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General
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Posted on 12-11-06 12:49
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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!
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General
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Posted on 12-11-06 12:54
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Oh.. it did not appear.. I am trying again...
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bibas100
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Posted on 12-11-06 1:35
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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...
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himalayantiger
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Posted on 12-11-06 2:34
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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.
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bibas100
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Posted on 12-11-06 10:16
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himalayan....i think tha answer was directed towards General right? My question comes from topology...
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RajaHarischandra
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Posted on 12-11-06 12:40
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Bibas. What is an a-cont. function? is your function real valued?
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bibas100
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Posted on 12-11-06 1:45
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Raja, Actually thats alpha and not a. Yea, its all on R.
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nepalean
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Posted on 12-11-06 3:52
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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???
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RajaHarischandra
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Posted on 12-11-06 4:11
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then what is an alpha-cont. function?
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General
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Posted on 12-11-06 4:47
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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!
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General
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Posted on 12-11-06 4:50
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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)
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