Discovering non-terminating inputs for multi-path polynomial programs

This paper investigates the termination problems of multi-path polynomial programs （MPPs） with equational loop guards. To establish sufficient conditions for termination and nontermination simultaneously, the authors propose the notion of strong/weak non-termination which under/over- approximates non-termination. Based on polynomial ideal theory, the authors show that the set of all strong non-terminating inputs （SNTI） and weak non-terminating inputs （WNTI） both correspond to tile real varieties of certain polynomial ideals. Furthermore, the authors prove that the variety of SNTI is computable, and under some sufficient conditions the variety of WNTI is also computable. Then by checking the computed SNTI and WNTI varieties in parallel, termination properties of a consid- ered MPP can be asserted. As a consequence, the authors establish a new framework for termination analysis of MPPs.     

一类n项和数的表达式

用Ｃｈｅｂｙｓｈｅ多项式的零点为节点的Ｌａｇｒａｎｇｅ多项式逼近高阶多项式时，误差公式中出现一类ｎ面和数。现给出此类和表达式，并用归纳法证明之。     

苯胺与聚硫橡胶复合膜阻抗表征

利用电化学交流阻抗的方法研究了苯胺与聚硫橡胶干态复合膜内的电荷传输问题，通过非线性最小二乘法拟合，得出了聚苯胺（ＰＡｎ）与聚硫橡胶不同配比原等效电路，并计算出其电荷的散系数和异相电子传递反应的交换电流。实验结果表明，干态膜中ＰＡｎ含量的增加，不但可以提高复合膜的导电性，而且可以提高反应活性。     

Prediction of Flexural Deformation of Reinforcement Concrete Beams with Polynomial Tension Stiffening Model

Based on an assumption of parabolic bond stress distribution,a simplified model with quartic polynomial function of the relative slip of steel bar and surrounding concrete for reinforced concrete (RC)tensile member was proposed. The post-cracking behavior as well as tension stiffening effect was considered in the new model. The relative slip of bending member could also be determined through the extension of the new model,which could be applied to obtaining the concentrated rotations at certain sections in order to predict the flexural deformation of RC beam. Several examples of four-point bending RC beams were approached to verify the new model,and the predictions of the flexural deflections of RC beams agreed well with experimental results. The new model can be extended to the application of partially corroded RC beam.     

B-值Dirichlet级数确定的整函数的(p,q)(R)级和(p,q)(R)型

利用Newton多边形研究了B-值Dirichlet级数确定的整函数的增长性,较方便地得到了B-值Dirichlet级数的(p,q)(R)级及型和下(p,q)(R)级与系数关系的若干结果.     

Pólya公式与色轨道多项式

色轨道多项式是色多项式与 Pólya计数公式的推广 .本文定义了色轨道多项式及其相应的概念如 P-图 ,SC-图等 ,给出了色轨道多项式的表达式和计算方法 ,讨论了色轨道多项式的基本性质 .作为它的一个应用 ,给了项链问题的具体计数公式     

电网检修排序问题

研究一个从实践中提出的电网检修排序（调度）问题，并证明了该问题的一般情形是ＮＰ－困难的，对其特殊情形给出了多项式时间的算法．     

弹性薄板弯曲问题的配线最小二乘法

应用单三角级数及最小二乘配线法解矩形薄板的弯曲问题。给出了算例 ,并把所得结果与相应的经典解作了比较     

轮换对称多项式通式的构造及初等轮换式的自动发现

通过改进算法的轮换对称多项式的通式构造程序,研究了初等轮换对称多项式的构造,编写Maple程序得到了3元到7元的初等轮换对称多项式;提出并编程实现列表乘法运算,为较多元多项式的线性表示及多项式的通式构造提供了强有力的工具;提出了3个猜想并编程实现部分验证.     

Jordan不等式的拓广及应用

借助于多项式判别系统和M ap le数学软件,建立了Jordan不等式新的拓广形式,由此得到关于Se iffert平均的3个含参双边不等式,并给出杨乐不等式的一个推广。