This article presents a complete proof of Mnëv’s Universality Theorem and and a first complete proof of Mnëv’s Universal Partition Theorem for oriented matroids. The Universality Theorem states that, for every primary semialgebraic set V there is an oriented matroid M, whose realization space is stably equivalent to V . The Universal Partition Theorem states that, for every partition V of IR in...

A Turing degree d bounds a principle P of reverse mathematics if every computable instance of P has a d-computable solution. P admits a universal instance if there exists a computable instance such that every solution bounds P. We prove that the stable version of the ascending descending sequence principle (SADS) as well as the stable version of the thin set theorem for pairs (STS(2)) do not ad...

Abstract This paper proposes a professional English translation corpus based on the binomial theorem coefficients. combines with vector space model to analyze similarity between machine and human in translation. The study results show that both can experience inaccuracies. is more objective accurate. established by this method help us solve problem of terminology research has specific reference...