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Jun
4
comment Laplace equation with periodic boundary conditions
Do you know the method of separation of variables?
Jun
4
comment Prove that the circle $S^1$ is not the boundary of any compact manifold with boundary in $\mathbb R^2-{(0,0)}$
If $S^1=\partial M$, then Stokes's theorem says $\int_{S^1} w=\int_M dw$, but $dw=0$ on $\mathbb R^2\setminus\{(0,0)\}$.
Jun
4
comment How to prove that operator is not compact in $L_2 (\mathbb{R})$
$A$ is even not well defined. For example, if $f(t)=e^{-t^2/4}$, then $(Af)(x)\equiv+\infty$.
Jun
4
answered $f_{n+1}(x):= \int_a ^x f_n(t)dt$, $\sum_{m=1} ^{\infty} f_m(x)$ is uniformly convergent
Jun
4
comment Is every vector space basis for $\mathbb{R}$ over the field $\mathbb{Q}$ a nonmeasurable set?
@AndréNicolas: Due to Steinhaus theorem, there is no measurable basis with positive measure.
Jun
4
comment A boundary version of Cauchy's theorem
I think the argument in your answer is just the same as the argument in the paper mentioned by @Potato in the question. I wonder, as asked in Potato's original question, is there any other proof without using Mergelyan's Theorem, at least when the boundary has some smoothness?
May
31
comment Simple non-closed geodesic.
I don't understand why you accepted Neal's answer. As Daniel Rust commented, it didn't answer your question, because it didn't show whether the non-closed geodedics could be simple or not.
May
31
comment Simple non-closed geodesic.
Could you please be more specific to explain how Hedlund's paper implies that there exists a simple dense geodesic?
May
29
revised Find all polynomials $P(x)$ satisfying this functional equation
deleted 4 characters in body
May
29
answered Find all polynomials $P(x)$ satisfying this functional equation
May
26
comment How can I show whether the series $\sum_{n=1}^\infty \frac{(-1)^n}{n(2+(-1)^n)} $ converges or diverges?
Denote $a_n=\frac{(-1)^n}{n(2+(-1)^n)}$. Note that $a_{2n-1}+a_{2n}=-\frac{1}{2n-1}+\frac{1}{6n}<-\frac{1}{3n}$.
May
25
comment Sequences with the following properties…
@Chung.J: Thank you!
May
25
answered Sequences with the following properties…
May
24
awarded  Good Answer
May
22
revised $(x+2)\cos\frac1{x+2} - x\cos\frac1x > 2$ for $x\in[1,\infty)$
deleted 41 characters in body
May
22
answered $(x+2)\cos\frac1{x+2} - x\cos\frac1x > 2$ for $x\in[1,\infty)$
May
21
revised What is my operator norm (cannot get good enough bounds).
added 1406 characters in body
May
21
comment What is my operator norm (cannot get good enough bounds).
@Norbert: I did use it. I just want to emphasize that since $B$ is compact, when can say more than $\|A\|^2=\|B\|$.
May
20
answered What is my operator norm (cannot get good enough bounds).
May
20
comment Let$ f : [0, 1]^2 \to R$ such that $f(x, y)$ is continuous in $x$ for each fixed $y$ and conversely also. Is $f $ continuous?
You may consider a function like $f(x,y)=\frac{xy}{x^2+y^2}$ when $(x,y)\ne (0,0)$ and $f(0,0)=0$.