Poly[2,7‐(9,9‐dihexylfluorene)‐alt‐pyridine] with donor‐acceptor architectures: A new series of blue‐light‐emitting alternating copolymers

A novel series of well‐defined alternating poly[2,7‐(9,9‐dihexylfluorenyl)‐alt‐pyridinyl] (PDHFP) with donor‐acceptor repeat units were synthesized using palladium (0)‐catalyzed Suzuki cross‐coupling reactions in good to high yields. In this series of alternating polymers, 2, 7‐(9,9‐dihexylfluorenyl) was used as the light emitting unit, and the electron deficient pyridinyl unit was employed to provide improved electron transportation. These polymers were characterized by ¹H‐NMR and ¹³C‐NMR, gel permeation chromatography (GPC), thermal analyses, and UV‐vis and fluorescence spectroscopy. The glass transition temperature of copolymers in nitrogen ranged from 110 to 148 °C, and the copolymers showed high thermal stabilities with high decomposition temperatures in the range of 350 to 390 °C in air. The difference in linkage position of pyridinyl unit in the polymer backbone has significant effects on the electronic and optical properties of polymers in solution and in film phases. Meta‐linkage (3,5‐ and 2,6‐linkage) of pyridinyl units in the polymer backbone is more favorable to polymer for pure blue emission and prevention of aggregation of polymer chain than para‐linkage (2,5‐linkage) of the pyridinyl units. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4792–4801, 2004     

On characterizing nilpotent lie algebras by their multiplierst(L) = 3,4,5,6

The nilpotent Lie algebras L of dimension n whose multipliers have dimension ½n(n-1)-t(L) have been found in [2] for t(L) = 0,1,2. Using a different method, we find similar results for t(L) = 3,4,5,6. The first author is extending the results to t(L) = 7 and 8.     

Tackling the edge dynamic graph colouring problem with and without future adjacency information

Many real world operational research problems, such as frequency assignment and exam timetabling, can be reformulated as graph colouring problems (GCPs). Most algorithms for the GCP operate under the assumption that its constraints are fixed, allowing us to model the problem using a static graph. However, in many real-world cases this does not hold and it is more appropriate to model problems with constraints that change over time using an edge dynamic graph. Although exploring methods for colouring dynamic graphs has been identified as an area of interest with many real-world applications, to date, very little literature exists regarding such methods. In this paper we present several heuristic methods for modifying a feasible colouring at time-step t into an initial, but not necessarily feasible, colouring for a “similar” graph at time-step \(t+1\). We will discuss two cases; (1) where changes occur at random, and (2) where probabilistic information about future changes is provided. Experimental results are also presented and the benefits of applying these particular modification methods are investigated.