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 Yearling
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1d
comment $f_1,f_2 \in L^q(\mu)$ and $\int_\mathcal{X}f_1gd\mu = \int_\mathcal{X}f_2gd\mu$ for all $g \in L^p(\mu)$ implies $f_1=f_2$ a.e.
Sorry - this was supposed to be $g = sgn(f_1-f_2)|f_1-f_2|^{p-1}$. Check whether this $g$ is in $L^q$.
1d
comment $f_1,f_2 \in L^q(\mu)$ and $\int_\mathcal{X}f_1gd\mu = \int_\mathcal{X}f_2gd\mu$ for all $g \in L^p(\mu)$ implies $f_1=f_2$ a.e.
Just use this $g$ and work out $ \int_X (f_1-f_2)g$. What is the result?
1d
comment Find all the primes that satisfy $p \mid 2^p - 1$
Looks good to me too. Now write it down properly.
1d
comment $f_1,f_2 \in L^q(\mu)$ and $\int_\mathcal{X}f_1gd\mu = \int_\mathcal{X}f_2gd\mu$ for all $g \in L^p(\mu)$ implies $f_1=f_2$ a.e.
Try $g = sign((f_1-f_2) \cdot |f_1-f_2|^{1/(p-1)}$.
2d
awarded  Yearling
Apr
15
comment Is a holomorphic function with zero derivative on a close connected set constant?
@Justin - the statement is true if the set has more than one point.
Apr
14
comment Is a holomorphic function with zero derivative on a close connected set constant?
This is because the set could be a single point. Take $f(z) = z^2$, where $f' = 0$ on $\{0\}$.
Apr
14
answered Numerically solving a steady state equation (diffusion reaction with monod kinetics)
Apr
13
comment How to convex problem with multiple constraints? $\underset{\mathbf{A}}{\text{minimize }} \|\mathbf{A}\|_F^2$
That doesn't make much of a difference. If $rank(X) > rank(S)$, there is no solution.
Apr
13
comment How to convex problem with multiple constraints? $\underset{\mathbf{A}}{\text{minimize }} \|\mathbf{A}\|_F^2$
If $n = m = r$, the matrix $S$ has full rank, and $X = 2S$, then $A = 2I$ and $\|A\|_1 = 2$. There is no solution of your problem in that case. More generally, if $rank(X) > rank(S)$, there is also no solution.
Apr
13
revised How to convex problem with multiple constraints? $\underset{\mathbf{A}}{\text{minimize }} \|\mathbf{A}\|_F^2$
edited tags
Apr
13
comment How to convex problem with multiple constraints? $\underset{\mathbf{A}}{\text{minimize }} \|\mathbf{A}\|_F^2$
1. Please explain your notation. 2. What makes you think there exists a solution $A$ with $\|A\|_1 = 1$?
Apr
11
comment What is $\lim_{n\to\infty} \frac{n}{\ln(n)} (n^{1/n}-1)$?
Set $h = \ln n/n$ for a moment. Can you rewrite the entire expression in terms of $h$? What happens to $h$ as $n \to \infty$?
Apr
10
answered Finding what $p$ does the series: $\sum_{n=1}^{\infty}\frac{\ln n}{n^p}$ converges
Apr
8
answered A trouble with the existence of an $C_{0}^{\infty}$- function $v,v>0$ such that $\int_{\Omega}hv^{\alpha}>0$
Apr
8
comment Closed form of the sum $\sum\limits_{n=0}^\infty \exp(-n^3)$
Mathematica doesn't know what to do with it. It does converge extremely quickly, though.
Apr
6
comment Eigen values of the operator $T : V \rightarrow V : T(p(t)) = p(t+1)$
Let $k$ be the degree of $p$. What is $p(t+k+1)$? Is that possible if $\lambda \ne 1$?
Apr
6
comment Multivariate Central Limit Theorem:
So the expected value of $A$ is given by eq. (1). Now use the same reasoning to verify (2).
Apr
5
comment Multivariate Central Limit Theorem:
What is the expected value of $A$? (This would be a matrix, but you should think of it as a vector). What is the covariance of $A$? This would be a tensor (a 4-dim array) but you should think of it as a matrix.
Apr
4
comment laplacian eigenvalues
If the domain is made smaller, the Rayleigh quotient is computed over a smaller set of functions and therefore its minimum cannot become smaller. This proves the inequality with $\ge$.