Affinity chromatography on vancomycin coupled to reversed phase liquid chromatography/ electrospray-ion trap mass spectrometry for the screening of combinatorial libraries

Summary The combination affinity chromatography-mass spectrometry can be drastically improved by introducing a reversed phase column prior to the mass spectrometric detection. The interactions of the macrocyclic antibiotic vancomycin with oligopeptides were used to illustrate the performance of the technique. A library of 36 peptides was successfully screened and the active compounds identified by electrospray MS⁽ⁿ⁾. The strong affinity of compounds ending with (D)-alanine and with (D)-alanine or an aromatic (D)-amino acid in the penultimate position with vancomycin was confirmed.     

无限维空间中的实零点定理

在本文中，我们建立了无限维空间中的实零点定理，同时从仿射空间的拓扑结构和域的序结构两个方面，分别刻划了适合无限维实零点定理的序域．此外，本文有例子表明，对任意的基数α，确实存在适合α维实零点定理的序域．     

Combinatorial synthesis of small-molecule libraries using 3-amino-5-hydroxybenzoic acid

Summary A non-peptide library of 2001 compounds has been prepared utilizing solid-phase techniques. The split/combine method was demonstrated to work well to form mixtures of compounds based on 3-amino-5-hydroxybenzoic acid as a core structure. The benzoic acid of the core structure served as the attachment point for the resin and the amino and hydroxy positions were variably substituted.     

Integer programming formulations of vehicle routing problems

Various mathematical formulations are available for situations represented by vehicle routing problems. The assignment-based integer programming formulations of these problems are more common and easy to understand. Such formulations are discussed in this paper and a much simpler formulation for the vechicle routing problem is presented for the case, when all the vehicles have the same load capacity and maximum allowable cost per route.     

Combinatorial synthesis and characterization of a ternary epitaxial film of Co and Mn doped Ge (0 0 1)

We report combinatorial molecular beam epitaxy synthesis and properties of a ternary epitaxial film of Co and Mn co-doped Ge grown on Ge (0 0 1) substrate. Structural effects were examined in situ by reflection high-energy electron diffraction and ex situ by microbeam X-ray diffraction techniques, and magnetic properties were probed by using magnetooptic Kerr effect. Ternary epitaxial phase diagrams have been studied for total doping concentrations up to 30 at.%, where regions of coherent epitaxy and rough disordered growth and those of near room temperature ferromagnetic ordering have been identified.     

Minimal cutwidth linear arrangements of abelian Cayley graphs

We find the minimal cutwidth and bisection width values for abelian Cayley graphs with up to 4 generators and present an algorithm for finding the corresponding optimal ordering. We also find minimal cuts of each order.     

Finding a feasible flow in a strongly connected network

We give a linear-time algorithm to find a feasible flow in a strongly connected network with fixed supplies and demands, each summing to a common value that is at most the minimum arc capacity. This algorithm speeds up the Goldberg-Rao maximum flow method by a constant factor.     

On the arithmetic product of combinatorial species

We introduce two new binary operations on combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series in the context of species. It allows us to introduce the notion of multiplicative species, a lifting to the combinatorial level of the classical notion of multiplicative arithmetic function. Interesting combinatorial constructions are introduced; cloned assemblies of structures, hyper-cloned trees, enriched rectangles, etc. Recent research of Cameron, Gewurz and Merola, about the product action in the context of oligomorphic groups, motivated the introduction of the modified arithmetic product. By using the modified arithmetic product we obtain new enumerative results. We also generalize and simplify some results of Canfield, and Pittel, related to the enumerations of tuples of partitions with the restrictions met.     

On the asymmetric representatives formulation for the vertex coloring problem

We consider the vertex coloring problem, which can be stated as the problem of minimizing the number of labels that can be assigned to the vertices of a graph G such that each vertex receives at least one label and the endpoints of every edge are assigned different labels. In this work, the 0-1 integer programming formulation based on representative vertices is revisited to remove symmetry. The previous polyhedral study related to the original formulation is adapted and generalized. New versions of facets derived from substructures of G are presented, including cliques, odd holes and anti-holes and wheels. In addition, a new class of facets is derived from independent sets of G. Finally, a comparison with the independent sets formulation is provided.