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Mechanical decision for a class of integral inequalities
Yang Lu1,3; Yu WenSheng1,2; Yuan RuYi2
2010-09-01
发表期刊SCIENCE CHINA-INFORMATION SCIENCES
卷号53期号:9页码:1800-1815
文章类型Article
摘要A class of integral inequalities is transformed into homogeneous symmetric polynomial inequalities beyond Tarski model, where the number of elements of the polynomial, say n, is also a variable and the coefficients are functions of n. This is closely associated with some open problems formulated recently by Yang et al. Using Timofte's dimension-decreasing method for symmetric polynomial inequalities, combined with the inequality-proving package BOTTEMA and a program of implementing the method known as successive difference substitution, we provide a procedure for deciding the nonnegativity of the corresponding polynomial inequality such that the original integral inequality is mechanically decidable; otherwise, a counterexample will be given. The effectiveness of the algorithm is illustrated by some more examples.
关键词Integral Inequality Symmetric Polynomial Inequality Timofte's Dimension-decreasing Method Successive Difference Substitution Mechanical Decision Inequality-proving Package Bottema
WOS标题词Science & Technology ; Technology
关键词[WOS]CYLINDRICAL ALGEBRAIC DECOMPOSITION ; SYMMETRIC POLYNOMIAL FUNCTIONS ; POSITIVITY ; ALGORITHM
收录类别SCI
语种英语
WOS研究方向Computer Science
WOS类目Computer Science, Information Systems
WOS记录号WOS:000281150500009
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文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/9944
专题综合信息系统研究中心
作者单位1.E China Normal Univ, Shanghai Key Lab Trustworthy Comp, Inst Software Engn, Shanghai 200062, Peoples R China
2.Chinese Acad Sci, Key Lab Complex Syst & Intelligence Sci, Inst Automat, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Lab Automated Reasoning & Programming, Chengdu Inst Comp Applicat, Chengdu 610041, Peoples R China
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Yang Lu,Yu WenSheng,Yuan RuYi. Mechanical decision for a class of integral inequalities[J]. SCIENCE CHINA-INFORMATION SCIENCES,2010,53(9):1800-1815.
APA Yang Lu,Yu WenSheng,&Yuan RuYi.(2010).Mechanical decision for a class of integral inequalities.SCIENCE CHINA-INFORMATION SCIENCES,53(9),1800-1815.
MLA Yang Lu,et al."Mechanical decision for a class of integral inequalities".SCIENCE CHINA-INFORMATION SCIENCES 53.9(2010):1800-1815.
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