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From: achenyo at on 13 Aug 2010 14:36
Hi,

I have the following two sets of equations:

integral of ((1/(lamda1+(lamda2*g0)))-(KNB/g1))*dF0(go)dF1(g1) = 1.................(1)

and

integral of ((g0/(lamda1+(lamda2*g0)))-(KNB*(g0/g1)))*dF0(go)dF1(g1) = GQ.......(2)

every other variable here is known except for amda1 and lamda2, how can I solve for lamda1 and lamda2.

Any suggestion will help.
From: Walter Roberson on 13 Aug 2010 15:08
achenyo at wrote:
> Hi,
> I have the following two sets of equations:
>
> integral of ((1/(lamda1+(lamda2*g0)))-(KNB/g1))*dF0(go)dF1(g1) =
> 1.................(1)
>
> and
>
> integral of ((g0/(lamda1+(lamda2*g0)))-(KNB*(g0/g1)))*dF0(go)dF1(g1) =
> GQ.......(2)
>
> every other variable here is known except for amda1 and lamda2, how can
> I solve for lamda1 and lamda2.

Your equations are probably not valid. The indefinite integral of any equation
does not equal an exact value: it equals a value plus an arbitrary constant.
You are thus trying to solve two equations in four unknowns.

Does your dF0(go) represent the differentiation of a known function F0, with
respect to unspecified variable, and then evaluating the differential at the
point g0 ? (note go vs g0 for one thing)

Does dF0(go)dF1(g1) represent the multiplication of dF0(go) with dF1(g1) ? You
were careful to use * to indicate multiplication everywhere else, so we are
left to wonder whether you wished to denote something different.

Which variables are the equations being integrated with respect to? If the
answer is either go or g1 then the integral cannot be treated as if dF0(go) or
dF1(g1) are just constants with known values and funny names.


*If* dF0(g0) and dF1(g1) are constants for the purpose of integration
(implying integration over lamda1, lamda2 or KNB) and if multiplication was
intended, and if the arbitrary constants are added in, and if the integration
just _happens_ to be over lamda1 in both cases, then the solution is:

lamda1 = g1 * (g0 - dF0(go) * dF1(g1) * Gq - dF0(go) * dF1(g1) * C2 + g0 * C1)
/ KNB / g0 / dF0(go) / dF1(g1) / (dF0(go) * dF1(g1) - 1)

lamda2 = -
(-dF0(g0)^2 * dF1(g1)^2 * KNB * g0 * exp((-Gq - C2 + g0 + g0 * C1) / g0 /
(dF0(g0) * dF1(g1) - 1)) - dF0(g0) * dF1(g1) * Gq * g1 - dF0(g0) * dF1(g1) *
C2 * g1 + KNB * g0 * dF0(g0) * dF1(g1) * exp((-Gq - C2 + g0 + g0 * C1) / g0 /
(dF0(g0) * dF1(g1) - 1)) + g0 * g1 + g0 * C1 * g1) / KNB / g0^2 / dF0(g0) /
dF1(g1) / (dF0(g0) * dF1(g1) - 1)

Notice the leading "-" on the value for lamda2 .
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