高分子物理中分子量不等式的一个证明

Proving Molecular Weight Inequality in Polymer Physics

从赫尔德不等式出发,分离散型和连续型两种情况对分子量不等式珚Mn≤珚Mη≤珚Mw≤珚Mz进行严密证明.对于离散型分子量不等式,通过对4种分子量两两作商、变形,利用离散型的赫尔德不等式证明分子量不等式.对于积分表示形式的连续型分子量不等式,利用连续型赫尔德不等式进行类似处理,证明了不等式.

The molecular weight inequality of Mn ≤Mη≤Mw≤Mz, of discrete type and continuous type is rigorously proved by applying H？lder inequality. For discrete type molecular weight inequality, four kinds of molecular weights are chosen and divided for quotients between every two, and deformed before the molecular weight inequality is proved by using discrete Hoelder inequality. And continuous molecular weight in the form of integral representation is proved by using continuous Hoeder inequality in the same manner.