User JacobsonRadical

8 votes

1 answer

491 views

Prove the zeros of a polynomial all lie in an annulus.

asked Aug 12, 2019 at 17:48

7 votes

1 answer

1k views

Find All Entire Functions that Satisfy Some Condition

asked Jul 23, 2019 at 12:25

7 votes

2 answers

370 views

Show that $f_{k}\longrightarrow f$ both weakly in $L^{p}$ and a.e. implies $|f_{k}|^{p}-|f|^{p}-|f_{k}-f|^{p}$ converges to $0$ in distribution

asked Mar 6, 2020 at 18:53

6 votes

2 answers

880 views

Confusion on the kernel and image of boundary map in terms of computing simplicial homology.

asked May 2, 2020 at 1:57

6 votes

2 answers

1k views

The relation between uniform integrability and dominated convergence theorem in the case of counting measure

asked Sep 21, 2020 at 1:07

6 votes

1 answer

100 views

Show that $X_{t}:=\alpha X_{t-1}+\epsilon_{t}$ is strictly stationary for $|\alpha|<1$ and $\epsilon_{t}$ i.i.d$~\sim N(0,\sigma^{2})$.

asked Jan 21 at 17:16

6 votes

2 answers

1k views

an odd degree polynomial with cyclic Galois group has root all real

asked May 2, 2018 at 3:36

6 votes

2 answers

2k views

An example of a non-commutative ring with multiplicative identity 1 in which the only (two sided) ideals are 0 and the whole ring

asked Nov 28, 2017 at 6:19

6 votes

2 answers

1k views

The Galois group is $\mathbb{Z_{4}}$ if and only if $\frac{\alpha}{\beta}-\frac{\beta}{\alpha}\in\mathbb{Q}$

asked Apr 11, 2018 at 12:47

6 votes

3 answers

1k views

Show that if X and Y are i.i.d random variables such that $\mathbb{E}(X-Y)^{2}<\infty$, then $\mathbb{E}X^{2}<\infty$

asked Nov 3, 2019 at 21:40

5 votes

1 answer

296 views

Conditional Probability --- Card Question

asked Oct 21, 2018 at 11:48

5 votes

1 answer

553 views

The properties of convex function on the closed unit interval $[0,1]$.

asked Nov 26, 2020 at 22:53

5 votes

1 answer

284 views

Show that the quotient norms fail to be a norm in the quotient space $\ell^{\infty}/c_{00}$.

asked Mar 2, 2021 at 6:08

5 votes

1 answer

749 views

Describe all the compact subsets of $\ell^{1}$ -- General Result Proved, Example Needed.

asked Oct 17, 2020 at 21:28

5 votes

1 answer

549 views

Derive an upper bound for the total variation of quadratic covariation [Exercise 1.5.7 in Karatzas and Shreve].

asked Apr 24, 2020 at 20:24

5 votes

2 answers

202 views

Solving the PDE $x_{1}\dfrac{\partial f}{\partial x_{1}}+x_{2}\dfrac{\partial f}{\partial x_{2}}=e^{f(x_{1},x_{2})}-\alpha.$

asked Mar 22, 2020 at 1:09

5 votes

1 answer

376 views

Dirichlet to Neumann operator in the unit ball with Fourier Analysis

asked Mar 6, 2020 at 20:14

5 votes

1 answer

562 views

Show that $\sigma(\text{elementary cylinders})=\sigma(\text{cylinders)}$.

asked Feb 12, 2020 at 22:49

5 votes

1 answer

1k views

Compute the characteristic function of Wiener Process (Brownian Motion).

asked Feb 14, 2020 at 18:13

4 votes

1 answer

486 views

Show that $(X_{t})_{t\in[0,1]}$ of i.i.d random variables with non-degenerate distribution has no continuous modification

asked Feb 17, 2020 at 1:03

4 votes

2 answers

289 views

(Proof Updated, Verification in Need) Show that $(s,t)\mapsto t\wedge s$ for $s,t\geq 0$ and $(s,t)\mapsto e^{-|t-s|}$ are positive semi-definite.

asked Feb 17, 2020 at 22:17

4 votes

1 answer

283 views

Explain a counter-example showing that Kolmogorov-Chentsov Theorem cannot be relaxed.

asked May 25, 2020 at 1:26

4 votes

2 answers

127 views

Show that $\phi(x):=\sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}(1+\frac{x^{2}}{n})^{n}}$ is differentiable on $\mathbb{R}$.

asked Jun 23, 2020 at 19:58

4 votes

1 answer

206 views

Discover the reason why two iterated integrals with different orders are not equal

asked Sep 20, 2020 at 20:48

4 votes

1 answer

324 views

Compute the $n$-fold iteration of an indefinite integral operator using integration by parts and induction.

asked Nov 20, 2020 at 17:53

4 votes

2 answers

425 views

Projection of an non-increasing sequence of closed convex subsets of a Hilbert space [Haim Brezis Exercise 5.5]

asked Apr 17, 2021 at 6:47

4 votes

1 answer

141 views

Geometric Intuition behind the genus of complex torus

asked Jul 3, 2021 at 11:30

4 votes

3 answers

592 views

If a ring has $A$ has a module decomposition into a direct sum of ideals, then each ideal is a ring.

asked Oct 28, 2021 at 15:45

4 votes

1 answer

74 views

Show that $\mathbb{P}(X>u)\leq\mathbb{E}(g(X)\mathbf{1}_{X>u})$ for all $u\in\mathbb{R}$ where $g(x)$ is nonnegative and weakly increasing.

asked Oct 15, 2023 at 19:11

4 votes

3 answers

136 views

Show that a function satisfies $|f(z)|<1$ for all $z$ in the open left half plane.

asked Jul 5, 2019 at 4:14

Stack Exchange Network

290 Questions

Prove the zeros of a polynomial all lie in an annulus.

Find All Entire Functions that Satisfy Some Condition

Show that $f_{k}\longrightarrow f$ both weakly in $L^{p}$ and a.e. implies $|f_{k}|^{p}-|f|^{p}-|f_{k}-f|^{p}$ converges to $0$ in distribution

Confusion on the kernel and image of boundary map in terms of computing simplicial homology.

The relation between uniform integrability and dominated convergence theorem in the case of counting measure

Show that $X_{t}:=\alpha X_{t-1}+\epsilon_{t}$ is strictly stationary for $|\alpha|<1$ and $\epsilon_{t}$ i.i.d$~\sim N(0,\sigma^{2})$.

an odd degree polynomial with cyclic Galois group has root all real

An example of a non-commutative ring with multiplicative identity 1 in which the only (two sided) ideals are 0 and the whole ring

The Galois group is $\mathbb{Z_{4}}$ if and only if $\frac{\alpha}{\beta}-\frac{\beta}{\alpha}\in\mathbb{Q}$

Show that if X and Y are i.i.d random variables such that $\mathbb{E}(X-Y)^{2}<\infty$, then $\mathbb{E}X^{2}<\infty$

Conditional Probability --- Card Question

The properties of convex function on the closed unit interval $[0,1]$.

Show that the quotient norms fail to be a norm in the quotient space $\ell^{\infty}/c_{00}$.

Describe all the compact subsets of $\ell^{1}$ -- General Result Proved, Example Needed.

Derive an upper bound for the total variation of quadratic covariation [Exercise 1.5.7 in Karatzas and Shreve].

Solving the PDE $x_{1}\dfrac{\partial f}{\partial x_{1}}+x_{2}\dfrac{\partial f}{\partial x_{2}}=e^{f(x_{1},x_{2})}-\alpha.$

Dirichlet to Neumann operator in the unit ball with Fourier Analysis

Show that $\sigma(\text{elementary cylinders})=\sigma(\text{cylinders)}$.

Compute the characteristic function of Wiener Process (Brownian Motion).

Show that $(X_{t})_{t\in[0,1]}$ of i.i.d random variables with non-degenerate distribution has no continuous modification

(Proof Updated, Verification in Need) Show that $(s,t)\mapsto t\wedge s$ for $s,t\geq 0$ and $(s,t)\mapsto e^{-|t-s|}$ are positive semi-definite.

Explain a counter-example showing that Kolmogorov-Chentsov Theorem cannot be relaxed.

Show that $\phi(x):=\sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}(1+\frac{x^{2}}{n})^{n}}$ is differentiable on $\mathbb{R}$.

Discover the reason why two iterated integrals with different orders are not equal

Compute the $n$-fold iteration of an indefinite integral operator using integration by parts and induction.

Projection of an non-increasing sequence of closed convex subsets of a Hilbert space [Haim Brezis Exercise 5.5]

Geometric Intuition behind the genus of complex torus

If a ring has $A$ has a module decomposition into a direct sum of ideals, then each ideal is a ring.

Show that $\mathbb{P}(X>u)\leq\mathbb{E}(g(X)\mathbf{1}_{X>u})$ for all $u\in\mathbb{R}$ where $g(x)$ is nonnegative and weakly increasing.

Show that a function satisfies $|f(z)|<1$ for all $z$ in the open left half plane.