User Svetoslav

34 votes

Prove that $\sin(x) + \cos(x) \geq 1$

answered Mar 9, 2016 at 17:59

21 votes

Accepted

A continuous function with positive and negative values but never zero?

answered Feb 26, 2016 at 17:28

12 votes

Accepted

Weak convergence in sobolev space

answered Sep 24, 2015 at 13:12

12 votes

Accepted

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f'(x)$ is continuous and $|f'(x)|\le|f(x)|$ for all $x\in\mathbb{R}$

answered Feb 8, 2016 at 11:54

7 votes

Accepted

Show that functional $f(x)=x'((a+b)/2)$ is bounded in $C^1([a,b])$ but unbounded in $C([a,b])$

answered Sep 25, 2015 at 13:38

7 votes

Accepted

Check whether the subsets $A, B$ of $M(2, \mathbb{R})$ are open or not and closed or not.

answered Sep 18, 2015 at 14:17

7 votes

Accepted

Can a smooth function have all derivatives positive for $x>0$ and $0$ at $x=0$?

answered Mar 6, 2016 at 3:06

6 votes

Name and proof of mathematical inequality

answered Sep 25, 2015 at 17:38

6 votes

True or False - Matrix Equation

answered Sep 26, 2015 at 11:25

5 votes

Accepted

The sum of integrals of a function and its inverse: $\int_{0}^{a}f+\int_{f(0)}^{f(a)}f^{-1}=af(a)$

answered Jan 29, 2016 at 15:24

5 votes

Accepted

L2 Matrix Norm Upper Bound in terms of Bounds of its Column

answered Feb 12, 2016 at 19:34

5 votes

Accepted

Compact operator in Hilbert spaces reach the maximum in the sphere.

answered Feb 3, 2016 at 19:48

5 votes

Inequalities with floor function

answered Feb 16, 2016 at 17:28

5 votes

Inequality from Analysis Qual

answered Feb 26, 2016 at 18:06

4 votes

How to prove $ \left(\sum\limits_{cyc}{xy}\right)^2 \ge3xyz(x+y+z)$ with $x,y,z$ being positive real numbers

answered Feb 16, 2016 at 16:20

4 votes

Accepted

Show that $K_1\cap K_2\cap \dots,K_N$ is compact

answered Feb 18, 2016 at 13:04

4 votes

Accepted

If a sequence of functions $(f_n)$ converges uniformly to $f$ on $[a,b]$ prove $f$ is integrable on $ [a,b]$.

answered Oct 2, 2015 at 14:12

4 votes

Accepted

Set $S={x^{3}+2x<4}$ bounded from above or below?

answered Sep 17, 2015 at 17:58

4 votes

Show that $a^k + 1$ is not always prime when $k$ is a power of $2$

answered Sep 15, 2015 at 12:55

4 votes

How to show square root of absolute of x, $\sqrt{|x|}$, is not Lipschitz continuous?

answered Jul 27, 2015 at 17:25

4 votes

Accepted

Weak convergence and convergence almost everywhere

answered Jul 29, 2015 at 16:35

4 votes

Accepted

Choose $\rho$ such that $\rho$-norm minimizes the matrix condition number

answered Jul 28, 2015 at 19:45

3 votes

Accepted

inner product of positive semi definite symmetric matrices

answered Jul 31, 2015 at 11:26

3 votes

inequality between matrix norms

answered Sep 12, 2015 at 10:49

3 votes

Accepted

Can we find a divergent Cauchy sequence?

answered Sep 25, 2015 at 11:57

3 votes

Accepted

Dirac Delta function and Lebesgue-measurability

answered Sep 23, 2015 at 11:41

3 votes

Accepted

Is $F(x)= \frac{1}{|x|^{r}}, (x\in \mathbb R)$ a distributiuon?

answered Sep 23, 2015 at 12:19

3 votes

Prove that $\lim_{n\to \infty} \int f_n ~d\mu = \int f ~d\mu$ in a measure space

answered Sep 28, 2015 at 20:27

3 votes

Accepted

How to prove this inequality (like triangle inequality)

answered Oct 9, 2015 at 15:22

3 votes

Accepted

Prove that D + A, where D is a diagonally positive matrix and A is a skew symmetric matrix, is always invertible

answered Oct 9, 2015 at 14:47

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175 Answers

Prove that $\sin(x) + \cos(x) \geq 1$

A continuous function with positive and negative values but never zero?

Weak convergence in sobolev space

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f'(x)$ is continuous and $|f'(x)|\le|f(x)|$ for all $x\in\mathbb{R}$

Show that functional $f(x)=x'((a+b)/2)$ is bounded in $C^1([a,b])$ but unbounded in $C([a,b])$

Check whether the subsets $A, B$ of $M(2, \mathbb{R})$ are open or not and closed or not.

Can a smooth function have all derivatives positive for $x>0$ and $0$ at $x=0$?

Name and proof of mathematical inequality

True or False - Matrix Equation

The sum of integrals of a function and its inverse: $\int_{0}^{a}f+\int_{f(0)}^{f(a)}f^{-1}=af(a)$

L2 Matrix Norm Upper Bound in terms of Bounds of its Column

Compact operator in Hilbert spaces reach the maximum in the sphere.

Inequalities with floor function

Inequality from Analysis Qual

How to prove $ \left(\sum\limits_{cyc}{xy}\right)^2 \ge3xyz(x+y+z)$ with $x,y,z$ being positive real numbers

Show that $K_1\cap K_2\cap \dots,K_N$ is compact

If a sequence of functions $(f_n)$ converges uniformly to $f$ on $[a,b]$ prove $f$ is integrable on $ [a,b]$.

Set $S={x^{3}+2x<4}$ bounded from above or below?

Show that $a^k + 1$ is not always prime when $k$ is a power of $2$

How to show square root of absolute of x, $\sqrt{|x|}$, is not Lipschitz continuous?

Weak convergence and convergence almost everywhere

Choose $\rho$ such that $\rho$-norm minimizes the matrix condition number

inner product of positive semi definite symmetric matrices

inequality between matrix norms

Can we find a divergent Cauchy sequence?

Dirac Delta function and Lebesgue-measurability

Is $F(x)= \frac{1}{|x|^{r}}, (x\in \mathbb R)$ a distributiuon?

Prove that $\lim_{n\to \infty} \int f_n ~d\mu = \int f ~d\mu$ in a measure space

How to prove this inequality (like triangle inequality)

Prove that D + A, where D is a diagonally positive matrix and A is a skew symmetric matrix, is always invertible