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user 21907
This tag is to be used only when re-tagging highly(!) off-topic questions where none of the actual tags would make sense; all actual tags the questioner has used are removed and something is needed to have some tag, which is enforced by the software, so this tag is used. However note that this tag is also used in the process of moderators deleting tags. Thus a question having this tag does most of the time not mean that somebody found it off-topic.
2
votes
Accepted
the relationship between integration by parts and surface integrals
This follows immediately from Green's formula, which says for $X$ vector field,
$\Omega$ open set,
$n$ the unit exterior normal to the boundary $\partial \Omega$
$$
\int_{\Omega}div X\ dx=\int_{\part …
- 16.2k
3
votes
Accepted
Fourier transform of a differential operator
Let me change slightly your notations and consider the quadratic form in $\mathbb R_{\xi,\eta}^2$
$$
Q(\xi,\eta)=\alpha \xi ^2+2\gamma \xi \eta+\beta \eta^2,
$$
where $\alpha, \beta$ are real paramete …
- 16.2k
2
votes
Rate of change of mass of a parameterized region
With $H$ the Heaviside function (characteristic function of $\mathbb R_+$),
you have
$$
M(t)=\int_{\mathbb R^n} f(x) H(t-h(x)) dx
$$
and thus, at least formally,
$$
\dot M(t)=\int_{\mathbb R^n} f(x) \ …
- 16.2k
5
votes
Fourier transform of Analytic Functions
The following basic result needs to be quoted on these matters of analyticity: the Paley-Wiener-Schwartz theorem gives a characterization of distributions with compact support. Let $u$ be a tempered d …
- 16.2k
1
vote
Estimating the flow when we know the vector field
Let $X=\sum_{1\le j\le n}a_j(x)\partial_{x_j}$ be a Lipschitz-continuous vector field on some open subset of $\mathbb R^n$. The flow is then Lipschitz-continuous: it is a consequence of Gronwall's in …
- 16.2k