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Apr
5
comment Computing $\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Theta)dS$
Please explain clearly what you mean by $\langle\cdot\rangle$. in the beginning of the question you write it as an integral, then you use other formulas...
Apr
5
comment Computing $\langle\sin(\gamma_i)\rangle= \int_{(S^2)^N} \sin(\gamma_i)p(\Theta)dS$
What about the following remark on the second page: "Please do not disseminate these notes. They are only intended for internal use within the context of the course. This is the first version of these notes"?? Do you think your teacher will appreciate posting the file on a public site?
Apr
4
comment Vector spaces and intersections
Nice counterexample.
Apr
3
comment Can all polygons outside of the largest inscribed rectangle in a convex polygon be concave
Use the applet in the end of this page: cgm.cs.mcgill.ca/~athens/cs507/Projects/2003/DanielSud to see that this rectangle is maximal.
Apr
3
comment All polynomials with no natural roots and integer coefficients such that $\phi(n)|\phi(P(n))$
Is $\phi(n)$ the Euler function?
Mar
31
comment Showing $2^{n_2} + 3^{n_3}+\cdots+9^{n_9}$ is dense in $\mathbb{R}^+$
I used $a^{-\infty}=0$ to keep notations simple. Of course it is intended to be understood as a limit.
Mar
31
comment Showing a piece-wise function is differentiable everywhere/Clarification
See this answer: math.stackexchange.com/a/47978/7327 You have a criteria to verify when a function defined on branches is differentiable.
Mar
31
comment In $\triangle ABC$, I is the incenter. Area of $\triangle IBC = 28$, area of $\triangle ICA= 30$ and area of $\triangle IAB = 26$. Find $AC^2 − AB^2$
@AGoogler: It's not really a method. You analyze what you're given and see what you can obtain out of that.
Feb
23
comment How do I solve $y'=\frac{x-y}{x+y}$?
Look at the relation between the numerator and the denominator in the integral. What happens when you differentiate the denominator?
Feb
22
comment If $AB$ and $BA$ are invertible matrices, are $A$ and $B$ square matrices?
Nice argument involving linear applications.
Feb
13
comment Car movement - differential geometry interpretation
It is not my answer I link to. When the question was unanswered here, I cross-posted it to MathOverflow.
Feb
13
comment Car movement - differential geometry interpretation
@janmarqz: I don't get it. What self promoting are you talking about?
Feb
13
comment Unreachable rubik cube positions.
Rotate a corner clockwise (or anticlockwise) and you won't be able to reach that position.
Jan
31
comment Simpler proof - Non atomic measures
@hot_queen: What do you mean?
Jan
17
comment proof of the full exchange lemma
Your index notations may be wrong... for example $\lambda_r\neq 0$ for some $k \leq t$??
Jan
17
comment proof of the full exchange lemma
I guess you mean $k<i$, not $k<1$.
Jan
12
comment Finding smallest delta available for permutations of a set of numbers
So that's a good, useful, mathematical answer? Just brute force through all 369600 solutions? I can hardly restrain myself not to downvote. I know the question is more suitable at math.stackexchange, but this answer is no better...
Jan
10
comment Is $f \in W^{1,1}[a,b]$ equivalent to $f$ absolutely continuous on $[a,b]$?
Yes, this is true. A proof can be found in: "One dimensional variational problems" by G. Buttazzo et al. starting from page 84.
Jan
9
comment How prove this inequality $\frac{2}{(a+b)(4-ab)}+\frac{2}{(b+c)(4-bc)}+\frac{2}{(a+c)(4-ac)}\ge 1$
@JackD'Aurizio: The function you consider is not convex on $(0,3)$ because it has a singularity at $x=k/4$ which is definitely in that interval since $K=abc \leq 1$.
Jan
9
comment How prove this inequality $\frac{2}{(a+b)(4-ab)}+\frac{2}{(b+c)(4-bc)}+\frac{2}{(a+c)(4-ac)}\ge 1$
@JackD'Aurizio: Have you tried your inequality for $a=b=c=1$? You obtain $1/2 \geq 3/4$... And your $K$ is not fixed, it depends on $a,b,c$, which doesn't make it a constant when trying to prove that your function is convex.