"зацепленная" система уравнений

English translation: concatenated/coupled system of equations

GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
Russian term or phrase:"зацепленная" система уравнений
English translation:concatenated/coupled system of equations
Entered by: Dimman

17:46 Jan 16, 2003
Russian to English translations [PRO]
Science - Mathematics & Statistics / math
Russian term or phrase: "зацепленная" система уравнений
Сложность решения системы (1) заключается в том, что она является "зацепленной" относительно неизвестных функций Wm, Xm, т.е. все неизвестные функции входят в каждое из m+1 уравнений данной системы.

и дальше по тексту

После исключения из (1) функции Wm получим независимую систему уравнений относительно Xm. Таким образом достигается "расцепление" системы (1) на известную классическую относительно Wкл и систему относительно исеомой функции Xmi.
Nik-On/Off
Ukraine
Local time: 19:06
concatenated/coupled
Explanation:
В принципе оба термина применяются. Я бы выбрал второй - тогда расцепление (не могу согласиться с Верой - именно РасЦепление) будет uncoupling
Selected response from:

Dimman
Russian Federation
Local time: 19:06
Grading comment
Спасибо всем, особенно Вере
4 KudoZ points were awarded for this answer



Summary of answers provided
3 +2linked set/system of equations or set/system of linked equations
Jack slep
5concatenated/coupled
Dimman
4Coupled
Vera Fluhr (X)
4system of interdependent equations
alla dunbar
4"Anchored" system of equations
Vera Fluhr (X)
1constrained system of equations/system of equations with binding constraints (a wild guess)
Montefiore


Discussion entries: 3





  

Answers


14 mins   confidence: Answerer confidence 1/5Answerer confidence 1/5
constrained system of equations/system of equations with binding constraints (a wild guess)


Explanation:

A completely wild guess:)

Constrained Nonlinear Systems

Mathematically, a Constrained Nonlinear System (CNS) model looks like:


find x

F(x) = 0
subject to L < x < U
G(x) < b

where F and x are of equal dimension and the variables x are continuous. The (possibly empty) constraints L < x < U are not intended to be binding at the
solution, but instead are included to constrain the solution to a particular domain or to avoid regions where F(x) is undefined. The (possibly empty) constraints
G(x) < b are intended for the same purpose and are silently converted to equations with bounded slacks.

The CNS model is a generalization of the square system of equations F(x) = 0. There are a number of advantages to using the CNS model type (compared to
solving as an NLP with a dummy objective, say), including:

A check by GAMS that the model is really square,
solution/model diagnostics by the solver (e.g. singular at solution, locally unique solution), and
potential improvement in solution times, by taking better advantage of the model properties.

For information on CNS solvers that can be used through GAMS see the Solver/Model type Matrix.

Montefiore
United States
Local time: 09:06
Native speaker of: Russian
PRO pts in category: 4
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53 mins   confidence: Answerer confidence 3/5Answerer confidence 3/5 peer agreement (net): +2
linked set/system of equations or set/system of linked equations


Explanation:
An offering.
Here are some examples. I presume in your case they are later "unlinked."

System of Equations: An Introduction
... Basically, the problem of finding some unknowns linked to each others
via equations is called a system of equations. For example,. and. ...
www.sosmath.com/matrix/system0/system0.html - 8k - Jan. 14, 2003 - Cached - Similar pages

Periodic behaviour and Differential Equations
A system of linked differential equations. ... This type of linked set of differential
equations is called a system of coupled differential equations. ...
www.ugrad.math.ubc.ca/coursedoc/ math100/notes/trig/dif2.html

PDF]1998: MULTI-FACTOR ANALYSIS OF FIRM-LEVEL PERFORMANCE THROUGH ...
... The model is a linked set of equations that attempt to capture how changes in one-factor
influences the level of another factor, and ultimately bottom-line ...
www.informs-cs.org/wsc98papers/207.PDF


    see above
Jack slep
Local time: 12:06
Works in field
Native speaker of: English
PRO pts in category: 35

Peer comments on this answer (and responses from the answerer)
agree  Yuri Geifman
54 mins
  -> Thanks, Yuri!

agree  Andrew Vdovin
17 hrs
  -> Vdovin, thanks!
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11 hrs   confidence: Answerer confidence 5/5
concatenated/coupled


Explanation:
В принципе оба термина применяются. Я бы выбрал второй - тогда расцепление (не могу согласиться с Верой - именно РасЦепление) будет uncoupling

Dimman
Russian Federation
Local time: 19:06
Native speaker of: Native in RussianRussian
PRO pts in category: 4
Grading comment
Спасибо всем, особенно Вере
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16 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
"Anchored" system of equations


Explanation:
Дмитрий, я еще вчера послала ответ, но из-за каких-то фокусов сети он не прошел. Во всяком случае, я его не вижу.
К сожалению, потерялись и все примеры.
А сейчас мне некогда их снова искать.
Так что - либо поверьте мне на слово, либо подождите до сегодняшнего вечера.

Как надоели эти неполадки сетевые, кто б знал!

Мое предположение насчет расщепления - действительно ошибочное. Я его стерла.

Vera Fluhr (X)
Local time: 18:06
Native speaker of: Native in RussianRussian, Native in FrenchFrench
PRO pts in category: 53
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20 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
system of interdependent equations


Explanation:
A lot of references confirming the term:

The model is more of a system of interdependent equations that are solved. Econometric models are usually characterized ...
http://www.mgmtguru.com/mgt499/TN6_3.htm

Given a larger system of equations, you must guard against deriving interdependent equations, as this does not lead to a solution. ...
http://kr.cs.ait.ac.th/~radok/math/mat1/mat129.htm

...estimates parameters in an interdependent system of linear regression equations. TSCSREG - time series cross section regression. ...
http://www.bham.ac.uk/is/stats/sas.htm

... The vector of innovations is modeled as an interdependent system of linear equations such that , where is normalized to have ones on the leading diagonal and ...
http://www.quantlet.de/scripts/bre/html/brehtmlnode16.html

The solution of the total interdependent system of equations is obtained iter- atively...
http://www.usm.uni-muenchen.de/people/adi/Download/Pauldrach...

... The equations describing the system are highly interdependent, and the magnetic forces felt by the pendulum at 5 milliseconds after release are highly ...
http://www.physlink.com/Education/AskExperts/ae437.cfm



--------------------------------------------------
Note added at 2003-01-17 13:50:45 (GMT)
--------------------------------------------------

Or:
INTERDEPENDENT SYSTEM OF EQUATIONS (the same meaning)

alla dunbar
Local time: 17:06
Native speaker of: Native in RussianRussian
PRO pts in category: 19
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1 day 22 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
Coupled


Explanation:
Я посмотрела сейчас в русских текстах - какие системы там называются зацепленными?
Таких систем я не нашла. Но нашла кучу "систем зацепленных/зацепляющихся уравнений". И такие уравнения действительно называются coupled, как пишет выше коллега bpz2001. Я привожу ниже все нужные ссылки, и Вы даже увидите, что системы из этих уравнений иногда тоже называют coupled systems.
Но у меня большое сомнение, что в Вашем контексте именно это имеется в виду. Во-первых, контекст не тот, а во-вторых, Вы сами говорите, что это слово стоит в кавычках, намекая тем самым на ненормативность употребления термина.
Итак, я Вам даю здесь все про термин Coupled, но сама продолжаю поиски тех ссылок про слово anchored, которые потерялись.

Как Вы видите, бывают даже цепочки (chains) из зацепленных уравнений:

Зацепленные (связанные) уравнения === Coupled equations
http://www.srcc.msu.su/num_anal/eng_math/redict/8.htm

. Цепочки зацепляющихся уравнений для функций Грина.
http://irc.spbu.ru/Deanery/Archive/1999_SN/progr/0232l5.htm

... S - kl (0) + U i a i a i a i a j (t);S - kl (0) (6) The appearance of higher order Green functions leads to an infinite chain of coupled equations for +- ijkl ...
http://arxiv.org/pdf/cond-mat/0010215

Электронно-конформационное взаимодействие. Система зацепляющихся уравнений типа Фоккера-Планка с добавочными членами, …..
http://www.moldyn.ru/bioinzhenerija/doc/lec.htm

... cases, approaches based on semiclassical one-body equations (Fokker-Plank, Boltzmann, Boltzmann ... n D (t, v) obey the following system of coupled equations [6]: n ...
...... is here studied with a Green-function method ... a differential operator in the original coupled system. ...
http://arxiv.org/pdf/nucl-th/9603027

... of an EM wave of frequency is given by where h is Plank's constant or 6.63X10 -34 Js. Finally there are the two coupled, differential equations that provide ...
http://users.wpi.edu/~ender3rd/paper.pdf

... The coupled transport equations, flux/force relations that relate ... The mechanically induced relative flow is determined by Green's function solution. ...
http://www-eaps.mit.edu/erl/research/theses/abstracts/Haarts...

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Note added at 2003-01-18 16:15:03 (GMT)
--------------------------------------------------

Хотя - не знаю - вот нашлась одна \"зацепляющаяся система\", и вроде контекст почти как у Вас:

Эту зацепляющуюся систему уравнений можно преобразовать в систему всего двух точных интегральных уравнений, называемую обобщенным уравнением Орнштейна ...
http://bsfp.media-security.ru/bsff2/bb05an6.htm

Прочитайте сами начало этой статьи, Дмитрий !
М.б. и правда - это то, что нужно?
Тогда приз - bpz2001.

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Note added at 2003-01-18 16:47:21 (GMT)
--------------------------------------------------

Я выяснила, что так называемые обобщенные уравнения Орнштейна-Цернике - это тоже \"зацепленная\" (coupled) система, но у нее есть специальное название : Replica system, ROZ equations. А \"зацеплением\", похоже, называют просто парную корреляцию (нет времени вчитываться как следует).

…….the total pair correlation functions h ij (r) which satisfy a set of coupled integral equations, the so-called replica Ornstein-Zernike (ROZ) equations [7]. As ...
http://arxiv.org/pdf/cond-mat/9504023

... system and then take the s ! 0 limit to obtain the integral equations for the original system, called the replica Ornstein Zernike (ROZ) equations. ...
http://tph.tuwien.ac.at/~paschinger/di7.ps

In this way Given and Stell [1-2] recently proposed a set of coupled integral equations, the so-called replica Ornstein-Zernike (ROZ) equations, relating the ...
htpp://www.icmp.lviv.ua/journal/zbirnyk.18/009/art09.ps.gz


    Reference: http://arxiv.org/pdf/nucl-th/9603027
    Reference: http://www.srcc.msu.su/num_anal/eng_math/redict/8.htm
Vera Fluhr (X)
Local time: 18:06
Native speaker of: Native in RussianRussian, Native in FrenchFrench
PRO pts in category: 53
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