Rational Solutions of High-Order Algebraic Ordinary Differential Equations

This paper considers algebraic ordinary differential equations(AODEs) and study their polynomial and rational solutions. The authors first prove a sufficient condition for the existence of a bound on the degree of the possible polynomial solutions to an AODE. An AODE satisfying this condition is called noncritical. Then the authors prove that some common classes of low-order AODEs are noncritical. For rational solutions, the authors determine a class of AODEs, which are called maximally comparable, such that the possible poles of any rational solutions are recognizable from their coefficients. This generalizes the well-known fact that any pole of rational solutions to a linear ODE is contained in the set of zeros of its leading coefficient. Finally, the authors develop an algorithm to compute all rational solutions of certain maximally comparable AODEs, which is applicable to 78.54% of the AODEs in Kamke's collection of standard differential equations.     

Improving solver performance through redundancy

It is well known that hierarchies of mathematical programming formulations with different numbers of variables and constraints have a considerable impact regarding the quality of solutions obtained once these formulations are fed to a commercial solver. In addition, even if dimensions are kept the same, changes in formulations may largely influence solvability and quality of results. This becomes evident especially if redundant constraints are used. We propose a related framework for information collection based on these constraints. We exemplify by means of a well-known combinatorial optimization problem from the knapsack problem family, i.e., the multidimensional multiple-choice knapsack problem (MMKP). This incorporates a relationship of the MMKP to some generalized set partitioning problems. Moreover, we investigate an application in maritime shipping and logistics by means of the dynamic berth allocation problem (DBAP), where optimal solutions are reached from the root node within the solver.     

迭代函数系统模型在生物序列分析中的应用

介绍了关于完全基因组及蛋白质序列的测度表示，迭代函数系统(IFS)模型在分形理论中已有较长时间的研究,在此我们提出用IFS模型及递归的IFS(RIFS)模型来拟合完全基因组与蛋白质序列的测度表示。我们发现在拟合完全基因组的测度表示时，RIFS模型比IFS模型好，但在拟合蛋白质序列的测度表示时IFS模型比RIFS模型好，从IFS模型或RIFS模型中估计的参数可以用来讨论与生物分类进化及蛋白质结构预测有关的问题。     

垂直热发射流场研究与计算机仿真

本文着重分析了垂直热发射单喷管流场自由双限制射流流场及其多组分流场参数的计算方法和复杂激波系的数值解,运用Godunov方法在386微机上进行了数学仿真,编制了CAD软件包。     

Mesenchymal stem cells within tumour stroma promote breast cancer metastasis

Mesenchymal stem cells have been recently described to localize to breast carcinomas, where they integrate into the tumour-associated stroma. However, the involvement of mesenchymal stem cells (or their derivatives) in tumour pathophysiology has not been addressed. Here, we demonstrate that bone-marrow-derived human mesenchymal stem cells, when mixed with otherwise weakly metastatic human breast carcinoma cells, cause the cancer cells to increase their metastatic potency greatly when this cell mixture is introduced into a subcutaneous site and allowed to form a tumour xenograft. The breast cancer cells stimulate de novo secretion of the chemokine CCL5 (also called RANTES) from mesenchymal stem cells, which then acts in a paracrine fashion on the cancer cells to enhance their motility, invasion and metastasis. This enhanced metastatic ability is reversible and is dependent on CCL5 signalling through the chemokine receptor CCR5. Collectively, these data demonstrate that the tumour microenvironment facilitates metastatic spread by eliciting reversible changes in the phenotype of cancer cells.