Applications of degree estimate for subalgebras

Let $K$ be a field of positive characteristic and $K$ be the free algebra of rank two over $K$. Based on the degree estimate done by Y.-C. Li and J.-T. Yu, we extend the results of S.J. Gong and J.T. Yu's results: (1) An element $p(x,y)\in K$ is a test element if and only if $p(x,y)$ does not belong to any proper retract of $K$; (2) Every endomorphism preserving the automorphic orbit of a nonconstant element of $K$ is an automorphism; (3) If there exists some injective endomorphism $\phi$ of $K$ such that $\phi(p(x,y))=x$ where $p(x,y)\in K$, then $p(x,y)$ is a coordinate. And we reprove that all the automorphisms of $K$ are tame. Moreover, we also give counterexamples for two conjectures established by Leonid Makar-Limanov, V. Drensky and J.-T. Yu in the positive characteristic case.Comment: 12 page

Multimedia Chinese Web Search Engines: A Survey

The objective of this paper is to explore the state of multimedia search functionality on major general and dedicated Web search engines in Chinese language. The authors studied: a) how many Chinese Web search engines presently make use of multimedia searching, and b) the type of multimedia search functionality available. Specifically, the following were examined: a) multimedia features - features allowing multimedia search; and b) extent of personalization - the extent to which a search engine Web site allows users to control multimedia search. Overall, Chinese Web search engines offer limited multimedia searching functionality. The significance of the study is based on two factors: a) little research has been conducted on Chinese Web search engines, and b) the instrument used in the study and the results obtained by this research could help users, Web designers, and Web search engine developers. By large, general Web search engines support more multimedia features than specialized one