Global Optimization in Any Minkowski Metric: A Permutation-Translation Simulated Annealing Algorithm for Multidimensional Scaling

It is well known that considering a non-Euclidean Minkowski metric in Multidimensional Scaling, either for the distance model or for the loss function, increases the computational problem of local minima considerably. In this paper, we propose an algorithm in which both the loss function and the composition rule can be considered in any Minkowski metric, using a multivariate randomly alternating Simulated Annealing procedure with permutation and translation phases. The algorithm has been implemented in Fortran and tested over classical and simulated data matrices with sizes up to 200 objects. A study has been carried out with some of the common loss functions to determine the most suitable values for the main parameters. The experimental results confirm the theoretical expectation that Simulated Annealing is a suitable strategy to deal by itself with the optimization problems in Multidimensional Scaling, in particular for City-Block, Euclidean and Infinity metrics.     

基于拉格朗日插值的签名方案的研究

提出基于拉格朗日插值的签名方案存在小数位问题,并通过引入向量计算机制以消除数字签名中的小数位问题,最后对其进行了证明.     

具有柱状夹杂无限体均匀变温问题的闭合解

研究具有柱状夹杂无限体的均匀变温问题，其中夹杂与基体材料不同但具有相同的剪切弹性模量。应用复变函数方法及其分区全纯函数理论，结合Riemann边值问题的研究成果，求得了问题的闭合解，作为特殊情形得到了单圆柱形夹杂时的精确解。     

矿区开采沉陷地质灾害防治研究

煤炭开采所引发的地质灾害中,以开采沉陷对人类环境的影响最为严重。文章就矿区开采沉陷所引发的地质灾害与防治对策进行了研究,并开发了相应的建筑群保护煤柱设计软件。     

基于时态关系模型的儿童保健系统的设计研究

根据当前时态数据模型的理论,为儿童保健管理信息系统建立了一个可行的时态关系模型,并对系统中的查询做了简单的描述,最后分析了这种建模方法的优缺点.