I can't seem to find any sort of concrete definition anywhere... it always seems a bit hand wavy :(
In particular I want to know what is an isomorphism between two banach algebras?
Thanks.
Homework Statement
f is a continuous function on [0,1]
M is the set of continuous functions on [0,1] which are 0 at 1 ... i.e. for all m in M, m(1) = 0
I want to know if it's true that
|f(1)| = \inf\{\sup\{|f(t)+m(t)|: t \in [0,1]\} : m \in M\}
The Attempt at a Solution
So...
Homework Statement
How can I calculate it for \frac{1}{1+cos^2(x)} by using the fact that \frac{1}{1+x^2} = 1 - x^2 + x^4 - ...?
Homework Equations
Given in the problem.
The Attempt at a Solution
I tried letting u = cos(x), then
\frac{1}{1+cos^2(x)} = \frac{1}{1+u^2} = 1...
Thanks for your help guys...
Yes Hurkyl I'm just doing functions on functions.
dx I'm a little confused - if g_{*}f=g\circ f as Hurkly says then we'd have f mapping A to B, then g mapping B to C ... wouldn't that be OK? Perhaps I'm missing something serious here :S ... could you give me a...
"push-forward" ?
Can someone help me understand what this is, in as simple terms as possible?
If I have a function f: A\rightarrow B and another one g:B\rightarrow C I know the "pullback" f^{*}g: A\rightarrow C is f^{*}g = g\circ f (correct?)
But what about the push forward f_{*}g? What...
This isn't homework per se... It's a question from a book I'm self-studying from.
If f is continuous on [a,b] and differentiable at a point c \in [a,b], show that, for some pair m,n \in \mathbb{N},
\left | \frac{f(x)-f(c)}{x-c}\right | \leq n whenever 0 \leq |x-c| \leq \frac{1}{m}...
I'm considering taking honours next year in statistics with a project in financial mathematics. I'm really looking forward to taking more classes in this area, but I have a couple of worries I'd like to air...
1. How smart do you really have to be? I think I'm above the curve, I can get high...
Yeah, I can see it's not periodic and hence must be apeiodic, but what's going on with that definition? My understanding of it is that there has to be a special (fixed) value of n where you can go from anyone state to all the others, including back to that state... but that doesn't seem to hold...
Homework Statement
Transition matrix is
0 0 1
0 0 1
(1/3) (2/3) 0
"argue that this chain is aperiodic"
Homework Equations
definition of aperiodicity - there must exist a time n such that there is a non-zero probability of going from state i to state j for all i & j
The...
my transition matrix is
0 0 1
0 0 1
(1/3) (2/3) 0
I'm supposed to argue that this chain is aperiodic,
A markov chain is aperiodic iff there exists a time n such that there is a positive probability of going from state i to state j for all i and j...
OK,
so Vout = 86/(860 x 0.06^2 x pi) = 8.84 m/s
then...
work (out) per unit mass = pressure rise/density + 0.5(Vout^2 - Vin^2) = 306.31 J/kg
Output Power = mass flow rate x work per unit mass = 26342.94 W
efficiency = 26342.94/31500 = 0.84
Is that right? The answer my lecturer...
it's one my lecturer picked out specifically from a fifth edition textbook... so I'd assume it's OK..
Thanks rainman, I think I've made some progress with it.. still a little stuck though...
from the volume rate of 0.1 m^3/s,
I get mass flow rate = 86 kg/s using m' = pv'
Also...
i left out the oil's density.. don't know if that makes a difference to your query though? word for word the question reads:
An oil pump is drawing 35kW of electric power while pumping oil with a density of 860kg/m^3 at a rate of 0.1m^3/s. The inlet and outlet diameters of the pipe are 8cm...