Towards Strong Duality in Integer Programming

We consider in this paper the Lagrangian dual method for solving general integer programming. New properties of Lagrangian duality are derived by a means of perturbation analysis. In particular, a necessary and sufficient condition for a primal optimal solution to be generated by the Lagrangian relaxation is obtained. The solution properties of Lagrangian relaxation problem are studied systematically. To overcome the difficulties caused by duality gap between the primal problem and the dual problem, we introduce an equivalent reformulation for the primal problem via applying a pth power to the constraints. We prove that this reformulation possesses an asymptotic strong duality property. Primal feasibility and primal optimality of the Lagrangian relaxation problems can be achieved in this reformulation when the parameter p is larger than a threshold value, thus ensuring the existence of an optimal primal-dual pair. We further show that duality gap for this partial pth power reformulation is a strictly decreasing function of p in the case of a single constraint. Dedicated to Professor Alex Rubinov on the occasion of his 65th birthday. Research supported by the Research Grants Council of Hong Kong under Grant CUHK 4214/01E, and the National Natural Science Foundation of China under Grants 79970107 and 10571116.     

On the deformation and fracture of porous materials

The constitutive behavior of porous materials (including the yield loci, the void growth rate, the macro stress-strain relation and the strain to localization instability) is examined based on the lower bound approach proposed by the present authors. These results are then compared with the experimental and the finite element results as well as those predicted by Gurson's equations. Emphasis is placed on approaching the real behavior from the upper and the lower bound analysis. Calculation is also made on the influence of void nucleation on the critical strain to instability and a modified strain-controlled nucleation criterion is proposed. Finally the instability and fracture of AISI4340 steel in plane strain tension is examined and comparison is made between theoretical and experimental results.     

动力学分析法测定银的进展

本文综述了动力学分析法测定银的发展概况.并对测定方法列表进行了比较,文章引用国内外文献90篇.     

三氮烯类化合物作为酸碱指示剂的研究及应用

本文报道了三氮烯类化合物作为酸碱指示剂的研究及应用.以我们新近合成的此类试剂之一——2-氯一4一硝基苯基重氮氨基偶氮苯为研究主要对象,分别讨论了有无表面活性剂存在、以及不同类型表面活性剂存在下,试剂的离解常数及变色区域.在TritonX-100存在下,其试剂的pKa=9.25±0.01,变色区域为pH8.40(黄)～10.0(紫);在CTMAB存在下,pKa=7.35士0.03,变色区域pH6.85～7.90;在混合表面活性剂TritonX-100-CTMAB存在下,pKa=8.20±0.05,变色域pH7.45～9.00(黄～紫).特别是在阳离子表面活性剂存在下,滴定终点颜色变化十分敏锐清晰,是一种优于酚酞和甲基橙的指示剂.最后并对此类试剂与表面活性剂的相互作用作了简单探讨.     

Intramammary expression and therapeutic effect of a human lysozyme-expressing vector for treating bovine mastitis

To develop a gene therapy strategy for treating bovine mastitis, a new mammary-specific vector containing human lysozyme (hLYZ) cDNA and kanamycin resistance gene was constructed for intramammary expression and clinical studies. After one time acupuncture or intracisternal infusion of healthy cows with 400 μg of the p215C3LYZ vector, over 2.0 μg/ml of rhLYZ could be detected by enzymatic assay for about 3 weeks in the milk samples. Western blotting showed that rhLYZ secreted into milk samples from the vector-injected cows had molecular weight similar to that of the natural hLYZ in human colostrums. Twenty days after the primary injection, the quarters were re-injected with the same vector by quarter acupuncture and even higher concentrations of rhLYZ could be detected. Indirect competitive ELISA of milk samples showed that the vector injection did not induce detectable humoral immune response against hLYZ. Clinical studies showed that twice acupuncture of quarters with the p215C3LYZ vector had overt therapeutic effect on clinical and subclinical mastitis previously treated with antibiotics, including disappearance of clinical symptoms and relatively high microbiological cure rates. These data provide a solid rationale for using the vector to develop gene therapy for treating bovine mastitis.     

水下沉桩施工新技术

肇庆换流站供水工程之一的五尺峡取水泵站施工中，在受施工条件限制的情况下，采用将钢筋混凝土预制桩改为开口钢管桩，将双排桩改为单排桩，尝试搭设水上竹平台作沉桩施工平台等措施均取得成功，保证了质量、安全、进度，降低了施工成本．     

非园断面通道层流摩擦阻力与换热理论研究的新进展

本文介绍作者近些年来对椭圆、矩形、扇形、任意三角形、正多边形、环形等各种非圆断面通道层流摩擦阻力与换热理论的研究成果，给出大量新的速度与温度场表达式，以及摩擦阻力与换热的新的计算公式。本文对传统的层流阻力与换热理论进行了一次系统的补充与完善，同时考虑到工程需要，对所有繁杂的理论公式都进行了化简，给出形式简单而且精度相当高的近似公式。     

局部对称共形平坦黎曼流形中具有平行平均曲率向量的子流形

本文把[1]的结论推广到了环绕空间是局部对称共形平坦的情形,即获得了:设M~是局部对称共形平坦黎曼流形N~+p(p>1)中具有平行平均曲率向量的紧致子流形,如果则M~位于N~+p的全测地子流形N~+1中。其中S,H分别是M~的第二基本形式长度的平方和M~的平均曲率,T_C、t_c分别是N~+p的Ricci曲率的上、下确界,K是N~+p的数量曲率。     

A necessary condition for the minimum of a quadratic form under rearrangements

A necessary condition is derived for a quadratic form p^tGp to be minimal among all permutations of the nonnegative nontrivial vector p. The quadratic form arises from the stability problem of a fixed-fixed taut string loaded with masses at equidistant points.     

双间隙加速管设计中几个问题的研究

对加速管的放电或击穿与绝缘环，电极材料，极间距离和真空度等因素的关系进行了分析，为加速管的设计提供了依据。以此研制的加速算运行正常。