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In my thesis, I want to explain that my experiment was set up in such a way that the sum of the two concentrations $~x~$ and $~y~$ is always constant, $$ x + y = \text{const.} $$

Is there a simple and concise term for this? I'm thinking of something like isothermal, which describes an area of equal temperature in chemistry, but in my case the sum of two different concentrations is always equal.

I'm asking here on Mathematics Stack Exchange because I believe that the term is likely a frequently used mathematical term. I seem to remember that there are different definitions of distances, with one of them being $~d=|x+y|~$ instead of $~d=\sqrt{x^2+y^2}~$, so maybe there is a term to describe this as an equidistant curve in relation to the former definition?

nmasanta
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PoorYorick
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    sum of concentrations is conserved; stay on the same contour line of $x+y$ – J. W. Tanner Jul 07 '19 at 13:53
  • $|x+y|$ isn't a norm in $R^2$, that's wrong. – Jakobian Jul 07 '19 at 14:11
  • You could say the two variables have a negative linear correlation. – Rai Jul 07 '19 at 14:17
  • @Jakobian, I just looked it up, what I was thinking of is the $L^p$ norm with $p=1$, which is also called rectilinear distance and is the distance used in taxicab geometry. Euclidean geometry uses the $L^p$ norm with $p=2$. You're probably right that it isn't a norm in $R^2$, but I never specified that. ;) – PoorYorick Jul 07 '19 at 14:55
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    @Alfredo, I thought about using that, but it does not specify that the sum is constant. $y = -ax$ would also be negatively linearly correlated, but $x - ax \neq \text{const.}$ – PoorYorick Jul 07 '19 at 14:58

2 Answers2

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In science, when a quantity remains constant, like the sum of concentrations in your example, we say it is conserved.

You could also say the sum of concentrations $x+y$ stays on the same contour line throughout the experiment.

That's all I can think of about this.

Good luck with your thesis!

J. W. Tanner
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  • +1 for the answer. I think another way to name this property would be invariance. The sum $x+y$ is invariant for the experiment. A third way would be to say that the sum $x+y$ is constrained to be a constant. – MachineLearner Jul 08 '19 at 04:43
  • Thanks for the recognition. I think your ideas are good too, @MachineLearner – J. W. Tanner Jul 08 '19 at 04:51
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I would describe the two concentrations as complementary. It doesn't precisely specify the situation, so you will still have to display/explain the explicit equation that you've shown to us, but it will highlight the relationship. (Complementary does have a precise definition when applied to angles; it means two angles that add up to 90 degrees. I think using it in your case is a pretty obvious generalization.)

JonathanZ
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