Concavity cuts for disjoint bilinear programming

We pursue the study of concavity cuts for the disjoint bilinear programming problem. This optimization problem has two equivalent symmetric linear maxmin reformulations, leading to two sets of concavity cuts. We first examine the depth of these cuts by considering the assumptions on the boundedness of the feasible regions of both maxmin and bilinear formulations. We next propose a branch and bound algorithm which make use of concavity cuts. We also present a procedure that eliminates degenerate solutions. Extensive computational experiences are reported. Sparse problems with up to 500 variables in each disjoint sets and 100 constraints, and dense problems with up to 60 variables again in each sets and 60 constraints are solved in reasonable computing times. Received: October 1999 / Accepted: January 2001?Published online March 22, 2001     

Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation

The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load.And an integral representations for the displacements of the semi-infinite elastic foundation was presented.The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semi- infinite elastic foundation.Some computational results and the analysis on the influence of parameters were presented.     

弹性地基上四边自由Reissner矩形中厚板的有限积分变换法

将弹性地基视为Winkler模型,利用二维有限积分变换的方法推导出了弹性地基上四边自由矩形中厚板位移和内力的精确解.由于在求解过程中不需要预先人为选取位移函数,而是从弹性地基上中厚板的基本方程出发,直接利用有限积分变换的数学方法求出可以完全满足四边自由边界条件,弹性地基上矩形中厚板问题的精确解,使得问题的求解更加合理.最后通过计算实例验证了所采用方法及所推导出的公式的正确性.     

银吸收边附近X射线衰减系数测量

在北京同步辐射装置的4B7A中能X光束线上,光源能区为2.1~6.0 keV,能量分辨大于5000,高次谐波小于0.1%,光源强度大于109光子/s。通过全能区多能点的透过率精确测量Ag样品质量厚度,然后采用Ag薄膜对单能X光子的透过率进行测量,给出了Ag薄膜在吸收边（3.4~3.9 keV）的衰减系数 。建立了Ag样品吸收边附近衰减系数同步辐射测量方法。通过不确定度分析给出衰减系数测量不确定度小于1％,填补了在该区间衰减系数的空白。     

An extremal bandwidth problem for bipartite graphs

This paper discusses the problem of finding the maximum number of edges E(m, n, B) in a bipartite graph having partite set sizes m and n and bandwidth B. Exact values for E(m, n, B) are found for many cases. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 278–289, 2000     

Short Disjoint Paths in Locally Connected Graphs

Chartrand and Pippert proved that a connected, locally k-connected graph is (k + 1)-connected. We investigate the lengths of k + 1 disjoint paths between two vertices in locally k-connected graphs with respect to several graph parameters, e.g. the k-diameter of a graph. We also give a generalization of the mentioned result. This research was partly done on a visit to the Institute of Systems Science of Academia Sinica (Beijing, China) under the project ME 418 of the Czech Ministery of Education. These authors are partly supported by the project LN00A056 of the Czech Ministery of Education.     

Disjoint paths, planarizing cycles, and spanning walks

We study the existence of certain disjoint paths in planar graphs and generalize a theorem of Thomassen on planarizing cycles in surfaces. Results are used to prove that every 5-connected triangulation of a surface with sufficiently large representativity is hamiltonian, thus verifying a conjecture of Thomassen. We also obtain results about spanning walks in graphs embedded in a surface with large representativity.

     

A Generalization of a Theorem of Dehon for Simple t-Designs

A generalization of a theorem of Dehon for simple t-designs is proved. Several new families of 4- and 5-designs having certain additional property regarding their block intersection numbers are obtained by applying this result.The author acknowledges the support of SFB Forschungsschwerpunkt-Geometrie Grant, University of Heidelberg.     

Generalized Steiner Triple Systems with Group Size g ≡0, 3 (mod 6)

Generalized Steirier triple systems, GS(2,3,n,g), are equivalent to maximum constant weight codes over an alphabet of size g 1 with distance 3 and weight 3 in which each codeword has length n. The necessary conditions for the existence of a GS(2,3,n,g) are (n-1)g≡0 (mod 2), n(n-1)g2≡0 (mod 6), and n≥g 2. These necessary conditions are shown to be sufficient by several authors for 2≤g≤11. In this paper, three new results are obtained. First, it is shown that for any given g, g≡0 (mod 6) and g≥12, if there exists a GS(2.3.n.g) for all n, g 2≤n≤7g 13. then the necessary conditions are also sufficient. Next, it is also shown that for any given g, g≡3 (mod 6) and g≥15, if there exists a GS(2,3,n,g) for all n, n≡1 (mod 2) and g 2≤n≤7g 6, then the necessary conditions are also sufficient. Finally, as an application, it is proved that the necessary conditions for the existence of a GS(2,3,n,g) are also sufficient for g=12,15.     

X-ray K-absorption edge shifts due to chemical combination

A possible explanation is given of the chemical shifts of x-ray K-absorption edges of metals when they undergo a chemical combination and form compounds. It is proposed that when a metal forms a compound its Fermi edge changes. It explains the numerical order as well as the nature of the chemical shifts. A fairly good agreement between the calculated and observed values has been obtained.