Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Re: Are elliptic functions orthogonal?
Posted:
Jan 20, 2013 11:50 PM
|
|
On Jan 20, 10:04 pm, h...@work.pk (Sycho) wrote:
> This just in to the alt.2600 news room. On Sun, 20 Jan 2013 17:22:01
> -0800 (PST) it was announced to all in a public briefing, Vaughan
> Anderson <vaughan.andur...@gmail.com> made the following declaration
> and shocked the world when the following was announced:
>
>
>
>
>
>
>
>
>
> >On Jan 18, 10:28 pm, h...@work.pk (Sycho) wrote:
> >> This just in to the alt.2600 news room. On Fri, 18 Jan 2013 14:58:51
> >> -0800 (PST) it was announced to all in a public briefing, Jeremy
> >> Sample <vaughan.andur...@gmail.com> made the following declaration and
> >> shocked the world when the following was announced:
>
> >> >Can an arbitrary function be uniquely expanded in a series solution of
> >> >elliptic integrals?
>
> >> >That is to say, can you apply an algorithm like the Fourier analysis,
> >> >(or Bessel, Legendre, etc.) to an arbitrary function, using elliptic
> >> >integrals instead of trigonometrics as the basis function?
>
> >> >I wonder if this could be a useful technique for reducing nonlinear
> >> >data, in systems where certain, simple cases are known to have
> >> >elliptic solutions.
>
> >> >Your scholarly input would be greatly appreciated, even if it means
> >> >referring me to journal articles, as long as they're by specific
> >> >authors.
>
> >> >TIA.
>
> >> They can be whatever you want them to be so long as you pay them
> >> enough "hush" money.
>
> >> Cookies also help.
>
> >What is it with you and cookies? The holidays are over, and it's time
> >to start on your New Year's resolution to lose weight. ;-)
>
> The dark side *always* has cookies. It's an unwritten law.
>
> >I believe that elliptic integrals (or functions), in general, are not
> >orthogonal, and therefore not suitable for use in series expansions.
> >But since they are not a discretely indexed function like Trigs,
> >Bessels, Legendres, etc. it may be possible to *find* values for the
> >elliptic control parameter that make them orthogonal, which would
> >impose a discrete index onto the functions.
>
> Everybody's got to believe in something. I, OTOH believe I'll have
> another beer.
>
> >There would be a continuum of families of these discretely indexed
> >elliptics. Also, the orthogonalization would have to be performed in
> >two dimensions, since elliptics are doubly periodic. If I'm lucky,
> >and this works, it would be a newly discovered kind of elliptic, and
> >it could advance the solution to a highly nonlinear, non-crypto
> >problem I'm working on. It might be enough to turn into a
> >dissertation, to finally wrap up the ol' PhD.
>
> >I gotta find the time to crunch the numbers. Wish me luck.
>
> Don't crunch numbers. Crunch cookies because they're tastier.
>
> HAIL FLUFFY!!1!!
> --
> If monsters ever sat around the campfire telling ghost stories, do you
> think it would start like this.. "It was a bright and sunny day..."
Exactly what do you mean by "cookie"?
|
|
|
|
