Mathematics
HeroZhang001's user avatar
HeroZhang001's user avatar
HeroZhang001's user avatar
HeroZhang001
  • Member for 10 months
  • Last seen this week
  • Henan, China
Profile Activity

12 Questions

Score Activity Newest Views
7 votes
2 answers
149 views

Assume $\int_0^\infty f(x)dx$ converges. Prove there exists $\xi\in[1,\infty)$ such that $\int_1^\infty \frac{f(x)}x dx=\int_1^\xi f(x)dx$.

4 votes
1 answer
255 views

Is $\{(\mathbb R,\phi)\}$ a smooth atlas for $\mathbb R$, where $\phi(x)=\left\{ \begin{array}{ll} x & x<0, \\ 2x& x\geq0~? \end{array} \right.$

4 votes
2 answers
124 views

Solution Verification: Compute $\int_{0}^{+\infty} \frac{\mathrm{e}^{-a x}-\mathrm{e}^{-b x}}{x} \sin x \mathrm{~d} x$, where $b>a>0$

3 votes
2 answers
339 views

Computing the De Rham Cohomology Group of Connected Sum $H_{\rm dR}^p(M_1 \# M_2)$

2 votes
1 answer
93 views

Proving the horizontal distribution is not involutive

2 votes
1 answer
124 views

Proving $\dim\{B\in {\rm M}(n,\mathbb{R}):BA^T=-AB^T\}=\frac{n(n-1)}{2}$ where $A\in {\rm O}(n)$ [duplicate]

2 votes
1 answer
87 views

Space pairs $(D^n,S^{n-1})$ and $(\mathbb R^n,\mathbb R^n\backslash\{0\})$ are NOT homotopy equivalent [duplicate]

1 vote
1 answer
145 views

GTM73 Hungerford's Algebra. Problem IV.6.4(ii)

0 votes
1 answer
117 views

Why does the Christoffel symbols in normal coordinate charts vanish only at point $p$, not vanish identically in an open neighborhood of $p$?

0 votes
2 answers
101 views

Find the volume of $\mathbb S^n$ (the surface area of $(n+1)$-dimensional unit ball) by using differential geometry

0 votes
1 answer
153 views

Computing the Euler Characteristic of $\mathbb{CP}^2 \# \mathbb{CP}^2$

-1 votes
1 answer
59 views

Computing the tangent space at the non-unit element of Lie group by using left translation

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