Question about Fourier transforms of gradient, curl and divergence
Consider a vector field $v:\mathbb{R}^3\rightarrow\mathbb{R}^3$. Denote by $F_u$ the Fourier transform of a scalar or vector field $u$. Can one finds an e...
Apr 18, 2026 1 VIEWS
Topic: General
5104 Articles 
Bipartite graph set cover
I don't know much about graph theory so I would need to know if the following problem has a positive answer or a reference. There is an undirected bi...
Apr 18, 2026 1 VIEWS
in Washer Method , is it important if we set the integral with respect of x or why when rotating a solid to find the volume?
consider the following question: find the volume of a solid bounded by $y=5/2-x$ and $y=1/x$, around $x=-1$. Know the answer is: $$\int_{0.5}^{2} \left(\f...
Apr 18, 2026 1 VIEWS
Prove $\sup(f+g) \le \sup f + \sup g$
Suppose $D$ is a nonempty bounded subset of reals. Let $f:D \to \mathbb R$ and $g:D \to \mathbb R$. Define $(f+g)(x)=f(x)+g(x)$. Prove $\sup(f+g)(D) \le \...
Apr 17, 2026 1 VIEWS
Quadratic vertex form - negative $h$ means it's on the right side of the graph?
When putting a quadratic equation in vertex form, I am having difficulty understanding why $h$ is negative when the location of the parabola goes to the r...
Apr 17, 2026 1 VIEWS
The Finishing Step to Showing that $1/(1-4x)^{1/2}$ generates the sequence $\binom{2r}{r}$
The Full Question: Show that $(1-4x)^{-\frac{1}{2}}$ generates the sequence $\binom{2n}{n}$, $n\in \mathbb N$ My Research How to show that $1 \over \sqrt{...
Apr 17, 2026 1 VIEWS
What does it mean when standard deviation is higher than the variance?
I am currently studying Wiener's process from Hull, and it says that the path of the process is jagged because when $\Delta t$ is small, the standard...
Apr 17, 2026 1 VIEWS
Find sigma, given Probability of normal distribution and mean.
In a factory sugar is packed in bags of normal weight $1000\text{ g}$. The actual weight $X$ (in $\text{g}$) can be modelled as a $N(\mu, \sigma_2)$-distr...
Apr 17, 2026 1 VIEWS
Does a function have to be one-to-one for it to have an inverse?
I am asked to find the inverse for $f(x)=x^3+\arctan(x+1)$ I graphed it on Desmos and found that it is one-to-one, so I assumed it does not have an invers...
Apr 17, 2026 1 VIEWS
Indefinite integral of secant cubed $\int \sec^3 x\>dx$
I need to calculate the following indefinite integral: $$I=\int \frac{1}{\cos^3(x)}dx$$ I know what the result is (from Mathematica): $$I=\tanh^{-1}(\tan(...
Apr 17, 2026 2 VIEWS
A conjecture related to a circle intrinsically bound to any triangle
Given a triangle $ABC$, whose (one of the) longest side is $AC$, consider the two circles with centers in $A$ and $C$ passing by $B$. (The part in italic ...
Apr 17, 2026 1 VIEWS
Tricking Dijkstra's Algorithm for negative weights
I'm doing this only for educationnal purposes, so when i was studying at college (i was computer science student) we've studied Dijkstra's ...
Apr 17, 2026 1 VIEWS