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age 46
visits member for 2 years, 7 months
seen 2 hours ago

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.
May
8
awarded  Yearling
Feb
5
revised Lower bound on chromatic number of a family of graphs
added 99 characters in body
Feb
5
answered Lower bound on chromatic number of a family of graphs
Jun
30
comment Smallest multiple whose digits are only ones and zeros
As far as I know, these kind of things just don't work well for divisors other than powers of 2, powers of 5 and a few other numbers like 3, 9 and 11 that are divisors of $10^n\pm 1$ for very small $n$.
Jun
30
answered Smallest multiple whose digits are only ones and zeros
Jun
29
comment If $K$ is an extension field of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=2$, prove that $K=\mathbb{Q}(\sqrt{d})$ for some square free integer $d$
If $K$ is $n$-dimensional, you get a relation between $1,\alpha,\ldots,\alpha^n$ by vector space stuff.
Jun
29
comment If $K$ is an extension field of $\mathbb{Q}$ such that $[K:\mathbb{Q}]=2$, prove that $K=\mathbb{Q}(\sqrt{d})$ for some square free integer $d$
You know that a basis for a subspace ($\mathbb Q$ in this case) can be extended to a basis for $K$. A suitable basis for $\mathbb Q$ is $\{1\}$. Say you extend it by $\alpha$. Can you show that $\alpha$ must satisfy a quadratic equation? Can you massage $\alpha$ into a $\beta$ of the form you want?
Jun
29
revised Where does directed random walk hit the boundary?
added 29 characters in body
Jun
28
comment Levy-Prokhorov metric question
Thanks. I noticed this after I posted. It shocks my faith in humanity that wikipedia might contain an error.