eigenket

13 ms·

151.
by eigenket 2y ago
As far as I know Rudin focuses on Fourier analysis on locally compact Abelian groups. There's been plenty of attention paid to doing Fourier analysis on other objects, especially compact Lie groups or symmetric spaces. Of course there
152.
by eigenket 2y ago
I don't think there's any interesting difference with different bases. Usually the base you represent stuff in is a relatively small number (because using very large bases is already wildly inefficient). I think it only usually ma
153.
by eigenket 2y ago
I have seen no evidence either way on that.
154.
by eigenket 2y ago
I don't think it's accurate to say the courts were in opposition to the PS government. PiS appointed lots of their own judges in their years in power who often decided along lines that PiS wanted. The biggest example of course bei
155.
by eigenket 2y ago
I haven't seen anything about that, but if she did then thats disapointing
156.
by eigenket 2y ago
There are not many examples of the government hacking opposition politicians an en leaking damaging material to friendly "news" agencies for political gain https://notesfrompoland.com/2023/12/18/poli
157.
by eigenket 2y ago
I don't think it's either necessary or appropriate for the government to be spying on its political opponents and then leaking damaging material to friendly "news" agencies https://notesfrompoland.com/202
158.
by eigenket 2y ago
I don't think it's reasonable to assume all EU governments (or even all Polish governments) will act the same as PiS do/did.
159.
by eigenket 2y ago
I think this isn't true (at least subjectively, for me). There are plenty of similar objects you can construct. This wikipedia page has a bunch of examples of Julia sets https://en.wikipedia.org/wiki/Julia_set#Exam
160.
by eigenket 2y ago
ASML, Dassault, Siemens...
161.
by eigenket 2y ago
Theres an easily accessible list here. Meta has been fined €1.2 billion, amazon €750 million, Google around €150 million across several fines. https://en.wikipedia.org/wiki/GDPR_fines_and_notices I don't see Micro
162.
by eigenket 2y ago
It did not develop exclusively from high German, as I wrote before and it was geographically widespread enough for clear Eastern vs Western dialects to emerge: https://en.wikipedia.org/wiki/Yiddish_dialects#Eastern_Yidd
163.
by eigenket 2y ago
I think calling something a Germanic language is a bit different to calling it a German language. I completely agree with your point about a "Germanic language" but I disagree about "a German language".
164.
by eigenket 2y ago
Not exclusively. It has elements from Hebrew and Aramaic (of course) as well as from various Slavic languages. A big chunk of it derives from High German but not all.
165.
by eigenket 2y ago
Fun fact: according to the etymology I could find online it's actually originally a German word (meaning client of a prostitute) that was borrowed by Yiddish, then borrowed in turn by Polish from Yiddish and also ended up in a couple o
166.
by eigenket 2y ago
On 64 bit computers you've been able to use 128 bit unsigned ints as a gcc extension for a long time now and the bit twiddling stuff works exactly as you'd expect. The relevant types are __int128 / unsigned __int128. Clang ha
167.
by eigenket 2y ago
It looks like you have to hold down the production phase button for a bit
168.
by eigenket 2y ago
> Light has infinite speed in its own reference frame. Or alternatively, light doesn't have a reference frame.
169.
by eigenket 2y ago
Is it obvious that such a distribution even exists?
170.
by eigenket 2y ago
I don't think this extra claim about polynomials which are a product of a complex linear term and a polynomial with real coefficients is true. Let a be distributed uniformly in (-1,1) and let b be distributed uniformly in the unit disk
171.
by eigenket 2y ago
This reasoning doesn't quite work. If you're multiplying a polynomial P by a linear factor L = (x-a) with a being a nonreal complex number then at least one of these statements is true 1. P does not have real coefficients 2. PL do
172.
by eigenket 2y ago
As far as your point in parentheses goes, I think wikipedia is either wrong or confusingly written (allowing complex factorisations of real polynomials makes what they're written consistent, but is a bit silly). See theorem (20) on pag
173.
by eigenket 2y ago
Yes, > 1 for any prime; everything else calculated via the product rule does indeed have a surprising amount to do with differentiation! If you take the usual polynomial functions in one variable (lets say x is the variable and all our t
174.
by eigenket 2y ago
This definition does actually have a surprising amount to do with differentiation. The definition works for any unique factorization domain and in particular for polynomials. It turns out that the definition here exactly matches the usual d
175.
by eigenket 2y ago
Yes
176.
by eigenket 2y ago
I think you're thinking about it in a slightly weird way, if I am understanding you correctly. Picking random roots would be a very different thing. Here were only dealing with polynomials whose complex roots come in conjugate pairs (I
177.
by eigenket 2y ago
A polynomial of order n has n roots (real and complex). A random polynomial has roughly log(n) of those be real and n - log(n) be nonreal. For large n, log(n) is tiny compared to n, so it's very surprising that over half the time the l
178.
by eigenket 2y ago
Its the same because the uniform distribution over (-x,x) can be obtained by taking a random variable uniformly distributed over (-1,1) and multiplying it by x. This doesn't change anything for the question about roots because the root
179.
by eigenket 2y ago
(1-x)/x - 1/x =1/x - 1 - 1/x = -1 Evaluating the expression naively near zero you're going to get wild numerical errors, but if you do the symbolic manipulation you're going to notice that it's just equal
180.
by eigenket 2y ago
That was the joke, I guess it wasn't appreciated ;)

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