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## Abstract

An index system for evaluating academic papers is constructed and verified based on the empirical analysis of papers that has gained the 6th Chinese Academy of Social Sciences Award for Outstanding Achievements. Some new index, such as paper discipline impact factor, discipline average cited rate per paper and discipline average downloaded rate per paper have been put forward in this paper. The empirical research results show that the ranking of papers calculated by this evaluation index system is in conformity with the awards determined by peer review in general, but still needs to be verified and improved in practice.

We prove that

for all integers n ≥ 1 and ɵ ≤ 8 ≤ π. This result refines inequalities due to Jackson (1911) and Turán (1938).