On the generalized Cauchy function and new Conjecture on its exterior singularities
文献类型：期刊论文
| 作者 | Wu Theodore Yaotsu |
| 刊名 | Acta Mechanica Sinica
 |
| 出版日期 | 2011 |
| 卷号 | 27期号:2页码:135-151 |
| 通讯作者邮箱 | tywu@caltech.edu |
| 关键词 | Uniform Continuity Of Cauchy'S Function Uniform Convergence Of Cauchy'S Integral Formula Generalized Hilbert-Type Integral Transforms Functional Properties And Singularity Distributions Solitary 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 article studies on Cauchy's function f(z) and its integral, (2 pi i)J[f(z)] equivalent to closed integral(C)f(t)dt/(t - z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D(+) bounded by C and the open domain D(-) outside C. (1) With f(z) assumed to be C(n) (n < infinity-times continuously differentiable) for all z is an element of D(+) and in a neighborhood of C, f (z) and its derivatives f((n))(z) are proved uniformly continuous in the closed domain <(D(+))over bar> = [D(+) + C]. (2) Cauchy's integral formulas and their derivatives for all z is an element of D(+) (or for all z is an element of D(-)) are proved to converge uniformly in (D(+)) over bar (or in (D(-)) over bar = [D(-) + C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f(z) and J[f(z)]) are shown extended to hold for the complement function F(z), defined to be C(n)for all z is an element of D(-) and about C. (4) The uniform convergence theorems for f(z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four generalized Hilbert-type integral transforms are proved. (5) Further, the singularity distribution of f(z) in D(-) is elucidated by considering the direct problem exemplified with several typical singularities prescribed in D(-). (6) A comparative study is made between generalized integral formulas and Plemelj's formulas on their differing basic properties. (7) Physical significances of these formulas are illustrated with applications to nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f(z) in domain D(-), based on the continuous numerical value of f(z)for all z is an element of (D(+)) over bar = [D(+) + C], is presented for resolution as a conjecture. |
| 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] | SOLITARY WAVES |
| 收录类别 | SCI ; EI |
| 原文出处 | http://dx.doi.org/10.1007/s10409-011-0446-8 |
| 语种 | 英语 |
| WOS记录号 | WOS:000292036300001 |
| 公开日期 | 2012-04-01 |
| 源URL | [http://dspace.imech.ac.cn/handle/311007/44992]  |
| 专题 | 力学研究所_环境力学重点实验室(2009-2011) |
| 推荐引用方式 GB/T 7714 | Wu Theodore Yaotsu. On the generalized Cauchy function and new Conjecture on its exterior singularities[J]. Acta Mechanica Sinica,2011,27(2):135-151. |
| APA | Wu Theodore Yaotsu.(2011).On the generalized Cauchy function and new Conjecture on its exterior singularities.Acta Mechanica Sinica,27(2),135-151. |
| MLA | Wu Theodore Yaotsu."On the generalized Cauchy function and new Conjecture on its exterior singularities".Acta Mechanica Sinica 27.2(2011):135-151. |
入库方式： OAI收割
来源：力学研究所
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