This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hype...This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.展开更多
Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. I...Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals ?nitely is de?ned. The containment relationships of function germs still satisfy ?nite k-determinacy under suffciently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented.展开更多
文摘This paper mainly gives a sufficient and necessary condition for an order of hyperplanes of a graphic arrangement being supersolvable. In addition, we give the relations between the set of supersolvable orders of hyperplanes and the set of quadratic orders of hyperplanes for a supersolvable arrangement.
基金Supported by the National Natural Science Foundation of China(11671070,11501051)NSF of Heilongjiang Province of China(QC2016008)the Project of Science and Technology of Jilin Provincial Education Department(JJKH2090547KJ)
文摘Mather gave the necessary and suffcient conditions for the ?nite determinacy smooth function germs with no more than codimension 4. The theorem is very effective on determining low codimension smooth function germs. In this paper, the concept of right equivalent for smooth function germs ring generated by two ideals ?nitely is de?ned. The containment relationships of function germs still satisfy ?nite k-determinacy under suffciently small disturbance which are discussed in orbit tangent spaces. Furthermore, the methods in judging the right equivalency of Arnold function family with codimension 5 are presented.
