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Hu Zhengtang
  • Member for 9 years, 7 months
  • Last seen more than 4 years ago
15 votes
Accepted

Show that the matrix $A^2 + I$ is invertible for all matrices $A$, where $A$ is an $n \times n$ symmetric matrix.

13 votes
Accepted

If $e^{itx_n}$ converges for every $t\in\mathbb R$, then does $x_n$ converge?

10 votes

Prove that if $\int f^2$ and $\int( f'')^2$ converge, so does $\int (f')^2$

10 votes

Quotient of two smooth functions is smooth

9 votes
Accepted

Prove that 360 divides (a-2)(a-1)a.a.(a+1)(a+2)

8 votes

Find the Maclaurin series of f(x)

7 votes

If $MM^{'}$ is positive definite, $M$ is invertible?

7 votes
Accepted

How to prove this inequality $\sin{\left(\frac{\pi}{2}ab\right)}\le\sin{\left(\frac{\pi}{2}a\right )}\sin{\left(\frac{\pi}{2}b\right)}$?

7 votes

Are there sometimes only finitely many square roots of a positive matrix?

7 votes
Accepted

Show that $A$ is symmetric, with $A \in M_n(\mathbb R)$

6 votes
Accepted

looking for a diffeomorphism (not C1)

6 votes

Integrating conjugate of polynomial

5 votes
Accepted

Composition of continious and analytic map

5 votes
Accepted

if $2f(x)+f''(x)=-xf'(x)$ show that $f(x)$and $f'(x)$ are bounded on $R$

5 votes
Accepted

Give an function $f$ which is holomorphic in a sector $S$ and continuous but not holomorphic on $\bar{S}$

5 votes
Accepted

Prove that $f(x)$ is integrable on $\mathbb{R}$.

4 votes

Prove $f(x)=ax+b$

4 votes
Accepted

The Bound of the 8th Derivative of an Analytic Function

4 votes

Order of matrices in $SL_2({\mathbb{F}_q})$

4 votes
Accepted

Is any norm on $\mathbb R^n$ invariant with respect to componentwise absolute value?

4 votes
Accepted

For what values will f(x) be necessarily one-one?

3 votes
Accepted

Finding a function

3 votes
Accepted

Does this property imply convergence?

3 votes

Convergence of double sum $\sum_{m, n}\frac{1}{m^p + n^k}$

3 votes
Accepted

How to prove $|xe^{-x^2}\int_{0}^{x}e^{t^2}dt-ye^{-y^2}\int_{0}^{y}e^{t^2}dt|<|x-y|$ for $x\ne y$

3 votes
Accepted

Partial derivatives of a function which is constant on the diagonal

3 votes
Accepted

$C[0,1]$ endowed with integral norms

3 votes

Zero of the derivative of ameromorphic function

3 votes

How prove this matrix inequality $\det(B)>0$

3 votes

real analysis and integral