In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a pol...In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.展开更多
It was proved that all continuous functions are topologically conjugate to their continuous iterative roots in monotonic cases. An interesting problem reads: Does the same conclusion hold in non-monotonic cases?We giv...It was proved that all continuous functions are topologically conjugate to their continuous iterative roots in monotonic cases. An interesting problem reads: Does the same conclusion hold in non-monotonic cases?We give a negative answer to the problem by presenting a necessary condition for the topological conjugacy,which helps us construct counter examples. We also give a sufficient condition as well as a method of constructing the topological conjugacy.展开更多
文摘In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.
基金supported by National Natural Science Foundation of China(Grant Nos.11301226 and 11301572)Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ13A010017)Chongqing Normal University Project(Grant No.13XLZ04)
文摘It was proved that all continuous functions are topologically conjugate to their continuous iterative roots in monotonic cases. An interesting problem reads: Does the same conclusion hold in non-monotonic cases?We give a negative answer to the problem by presenting a necessary condition for the topological conjugacy,which helps us construct counter examples. We also give a sufficient condition as well as a method of constructing the topological conjugacy.
