LuboŇ° Motl

Czech Republic

motls.blogspot.com

Age: 42

Hi, I am a string theorist and a publicist.

1d
comment Did North African countries have a police in the 18th/19th Century?
Hi, look e.g. at ottoman-uniforms.com/ottoman-police-1840-to-1918 - BTW in Los Angeles, they didn't think that the Ottoman Police was good see cdnc.ucr.edu/cgi-bin/cdnc?a=d&d=LAH18951103.2.84
1d
answered Proving the convergnce of a sequence
1d
comment Simplify exponential equation
This is almost certainly an equation that can't be solved analytically for general values of $A_1,A_2,c_1,c_2$.
1d
answered Finding all permutations which satisfy given condition
1d
comment Did North African countries have a police in the 18th/19th Century?
You may get different results for different countries etc. For example, Libya was in the Ottoman Empire before it became Italian in the 1920s. In the Ottoman Empire,there was first police in 1845. It could spread to other places of the empire soon.
1d
comment Proving the convergnce of a sequence
Have you tried to find the change of the distances from the -3 fixed point, just like you did for +2? One always gets attracted to +2, and repelled from -3, so one ends up with the constant sequence at -3 and the same limit if you start with -3. Otherwise, even for -2.99 or -3.01, you will end up with +2.
1d
comment Proving the convergnce of a sequence
You should first find the candidate limit because you have to do it, anyway, and it's in fact simpler than to prove the existence of the limit. If there is a limit, what can you say about $a_{n+1}-a_n$ for a large enough $n$? What does it imply?
Feb
4
comment What progress, compared to the Americans, did the Germans make on constructing a nuclear weapon during WW2?
See en.wikipedia.org/wiki/German_nuclear_weapon_project for some non-conspiracy facts about the project. I would emphasize that Heisenberg, a top German theorist who could have known better, incorrectly estimated that one needed much more uranium,perhaps a ton, for a bomb, and that contributed to their skepticism about the feasibility of the concept. They weren't anywhere close to the bomb.
Feb
4
comment Is the prime counting function differentiable?
But aside from the naive definition of the derivative, it's very useful to write the jumps in terms of the Dirac delta-function, $\theta'(x)=\delta(x)$, and analytically, $\delta(x)$ may moreover be written via $1/(x-i\epsilon)=i\pi\delta(x)$. The form of the delta-function (i.e.a piece of the OP's derivative) on the left-hand side is analytic in a half-plane and this is helpful in various manipulations with $\pi(x)$. While the "undergrad" statement is that the derivative doesn't exist, the moral answer is that it not only does but it may be very useful.
Feb
4
comment How did the letter "v" come to represent the voiced labio dental fricative?
Is it an accident that the Cyrillic letter "B" is equivalent to the Latin "V"? Was this fact true before the phonetic changes in Latin you talk about, and if it was, wasn't it really the cause? I mean, people could have confused the letter because in a different alphabet, one meant the other. Or, if Cyrillic were really made 800 years after the phonetic changes above ;-), wasn't the choice of the letters in Cyrillic script influenced by the confusion in Latin?
Feb
4
comment The drop/weakening of "h" sound in General American English
The page on H-dropping says that Americans generally do not H-drop.
Feb
4
comment When were quarks discovered?
If it's hard to deal with Wikipedia, click here and read a few paragraphs: en.wikipedia.org/wiki/Quark#History
Feb
4
comment How does the Moon influence atmospheric pressure?
Thanks ;-) In particle physics, it's being used in this way the two of us understood since early 1990s when Paul Ginsparg established two archives at arxiv.org, particle physics "theory" and "phenomenology". The latter - new term in particle physics - was meant to be an application of science to actual phenomena, with the focus on what is observed (phenomena), not what is behind it. It contrasts with "theory" that tries to explain the reasons as carefully as you can. That's very different from psychology and philosophy where "phenomenology" studies (phenomenon of) consciousness only.
Feb
4
comment Ferromagnets - Permanent?
The point is that you can't really "fully demagnetize" a ferromagnetic material everywhere. When a ferromagnetic material is no overall magnetic field, it only means that it's divided to lots of small domains which are individually magnetized but in total, they mostly cancel. Small enough domains of a ferromagnetic material are always "permanent magnets". And yes, I think that it's the same for ferrimagnets. The residual field may also differ in small domains but they may be aligned.
Feb
4
comment How does the Moon influence atmospheric pressure?
I am sure we have similar confusions. I don't know the full theory myself. Their paper is too phenomenological for me. A discussion could also start here: motls.blogspot.com/2016/02/does-moon-cause-more-rain.html?m=1
Feb
4
revised How does the Moon influence atmospheric pressure?
added 276 characters in body
Feb
4
answered How does the Moon influence atmospheric pressure?
Feb
4
answered Ferromagnets - Permanent?
Feb
4
comment How many solution are there to equation $f(x)=f(f(x))$ given the following function?
One may also prove that $f(x)=x$ and $f(x)=6-x$ have no solutions outside these two intervals, and all these four solutions are different from each other because $f(x)=x$ and $f(x)=6-x$ could only be obeyed by the same $x$ if $x=6-x$ i.e. $x=3$ but that's clearly not a solution.
Feb
4
comment How many solution are there to equation $f(x)=f(f(x))$ given the following function?
@N74: to prove it, one really wants to say (and see from the graph, whatever it is, or from the explicit form of the function with $824-(x-3)^{10}$) that the function $f(x)-x$ is monotonic around the points $x=1+\epsilon$ (e.g. in the interval 0.5-1.5) and $x=5-\epsilon$ (in 4.5-5.5), so by monotonicity and continuity, one finds exactly 1 solution of $f(x)=x$ in each interval. Similarly, one finds a pair of solutions to $f(x)=6-x$ in these two intervals which is also OK. The monotonicity follows from the graph visually and from monotonicity of $y=x$.
1 2 3 4 5