On resolution to Wu's conjecture on Cauchy function's exterior singularities
文献类型：期刊论文
| 作者 | Wu TY |
| 刊名 | Acta Mechanica Sinica
 |
| 出版日期 | 2011 |
| 卷号 | 27期号:3页码:309-317 |
| 通讯作者邮箱 | tywu@caltech.edu |
| 关键词 | Cauchy Function Singularity Distribution Wu'S Conjecture Resolution By Induction Perturbation-Series Waves |
| ISSN号 | 0567-7718 |
| 产权排序 | [Wu, Theodore Yaotsu] CALTECH, Pasadena, CA 91125 USA; [Wu, Theodore Yaotsu] Chinese Acad Sci, Inst Mech, Beijing 100864, Peoples R China |
| 通讯作者 | Wu, TY (reprint author), CALTECH, Pasadena, CA 91125 USA |
| 合作状况 | 国际 |
| 中文摘要 | This 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. |
| 学科主题 | Engineering; Mechanics |
| 分类号 | 二类 |
| 类目[WOS] | Engineering, Mechanical ; Mechanics |
| 研究领域[WOS] | Engineering ; Mechanics |
| 关键词[WOS] | PERTURBATION-SERIES ; WAVES |
| 收录类别 | SCI ; EI |
| 原文出处 | http://dx.doi.org/10.1007/s10409-011-0465-5 |
| 语种 | 英语 |
| WOS记录号 | WOS:000292036800001 |
| 公开日期 | 2012-04-01 |
| 源URL | [http://dspace.imech.ac.cn/handle/311007/44927]  |
| 专题 | 力学研究所_非线性力学国家重点实验室 |
| 推荐引用方式 GB/T 7714 | 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.(2011).On resolution to Wu's conjecture on Cauchy function's exterior singularities.Acta Mechanica Sinica,27(3),309-317. |
| MLA | Wu TY."On resolution to Wu's conjecture on Cauchy function's exterior singularities".Acta Mechanica Sinica 27.3(2011):309-317. |
入库方式： OAI收割
来源：力学研究所
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