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Apr
17
comment Integer solution to the equation
Ummm.. (1) this is not linear algebra; and (2) where does this problem come from?
Jan
28
accepted Measurability Question?
Jan
28
comment Measurability Question?
@PaulMcKenney: In that case it is direct. I just didn't know the definition. Thanks!
Jan
27
comment Measurability Question?
Sorry. I'm still having trouble seeing the connection between not being a reverse well ordering; and having an increasing subsequence.
Jan
27
comment Measurability Question?
Thanks for the answer. Is it clear that $x\in A$ if and only if my original condition holds?
Jan
27
revised Measurability Question?
added 24 characters in body
Jan
27
comment Measurability Question?
Sorry. Yes the functions map into $\mathbb R$ (and are measurable with respect to the Borel $\sigma$-algebra on $\mathbb R$ and $\mathcal B$ on $X$). [Question edited to clarify this point]
Jan
27
awarded  Nice Question
Jan
27
asked Measurability Question?
Dec
15
awarded  Caucus
Oct
15
comment 1 dimensional flows and phase portraits
I flagged it for a moderator for possible transfer (I'm not sure if this the right course of action, but I have no doubt I'll be set right if this isn't the right thing...)
Jun
19
comment How can I find a tranformation matrix/Mathematical relation between two 5th degree polynomial curves in space?
This question appears to be off-topic because it duplicates something posted simultaneously on MSE
May
14
comment Squaring the plane, with consecutive integer squares. And a related arrangement
Quite interesting. But I don't think this belongs on this web site. The AG tag is certainly wrong. Combinatorial geometry maybe. I think you could try asking this on MSE. For what it's worth, I have a paper with some similar pictures: math.uvic.ca/faculty/aquas/papers/paper43.pdf
Mar
26
comment An example of a homeomorphism on $[0,1]^2$ with constant Jacobian determinant $\pm1$
You're looking for area preserving diffeomorphisms of the square. There are old theorems guaranteeing that there are lots of these. I don't have a reference right now.
Mar
18
comment conditional expectation of discrete random variable given sum constraint
The proof of the first is that $Z=E[X_i|X_1+\ldots+X_k=n]$ is the same for each $i$. Adding all $k$ of these $Z$'s, you get $E[X_1+\ldots+X_k|X_1+\ldots+X_k=n]=n$, so that $Z=n/k$. Similarly for the squares, you have $E[X_1^2|X_1+\ldots+X_k=n]=(1/k)E[X_1^2+\ldots+X_k^2|X_1+\ldots+X_k=n]$. The minimum value of the quantity in the expectation occurs when all the $X_i$ are equal to $n/k$, and so there is an inequality: $E[X_1^2|X_1+\ldots+X_k=n]\ge (n/k)^2$.
Mar
8
comment Counting function for sums of three squares
Just sum the geometric progression: 1/8 are of this form with n=0; 1/32 are of this form with n=1; 1/128 are of this form with n=2 etc. these are disjoint subsequences.
Mar
6
comment Is this a valid way to prove that this infinite sum is divergent?
You don't tell us what level of courses you've taken. Basically everything you've done is fine. How you justify the steps you take depends on what techniques you've learned to manipulate things (but what you've done can be defended no matter what level of formality you're using).
Sep
10
comment Monotonic log det function?
Try taking this to Math.stackexchange.com Also you can radically simplify the expression you're asking about, so why not do that before posting?
Sep
4
comment integrate moments normal distribution between finite limits
which part of this q is about research level mathematics?
Sep
3
comment A vector with fixed correlation with existing vector, is it always possible?
You should have square roots in your denominator. If $X=(1,0,0,0,0,0)$, then $Y=(r,\sqrt{1-r^2},0,0,0,0)$ will do the trick.