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《Mathematics in Practice and Theory》 2007-01
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A Note on Sturm Theorem

XIE Lie-jun(Faculty of Science,Ningbo University,Ningbo Zhejiang 315211,China)  
Classical Sturm theorem is used to tell the number of distinct roots of polynomials in arbitrary interval.Yet it fails to give more information such as multiplicities of roots.We define the generalized Sturm sequence,and a necessary and sufficient condition for all the roots of polynomials of any degree in given interval have even or odd multiplicity is presented.Also,we discuss the problem of the non-negative and non-positivity of polynomials as application.
【Fund】: 宁波大学重点科研基金(XK200453)
【CateGory Index】: O156
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【Co-references】
Chinese Journal Full-text Database 10 Hits
1 LIU Ru-chen (Department of preparatory Courses,Liaoning College of Communication,Senyang 110122,China);Positive Solutions of Singular Nonlinear Sturm-Liouville Problems[J];Journal of Changchun Teachers Coliege;2005-12
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7 CHENG Chuan-rui(Luohe Vocational and Technical College, Luohe 462000,China);Feature Value of Sturm-Liouville[J];Journal of Nanyang Teachers College;2005-03
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9 WEI Guang-sheng, XU Zong-ben (College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi, 7W06S, P. R. China; Research Center for Applied Mathematics and Institute for Information and System Science, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P. R. China);Left-definite Boundary Conditions of Regular Sturm-Liouville Problems[J];Advances in Mathematics;2006-02
10 WEI Guang-sheng (1.College of Mathematics and Information Science,Shaanxi Normal University,Xi'an,Shaanxi,710062,P.R.China;2.Research Center for Applied Mathematics and Institute for Information and System Science,Xi'an Jiaotong University,Xi'an,Shaanxi,710049,P.R.China);Left-definite Spaces of Regular Sturm-Liouville Problems[J];Advances in Mathematics;2006-04
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