| 1. | Th 3 . 2 nontrivial projections are ci operators
非平凡的投影算子也是“算子 |
| 2. | Is not disturbed by appending a " good " nontrivial multiplicative factor to
以“好的”而非平凡的乘积因子， 1 -级相关函数 |
| 3. | Data mining , also known as knowledge discovery in database , is finding information in very large database for decision maker to make decision
数据挖掘又称数据库中知识发现，是从大量数据中用非平凡的方法发现有用的知识。 |
| 4. | It is for this reason that data mining , to discover useful knowledge from amount of data by uncommon methods , has developed very quickly
数据挖掘? ?用非平凡的方法从大量数据中发现有用的知识，正是应此要求而迅速发展起来的一门科学。 |
| 5. | Theorem 2 . 4 let g be a non - abelian inner - finite group , each non - trivial proper subgroup of g is prime order cyclic group if and only if g is a simple group ; each proper subgroup of g is nilpotent ; and each non - trivial subgroup of g is self - normalizer
4设g是非阿贝尔的内有限群，则g的每个非平凡真子群都是素数阶循环群的充分必要条件是g是单群， g的每个真子群幂零且g的每个非平凡的真子群自正规化定理2 |
| 6. | Web mining is the traditional data mining technology used in web , attempting to find implicative , unknown , and non - trivial schema which has potential application from the innumerable web file assembly and the data information which can be gotten when the user browse web
Web挖掘是传统数据挖掘技术在web环境下的应用，试图从大量的web文档集合和用户浏览web的数据信息中发现蕴涵的、未知的、有潜在应用价值的、非平凡的模式。 |
| 7. | Let f be a biquadratic polynomial , then ( 1 ) the julia set of f is connected if and only if the orbits of all critical pionts are bounded ; ( 2 ) the julia set of f is totally disconnected if and only if every connected component of the filled julia set of f containing critical points is not periodic under iterations : ( 3 ) if f does not satisfy the conditions ( 1 ) and ( 2 ) , then the julia set of f has infinitely many non - trivial connected components , where a component is trivial if it contains only one point
A集是完全不连通的当且仅当f的任何临界声、不属于填充julm集的周期分支内。你当j的临界卢、不满足条件小， ” j时， f的几ha集有可数个非平凡的连通分支，这里，一个分支是平凡的，如果它仅由一个卢、组成。 。 |
| 8. | In chapter 3 , we will estimate the first eigenvalue of laplacian from below on manifolds with a little negative curvature . in chapter 4 , we will prove the existence of bounded nontrivial harmonic functions on some classes of complete manifolds which will generalize the results of s . y . cheng ' s
在第三章，我们将给出具有小负曲率的流形上laplace算子的第一特征值的下界估计；第四章，我们会给出一类完备非紧流形上非平凡的有界调和函数的存在性，推广了s . y . cheng的结果。 |
| 9. | Data mining is an important research subject in the field of information technology . it means a process of nontrivial extraction of implicit , previously unknown and potentially useful information from data in databases or datawarehouses . it involves such subject areas as database , artificial intelligence , machine learning and statistics . classification analysis is an important data mining problem
数据挖掘( datamining )是信息处理技术研究领域的一项重要课题。它是指从大型数据库或数据仓库中提取隐含的、未知的、非平凡的以及有潜在应用价值的信息或模式的过程。 |
| 10. | The article stated here will give some remarks to the following equation in two cases : for the case > 0 , the equation expresses the eigenvalue of the laplacian while for the case = 0 , it is the existence of nontriv - ial bounded harmonic functions on complete noncompact manifolds
本文中我们主要分两种情况来讨论了关于laplace算子的方程： u + u = 0 ， r ~ + { 0 }对应于0 ，是riemann流形上laplace算子的特征值问题，而对应于= 0则是完备非紧流形上非平凡的有界调和函数的存在性问题。 |
