User Gabrielek

6 votes

1 answer

217 views

Problem in the theory of finding the unique solution of $-u'' = \delta_0$ and $-u'' + cu= \delta_0$

ordinary-differential-equations sobolev-spaces distribution-theory

asked Jan 26, 2021 at 16:22

5 votes

1 answer

72 views

Poiseuille flow: can I avoid the simplification that $u=u(y)$?

partial-differential-equations mathematical-physics fluid-dynamics

asked Mar 25, 2021 at 11:06

4 votes

1 answer

158 views

How to solve explicitly the Dirichlet problem (in dimension 2) with boundary data $f(e^{i\theta}) := ( \sin(\theta) - \cos(2\theta))^2$

partial-differential-equations definite-integrals

asked Jan 13, 2021 at 10:28

3 votes

1 answer

101 views

Suppose $f,g$ are two absolutely continous functions in an interval $[a,b]$. Show $fg \in AC[a,b]$.

solution-verification absolute-continuity

asked Jan 28, 2021 at 16:31

3 votes

1 answer

43 views

A different music "shuffle" feature

probability probability-theory

asked Feb 11, 2021 at 9:12

2 votes

1 answer

138 views

Show that $H(x) := |x|^{-1} u(x/|x|^2) $ is harmonic if $u$ is harmonic

harmonic-functions

asked Jan 6, 2021 at 14:05

2 votes

2 answers

120 views

How to derive Bernoulli's theorem for an elastic fluid from Lamb's equation

mathematical-physics fluid-dynamics

asked Mar 26, 2021 at 15:35

2 votes

0 answers

26 views

Example of function that is in $C^\infty([0,\infty))\cap L^1((0,\infty))$ but not in $W^{1,1}(0,\infty)$

solution-verification sobolev-spaces smooth-functions

asked Jan 16, 2021 at 14:06

2 votes

1 answer

77 views

Question on integration: $\int_{k}^{k+1}\int_{k}^{k+1}\frac{1}{x^2+y^2}dxdy$

integration measure-theory

asked Sep 5, 2019 at 9:28

2 votes

1 answer

101 views

Artin's lemma and some morphisms.

abstract-algebra field-theory

asked Dec 30, 2019 at 15:21

2 votes

1 answer

106 views

Show that the sequence $\frac{0}{1}, \frac{0}{2}, \frac{1}{2}, \frac{0}{3}, \frac{1}{3}, \frac{2}{3}, \dots \frac{k-1}{k}$ is equidistributed mod 1

sequences-and-series elementary-number-theory equidistribution

asked Mar 23, 2020 at 15:35

1 vote

1 answer

47 views

Question about the convolution $\mathbb{1}_{[0,1]} * \mathbb{1}_{[0,1]}$

real-analysis convolution

asked Mar 25, 2020 at 15:23

1 vote

1 answer

40 views

Show that an operator is continuous

operator-theory

asked Jun 29, 2020 at 10:20

1 vote

2 answers

117 views

Show that there exist $f_1 \in L^{p_1}$ and $f_2 \in L^{p_2}$ such that $f = f_1 +f_2$.

lp-spaces

asked Jun 29, 2020 at 14:28

1 vote

1 answer

283 views

Doubt about Jacobson Basic Algebra I

abstract-algebra

asked Dec 31, 2019 at 10:57

1 vote

1 answer

79 views

Evaluate $\lim_{n \rightarrow \infty} \int_0^{+\infty} \frac{e^{-n^2x}}{\sqrt{|x-n^2|}} dx$

integration limits measure-theory lebesgue-integral

asked Aug 31, 2019 at 8:23

1 vote

1 answer

48 views

Lebesgue integrability $e^{-\frac{y}{x}}\frac{sen(x)}{y}$

lebesgue-integral

asked Aug 31, 2019 at 13:57

1 vote

1 answer

66 views

Some questions about $\sum_{n=1}^{\infty} (2z)^{-n^2}$

complex-analysis

asked Nov 29, 2019 at 16:54

1 vote

1 answer

44 views

Rouché's theorem about the equation $\log(z + 3) + z = 0$ in $D_{1/4}(0)$

complex-analysis

asked Nov 30, 2019 at 9:57

1 vote

0 answers

46 views

Some question on $F(z) := \sum_{n=1}^{\infty} \frac{1}{n} \text{log} \Big(1+\frac{z}{n} \Big)$

complex-analysis

asked Dec 12, 2019 at 16:51

1 vote

4 answers

81 views

Show $ ( \sin(\theta) - \cos(2\theta))^2 = 1+ \sin(\theta) - \sin(3 \theta) - \frac{1}{2}\cos(2 \theta) + \frac{1}{2}\cos(4 \theta) $

trigonometry

asked Jan 22, 2021 at 14:29

1 vote

0 answers

54 views

Proof of the conservation law for the mass

mathematical-physics

asked Mar 3, 2021 at 15:13

1 vote

0 answers

34 views

Is the Fourier series independent from the basis used in its calculation?

fourier-analysis fourier-series

asked Jun 17, 2021 at 15:05

1 vote

1 answer

99 views

Problem using Bessel's inequality to prove that an orthonormal system is complete in Vitali-Dalzell theorem.

solution-verification proof-explanation fourier-analysis hilbert-spaces

asked Jun 17, 2021 at 16:07

1 vote

2 answers

111 views

Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that $f(x^2 + y + f(y)) = 2y + (f(x))^2$ [duplicate]

functional-equations

asked Feb 15, 2021 at 17:38

1 vote

1 answer

67 views

How to solve $\frac{\partial V}{\partial t} + x + \frac{\partial V}{\partial x}- \frac{1}{2} \frac{1}{\left(\frac{\partial V}{\partial x}\right)} = 0$

partial-differential-equations optimal-control

asked Feb 17, 2021 at 16:58

1 vote

0 answers

33 views

Compute the Discrete Fourier Transform (DFT) of the 4-point signal $f = [3, 2, 5, 1]$.

discrete-mathematics solution-verification fourier-analysis fourier-transform

asked Jun 23, 2021 at 15:34

1 vote

1 answer

71 views

Take $f$ in $L^1(\mathbb{R})$, define $g(x) := f (ax + b)$. Compute the Fourier transform of $g$ in terms of that of $f$.

fourier-analysis fourier-transform

asked Jun 24, 2021 at 16:54

1 vote

0 answers

23 views

Help in the choice of the best coefficients to study the convergence of the finite element method for PDE

finite-element-method elliptic-equations elliptic-operators

asked Jul 6, 2021 at 8:30

1 vote

1 answer

38 views

How to discretize the trilinear form $m(w;,u,v) := \int_\Omega w^{2p} u \ v$ to get a matrix for FEM methods

partial-differential-equations solution-verification finite-element-method

asked Oct 7, 2021 at 7:34

Stack Exchange Network

current community

your communities

more stack exchange communities

55 Questions

Problem in the theory of finding the unique solution of $-u'' = \delta_0$ and $-u'' + cu= \delta_0$

Poiseuille flow: can I avoid the simplification that $u=u(y)$?

How to solve explicitly the Dirichlet problem (in dimension 2) with boundary data $f(e^{i\theta}) := ( \sin(\theta) - \cos(2\theta))^2$

Suppose $f,g$ are two absolutely continous functions in an interval $[a,b]$. Show $fg \in AC[a,b]$.

A different music "shuffle" feature

Show that $H(x) := |x|^{-1} u(x/|x|^2) $ is harmonic if $u$ is harmonic

How to derive Bernoulli's theorem for an elastic fluid from Lamb's equation

Example of function that is in $C^\infty([0,\infty))\cap L^1((0,\infty))$ but not in $W^{1,1}(0,\infty)$

Question on integration: $\int_{k}^{k+1}\int_{k}^{k+1}\frac{1}{x^2+y^2}dxdy$

Artin's lemma and some morphisms.

Show that the sequence $\frac{0}{1}, \frac{0}{2}, \frac{1}{2}, \frac{0}{3}, \frac{1}{3}, \frac{2}{3}, \dots \frac{k-1}{k}$ is equidistributed mod 1

Question about the convolution $\mathbb{1}_{[0,1]} * \mathbb{1}_{[0,1]}$

Show that an operator is continuous

Show that there exist $f_1 \in L^{p_1}$ and $f_2 \in L^{p_2}$ such that $f = f_1 +f_2$.

Doubt about Jacobson Basic Algebra I

Evaluate $\lim_{n \rightarrow \infty} \int_0^{+\infty} \frac{e^{-n^2x}}{\sqrt{|x-n^2|}} dx$

Lebesgue integrability $e^{-\frac{y}{x}}\frac{sen(x)}{y}$

Some questions about $\sum_{n=1}^{\infty} (2z)^{-n^2}$

Rouché's theorem about the equation $\log(z + 3) + z = 0$ in $D_{1/4}(0)$

Some question on $F(z) := \sum_{n=1}^{\infty} \frac{1}{n} \text{log} \Big(1+\frac{z}{n} \Big)$

Show $ ( \sin(\theta) - \cos(2\theta))^2 = 1+ \sin(\theta) - \sin(3 \theta) - \frac{1}{2}\cos(2 \theta) + \frac{1}{2}\cos(4 \theta) $

Proof of the conservation law for the mass

Is the Fourier series independent from the basis used in its calculation?

Problem using Bessel's inequality to prove that an orthonormal system is complete in Vitali-Dalzell theorem.

Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that $f(x^2 + y + f(y)) = 2y + (f(x))^2$ [duplicate]

How to solve $\frac{\partial V}{\partial t} + x + \frac{\partial V}{\partial x}- \frac{1}{2} \frac{1}{\left(\frac{\partial V}{\partial x}\right)} = 0$

Compute the Discrete Fourier Transform (DFT) of the 4-point signal $f = [3, 2, 5, 1]$.

Take $f$ in $L^1(\mathbb{R})$, define $g(x) := f (ax + b)$. Compute the Fourier transform of $g$ in terms of that of $f$.

Help in the choice of the best coefficients to study the convergence of the finite element method for PDE

How to discretize the trilinear form $m(w;,u,v) := \int_\Omega w^{2p} u \ v$ to get a matrix for FEM methods