Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler charact...Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by a cyclic L∞-algebra L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that the Behrend function depends only on the formal neighborhood of the moduli space.展开更多
Basing on results of Xu and Qin [10], and Guo [12] on cyclotomic elements in K2F for local fields F, we prove that every element in K2Q is a finite or infinite product of cyclotomic elements. Next, we extend this resu...Basing on results of Xu and Qin [10], and Guo [12] on cyclotomic elements in K2F for local fields F, we prove that every element in K2Q is a finite or infinite product of cyclotomic elements. Next, we extend this result to finite extensions of Q satisfying some additional conditions.展开更多
The symmetric dynamical model of a Cournot duopoly based on conjectural variation is established.Local stability of the equilibrium point is analyzed and the invariant sets are given.Then,dynamic behavior is studied b...The symmetric dynamical model of a Cournot duopoly based on conjectural variation is established.Local stability of the equilibrium point is analyzed and the invariant sets are given.Then,dynamic behavior is studied by numerical simulation.With the change of gradient adjustment parameters,the routes to chaos vary.Synchronization occurs along the invariant sets accompanied by the on-off intermittency through the analysis of transverse stability.Coexistence of multiple attractors and structure of basins of attraction being more complex indicate more complicated bifurcation phenomena.展开更多
In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn...In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn（x） is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.展开更多
基金Supported by Simon Foundation Collaboration Grants(Grant No.311837)
文摘Abstract We define the motivic Milnor fiber of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topo- logical Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by a cyclic L∞-algebra L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that the Behrend function depends only on the formal neighborhood of the moduli space.
文摘Basing on results of Xu and Qin [10], and Guo [12] on cyclotomic elements in K2F for local fields F, we prove that every element in K2Q is a finite or infinite product of cyclotomic elements. Next, we extend this result to finite extensions of Q satisfying some additional conditions.
基金National Natural Science Foundation of China(Nos.11962011,61463027)Humanities and Social Sciences from the Ministry of Education of China(No.15YJC820007)。
文摘The symmetric dynamical model of a Cournot duopoly based on conjectural variation is established.Local stability of the equilibrium point is analyzed and the invariant sets are given.Then,dynamic behavior is studied by numerical simulation.With the change of gradient adjustment parameters,the routes to chaos vary.Synchronization occurs along the invariant sets accompanied by the on-off intermittency through the analysis of transverse stability.Coexistence of multiple attractors and structure of basins of attraction being more complex indicate more complicated bifurcation phenomena.
文摘In ＂Elements of small orders in K2（F）＂ （Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.）, the author investigates elements of the form {α, Фn（α）} in the Milnor group K2F of a field F, where Фn（x） is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F.
