1
$\begingroup$

I came across this expression in the documentation for some software:

$\displaystyle\sum\limits_{j=1}^c\alpha_{i*(j)k}q_j=Q_k$

Here, $\alpha$ is the element of a matrix with the rather curious index "$i*(j)k$", which the documentation describes as being a mapping function from the elements of one matrix to another. I have never seen this notation before in my life, specifically the use of the multiplication operator and the parentheses. I am familiar with Einstein notation for matricies, but this does not seem to be related to that. It is possible that this is just a typo in the documentation, but in case anyone can make sense of it, please help me understand! Thanks.

$\endgroup$
  • $\begingroup$ A further perplexity of that definition is the meaning of "$i$" in there. Is there context for that? $\endgroup$ – Semiclassical Sep 25 '14 at 15:56
  • $\begingroup$ The software is for analyzing chemical reactions; "$i$" in this case is the index of a chemical element that appears in the reaction. For example, $i=1$ is carbon, $i=2$ is hydrogen, etc. $\endgroup$ – Carlton Sep 25 '14 at 16:03
  • $\begingroup$ Gotcha. Best I can guess is that they intend it as $\alpha_{i*(j),k}$ i.e. $\alpha$ as an array. But that still leaves the $i*(j)$ mysterious. $\endgroup$ – Semiclassical Sep 25 '14 at 16:13
  • $\begingroup$ Yes, I forgot to mention that $\alpha$ is a 2D matrix/array, so it definitely needs a comma in there somewhere to denote the two indicies. I think you're correct in that there's a missing comma. $\endgroup$ – Carlton Sep 25 '14 at 16:19
  • $\begingroup$ I'm guessing the star is there in order to visually separate $a_i$, the array for a particular chemical element, from the indices $j$ and $k$? But this still doesn't explain the parentheses on $(j)$, so who knows... $\endgroup$ – alexis Sep 25 '14 at 16:29
1
$\begingroup$

As far as I can tell, this obscure notation was invented by the authors of the paper. In short, there are two vectors $I$ and $J$, and by definition $J$ is a subset of $I$. Therefore, any element $J_j$ has a corresponding element $I_i$, and the mapping function between these two elements is denoted by "$i*(j)$". In practice, this is used to say that when the index $j$ is used (such as in the summation in my original post), we can instead map it to a corresponding index $i$ and pull the value of interest from $I$ instead of $J$.

The paper in which I found this is publically available if anyone cares to read it. It is technical report number AD/A-002 791 by Stanford Research Institute, from March 1974. The title is "Tiger Computer Program Documentation". A Google search for the title should give you a link to the report as hosted on www.dtic.mil. The equation of interest is on page I-B-4, second full paragraph.

Thanks to all who helped.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.