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метод соместного обращения интегральных преобразований

English translation: inversion of the joint transform (by Cagniard's method)

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18:06 Feb 12, 2005
Russian to English translations [PRO]
Science - Mathematics & Statistics
Russian term or phrase: метод соместного обращения интегральных преобразований
Применяя интегральные преобразования Лапласа и Фурье и метод соместного обращения интегральных преобразований (метод Каньяра), получим аналитическое решение задачи.

Каньяр -- Cagniard
Nik-On/Off
Ukraine
Local time: 04:41
English translation:inversion of the joint transform (by Cagniard's method)
Explanation:
На Amazon.com продается книжка Transform Methods for Solving Partial Differential Equations by Dean G. Duffy, вот названия некоторых глав:

...
The Solution of Partial Differential Equations by Laplace Transforms
The Solution of Partial Differential Equations by Fourier Transforms
The Joint Transform Method
The Solution of Partial Differential Equations Using the Joint Transform Method
Inversion of the Joint Transform by Cagniard's Method
The Modification of Cagniard's Method by De Hoop
...
http://www.amazon.com/exec/obidos/tg/detail/-/0849373743/102...
Selected response from:

Natalie
Poland
Local time: 03:41
Grading comment
В общем, после долгих раздумий и поисков я решил остановиться на этом варианте.
Всем огромное спасибо!
4 KudoZ points were awarded for this answer

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Summary of answers provided
4joint converse of integral transforms
Dimman
4inversion of the joint transform (by Cagniard's method)
Natalie
2 +1Cagniard-de Hoop method; method of inverse [integral] transformation
Kirill Semenov
3double inverse transform of the integral
David Knowles
3[Cagniard de Hoop] combined integral transform inversion technique
olganet
3the joint inverse of the integral transformations (the Cagniard method),Dorene Cornwell


Discussion entries: 9





  

Answers


2 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5
метод соместного обращения интегральных преобразований
the joint inverse of the integral transformations (the Cagniard method),


Explanation:
My calculus is rusty and this example is posted just to give something to check on--Look for English sites.

Applying the LaPlace and Fourier integral transformations [transforms is probably fine shorthand] and the joint inverse of the integral transformations (the Cagniard method), we get an analytic solution of this problem


This is definitely going to be an Inverse, not a converse

Dorene Cornwell
Local time: 18:41
Works in field
Native speaker of: English
PRO pts in category: 15
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3 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5
метод соместного обращения интегральных преобразований
[Cagniard de Hoop] combined integral transform inversion technique


Explanation:
Cagniard-de Hoop method of Laplace inversion. ...
www.ndt.net/abstract/wcndt96/data/223.htm

PDF] Lacunae of a Two-Dimensional Piezoelectric Characteristic ...
File Format: PDF/Adobe Acrobat - View as HTML
... This was achieved by using an integral transform inversion technique

The inversion of the Laplace transform is performed using the Cagniard-de Hoop method (Cagniard L., “Reflection and refraction of progressive seismicwaves”, 1962, McGraw-Hill, New York. Fig. 3.
wwwsoc.nii.ac.jp/jsac/analsci/special/079.pdf

Most of the works on transient motion employed integral transform
methods and the Cagniard de Hoop inversion technique. ...
www.journals.royalsoc.ac.uk/index/JVCX7U68QJ98JG7J.pdf


... of problems can be obtained by integral transform methods in ... technique (Noble, 1958)
and the Cagniard-de Hoop method (de Hoop, 1958) of Laplace inversion. ...
www.kluweronline.com/article.asp?PIPS=319734&PDF=1

olganet
Local time: 21:41
Native speaker of: Native in RussianRussian
PRO pts in category: 8
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3 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
метод соместного обращения интегральных преобразований
inversion of the joint transform (by Cagniard's method)


Explanation:
На Amazon.com продается книжка Transform Methods for Solving Partial Differential Equations by Dean G. Duffy, вот названия некоторых глав:

...
The Solution of Partial Differential Equations by Laplace Transforms
The Solution of Partial Differential Equations by Fourier Transforms
The Joint Transform Method
The Solution of Partial Differential Equations Using the Joint Transform Method
Inversion of the Joint Transform by Cagniard's Method
The Modification of Cagniard's Method by De Hoop
...
http://www.amazon.com/exec/obidos/tg/detail/-/0849373743/102...


Natalie
Poland
Local time: 03:41
Native speaker of: Native in RussianRussian
PRO pts in category: 44
Grading comment
В общем, после долгих раздумий и поисков я решил остановиться на этом варианте.
Всем огромное спасибо!
Login to enter a peer comment (or grade)

2 mins   confidence: Answerer confidence 4/5Answerer confidence 4/5
метод соместного обращения интегральных преобразований
joint converse of integral transforms


Explanation:
imho

--------------------------------------------------
Note added at 3 hrs 44 mins (2005-02-12 21:51:29 GMT)
--------------------------------------------------

согласен, inverse здесь лучше. Inversion мне кажется сюда не подходящим

Dimman
Russian Federation
Local time: 04:41
Native speaker of: Native in RussianRussian
PRO pts in category: 4

Peer comments on this answer (and responses from the answerer)
neutral  Jack Slep: I'm more inclined to think "joint inversion."
40 mins
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1 day3 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5
метод соместного обращения интегральных преобразований
double inverse transform of the integral


Explanation:
This is the closest I can come up with, but it may not be right!

... directly from the boundary-value problem in the integral transform domain into a ... The double inverse transform is performed based on Cagniard's method and ...

... recently, another approach of the inverse problem of ... is usually done using a double integral transform expressed as a ... It is inverted using the Cagniard de Hoop ...



    Reference: http://www.ingentaconnect.com/content/rsl/rpa/2000/00000456/...
    Reference: http://www.kluweronline.com/article.asp?PIPS=420652&PDF=1
David Knowles
Local time: 02:41
Works in field
Native speaker of: Native in EnglishEnglish
PRO pts in category: 27
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2 hrs   confidence: Answerer confidence 2/5Answerer confidence 2/5 peer agreement (net): +1
метод соместного обращения интегральных преобразований
Cagniard-de Hoop method; method of inverse [integral] transformation


Explanation:
Судя по ссылкам, обычно ничего не уточняется:

Cagniard-de Hoop method,

в лучшем случае:

Cagniard-de Hoop method of inverse transformation.

Опускают даже слово integral, а этой "совместности" ну нигде в упор не видно.

4pPA3 Space-time domain acoustic wave fields in media with ...
... type method consists of the transform domain Neumann series solution or WKBJ iterative solution, and the Cagniard--De Hoop method of inverse transformation. ...
www.auditory.org/asamtgs/asa94mit/4pPA/4pPA3.html - 2k - Cached - Similar pages

Publications
... Univ. of Munchen (Germany) , 3-5 October 1996 MCM Bakker "Avoiding superposition integrals using the Cagniard-De Hoop integral transformation method", Paper ...
www.mechanics.citg.tudelft.nl/~bakker_m/reports.html - 6k


Linear Elastic Waves
... The famous Cagniard-de Hoop method is used to invert the integral transforms in calculating the transient, out-of-plane radiation excited by a line source at ...
www.iop.org/EJ/abstract/0959-7174/12/2/701

IngentaConnect Article: Exact transient full-field analys... ...
... transient solutions for dynamic shear stresses, displacement and stress-intensity factor are obtained by using the Cagniard-de Hoop method of Laplace inversion ...
www.ingentaconnect.com/content/ rsl/rpa/2005/00000461/00002054/art00010

Ну и так далее. Нет совместного.

--------------------------------------------------
Note added at 1 day 20 hrs 9 mins (2005-02-14 14:16:41 GMT)
--------------------------------------------------

Чтоб тебя вконец доконать и запутать -- вот еще чего накопалось: \"multiple inverse transforms\":

[PDF] Electromagnetic field scattering by a triangular aperture +
File Format: PDF/Adobe Acrobat
... for the transformed initial and boundary conditions, and multiple inverse transforms may be ... Here, Bx (z = +) is the multidimensional Laplace transform of the ...
ao.osa.org/ViewMedia.cfm?id=22838&seq=0

The MathFinance Newsletter #92
... Mathematical issues at stake include: multiple inverse Fourier transform techniques, issues of smooth and continuous pasting in free boundary and optimal ...
www.mathfinancenews.com/MFW_090204.html

[PDF] Cover Page -- contact information
File Format: PDF/Adobe Acrobat - View as HTML
... they can be scalars, vectors, continuous or discrete functions, or Laplace or Z transform domain functions. ... we suggest constructing a multiple inverse function ...
www.bgu.ac.il/~akarniel/pub/KarnielMeirInbar_WC2000.pdf

[PDF] arXiv:nucl-th/9409001 v1 2 Sep 1994
File Format: PDF/Adobe Acrobat - View as HTML
... Furthermore, the multiple inverse Laplace transform used to determine the nuclear density of states from the Grand-Canonical partition ...
arxiv.org/pdf/nucl-th/9409001

Kirill Semenov
Ukraine
Local time: 04:41
Works in field
Native speaker of: Native in RussianRussian
PRO pts in category: 125

Peer comments on this answer (and responses from the answerer)
agree  Alya: чаще всего просто "Cagniard-de Hoop method" без уточнений / сдается мне, что "совместное обращение..." -- это нововведение автора переводимого текста. В рунете главным образом упоминается "просто" метод Каньяра - де Хоопа; это выражение не используется
32 mins
  -> ну, тут уже дело принципа и хочется понять, что такое "совместное" :) + Я раскопал один сайт, где "совместное обращение" (с другой математикой, правда, связан), но там слово "совместное" закавычено было.
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