Recent advances in lattice gauge theories

Recent progress in the field of lattice gauge theories is briefly reviewed for a nonspecialist audience. While the emphasis is on the latest and more definitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.     

An adaptive memory algorithm for the k-coloring problem

Let G=(V,E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1,…,k}) to each vertex of G so that no edge has both endpoints with the same color. The adaptive memory algorithm is a hybrid evolutionary heuristic that uses a central memory. At each iteration, the information contained in the central memory is used for producing an offspring solution which is then possibly improved using a local search algorithm. The so obtained solution is finally used to update the central memory. We describe in this paper an adaptive memory algorithm for the k-coloring problem. Computational experiments give evidence that this new algorithm is competitive with, and simpler and more flexible than, the best known graph coloring algorithms.     

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.     

NMR determination of the composition of balsams from scotch pine resin

We have used ¹H and ¹³C NMR spectroscopy to study the composition of pine resin balsams from Scotch pines grown in different regions of the Republic of Belarus. We have established that their chemical composition does not depend very much on the region where they are grown or the level of contamination of the forests by radioactive and industrial emissions. Prolonged storage of the balsams leads to a substantial change in their compositions, due to isomerization of the resin acids. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 3, pp. 411–415, May–June, 2008.     

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.     

An improved ant colony optimisation heuristic for graph colouring

The focus of this paper is an ant colony optimisation heuristic for the graph colouring problem. We start by showing how a series of improvements enhance the performance of an existing ant colony approach to the problem and then go on to demonstrate that a further strengthening of the construction phase, combined with a tabu search improvement phase, raise the performance to the point where it is able to compete with some of the best-known approaches on a series of benchmark problems.     

Balanced decomposition of a vertex-colored graph

A balanced vertex-coloring of a graph G is a function c from V(G) to {−1,0,1} such that ∑{c(v):v∈V(G)}=0. A subset U of V(G) is called a balanced set if U induces a connected subgraph and ∑{c(v):v∈U}=0. A decomposition V(G)=V₁∪?∪V_r is called a balanced decomposition if V_i is a balanced set for 1≤i≤r.In this paper, the balanced decomposition number f(G) of G is introduced; f(G) is the smallest integer s such that for any balanced vertex-coloring c of G, there exists a balanced decomposition V(G)=V₁∪?∪V_r with |V_i|≤s for 1≤i≤r. Balanced decomposition numbers of some basic families of graphs such as complete graphs, trees, complete bipartite graphs, cycles, 2-connected graphs are studied.     

On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree

A different approach is given to recent results due mainly to R. C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The techniques developed are based on some results of matching polynomials and used a work by O. L. Heilmann and E. H. Lieb on an apparently unrelated topic.      

Synthesis, Characterization and Inclusion Properties of an Iron(II) Polyimine Complex Derived from 2,6-Diacetylpyridine and an Aliphatic Polyamine

A novel multibinding species has been obtained by attaching four aliphatic polyamine chains to an iron(II)-polyimine centre, derived from 2,6-diacetylpyridine. Molecular simulations for the complex corroborate the evidence from 1H NMR spectroscopy of a symmetric structure, with the four polyamines displaying a tetrahedral arrangement around the metal centre. The protonated polyamine complex interacts with hexacyanoferrate(II) ions, leading to an inclusion compound which has been characterized based on vibrational and Mössbauer spectroscopy, and on cyclic voltammetry.     

双核铂的Pt2（CN）4（CNC4H9）4的发光机制及Pt...Pt间互作用的从头计算研究

利用从头算ＭＰ２方法优化了Ｐｔ（ＣＮ）２（ＣＮＣＨ３）２，Ｐｔ（ＣＮ）２（ＣＮＣＨ３）２－（ＮＣＣＨ３）２．「Ｐｔ（ＣＮ）２．（ＣＮＣＨ３）２」２的在态几何结构，利用单激发的组态相互作用方法（ＣＩＳ）计算了固态和乙氰溶液中标题化合物的发射光谱，并对激发态的几何结构进行了优化，结果表明，基态时，Ｐｔ．．．ＮＣＣＨ３之间的距离较大（０．４０６ｎｍ），说明溶剂分子与Ｐｔ原子之间存在较小的范德华作用；而激发时，Ｐｔ．．．ＮＣＣＨ３之间的距离减小（０．２５７ｎｍ），说明此时Ｐｔ．．．ＮＣＣＨ３之间相互作用较强，由于这种作用使乙氰溶液中该物质的发光性质与不考虑溶剂效应时相比差异较大，其发射光谱不可我谱区，固态时，此化合物为直线链状结构，ＭＰ２计算得到：基态时「Ｐｔ（ＣＮ）２（ＣＮＣＨ３）２」２中Ｐｔ．．．Ｐｔ之间的距离为０