Skip to main content
Eugene Zhang's user avatar
Eugene Zhang's user avatar
Eugene Zhang's user avatar
Eugene Zhang
  • Member for 9 years, 3 months
  • Last seen this week
53 votes

Frobenius norm of product of matrix

50 votes
Accepted

How to prove limit of measurable functions is measurable

40 votes

A ring in which the two operations are equal is {0}

26 votes
Accepted

How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$.

13 votes
Accepted

Suppose $a_n>0$ and $\sum_{n=1}^{\infty}{a_n}$ diverges. Determine convergence of $\sum_{n=1}^{\infty}{\frac{a_n}{s_n^2}}$, where $s_n=\sum^n a_n$.

11 votes

Proving the inequality $|e^z-1|\leq e^{|z|}-1$

10 votes
Accepted

Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$

10 votes
Accepted

Prove that a regular Lindelöf topological space is normal

9 votes
Accepted

Let $R$ be a ring. Define a circle composition ◦ in R by $a ◦ b =a+b-ab$, $a, b ∈ R$.

9 votes

Power Set of $X$ is a Ring with Symmetric Difference, and Intersection

9 votes
Accepted

If $f: \mathbb{C} \rightarrow \mathbb{C}$ is analytic and $\lim_{z \to \infty} f(z) = \infty$ show that $f$ is a polynomial

9 votes
Accepted

Is the matrix $A$ positive (negative) (semi-) definite?

9 votes
Accepted

Improper integral $\int_0^\infty \frac{\sin(x)}{x}dx$ - Showing convergence.

7 votes
Accepted

$\sum_{n=1}^{\infty} \frac{1}{(n+1)!} \prod_{k=1}^{n} f(k)$ diverges

7 votes
Accepted

Proof: Derivative of $(-1)^{x}$

7 votes
Accepted

Counter example for $(A \times B) \cap (C \times D) = (A \cap C ) \times (B \cap D)$

7 votes

Pointwise convergence implies $L^p$

7 votes
Accepted

Show there exists $\xi \in [a,b]$ such that $g(\xi)\int_a^\xi f(x)\text{d}x=f(\xi)\int_\xi^b g(x)\text{d}x$

7 votes

Interior and boundary of $\mathbb{Q}$ in $\mathbb{R}$

7 votes

Show that $\int _{-\infty}^\infty f(x) dx>0 $ .

7 votes

Probability Theory, Symmetric Difference

7 votes
Accepted

There exist meager subsets of $\mathbb{R}$ whose complements have Lebesgue measure zero

7 votes
Accepted

Show that $\lfloor(2+\sqrt{3})^n\rfloor$ is an odd integer whenever n is a nonnegative integer

7 votes

Boundary of the intersection of two open sets in $\mathbb{R}^n$

6 votes
Accepted

$\sup_x(f) = \sup_x (g)$ . Show that there exists a $t$ such that $ f^2(t) + 5f(t) = g^2 +5g(t).$

6 votes

find the limit of one sequence $\lim_{ n \to \infty } \cos(\frac{\pi}{2n + 1})\cos(\frac{2\pi}{2n + 1})...\cos(\frac{n\pi}{2n + 1}) $

6 votes
Accepted

Find the sum of the $\sum_{m=k}^{+\infty}\binom{m}{k}(1-p)^k\cdot p^{m-k}$

6 votes

Does this one line proof for equivalence of union of closures make any sense?

6 votes
Accepted

Given an entire function which is real on the real axis and imaginary on the imaginary axis, prove that it is an odd function.

6 votes
Accepted

How to calculate $\sum_{m=1}^{N}\binom{m+k-1}{m}$.

1
2 3 4 5
18