Hi , is the following correct ?
(an outline of the proof )
Given an arbitrary Cauchy sequence (f_{n})
we have that
\forall \epsilon > 0, \exists n_{\epsilon} \leq m < n \, s.t \sup_{0 \leq x < \infty} \frac{|f_{n}(x) - f_{m}(x)|}{x^{2} + 1} < \epsilon
g_{n}(x) = f_{n}(x)/(x^{2} + 1)...
Let F = \left\{f : [0, \infty) \rightarrow R, norm(f) = \sup_{x \in [0,\infty)} \frac{|f(x)|}{x^{2} + 1} < \infty\right\}
Is F complete , under the given norm ?
My approach was to look at the pointwise limit of an arbitrary Cauchy sequence, but I am not able to prove that it converges in...
Hi,
A Markov chain is aperiodic if all the states are in one class (as periodicity is a class property and the chain itself is called aperiodic in your case) and starting from state i, there is a non-zero probability of transition to state i (this is of course given by your definition of d(i))...
Hi,
if f(t) >= 0 for t >=0, then using (g(x/t) + 1) would be a better idea ?
Now if
f(t) = f^{+}(t) - f^{-}(t) ,
where f^{+}(t) and f^{-}(t) denotes max(f(t),0) and max(-f(t),0) respectively
then one can use g(x/t) + 1 for f+(t) and g(x/t) - 1 for f-(t) to obtain a bound.
Sorry but what is "i" ? I did not understand what this means.
Why is it not needed if x is a function ? And could you please point me to some easy references on calculus for functionals ?
Thank you !
Hi all,
I was reading a paper in which implicit differentiation was used as follows
x \in R, \lambda \in R
Given G(x,\lambda) = 0
\frac{\partial G(x,\lambda)}{\partial x} \frac{\partial x}{\partial \lambda} + \frac{\partial G(x,\lambda)}{\partial \lambda} = 0
My doubt is...
Use of "method of undetermined coefficients"
Hi all,
Suppose I have a equation
f(z+1) - f(z) = z^{1/2} , \forall z \geq 0 eq (1)
then is it possible to solve this equation by the method of undetermined coefficients ?
It is usually seen in textbooks that the forcing function is taken to be...