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Mechanical decision for a class of integral inequalities
Yang Lu1,3; Yu WenSheng1,2; Yuan RuYi2
Source PublicationSCIENCE CHINA-INFORMATION SCIENCES
2010-09-01
Volume53Issue:9Pages:1800-1815
SubtypeArticle
AbstractA 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.
KeywordIntegral Inequality Symmetric Polynomial Inequality Timofte's Dimension-decreasing Method Successive Difference Substitution Mechanical Decision Inequality-proving Package Bottema
WOS HeadingsScience & Technology ; Technology
WOS KeywordCYLINDRICAL ALGEBRAIC DECOMPOSITION ; SYMMETRIC POLYNOMIAL FUNCTIONS ; POSITIVITY ; ALGORITHM
Indexed BySCI
Language英语
WOS Research AreaComputer Science
WOS SubjectComputer Science, Information Systems
WOS IDWOS:000281150500009
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Document Type期刊论文
Identifierhttp://ir.ia.ac.cn/handle/173211/9944
Collection综合信息系统研究中心
Affiliation1.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
Recommended Citation
GB/T 7714
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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