Abstract
Function P-sets which is composed of function internal P-set and function outer P-set, is a function set pair and has dynamic and law characteristics. Based on function P-sets, this paper presents the concepts such as data law, - data law, -data law and bi-data law, and then -data law theorem, -data law theorem, bi-data law band theorem, data law recovery theorem, bi-data law identification theorem and law identification criterion are proposed. By using these results, teaching effect analysis is obtained and applications on bilingual education are given. Function P-sets is a new method in the research of dynamic data system.
Highlights
In 2008, Refs.(SHI Kai-quan. 2008)(SHI Kai-quan. 2009) originated P-sets ( X F, X F ) by introducing dynamic characteristic into general set X .Refs. (SHI Kai-quan Shi, Li Zhang. 2009)(YU Xiu-qing. 2010) (YU Xiu-qing. 2010) (SHI Kai-quan&Tingcheng Chang. 2005) (SHI Kai-quan &LI Xiu-hong, 2010) discussed application in many fields
P-set QF and function outer P-set QF together, they have dynamic and law characteristic. It is to say: when functions in function set Q are transferred out from Q, Q becomes function internal P-set QF, on the other hand,when functions out of Q are transferred into Q, Q becomes function outer P-set QF, function P-sets has dynamic characteristic
Theorem 4.2 If ( p(x)iF, p(x)iF ) and ( p(x)Fj, p(x)Fj ) are bi-data laws generated by function P-sets (QiF,QiF )
Summary
In 2008, Refs.(SHI Kai-quan. 2008)(SHI Kai-quan. 2009) originated P-sets ( X F , X F ) by introducing dynamic characteristic into general set X .Refs. (SHI Kai-quan Shi, Li Zhang. 2009)(YU Xiu-qing. 2010) (YU Xiu-qing. 2010) (SHI Kai-quan&Tingcheng Chang. 2005) (SHI Kai-quan &LI Xiu-hong, 2010) discussed application in many fields. 2005) (SHI Kai-quan &LI Xiu-hong, 2010) discussed application in many fields. P-set QF and function outer P-set QF together, they have dynamic and law characteristic. Based on above content and features of function P-sets, the concepts of data law, F -data law, F -data law and bi-data law are proposed, the bi-data law band theorem, recovery theorem and identification theorem are given, and identification criterion of data law are put forward Using these results, this paper gives teaching effect analysis modal (TEAM) and discusses application of TEAM on bilingual education in university. 3. Data law and its characteristics Definition 1 Given finite function set . Proof Assumed that Q {u1, u2 , , um} is the given finite function set and yi {yi,, yi,2 , , yi,n 1} is the data set of ui. Theorem 3.2 ( F -data law theorem) If p(x) is data law generated by function set Q , there exists an F. Its proof is similar to the theorem 3.7, so omitted
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