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On resolution to Wu's conjecture on Cauchy function's exterior singularities
Wu TY; Wu, TY (reprint author), CALTECH, Pasadena, CA 91125 USA
Source PublicationActa Mechanica Sinica
2011
Volume27Issue:3Pages:309-317
ISSN0567-7718
AbstractThis is a series of studies on Wu's conjecture and on its resolution to be presented herein. Both are devoted to expound all the comprehensive properties of Cauchy's function f(z) (z = x + iy) and its integral J[f(z)] equivalent to (2 pi i)(-1) closed integral(C)f(t)(t - z)(-1)dt taken along the unit circle as contour C, inside which (the open domain D (+)) f(z) is regular but has singularities distributed in open domain D (-) outside C. Resolution is given to the inverse problem that the singularities of f(z) can be determined in analytical form in terms of the values f(t) of f(z) numerically prescribed on C (|t| = 1), as so enunciated by Wu's conjecture. The case of a single singularity is solved using complex algebra and analysis to acquire the solution structure for a standard reference. Multiple singularities are resolved by reducing them to a single one by elimination in principle, for which purpose a general asymptotic method is developed here for resolution to the conjecture by induction, and essential singularities are treated with employing the generalized Hilbert transforms. These new methods are applicable to relevant problems in mathematics, engineering and technology in analogy with resolving the inverse problem presented here.
KeywordCauchy Function Singularity Distribution Wu's Conjecture Resolution By Induction Perturbation-series Waves
Subject AreaEngineering ; Mechanics
DOI10.1007/s10409-011-0465-5
URL查看原文
Indexed BySCI ; EI
Language英语
WOS IDWOS:000292036800001
WOS KeywordPERTURBATION-SERIES ; WAVES
WOS Research AreaEngineering ; Mechanics
WOS SubjectEngineering, Mechanical ; Mechanics
Classification二类
Citation statistics
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/44927
Collection非线性力学国家重点实验室
Corresponding AuthorWu, TY (reprint author), CALTECH, Pasadena, CA 91125 USA
Recommended Citation
GB/T 7714
Wu TY,Wu, TY . On resolution to Wu's conjecture on Cauchy function's exterior singularities[J]. Acta Mechanica Sinica,2011,27(3):309-317.
APA Wu TY,&Wu, TY .(2011).On resolution to Wu's conjecture on Cauchy function's exterior singularities.Acta Mechanica Sinica,27(3),309-317.
MLA Wu TY,et al."On resolution to Wu's conjecture on Cauchy function's exterior singularities".Acta Mechanica Sinica 27.3(2011):309-317.
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