拓扑量子场理论与相交指标

该文构造了一新的上同调型拓扑量子场理论并证明了其配分函数是相交指标 (crossingindex)     

Proving total dual integrality with cross-free families—A general framework

We present a theorem stating that certain classes of linear programming problems have integer optimal (primal and dual) solutions. The theorem includes as special cases earlier results of Johnson, Edmonds and Giles, Frank, Hoffman and Schwartz, Gröflin and Hoffman, and Lawler and Martel. The proof method consists of deriving total dual integrality for the corresponding system of linear inequalities from the total unimodularity of certain ‘cross-free’ subsystems. The scheme presented here differs from the one proposed earlier by Grishuhin in that Grishuhin requires the total unimodularity of cross-free subsystems in the axioms, whereas here this follows from easier verifiable axioms.     

Bosonization theory for tunneling spectra in smooth edges of quantum Hall systems

We calculate the spectral function of a smooth edge of a quantum Hall system in the lowest Landau level by means of a bosonization technique. We obtain a general relationship between the one electron spectral function and the dynamical structure factor. The resulting – characteristics exhibit, at low voltage and temperature, power law scaling, generally different from the one predicted by the chiral Luttinger liquid theory, and in good agreement with recent experimental results.     

On k-planar crossing numbers

The k-planar crossing number of a graph is the minimum number of crossings of its edges over all possible drawings of the graph in k planes. We propose algorithms and methods for k-planar drawings of general graphs together with lower bound techniques. We give exact results for the k-planar crossing number of K_2k+1,q, for k?2. We prove tight bounds for complete graphs. We also study the rectilinear k-planar crossing number.     

The Crossing Number of C(mk;{1, k})

Calculating the crossing number of a given graph is, in general, an elusive problem. Garey and Johnson have proved that the problem of determining the crossing number of an arbitrary graph is NP-complete. The crossing number of a network(graph) is closely related to the minimum layout area required for the implementation of a VLSI circuit for that network. With this important application in mind, it makes most sense to analyze the the crossing number of graphs with good interconnection properties, such as the circulant graphs. In this paper we study the crossing number of the circulant graph C(mk;{1,k}) for m3, k3, give an upper bound of cr(C(mk;{1,k})), and prove that cr(C(3k;{1,k}))=k.Research supported by Chinese Natural Science Foundation     

A Lower Bound for the Rectilinear Crossing Number

We give a new lower bound for the rectilinear crossing number of the complete geometric graph K_n. We prove that and we extend the proof of the result to pseudolinear drawings of K_n. Dedicated to the memory of our good friend and mentor Víctor Neumann-Lara. Received: April, 2003 Final version received: March 18, 2005     

Hopping conductivity and activated transport in InxGa1-xAs quantum wells

We present measurements of the diagonal R_xx and off-diagonal R_xy magnetoresistance under quantum Hall conditions on several high electron mobility transistors (HEMT) based on In_xGa_1-xAs quantum wells. From the magnetoresistance tensor we obtain the longitudinal conductivity σ _xx . We study the transport mechanisms near the σ _xx minima at temperatures ranging between 2 K and 35 K; activated transport is the dominant mechanism for temperatures above 7 K while variable range hopping conductivity is significant for lower temperatures. We show that electron-electron correlations should be taken into account to explain the conductivity vs temperature behaviour below 5 K. Finally, we study the behaviour of the localization length as a function of Landau level filling and obtain a critical exponent γ = 3.45±0.15. Received 6 June 2001 and Received in final form 16 October 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.