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185 Answers

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24
Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
14
How to show that $f'(x)<2f(x)$
9
Is $AB+BA$ is positive definite too if $A$ and $B$ are positive definite?
8
Find $f(i)$ for an entire function satisfying given conditions.
8
$|\operatorname{Im}f(z)|\leq |\operatorname{Re}f(z)|$ then $f$ is constant
8
Trace of $A$ if $A =A^{-1}$
7
Zeros of a cubic polynomial with rational coefficients
7
boundedness of an operator
7
$f: \Bbb N→ \Bbb N$ , $f\big(f(m) +f(n)\big)=m+n$ $\space$ for all $m,n∈\Bbb N$
7
Compact linear operator from $L^p (\mathbb R)$ to $L^p (\mathbb R)$
7
Finite simple group with subgroups of same order
7
Differential equation with unusual form of initial values
6
Choosing a linear map $(\mathbb{Z}/2\mathbb{Z})^n \rightarrow \mathbb{Z}/2\mathbb{Z}$ which is nonzero on half of a sequence of vectors
6
Application of Liouville's Theorem
6
is it possible to construct a continuous bijective map from $\mathbb{R}$ to $\mathbb{R^{2}}$
6
differentiable function, prove $f=0$
6
Operators on $C([0,1])$ that is compact or not.
5
Prove that $c^3f(c)+c f(c)\ge1$
5
Prove that there are $n$ pairwise distinct numbers $t_1,t_2,…,t_n$ in $(0,1)$, such that $\sum_{i=1}^n\frac{k_i}{f'(t_i)}=\sum_{i=1}^n k_i$
5
Does $f_n \to 0$, a.e., implies $\int_{\mathbb R} \sin(f_n(x)) dx \to 0$, when each $f_n \in L^1$
5
Prove that $f(x)$ be a constant
4
Application of Open Mapping Theorem
4
$P(|X|\ge\lambda a)\ge (1-\lambda)^2a^2$ for $0\le \lambda \le 1$
4
Sum of eigenvalues and singular values
4
The sum of the series $\sum_{n=0}^{\infty}\frac{\epsilon_n}{n!}$ is an irrational number
4
$f$ maps measurable sets to measurable sets
4
How prove this integral inequality $\int_{0}^{s}f(x)\,dx\le\int_{s}^{1}f(x)\,dx\le\dfrac{s}{1-s}\int_{0}^{s}f(x)\,dx$
4
Let $f:[a,b]\to\mathbb R$ be Riemann integrable and $f>0$. Prove that $\int_a^bf>0$. (No Measure theory)
4
if $\sum_{n=1}^{\infty }a_{n}$ converges ($a_{n}$ are non negatives), study the convergence of the serie $\sum_{n=1}^{\infty }\sqrt{\frac{a_{n}}{n}}$
4
Prove that there is a $\delta$ such that $\int_{0}^{1} (f(x))^2dx\leq \delta$$\int_{0}^{1} (f'(x))^2dx$ for all $f$ with these conditions
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