Can anybody help me to solve the following first order conditions for . All these variables should be independent of one another, i.e., the right hand side of the solution should contain only constants . [There are 4 equations and only 4 unknowns and looks the solution is possible but I am not reaching to the destination].

I appreciate if any of Sajha friends provide me some hints to solve this!

Oh.. it did not appear.. I am trying again...

Hey guys,
Can you folks help me solve the following problems , if you may....Thanks in advance...

1.a function, f is defined on [a,b], and α>0, f is continuous at Xo E [a,b]. Prove f is α-continuous at Xo.

2. f is defined on [a,b], and α>0, Dα={x E[a,b] such that f is not α-continuous at X}
Prove Dα is compact.

I know these problems should not be that hard...but my brain is real dumb these days...

bibas, its been a long while..i haven't done those stuf...so don't remember offhand....but general...your solutions should be easy. If you have four unknows...say w,x,y,z....all u got to do is find three equations....in terms of w,x,y...by equating all of them to z and solve using simulataneous equation. lets say u have sth like
7w+3x+4y-z=0.........(i)
6w+2x+10y-2z=0.......(ii)
..........................
..........................
you can take like (i) and (ii), so that u will have sth like,
7w+3x+4y=3w+x+5y
i.e.4w+2x-y=0...............(a)....Similarly u can find other three solutions...by taking two other equations out of the four....and solve the three unknowns using simulataneous equation. Hope that helps.

himalayan....i think tha answer was directed towards General right?

My question comes from topology...

Bibas. What is an a-cont. function? is your function real valued?

Raja,
Actually thats alpha and not a. Yea, its all on R.

The answer for General is straight forward. 4 equations, 4 variable; a piece of cake.
Do as tiger has shown by eliminating one by one e.g reduce the equations to 3 variables frm first 2 equations. Then go for third and finally for the fourth. At this step, u will be remained with one variable and one equations.
If you dont like to go this way, use MATHCAD or MATLAB, thise softwares give you the answer in less than a min. Or use Texas instrument, it also gives you the answer.
But you already have a vague question. You have stated following equations, but where are the equations???

then what is an alpha-cont. function?

I could not include the file, I am typing here. If some confusion about understanding the equations, please ask me. "n", "ni" and "j" are suffixes.
----------Problem-----------

An+Rni * B = Kni/Tni for all "n" and "i" ---------------------------------------------(1)
Sum over n (An)+Rj *B = [Sum over n (Knj)]/Bj for all "j"------------------------(2)
Sum over i (Tni)+sum over j (tj) =T for all "n"--------------------------------------(3)
Sum over n and sum over i (Tni * Rni)+sum over j (Tj*Rj)= C ------------------(4)

From these equations, I have to solve for unknowns "Tni" and "Tj" in terms of knowns Rni, Rj, Kni, Knj, T and C. Condition is: the solution for "Tni" should be independent of "An" , "B" and "Tj". Similarly, solution for "Tj" should be independent of of "An" , "B" and "Tni".


-------------Problem ends-------------

Please somebody help me!

Correction"
(1) In Right hand side of Equation (2), "Bj" should be "Tj"
(2) "tj" in equation (3) should be "Tj"

The correct one is shown below:

An+Rni * B = Kni/Tni for all "n" and "i" ---------------------------------------------(1)
Sum over n (An)+Rj *B = [Sum over n (Knj)]/Tj for all "j"------------------------(2)
Sum over i (Tni)+sum over j (Tj) =T for all "n"-------------------------------------(3)
Sum over n and sum over i (Tni * Rni)+sum over j (Tj*Rj)= C ------------------(4)