Influence of the capillarity on a creeping film flow down an inclined plane with an edge

Summary In creeping flows of thin films, the capillarity can play a dominant role. In this paper, the creeping film flow down an inclined plane with an edge is considered. The influence of the capillarity on the velocity and the film surface is studied analytically, numerically and experimentally. Received 12 April 1999; accepted for publication 9 May 1999     

Path coupling using stopping times and counting independent sets and colorings in hypergraphs

We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q‐colorings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

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.     

A conjecture of Borodin and a coloring of Grünbaum

In 1976, Borodin conjectured that every planar graph has a 5‐coloring such that the union of every k color classes with 1 ≤ k ≤ 4 induces a (k—1)‐degenerate graph. We prove the existence of such a coloring using 18 colors. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:139–147, 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.     

刀口定量检验技术的研究

主要介绍了天文镜面加工的中的刀口定量检验技术，包括阴影图像ＣＣＤ实时采集，图像处理，定量计算。     

Solving some NP-complete problems using split decomposition

We show how to use the split decomposition to solve some NP-hard optimization problems on graphs. We give algorithms for clique problem and domination-type problems. Our main result is an algorithm to compute a coloration of a graph using its split decomposition. Finally we show that the clique-width of a graph is bounded if and only if the clique-width of each representative graph in its split decomposition is bounded.     

A local structure theorem on 5‐connected graphs

An edge of a 5‐connected graph is said to be contractible if the contraction of the edge results in a 5‐connected graph. Let x be a vertex of a 5‐connected graph. We prove that if there are no contractible edges whose distance from x is two or less, then either there are two triangles with x in common each of which has a distinct degree five vertex other than x, or there is a specified structure called a K₄^?‐configuration with center x. As a corollary, we show that if a 5‐connected graph on n vertices has no contractible edges, then it has 2n/5 vertices of degree 5. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 99–129, 2009