Hans Engler
Reputation
4,666
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
 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 Apr15 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. Apr14 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 $\{0\}$. Apr14 answered Numerically solving a steady state equation (diffusion reaction with monod kinetics) Apr13 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. Apr13 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. Apr13 revised How to convex problem with multiple constraints? $\underset{\mathbf{A}}{\text{minimize }} \|\mathbf{A}\|_F^2$ edited tags Apr13 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 $\|A\|_1 = 1$? Apr11 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 $n \to \infty$? Apr10 answered Finding what $p$ does the series: $\sum_{n=1}^{\infty}\frac{\ln n}{n^p}$ converges Apr8 answered A trouble with the existence of an $C_{0}^{\infty}$- function $v,v>0$ such that $\int_{\Omega}hv^{\alpha}>0$ Apr8 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. Apr6 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 $\lambda \ne 1$? Apr6 comment Multivariate Central Limit Theorem: So the expected value of $A$ is given by eq. (1). Now use the same reasoning to verify (2). Apr5 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. Apr4 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 $\ge$.