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Is there a transform which "simplifies" finding of minima or maxima? Or to put the question more generally, what are the "frequency domain" analogues for extrema finding for various transforms, such as the Fourier, Laplace, and Mellin transforms? (Or any others, if a straightforward analogue exists.) I'm looking at a class of non-trivial minimization problems, and am wondering if a transform might help with conceptualizing them, much like the Fourier transform helps with conceptualizing wave behavior with its time domain/frequency domain duality. -- 76.201.158.47 ( talk) 00:37, 19 July 2009 (UTC)
So I find myself wanting to write some ordered n-tuples of the form , except that in place of I have a longer expression, long enough that I don't want to write it twice, and the context in which this appears is such that I can't easily write a separate "where" clause as I usually would (). If I had a similar problem on the right hand side I could solve it easily by writing , but I don't think I've ever seen an analogous notation for the elements of a Cartesian product, even though one ought to exist. just looks silly. Has any prominent source ever defined a notation for this, or, failing that, can anyone suggest something that looks good? I have the full resources of LaTeX at my disposal. -- BenRG ( talk) 11:35, 19 July 2009 (UTC)
I once used (X i : i ∈ B) in a published paper.
The idea was that B was some subset of the index set {1, ..., n). E.g. if B = {2, 4, 9} then
That may not be exactly what you need, since in the "tuples" I was using the order didn't actually matter and since B was simply a set, I couldn't have written
in this notation. But I didn't need that. Maybe you can play with variations on this theme and find one that suits your purpose. I didn't explain the notation; it seemed self-explanatory in the context in which I used it. Michael Hardy ( talk) 14:38, 19 July 2009 (UTC)
I don't understand the question. Could you be looking for the projection map ? 67.117.147.249 ( talk) 23:28, 19 July 2009 (UTC)
Mathematics desk | ||
---|---|---|
< July 18 | << Jun | July | Aug >> | July 20 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Is there a transform which "simplifies" finding of minima or maxima? Or to put the question more generally, what are the "frequency domain" analogues for extrema finding for various transforms, such as the Fourier, Laplace, and Mellin transforms? (Or any others, if a straightforward analogue exists.) I'm looking at a class of non-trivial minimization problems, and am wondering if a transform might help with conceptualizing them, much like the Fourier transform helps with conceptualizing wave behavior with its time domain/frequency domain duality. -- 76.201.158.47 ( talk) 00:37, 19 July 2009 (UTC)
So I find myself wanting to write some ordered n-tuples of the form , except that in place of I have a longer expression, long enough that I don't want to write it twice, and the context in which this appears is such that I can't easily write a separate "where" clause as I usually would (). If I had a similar problem on the right hand side I could solve it easily by writing , but I don't think I've ever seen an analogous notation for the elements of a Cartesian product, even though one ought to exist. just looks silly. Has any prominent source ever defined a notation for this, or, failing that, can anyone suggest something that looks good? I have the full resources of LaTeX at my disposal. -- BenRG ( talk) 11:35, 19 July 2009 (UTC)
I once used (X i : i ∈ B) in a published paper.
The idea was that B was some subset of the index set {1, ..., n). E.g. if B = {2, 4, 9} then
That may not be exactly what you need, since in the "tuples" I was using the order didn't actually matter and since B was simply a set, I couldn't have written
in this notation. But I didn't need that. Maybe you can play with variations on this theme and find one that suits your purpose. I didn't explain the notation; it seemed self-explanatory in the context in which I used it. Michael Hardy ( talk) 14:38, 19 July 2009 (UTC)
I don't understand the question. Could you be looking for the projection map ? 67.117.147.249 ( talk) 23:28, 19 July 2009 (UTC)