Trick for applying Rouche's Thorem to find zeros of complex polynomial

It involves proper selection of f and g such that |g|<|f|
Trick : Always chose the f(z) to be a monomial from the given polynomial   terms.

interpolation on sobolev spaces

for 0<theta<1
 and a,b be positive numbers then
c=theta*a+(1-theta)*b

then a new sobolev space  S^c is given by  =[S^a ,S^b] for given theta such that  c=theta*a+(1-theta)*b

Reference: Thm 2.6.3 page 92 in Kesavan's book of "functional analysis and applications"
 
Note: Deducing norms is trivial

Why western pairs are bad at living together

There girls don't compromise on a relation, where as the Indian subcontinent girls are very good at.
   as there is a famous saying,
"Indian wife, American salary , British Home , German car"

Research vs cooking (Culinary art)

i see a very strong correlation between the art of cooking and scientists

IIT GATE 13 MATHEMATICS Problem 31 on determinant of a Matrix transformation by a different basis