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Re: [Phys-l] cosmology question



On 5/25/2011 1:53 PM, David Bowman wrote:

[bw]
x*(dx/dt)2/H_02 = [Omega]_m + (1 - [Omega]_m - [Omega]_lambda)*x + [Omega]_lambda*x3

Alpha offers this in response:x(t) = (zeta|-> integral_1^zeta xi/(_lambda xi^3 omega-_lambda xi
omega-_m xi omega+_m omega+xi) dxi)^(-1)(c_1+(3 t)/4)

Quite! :-)

Brian W
Who or what is Alpha,& how does his/her/its response follow from what I wrote? I cannot parse the response. Please translate it into something readable.

For some reason Brian stripped the ^ symbols from my version of the Friedmann equation, which ought to have been copied above as:

x*(dx/dt)^2/H_0^2 = [Omega]_m + (1 - [Omega]_m - [Omega]_lambda)*x + [Omega]_lambda*x^3 .

Brian's comment suggests to me that maybe some readers may not understand my notation as far as reducing mathematical equations into an ASCII form.
So here is a dictionary of my notation:

* = multiply by.

/ = divide by.

+ = add to.

- = subtract from (when a binary operation) or negate (when a unary operation).

^ = raised to the power of (i.e. what immediately follows is a right side superscript on what immediately preceeds the symbol).

_ = lower right susbscript (what immediately follows is a right side subscript on what immediately preceeds the symbol).

[greek letter] = the corresponding symbol for the greek letter named in [...], (e.g. [Omega] = capital letter omega, [pi] = lower case letter pi).

dx/dt = the derivative of x with respect to t.

(...) = parentheses indicating a pending operation is to be performed on the whole evaluated value of of whatever expression ... is inside them.

^ and _ symbols take precedence over * and / symbols which, themselves, take precedence over + and - symbols.

BTW, when raising a subscripted quantity to a power the whole quantity is raised to the power, not just the subscript. So in the above Friedmann equation H_0^2 = (H_0)^2 = the square of the Hubble parameter, H_0, rather than an H with a subscript which is the square of zero.

So could Brian please translate Alpha's response into a notation compatible with the above scheme?

Thanks.

David Bowman
I think I may have offended you with my unseemly lunchtime haste, David.
Moreover, I likely pasted your Friedmann equation into the Alpha computational engine
in incomplete form. So this afternoon, I cut and pasted the equation again,
and took a screen shot of the Alpha effort.
This is how you could access this server:
http://www.wolframalpha.com/

About Alpha: I seem to recall that when a list-member inquired about the fourier transforms of
some inverse transcendental expressions last year, it was Alpha who was the sole responder.

Though it is certainly the case that Alpha can produce results from materials
where I am speechless, it too, has its naivete, and here it tries out on your equation:

_http://s880.photobucket.com/albums/ac6/betwys/DavidBowmans%20Universe/_

*http://tinyurl.com/3ztue8g
*

It seems to be making heavy weather of the [Omega]_lambda notation, and appears to be
assuming some constructs that were unintended. But how much less did I understand!
It would be pleasant to be able to follow the notes of the most mathematically adept,
but this is unlikely - and I must content myself with crutches of this kind.

Sincerely


Brian Whatcott