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Eclipse Sun's user avatar
Eclipse Sun's user avatar
Eclipse Sun
  • Member for 10 years, 1 month
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16 votes
2 answers
2k views

An asymptotic expression of sum of powers of binomial coefficients.

9 votes
0 answers
138 views

$GL_2(R)$ action on binary cubic forms

7 votes
2 answers
125 views

Prove a function is in $L^2[0,1]$

6 votes
2 answers
124 views

Find a countable set with the given property.

5 votes
1 answer
367 views

Phase curve of $\ddot{x}=-x,\ddot{y}=-y$

5 votes
1 answer
420 views

Power series expansion of Blaschke product

5 votes
1 answer
161 views

Compute a multiple integral.

5 votes
3 answers
366 views

A sequence of random variables with bounded variance

5 votes
2 answers
124 views

Show that the map is onto

4 votes
1 answer
843 views

Find the natural boundary of $\sum_{n=1}^\infty \frac{z^n}{1-z^n}$

4 votes
0 answers
108 views

Show that a group is trivial [duplicate]

3 votes
0 answers
74 views

Uniqueness of prime factorization of ideals

3 votes
1 answer
70 views

A cover of Locally connected space with certain compactness property

3 votes
2 answers
673 views

What is the sufficient and necessary condition for changing the order of summation?

3 votes
1 answer
99 views

Homorphism from $B(G)$ to $\mathbb{Z}$

3 votes
0 answers
175 views

Generalization of Sylow's third theorem

3 votes
1 answer
228 views

Show that Mergelyan's theorem cannot extend to the case in which $S^2-K$ has infinitely many components.

3 votes
1 answer
74 views

Show that there exists a sequence of functions $\{f_n:[0,1]\to\mathbb C\}$ satisfying the given condition.

3 votes
2 answers
70 views

Show that $\sum_k\omega_k^2=\infty$ a.e. if $\{\omega_k\}$ is an orthonormal basis

2 votes
1 answer
232 views

Construct a smooth function on $T^2$ that has exactly three critical points

2 votes
1 answer
1k views

First homology group of non-orientable manifold

2 votes
1 answer
416 views

Is there an open subspace of a locally compact space that is not locally compact?

2 votes
0 answers
189 views

Homeomorphism between $\mathbb{Q}\cap[0,1]$ and $\mathbb{Q}\cap(0,1)$ [duplicate]

2 votes
2 answers
61 views

Show that $\int_{|x|<R}\frac{|f(x)|}{|x|}\mathrm dx=o(R),\quad R\to\infty.$

2 votes
2 answers
1k views

Prove a metric space is compact, if every infinite subset in it has a limit point.

2 votes
1 answer
80 views

Prove that $\lim_{n \to \infty}3nx_n^3 = 1$.

2 votes
2 answers
1k views

Cardinal number of the set of all one-to-one mappings of $A$ onto itself. [closed]

2 votes
1 answer
65 views

measures on the Borel field generated by a field.

2 votes
1 answer
748 views

Bounded holomorphic function on an unbounded region

2 votes
0 answers
454 views

Projection from group algebra to an irreducible representation