Hi, I'm studying about the bisection method for the first time. If we approach a problem with this method, how do we select the tolerance? Any help would be appreciated, thanks.
@user1952009 feel free to help with comments/answers in any of my questions. My purpose is improve my abilities in mathematics. Many thanks for your help.
@arctic OK, so I buy your description. Fibers are lines x = ky, which are embedded S^3's
@Danu It's not interesting that there are infinitely many such things with bases projective spaces. It is interesting that there are finitely many bundles with base, total space and fiber all spheres.
If $\mathcal S$ is a sheaf of groups, then you can of course define $H^0(\mathcal S)$, but also $H^1(\mathcal S)$. This is a set - no group structure whatsoever. You cannot define higher cohomology.
So in most problems, I find that the tricky part is figuring out whether there are any theorems that are applicable, by looking at things in the right way.
In this problem, the tricky part is that we know way too much, so we'd be toying with things back and forth until we find which theorem actually takes us to the solution
I really dislike working with definitions of spin and spin^c as groups... I much prefer defining a spin^c structure in terms of Clifford multiplication
So the task is to prove that for $1 < p < \infty$, if you consider some sequence $\underline{x}_n\in \ell^p$ which converges to $\underline{x}$ weakly, and also that $\|\underline{x}_n\| \rightharpoonup \|\underline{x}\|$, that the sequence converges strongly.
I've got two ways in mind for going about this
One would be to use that $(\ell^p)^* \simeq \ell^q$ and play with it from there
The other would be that weak convergence in $\ell^p$ is equivalent to convergence in each coordinate
Would you guys agree with me that the latter is probably a more fruitful way to go about this problem?
Hello, I think I misunderstand what is being asked of me here: http://i.imgur.com/kIooVcW.png could someone elaborate ?
although you've removed your response, assuming it was valid, does being asked for continuity on the left not mean i find which value f(x) is approaching from the left? I'm thinking I may have misunderstood the question completely
So, I came across this statistics question, and I believe it's a Negative Binomial Distribution. Can anyone confirm? Here is the question: Accidents recur in a factory at the rate of $3$ per week. Assume that accidents happen randomly and independently of each other. What is the probability that there is at most $1$ accident in a week?
Given that $R_{i}$ are rings, I need to prove that
$char(R) = char(R_{1} \bigoplus R_{2} \bigoplus \cdots \bigoplus
R_{n}) = lcm(char(R_{1}), char(R_{2}), \cdots, char(R_{n}))$
Recall that the characteristic of a ring $S$, denoted $char(S)$, is the smallest positive integer $n$ such that $...
@MacroGuy You can take the logarithm of both sides. In this example, I'd first divide both sides by one of the exponentials so there's only one $t$ to worry about.
@AkivaWeinberger Yah, not really sure. It should be connected in Zariski though
(I don't really know AG, so I may be mistaken)
@AkivaWeinberger Maybe you can try to break it into a bunch of 1 complex dimensional pieces, and use some complex analysis to see if you can get them to fit together. Anyway I have been up way to long I should leave
Given that $R_{i}$ are rings, I need to prove that
$char(R) = char(R_{1} \bigoplus R_{2} \bigoplus \cdots \bigoplus
R_{n}) = lcm(char(R_{1}), char(R_{2}), \cdots, char(R_{n}))$
Recall that the characteristic of a ring $S$, denoted $char(S)$, is the smallest positive integer $n$ such that $...
