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à partie d’une droite

English translation: [from/with/using/based on] a subset of a straight line

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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
French term or phrase:à partie d’une droite
English translation:[from/with/using/based on] a subset of a straight line
Entered by: Claire Chapman
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16:00 Nov 10, 2007
French to English translations [PRO]
Tech/Engineering - Energy / Power Generation / Hydropower plants
French term or phrase: à partie d’une droite
Bonjour,

Voici une phrase d'un document sur l'énergie hydroélectrique.

"Les équations et les coefficients de corrélation indiqués sont issus d’une interpolation à partie d’une droite (méthode des moindres carrés)."

Je voudrais juste de l'assitance sur "à partie d’une droite:
Je n'en ai aucune idée.

Je vous remercie par avance.
Bon weekend.

Richard
Richard Levy
United States
Local time: 04:22
[from/with/using/based on] a subset of a straight line
Explanation:
Well, in the domain of mathematics, "une partie" is a subset, and "une droite" is a straight line. Note, that in certain contexts, it might sound better in English to say "the elements of a subset" such as when the sentence gives reference to the specific members of the subset, as opposed to an overall reference to just the subset.

Equations de droites définies à partie de points
http://pilat.free.fr/pilat/exos/flash/ana2.swf

Pour tracer une **droite à partie** de son équation, il suffit de connaître deux points. Le plus simple est de prendre l'intersection avec les axes, c'est-à-dire de considérer successivement x = 0 et y = 0 (sauf si la droite est parallèle à un axe, auquel cas le tracer est trivial). On peut aussi prendre l'ordonnée à l'origine et un point « éloigné » (c'est-à-dire au bord de la figure tracée sur le papier, par exemple considérer x = 10 si l'on va jusqu'à 10), ou encore deux points éloignés (un à chaque bord de la figure) ; en effet, plus les points sont éloignés, plus le tracé de la droite est précis.
http://www.rinnovamento.it/g/ge/geometrie_analytique.html

2eme question on pose z=x+iy je dois trouver la **partie réelle et la partie imaginaire** de Z=(z-2+i)/(z+2i) et vérifier que Re(Z)=(x^2+y^2-2x+3y+2)/(x^2+(y+2)^2)
j'ai essayé plusieurs techniques de développement mais je n'arrive pas à isoler i pour obtenir una forma a + ib ( a partie réelle , b partie imaginaire)
http://carremaths.yellis.net/phpBB2/viewtopic.php?p=40160

Wikipédia – Sous-ensemble
En mathématiques, un ensemble A est un sous-ensemble ou **une partie** d’un ensemble B, ou encore B est sur-ensemble de A, si tout élément du sous-ensemble A est aussi élément du sur-ensemble B. Il peut par contre y avoir des éléments de B qui ne sont pas éléments de A (voir le diagramme à droite). La relation entre A et B s'appelle l'inclusion….
http://fr.wikipedia.org/wiki/Sous-ensemble

Wikipedia - SubSet
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide. The relationship of one set being a subset of another is called inclusion or containment….
http://en.wikipedia.org/wiki/Subset

To generate 2D sections using the elements of each subset. The number of sections to be generated depends on several factors - the number of the initial ones, the complexity of the 3D objects and the needed reconstruction and visualization accuracy.
http://jan.ucc.nau.edu/nms35/interpolation_approach.htm

--------------------------------------------------
Note added at 1 day3 hrs (2007-11-11 19:18:31 GMT)
--------------------------------------------------

Without seeing the document, I don’t know what they are doing with it. However, with interpolation, one takes the elements (the known data points) and uses a mathematical formula to connect the elements (data points). Let’s say, you have sampled a sound wave so many times a second. You put the data that you know on the graphs and connect them with a line. That (linear interpolation) is the most basic form of interpolation. However, as you look at the graph, you can see that the lines don’t reflect how the sound waves really look because true sound waves form curved lines and not a series of straight lines that are connected. More advanced forms of interpolation try to reshape the sound wave by using a mathematical formula to calculate what the true shape of the sound wave would have been from the known elements in order to create a more accurate representation of the sound wave.

As I said, linear interpolation is the simplest form. The Wikipedia pages that I gave you before go into detail for more advanced methods. Examples of usage in hydroelectric plants are shown below:

Baker River Hydroelectric Project
1. Skagit River flow at each survey site estimated using middle Skagit flow routing model.
2. Measured backwater sloughs represent a subset of the 16 backwater sloughs identified during field surveys.
3. Backwater slough length at each site measured during field surveys; backwater slough width measured at series of 10 to 20 transects.
4. Solid lines represent interpolation between measured points; dashed lines represent extrapolation beyond measured data.
http://www.pse.com/energyEnvironment/hydroPDFs/baker/studies...

DRAFTAn Approximate Method to Assess the Peaking Capability of the NW Hydroelectric System
The second section of this file is a linear interpolation table for full gate flow versus HK.
Projects that have the HK entry 0 are assumed to have constant full gate flow as shown.
http://www.nwcouncil.org/energy/resource/meetings/2005_10/pe...

(3) Minimum runoff-duration curves for various frequencies, as shown in Figure 12-3 are obtained by plotting points from the low-flow frequency curves on logarithmic paper. The flow rates are converted to volumes (millions of cubic meters in this example). The logarithmic scales simply permit more accurate interpolation between durations represented by the frequency curves.
http://www.usace.army.mil/publications/eng-manuals/em1110-2-...

If I haven't made it clear, or if you need more help, please let me know :-)

--------------------------------------------------
Note added at 1 day4 hrs (2007-11-11 20:15:32 GMT) Post-grading
--------------------------------------------------

You're welcome, Richard! And Thank YOU! :-)
Selected response from:

Claire Chapman
Local time: 04:22
Grading comment
Thanks so much for your help on this quite difficult topic.
4 KudoZ points were awarded for this answer

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Summary of answers provided
3 +1[from/with/using/based on] a subset of a straight line
Claire Chapman
3section of a straight linexxxmistahara


Discussion entries: 8





  

Answers


44 mins   confidence: Answerer confidence 3/5Answerer confidence 3/5
section of a straight line


Explanation:
interpolation à la partie d’une droite

xxxmistahara
Local time: 11:22
Native speaker of: Native in RomanianRomanian

Peer comments on this answer (and responses from the answerer)
neutral  Claire Chapman: A subset of a line is a section of the line but there does not appear to be a mistake in the grammar of the original sentence. See the references that I posted.
35 mins
  -> that's it, thanks
Login to enter a peer comment (or grade)

1 hr   confidence: Answerer confidence 3/5Answerer confidence 3/5 peer agreement (net): +1
[from/with/using/based on] a subset of a straight line


Explanation:
Well, in the domain of mathematics, "une partie" is a subset, and "une droite" is a straight line. Note, that in certain contexts, it might sound better in English to say "the elements of a subset" such as when the sentence gives reference to the specific members of the subset, as opposed to an overall reference to just the subset.

Equations de droites définies à partie de points
http://pilat.free.fr/pilat/exos/flash/ana2.swf

Pour tracer une **droite à partie** de son équation, il suffit de connaître deux points. Le plus simple est de prendre l'intersection avec les axes, c'est-à-dire de considérer successivement x = 0 et y = 0 (sauf si la droite est parallèle à un axe, auquel cas le tracer est trivial). On peut aussi prendre l'ordonnée à l'origine et un point « éloigné » (c'est-à-dire au bord de la figure tracée sur le papier, par exemple considérer x = 10 si l'on va jusqu'à 10), ou encore deux points éloignés (un à chaque bord de la figure) ; en effet, plus les points sont éloignés, plus le tracé de la droite est précis.
http://www.rinnovamento.it/g/ge/geometrie_analytique.html

2eme question on pose z=x+iy je dois trouver la **partie réelle et la partie imaginaire** de Z=(z-2+i)/(z+2i) et vérifier que Re(Z)=(x^2+y^2-2x+3y+2)/(x^2+(y+2)^2)
j'ai essayé plusieurs techniques de développement mais je n'arrive pas à isoler i pour obtenir una forma a + ib ( a partie réelle , b partie imaginaire)
http://carremaths.yellis.net/phpBB2/viewtopic.php?p=40160

Wikipédia – Sous-ensemble
En mathématiques, un ensemble A est un sous-ensemble ou **une partie** d’un ensemble B, ou encore B est sur-ensemble de A, si tout élément du sous-ensemble A est aussi élément du sur-ensemble B. Il peut par contre y avoir des éléments de B qui ne sont pas éléments de A (voir le diagramme à droite). La relation entre A et B s'appelle l'inclusion….
http://fr.wikipedia.org/wiki/Sous-ensemble

Wikipedia - SubSet
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide. The relationship of one set being a subset of another is called inclusion or containment….
http://en.wikipedia.org/wiki/Subset

To generate 2D sections using the elements of each subset. The number of sections to be generated depends on several factors - the number of the initial ones, the complexity of the 3D objects and the needed reconstruction and visualization accuracy.
http://jan.ucc.nau.edu/nms35/interpolation_approach.htm

--------------------------------------------------
Note added at 1 day3 hrs (2007-11-11 19:18:31 GMT)
--------------------------------------------------

Without seeing the document, I don’t know what they are doing with it. However, with interpolation, one takes the elements (the known data points) and uses a mathematical formula to connect the elements (data points). Let’s say, you have sampled a sound wave so many times a second. You put the data that you know on the graphs and connect them with a line. That (linear interpolation) is the most basic form of interpolation. However, as you look at the graph, you can see that the lines don’t reflect how the sound waves really look because true sound waves form curved lines and not a series of straight lines that are connected. More advanced forms of interpolation try to reshape the sound wave by using a mathematical formula to calculate what the true shape of the sound wave would have been from the known elements in order to create a more accurate representation of the sound wave.

As I said, linear interpolation is the simplest form. The Wikipedia pages that I gave you before go into detail for more advanced methods. Examples of usage in hydroelectric plants are shown below:

Baker River Hydroelectric Project
1. Skagit River flow at each survey site estimated using middle Skagit flow routing model.
2. Measured backwater sloughs represent a subset of the 16 backwater sloughs identified during field surveys.
3. Backwater slough length at each site measured during field surveys; backwater slough width measured at series of 10 to 20 transects.
4. Solid lines represent interpolation between measured points; dashed lines represent extrapolation beyond measured data.
http://www.pse.com/energyEnvironment/hydroPDFs/baker/studies...

DRAFTAn Approximate Method to Assess the Peaking Capability of the NW Hydroelectric System
The second section of this file is a linear interpolation table for full gate flow versus HK.
Projects that have the HK entry 0 are assumed to have constant full gate flow as shown.
http://www.nwcouncil.org/energy/resource/meetings/2005_10/pe...

(3) Minimum runoff-duration curves for various frequencies, as shown in Figure 12-3 are obtained by plotting points from the low-flow frequency curves on logarithmic paper. The flow rates are converted to volumes (millions of cubic meters in this example). The logarithmic scales simply permit more accurate interpolation between durations represented by the frequency curves.
http://www.usace.army.mil/publications/eng-manuals/em1110-2-...

If I haven't made it clear, or if you need more help, please let me know :-)

--------------------------------------------------
Note added at 1 day4 hrs (2007-11-11 20:15:32 GMT) Post-grading
--------------------------------------------------

You're welcome, Richard! And Thank YOU! :-)

Claire Chapman
Local time: 04:22
Native speaker of: Native in EnglishEnglish
PRO pts in category: 4
Grading comment
Thanks so much for your help on this quite difficult topic.

Peer comments on this answer (and responses from the answerer)
agree  xxxmistahara
6 mins
  -> Thank you, mista :-)
Login to enter a peer comment (or grade)




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Changes made by editors
Nov 11, 2007 - Changes made by Claire Chapman:
Created KOG entryKudoZ term » KOG term


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