Investigation into the ROMP copolymerization of peptide‐ and PEG‐functionalized norbornene derivatives

The ring‐opening metathesis polymerizations (ROMP), using RuCl₂ (PCy₃)₂CHPh, of a series of peptide‐functionalized norbornene derivatives have been investigated. Incorporation of a PEG‐monomer was found to prevent premature precipitation of polymer strands during the course of polymerization reactions and yield water compatible polymers in high conversions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3178–3190, 2007     

The Livsic Cocycle Equation for Compact Lie Group Extensions of Hyperbolic Systems

In this article we extend well-known results of Livsic on theregularity of measurable solutions to the cocycle equation.Livsic proved a regularity result for real valued cocycles,but for compact Lie group valued cocycles his result was restrictedto coboundaries (that is, trivial or constant cocycles). Inthis article we prove the complete result. We present several useful applications of these results.     

Globally Linked Pairs of Vertices in Equivalent Realizations of Graphs

A two-dimensional framework (G,p) is a graph G = (V,E) together with a map p: V → ℝ². We view (G,p) as a straight line realization of G in ℝ². Two realizations of G are equivalent if the corresponding edges in the two frameworks have the same length. A pair of vertices {u,v} is globally linked in G if %and for all equivalent frameworks (G,q), the distance between the points corresponding to u and v is the same in all pairs of equivalent generic realizations of G. The graph G is globally rigid if all of its pairs of vertices are globally linked. We extend the characterization of globally rigid graphs given by the first two authors [13] by characterizing globally linked pairs in M-connected graphs, an important family of rigid graphs. As a byproduct we simplify the proof of a result of Connelly [6] which is a key step in the characterization of globally rigid graphs. We also determine the number of distinct realizations of an M-connected graph, each of which is equivalent to a given generic realization. Bounds on this number for minimally rigid graphs were obtained by Borcea and Streinu in [3].     

Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

Solid-phase synthesis of imidazo[4,5-b]pyridin-2-ones and related urea derivatives by cyclative cleavage of a carbamate linkage

A solid-phase synthesis of substituted cyclic urea derivatives as potential heterocyclic library scaffolds is described. 2-Amino-3-nitropyridine is attached to Wang resin via a carbamate linkage. Reduction of the nitro group was achieved with SnCl(2).2H(2)O. Reductive alkylation with a range of substituted benzaldehydes followed by cyclative cleavage afforded a small library of 3-substituted imidazo[4,5-b]pyridine-2-ones in 33-45% yield and 59-88% purity. Subsequently, this methodology was applied to the synthesis of 3-substituted imidazo[4,5-f]quinolin-2-ones.     

On-line on-chip post-column derivatisation reactions for pre-ionisation of analytes and cluster analysis in gradient micro-liquid chromatography/electrospray mass spectrometry

A system is presented that demonstrates the principle of on-line and on-chip post-column derivatisation reactions in micro-high-performance liquid chromatography (micro-HPLC) hyphenated to electrospray time-of-flight mass spectrometry (ESI-TOFMS). In this micro-HPLC-chip-MS set-up, the analytes are separated using gradient micro-HPLC and subsequently derivatised on-chip and detected. One of the major limitations of MS detection is its dependency on the degree of ionisation, which is widely variable and compound-specific. Optimising and controlling the degree of ionisation in a simple manner would allow MS detection to be truly generic. One way of achieving this is by pre-ionisation of analytes using simple derivatisation procedures that are both rapid and quantitative. Performing this in situ on the system described here overcomes issues of sample handling and efficiency losses when time-consuming "bench chemistry" is necessary prior to analysis. The power of the system is demonstrated by the separation of primary and secondary amines, which are subsequently derivatised with a positively charged phosphonium complex and detected in an enhanced manner. Typically, molecular cations (M(+)) are detected showing that the ionisation process is dominated by the phosphonium species, leading to more constant ionisation for a variety of compounds. In addition, stable isotopically labelled ((12)C/(13)C)-phosphonium reagent is used for the reactions, allowing for inherent signal/noise (S/N) improvement and automated data processing using cluster analysis. A similar reaction scheme is used for the derivatisation of ketones and aldehydes, also demonstrating dramatic increases in sensitivity, especially with increasing temperature. Minimal loss in chromatographic fidelity in terms of retention times is observed by the introduction of the micromixer chip into the system. Optimal flow rates in micro-HPLC and ESI-MS are compatible with flow rates for the chip as well as a multitude of in-line optical detectors including UV and fluorescence. In addition, the micromixer chip can be positioned pre-column if preferred. The system is robust, easily fully automated and applicable to a wide variety of reactions. The system has a major advantage in its simple robust connection to the "normal scale" outside world.