with the d-dimensional cyclic polytope with n vertices, C(n,d), and the set of its triangulations, S(n,d). We show that there is a bijection between S(n,d) and certain partitions of the set of increasing d-tuples on the integers 1 to n–1. We give a combinatorial characterization of the second higher Stasheff–Tamari poset, which is a partial ordering of S(n,d), and we determine its 2-dimension. There is a well-known representation of triangulations of an n-gon by right bracket vectors. We generalize this to cyclic polytopes of higher dimensions.     

A note on canonical functions

We construct a generic extension in which the ℵ₂nd canonical function on ℵ₁ exists. Supported by NSF and by a Fulbright grant. Publ. 378. Partially supported by the B.S.F.     

Approximating the single source unsplittable min-cost flow problem

In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. Moreover, the total cost must not exceed a given budget. This problem has been introduced by Kleinberg [7] and generalizes several NP-complete problems from various areas in combinatorial optimization such as packing, partitioning, scheduling, load balancing, and virtual-circuit routing. Kolliopoulos and Stein [9] and Dinitz, Garg, and Goemans [4] developed algorithms improving the first approximation results of Kleinberg for the problem of minimizing the violation of edge capacities and for other variants. However, known techniques do not seem to be capable of providing solutions without also violating the cost constraint. We give the first approximation results with hard cost constraints. Moreover, all our results dominate the best known bicriteria approximations. Finally, we provide results on the hardness of approximation for several variants of the problem. Received: August 23, 2000 / Accepted: April 20, 2001?Published online October 2, 2001     

Enhanced four-wave mixing in mercury isotopes, prepared by stark-chirped rapid adiabatic passage

We demonstrate significant enhancement of four-wave mixing in coherently driven mercury isotopes to generate vacuum-ultraviolet radiation at 125 nm. The enhancement is accomplished by preparation of the mercury atoms in a state of maximum coherence, i.e. maximum nonlinear-optical polarization, driven by Stark-chirped rapid adiabatic passage (SCRAP). In this technique, a pump laser at 313 nm excites the two-photon transition between the ground state 6s²¹S₀ and the target state 7s ¹S₀ in mercury. A strong, off-resonant radiation field at 1064 nm generates dynamic Stark shifts. These Stark shifts serve to induce a rapid adiabatic passage process on the two-photon transition. During the process a coherent superposition of the two states is established, which enhances the nonlinear-optical polarization in the medium to the maximum possible value. The maximum coherence permits efficient four-wave mixing of a pump laser and an additional probe laser at 626 nm. The efficiency is further enhanced, as the SCRAP process allows to stimulate the complete set of different mercury isotopes to participate in the frequency conversion process. This enlarges the effective atomic density of the medium. Thus, we observe the generation of vacuum-ultraviolet radiation at 125 nm enhanced by more than one order of magnitude with respect to conventional frequency conversion. Parallel to the frequency conversion process, we monitored the evolution of the population in the medium by laser-induced fluorescence. These data demonstrate efficient coherent population transfer by SCRAP.     

Correlated and non-correlated growth kinetics of pentacene in the sub-monolayer regime

We present a study of the growth kinetics of pentacene monolayer islands on SiO₂ in the submonolayer regime by using Atomic Force Microscopy (AFM). Two distinct growth modes, namely correlated growth (CG) and non-correlated growth (NCG), have been identified by Voronoi tesselation. These two modes are characterized by different island growth kinetics. In the case of correlated growth, the average island size 〈A〉 scales with deposition time t i.e. 〈A〉 ∝ t whereas for non-correlated growth, 〈A〉 ∝ t². The CG and NCG regimes are defined by the level of re-evaporation which determines the capture zones around the islands: Wigner-Seitz cells for CG and coronas of width λ_D (λ_D is the mean diffusion distance on SiO₂ before re-evaporation) for NCG. A simple model is proposed to reproduce the experimental growth kinetics in both modes.     

Cayley graphs of finitely generated groups

There does not exist a Borel choice of generators for each finitely generated group which has the property that isomorphic groups are assigned isomorphic Cayley graphs.