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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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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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4 ZHUANG Rong-kun(Dept.of Math.,Huizhou Univ.,Huizhou 516015,China; Dept.of Math.,Zhongshan Univ.,Guangzhou 510275,China);Oscillation comparison theorems of solutions for second order nonlinear elliptic differential equations[J];Applied Mathematics A Journal of Chinese Universities;2005-02
5 Cheng Chonggao (Huanggang Educational Institute, Huanggang,Hubei) Deng Zongqi (Central China Normal University,Wuhan);ON STURM COMPARISON THEOREMS FOR THE DERIVATIVE FUNCTIONS OF SOLUTIONS OF LINEAR SECOND ORDER DIFFERENTIAL EQUATIONS[J];Journal of Central China Normal University(Natural Sciences);1991-03
6 MA Na-rui~1,FU Shou-zhong~(2,3),WEI Guang-sheng~1(1.Department of Mathematics and Information Science,School of Science,Chang′an University,Xi′an 710064,China;2.School of Science,Xi′an Jiaotong University,Xi′an 710049,China;3.Department of Computer Science,Zhaoqing University,Zhaoqing 526061,China);A Class of Inverse Sturm-Liouville Eigenvalue Problems[J];Acta Scientiarum Naturalium Universitatis NeiMongol;2006-05
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
8 LIU Ru-chen(Liaoning Vocational College of Communication,Shenyang 110122,China);Positive Solutions of Singular NonlinearSturmLiouville Problems[J];Transactions of Shenyang Ligong University;2006-02
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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