Big Oh !!

This is what i spent doing for the first one hour of my work time today.

given g1=O(f1) and g2=O(f2)
there exists x1, x2, c1 and c2

g1)x) < c1*f1(x), x>x1
g2(x) < c2*f2(x), x>x2

now x3 = max(f1,f2), c3=max(c1,c2)
therefore g1(x) < c3*f1(x), x>x3
g2(x) < c3*f2(x), x>x3

g1(x) + g2(x) < (f1(x) + f2(x)), x>x3
g1+g2 = O (f1+f2)

given f1(x)+ f2(x) < 2*max(f1(x), f2(x))
you have your lemma as well.

f1(x) + f2(x) < 2*max(f1(x), f2(x))

All considered functions mutually are monotone non-dcreasing functions and moreover their second derivatives aer non-negative. so there exists large enough x3>x2 such that

either f1(x)>f2(x) or f2(x)>f1(x) for all x>x3. with out loss of generality assume that f1(x)>f2(x). Then we deduce that,
2*E0*f1(x0 < g1(x) + g2(x) < 2* E1*f1(x) forall x>x3

if f1(x) > f2(x) which is equivalent to g1+g2 = O(f1)
iff1(x) < f2(x) forall x>x3
then g1+g2=O(f2)

Saturday was too much of alcohol. we were celebrating Birthday of one of my friends in Hyderababd. i should seriously check on my alcohol intake.



U-Boot has been fun to work on but its equally been difficult for me to digest most of it. the whole of last week i spent on getting the new cpu support into U-Boot. With lots of cross refrencing and google help, managed to get the flash drivers and ethernet drivers working with U-Boot. Most of the Cpu related work has been done. But i have been completely stuck with board side. Since my project involves a new board, built from scratch, i have been having a terrible time understanding the whole thing. currently hacking on early initialization part of the board and i have just two more days to get this whole stuff running.

Which ever organization i go to(not many, this is my third now) i always get the USB related work assigned to me. long back in the project i spent about a week hacking on the USB stack and back porting it. Now the managers want me to take over the rest of the USB related development work, which is not my responsibility. Plus have to still hack on the framebuffer driver and write a driver for the graphics controller.....i need a holiday....

currently reading The Bell Curve