Comprehensive Two‐Dimensional Gas Chromatography with a Rotating Thermal Desorption Modulator and Independently Temperature‐Programmable Columns

In comprehensive two‐dimensional gas chromatography, two individual separations are coupled by means of a rotating thermal desorption modulator interface. The injection pulse introduced via the interface onto the second column should be as short as possible. Parameters affecting the modulator operation are studied. In the set‐up used in this study, the temperature of the second column can be programmed independently from that of the first column. Optimization of the second‐dimension separation to minimize peak broadening and maximize resolution is discussed and an elegant approach to determine second‐dimension retention times using a non‐constant modulation frequency is demonstrated. The high separation power of the comprehensive system is demonstrated by the analysis of technical and biota samples containing chlorinated biphenyls and toxaphene.     

Cost Based Filtering for the Constrained Knapsack Problem

We present cost based filtering methods for Knapsack Problems (KPs). Cost based filtering aims at fixing variables with respect to the objective function. It is an important technique when solving complex problems such as Quadratic Knapsack Problems, or KPs with additional constraints (Constrained Knapsack Problems (CKPs)). They evolve, e.g., when Constraint Based Column Generation is applied to appropriate optimization problems. We develop new reduction algorithms for KP. They are used as propagation routines for the CKP with (nlogn) preprocessing time and (n) time per call. This sums up to an amortized time (n) for (logn) incremental calls where the subsequent problems may differ with respect to arbitrary sets of necessarily included and excluded items.     

Kazhdan-Lusztig Cells and the Murphy Basis

Let H be the Iwahori–Hecke algebra associated with S_n,the symmetric group on n symbols. This algebra has two importantbases: the Kazhdan–Lusztig basis and the Murphy basis.We establish a precise connection between the two bases, allowingus to give, for the first time, purely algebraic proofs fora number of fundamental properties of the Kazhdan–Lusztigbasis and Lusztig's results on the a-function. 2000 MathematicsSubject Classification 20C08.     

Kazhdan-Lusztig Cells, q-Schur Algebras and James' Conjecture

We consider the Dipper–James q-Schur algebra S_q(n, r)_k,defined over a field k and with parameter q 0. An understandingof the representation theory of this algebra is of considerableinterest in the representation theory of finite groups of Lietype and quantum groups; see, for example, [6] and [11]. Itis known that S_q(n, r)_k is a semisimple algebra if q is nota root of unity. Much more interesting is the case when S_q(n,r)_k is not semisimple. Then we have a corresponding decompositionmatrix which records the multiplicities of the simple modulesin certain ‘standard modules’ (or ‘Weyl modules’).A major unsolved problem is the explicit determination of thesedecomposition matrices.     

High-yield solution-phase synthesis of di- and trinucleotide blocks assisted by polymer-supported reagents

A new solution-phase phosphoramidite approach is reported for oligonucleotide synthesis employing recyclable solid-supported reagents. It uses polyvinyl pyridinium tosylate as the activator of a nucleoside-3'-O-phosphoramidite in the coupling step with a 5'-OH nucleoside or dinucleotide. The resulting phosphite triester was either sulfurized or oxidized using polystyrene-bound trimethylammonium tetrathionate or periodiate. This method avoids complicated purification steps, as excess reagents are easily removed by filtration. [reaction: see text]