吉林师范大学学报(自然科学版)
吉林師範大學學報(自然科學版)
길림사범대학학보(자연과학판)
JILIN NORMAL UNIVERSITY JOURNAL(NATURAL SCIENCE EDITION)
2014年
4期
6-10,21
,共6页
1-参数勒让德开折%多重勒让德开折%生成族%多重函数芽%余维估计
1-參數勒讓德開摺%多重勒讓德開摺%生成族%多重函數芽%餘維估計
1-삼수륵양덕개절%다중륵양덕개절%생성족%다중함수아%여유고계
one-parameter Legendrian unfolding%multi-Legendrian unfolding%multi-germ%estimate of codimen-sions
本文给出1-参数勒让德开折与多重勒让德开折的定义并讨论它们的生成族的构造,证得多重函数芽的K-余维估计定理,该结果是对克莱罗型微分方程与完全可积一阶偏微分方程几何奇点进行半局部分类的基础。
本文給齣1-參數勒讓德開摺與多重勒讓德開摺的定義併討論它們的生成族的構造,證得多重函數芽的K-餘維估計定理,該結果是對剋萊囉型微分方程與完全可積一階偏微分方程幾何奇點進行半跼部分類的基礎。
본문급출1-삼수륵양덕개절여다중륵양덕개절적정의병토론타문적생성족적구조,증득다중함수아적K-여유고계정리,해결과시대극래라형미분방정여완전가적일계편미분방정궤하기점진행반국부분류적기출。
The notions of one-parameter Legendrian unfolding and multi-Legendrian unfolding are given,and the structures of their generating families are studied. The theorem of estimate of codimensions for multi-germs under K-equivalence is proved. The results are the basis of semi-local classification of geometric singulatities for the differential equations of Clairaut type and completely integrable holonomic systems of first-order differential equations.