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bio website math.ntnu.no/~hanche
location Trondheim, Norway
age
visits member for 3 years
seen 2 hours ago

Jan
6
comment How does an Iterated Integral Work?
The formula involving $I$ seems to be just a definition of $I$. The second equality is trivially true: It reflects the fact that it doesn't matter what letter you use for the integration variable in an integral. The interesting question is why is $J=I^2$ …
Jan
3
revised Disproving cantor's diagonalisation
edited tags
Jan
2
comment Showing that $\inf\left|x-p\right|$ is continuous
@rat You got it!
Jan
1
comment Showing that $\inf\left|x-p\right|$ is continuous
@rat If $a>f(q)$ then there is some $x\in X$ with $|x-q|<a$. Then $|x-p|<a+|p-q|$, and of course $f(p)\le |x-p|$ … I skipped some detail, but does this help?
Jan
1
comment Showing that $\inf\left|x-p\right|$ is continuous
@rat You need to employ the definition of infimum. Can you see why the final inequality in my answer is equivalent to $f(p)\le|x-q|+|p-q|$ for all $x\in X$?
Jan
1
answered Showing that $\inf\left|x-p\right|$ is continuous
Dec
29
comment construct $\mathcal{O}(h^2)$ finite difference scheme for $(a(x)\cdot u'(x))'$ operator
I replaced an asterisk of yours by a dot. Asterisks are for convolutions! (Pet peeve of mine, sorry.)
Dec
29
revised construct $\mathcal{O}(h^2)$ finite difference scheme for $(a(x)\cdot u'(x))'$ operator
Better formatting
Dec
29
comment construct $\mathcal{O}(h^2)$ finite difference scheme for $(a(x)\cdot u'(x))'$ operator
Does the asterisk denote convolution? I'm guessing not, but it's hard to be sure sometimes. Also, perhaps due to not being a numerical analyst, I don't understand what a difference sceme for an operator is. What is the underlying problem?
Dec
28
comment Prove: $abc\geqslant 162$
There are well known inequalities connecting various kinds of averages (weighted or not) – arithmetic, geometric, harmonic etc. Do you know these, and have you tried applying them?
Dec
26
answered How to prove that $(x-a)^{2} \cdot f(x) $ is differentiable only at $a$, where $f(x)$ is the Dirichlet function?
Dec
23
comment How do I evaluate the following integral $\int_{-\infty}^{\infty} e^{-\sigma^2 x^2/2}\; \mathrm dx$?
Try searching this site for Gaussian integral. You can't find an expression for the antiderivative, by the way, other than the one with erf (full name: error function, which see).
Dec
21
revised Solving cauchy hyperbolic second order pde
Fixed up align usage
Dec
20
awarded  Caucus
Dec
19
answered Given matrix P such that $P^{102 } =0 $ , to show that $P^{2} = 0$.
Dec
17
comment Intuitively, why is the Gaussian the Fourier transform of itself?
The link you gave at the end results in a “request denied” error. Do you know of any other source?
Dec
17
answered Inequality $a^2b^2+2(a+b)\geq 4ab+1$
Dec
17
comment Inequality $a^2b^2+2(a+b)\geq 4ab+1$
The slightly (but only slightly) flippant answer is: Don't do that, then. To be less flippant, what you have discovered is that the inequality you used is to rough an estimate to work. So you'll need to abandon that approach and try something different.
Dec
17
comment Interchange of derivatives
(2) should be okay if you just add a term $\partial L/\partial t$ on the left. For (1), it is not even clear what $\partial\dot L/\partial\dot q$ should mean. I suppose $\dot L$ is a total derivative of $L$, but then that is only defined along some curve, and you can't differentiate it in the $\dot q$ direction. To elaborate a bit, $d/dt$ is a total derivative along a curve. It doesn't mix well with partial derivatives. A proper answer requires more time than I have available right now.
Dec
17
comment Prove inequalities with induction
Exactly. As an exercise in induction, the problem is unfortunately worthless. (On a side note, be careful in writing stuff like $P(2):2+\sqrt{2}>2 \Rightarrow true$ like you did above, for any statement, true or false, implies any true statement. It's one of the oddities of mathematical logic as opposed to everyday use of language. Perhaps you meant the arrow to mean “evaluates to” or something like that, but then you should have chosen a different style arrow to avoid confusion.)