N阶幻体及其初等性质

幻方和幻立方是组合数学中古老问题,它们体现了数字间关系的优美性与和谐性.本文基于幻方和幻立方的理论引入了幻体,给出了其存在性定理的证明,并进一步讨论了幻体的初等性质.     

判别线性不等式组相容性的ALN法

本文将ＡＢＳ算法应用到线性不等式组上．给出了一种判别ＡＸ＜０的相容性的方法．     

The Experimental and Theoretical Research of “Local Resonance“ in Ultrasonic Honing System

In 1982, Professor Fang Guoliang found the “Non full resonance“ phenomenon in a tool system while he use the thin-long tool ultrasonically machining deep-small hole. He called it as “local resonance“. Also this “Non full resonance“ phenomenon was discovered in the ultrasonic drilling and the ultrasonic honing system later. To its mechanism, professor Fang thought that the coupling of long-thin tool bar and driving system is weak, so the tool bar can vibrate independently, but the quantitative relation betwe...     

多个矩阵之和与积的特征值关系问题

给出了3个以上矩阵之和与积的特征值之间的若干等价关系.     

奇异矩阵的Krylov方法的误差分析比较

Krylov方法是求解线性方程组Ax=b,A∈CN×N,b∈CN的一种迭代方法,当A非奇异时,已有很好研究.而当A奇异或接近奇异阵时,在一定的假定条件下,Krylov方法的解与范教最小的最小二乘解A+b之间的差是可以估计出来的.     

应用核磁共振实验实现量子计算的注记

从量子力学的基本原理出发,阐述了利用核磁共振进行量子计算的实验方法,澄清了有关文献中若干容易混淆而又十分重要的概念,并进一步报道CNOT门操作的实验方法和结果.实验结果与理论的预言一致.     

矩阵的相似准直和与群逆

首先引入矩阵的相似准直和的定义,讨论了它和群逆的关系,得到了一些性质和应用。     

Fuzzy－AHP投入产出模型及其在地方电网理论电价研究中的应用

本文提出了应用Fuzzy-AHP编制投入产出表和建立投入产出模型的方法, 并用来研究地方电网理论电价问题, 以某县为例进行了验证, 结果表明方法和模型是合理可行的。     

最小二乘解存在的充分必要条件

本文提出了当观测值的权矩阵为正定或半正定的前提下，其最小二乘解存在的充分必要条件为并以间接平差为例验证了该结论的正确性。     

On the sign of the optimal combining weights under the error-variance minimizing criterion

Building on the well-known measure of the optimal combining weights under the error-variance minimizing criterion, this note has extended the sign-determination rule to the case of combining more than two competing forecasts. The algebraic rule derived provides a quick way to check the sign of each combining weight without directly comparing the correlation and variances of individual forecasting errors.