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May
17
comment Geometric mean of prime gaps?
This is fantastic. I was wondering why my numerical data seemed a little off - I did not take $N$ to be anywhere near large enough!
May
11
answered Geometric mean of prime gaps?
May
7
revised If I flip a coin $n$ times, what is the expected maximum number of heads or tails in a row?
edited title
May
7
revised If I flip a coin $n$ times, what is the expected maximum number of heads or tails in a row?
added 123 characters in body
May
7
answered If I flip a coin $n$ times, what is the expected maximum number of heads or tails in a row?
May
7
comment If I flip a coin $n$ times, what is the expected maximum number of heads or tails in a row?
@JMoravitz: I cleaned up the question a bit as the part about an infinite number of flips does not seem well phrased.
May
7
revised If I flip a coin $n$ times, what is the expected maximum number of heads or tails in a row?
Cleaned up this question a bit.
May
5
comment Counting the number of paths on a graph
+1, this is the only correct answer here.
May
5
comment Counting the number of paths on a graph
@F.M. The answer you accepted is not correct, and does accurately address your question.
May
5
answered For a PAC learnable hypothesis Show that its sample complexity $m_{\mathcal{H}}$ is monotonically non-increasing in each of its parameters
May
5
revised ANSML - Proving of the matrix identity $\nabla_AtrABA^TC = CAB+C^TAB^T$
added 1 character in body
May
5
comment ANSML - Proving of the matrix identity $\nabla_AtrABA^TC = CAB+C^TAB^T$
For the fourth identity, what does $|A|$ mean? Is it the Frobenius norm, some other norm, or simply the absolute value of the entries of the matrix? Also I think a trace is missing as well, as this gradient is for functions from matrices to the real numbers. In any case I would recommend asking one question per post on Math.Stackexhange.
May
5
answered ANSML - Proving of the matrix identity $\nabla_AtrABA^TC = CAB+C^TAB^T$
May
5
revised High Dimensional Rotation Matrices As Product of In-Plane Rotations
Added tags and dollar signs
May
4
answered High Dimensional Rotation Matrices As Product of In-Plane Rotations
Apr
27
comment Squarefree products of a class of primes
Let $S\subset\mathcal{P}$ be some subset of primes with relative density $\delta$. Let $A$ be the set of integers which can be written as products of primes in $S$. Then we expect that $$\sum_{n\leq x}1_A(n)\sim\frac{kx}{(\log x)^{1-\delta}}$$ for some constant $k$ depending on $S$. We may need $S$ to be reasonably well behaved, such as the example of primes congruent to $s$ mod $m$, but in general this is the statement that we should be looking to prove. This is related to the singularity at $s=1$.
Apr
13
comment Integral of a square compared to the square of an integral
This can also be proven using Parsevals theorem.
Apr
13
comment Integral of a square compared to the square of an integral
What you are trying to prove is false. The $L^2$ norm does not equal the $L^1$ norm in general for constant functions. Notice that $\int C^2 =(b-a)C^2$ whereas $(\int C )^2 = (b-a)^2 C^2$.
Apr
13
comment Heuristic explanation for oscillatory behavior of first $n$ primes' multiples
What are you plotting? This question is not clear.
Apr
13
comment evaluate $\int \frac{\tan x}{x^2+1}\:dx$
I am going to guess that if this is coming from a homework, the intended question was $\int \text{arctan}(x)/(x^2+1)dx$ which has a nice form.