1) difference substitution
差分代换
1.
For the difficulties and problems during proving the homogeneous polynomials inequalities by the difference substitution,we give a solution way and comment on the Bottema software and the difference substitution of general polynomial.
针对差分代换证明齐次多项式不等式存在的困难和问题,提出了一种解决方法,并对Bottem a软件和一般多项式差分代换DS(F)进行了评价。
2.
The main results are the following:with the proper hypotheses,if the problems of inequalities involving symmetric homogeneous functions can be settled via the theory of majorizations or the trivial non-negative of difference substitution,then these problems also can be settled by quasimonotone function method.
获得的主要结果是:在适当的假设下,如果涉及齐次对称函数的不等式问题可用优超理论或差分代换平凡非负方法处理,那么这类问题也能用拟单调函数方法处理。
2) difference replacement
差分代换
1.
Study of multi-nomial semi-positive definiteness in real number field by the means of difference replacement;
用差分代换研究实数域中多项式的半正定性
2.
A difference replacement demonstration of the geometric inequalities of acute triangle and the corresponding application program
锐角三角形几何不等式的差分代换证法及应用程序
3) SDS
差分代换
1.
Combining RFD with SDS,the program can automatically prove an extensive class of geometric inequalities involving radicals.
将RFD算法和差分代换方法相结合,给出了一大类具有相当难度的几何不等式的机器证明。
4) successive difference substitution
逐次差分代换
1.
Recently a method based on successive difference substitution has been developed by Yang to prove positive semi-definition of polynomials,and its corresponding program tsds has been realized in MAPLE.
近年来由杨路等提出了一种利用逐次差分代换以证明多项式非负性的方法,并在MAPLE平台编写了相应程序。
6) set sequence of difference substitution
差分代换集序列
补充资料：代换法则
代换法则
substitution rule
代换法则[s一山stituti叨n此:，10及eT阴oB阴np姗加]，亦称代换规则 逻辑一数学演算中的推导法则(derjvation rLde)之一代换法则有各种不同形式.例如，在命题演算(proposit，0，1:LI ealculus)中，代换法则是用一个公式代换命题变兀在命题公式中的所有的出现.在谓词演算戈Pfe山cate calculus)中，它是:a)用一个公式代换谓词公式中的谓词变元(predieatev::riable)(这里需要遵守一系列关于个体变元出现的限制以避免变元碰撞(二1llable collision)，即出现在公式中的自由变元通过代换变为约束变元);b)项的代换法则是用一个项代换渭同公式中相应类型的个体变元的自由出现(这里也必须避兔变兀碰撞).
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条