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Feb
2
comment In a directed graph, every vertex has exactly seven edges coming in. What can one always say about the number of edges going out of its vertices?
I think you can solve this just by remembering that the total sum of the indegrees (in this case 7*n, where n is the number of nodes) must equal the total sum of the outdegrees. BTW, in 4), did you mean "some vertex" or "all vertexes"?
Feb
2
comment Sampling from a given pdf
Is this real-life sampling for specific given constants (in which case you can use numerical methods) or are you trying to find a general 'formula' for sampling?
Feb
1
comment Which is more appropriate here: multiplicative or additive error?
There shouldn't be two cases. I'm using e to mean epsilon above. It should just be a single multiplication.
Feb
1
comment Which is more appropriate here: multiplicative or additive error?
Hint: what's (x+e)*(y+e) and which of the above models is that closest to for small values of e?
Feb
1
comment For any $n^2+1$ closed intervals of $\mathbb R$, prove that $n+1$ of the intervals share a point or $n+1$ of the intervals are disjoint
My gut feeling is that this isn't actually true, at least without some additional conditions. Of course, my gut could be wrong.
Jan
27
comment Calculating Down Range and Cross Range Coordinates
In spherical coordinates, r usually refers to a radius (or distance), which is always a positive number. You might be doing things differently and having r refer to both radius and direction. I suggest at least trying the standard spherical coordinates model.
Jan
27
awarded  Autobiographer
Jan
27
comment $X^4 - 4Y^4 = -Z^2$ has no solutions in non zero integers
See @ArnieDris answer.
Jan
27
comment Sine wavelength in terms of arc length and amplitude
There's no way to avoid elliptic functions here, but tinyurl.com/hcldrcf may help
Jan
27
comment Solve in integers $b^{11}-1=a^{2016}+a^{2015}+\dots+1$
Since 2017 is prime, Fermat's Little Theorem might be involved?
Jan
27
comment $X^4 - 4Y^4 = -Z^2$ has no solutions in non zero integers
Just a thought: did you consider difference of squares on the left side?
Jan
27
comment Show $1$ is the only positive odd integer value of $k$
Is there a question here, or are you just asking us to check your proof?
Jan
27
comment Prove: $a^2\left ( \frac{b}{c}-1 \right )+b^2\left ( \frac{c}{a}-1 \right )+c^2\left ( \frac{a}{b}-1 \right ) \geq 0$.
I suspect this is some bizarre form of the triangle inequality.
Jan
27
revised If $f(x),g(x)$ are two differentiable functions such that $f'(x)=g(x)$, $|f(x)|<1$ and $f(0)^2+g(0)^2=9$
corrected interval for left side of g(0) membership
Jan
27
suggested approved edit on If $f(x),g(x)$ are two differentiable functions such that $f'(x)=g(x)$, $|f(x)|<1$ and $f(0)^2+g(0)^2=9$
Jan
27
comment If $f(x),g(x)$ are two differentiable functions such that $f'(x)=g(x)$, $|f(x)|<1$ and $f(0)^2+g(0)^2=9$
Possible hint: assume for contradiction that g(c)*g''(c) <= 0 for all c in (-3,3). In particular, this means g(c) and g''(c) have opposite signs (unless one of them happens to be 0 at a given point). Not sure if this will help, but it may.
Jan
26
revised Infinite exponentials
corrected confusion between sequence terms and series terms, offered other way to exponeniate
Jan
26
answered Question on Gambler's Ruin
Jan
26
comment Infinite exponentials
My original version started with "this doesn't answer your question, but is too long for a comment...". Must stop revising myself! (you could also argue that I answered the question for one possible interpretation)
Jan
26
answered Infinite exponentials