The elections in that year still did not distinguish votes in the electoral college for president and for vice-president. And in the first vote they were tied.
What if Burr manages the majority in the first vote and becomes president, with Jefferson as vice-president?
Alfred was a brilliant king bu he just managed to save Wessex (not an easy feat) and keep parts of Mercia, but Æthelstan extended the kingdom to East Anglia, Northumbria and even became overlord of the Scots and Britons. He was the first king of England, but his grandfather is much more famous, why is that?
Are there (almost) continuous real functions such that
f(f(x)) = -x
?
Obviously, there are complex solutions, trivially f(x) = ix.
I have tried with rational functions of the form
y = (a x + b)/(c x + d)
but they do not produce real results.
Could it be that there are no real solutions?
To make some numerical simulations of the radioactivity and heat production of the spent fuel in the pools, I'd need a more or less complete and precise table of isotopic composition of the fuel as it is extracted from the reactor and placed in the pool.
I understand that this composition depends on several factors (enrichment, time and position in the vessel, model of the reactor,...), but if you can link a reference that provides this table for a particular case I'd be very grateful.
I'm now exploring the results listed in SFCOMPO (https://www.oecd-nea.org/jcms/pl\_21515/sfcompo-2-0-spent-fuel-isotopic-composition) that has tables of this type, but any help is welcome.
I know how to solve this using Cartesian geometry. I put the triangle well placed on the complex plane with r=1, the center at the origin and one of the vertices at z=2. Then expanding the expression
S = |e^(iθ) - 2|^4 + |e^(iθ) - 2e^(i(2π/3))|^4 + |e^(iθ) - 2e^(-i(2π/3))|^4
and using that
cos(x) + cos(x + 2π/3) + cos(x - 2π/3) = 0
I get S = 99, for every point on the circle.
But, is there a simpler solution using geometrical theorems?
I'm working on a alternate timeline in which WW1 ended en 1916. The point of departure is a success of the Italian campaign in 1915 at the Isonzo river. That makes the British empire, in another Churchill change of opinion, to abandon the Gallipoli campaign and instead move the British and Anzac trops to Northern Italy. The break the Austrian resistance at the Isonzo and the Brennero pass.
Then, the Hungarians see the change of winds and declare independence and neutrality in the conflict. The crumbling Austrian defense force the German empire to move troops to the south, and this allows to break the front in Belgium, while Brusilov break it in Poland.
By the summer of 1916, the central powers surrender.
What then?
Major changes are that there is no American intervention, no Wilson plan, no League of Nations. Instead the Entente (plus Italy) force a rendition where their empires simply divide and annex parts of the defeated.
In Russia, the peace and demobilization of troops, that return home, could prevent the revolution?
Also, there is no Alllenby campaign in Palestine and Syria. Instead the Ottoman Empire is mostly untouched at the end of the war. Would the partition happen anyway?
What are your ideas for the consequences of the war ending in the summer of 1916?
I have already created alternate histories for Russia and Germany after the war,,, but any suggestion is welcome.
What would happen in the UK, for instance, could a civil war start because of Ireland?
What about France?
And the Balkans and Hungary? In my alternate history, the Hungarian secession does not save them. Croatia declares independence, while Romanians and Slovaks rise in revolt.
Unene has an introductory but very extensive book (1600+ pages) on CANDU reactors
https://www.unene.ca/essentialcandu/
This books deals on all aspects of the technology: fundamentals, nuclear, thermalhydraulics, electrical systems, protection, fuel... for CANDU reactors.
Is there a book (or web resource) similar for PWRs?
I have Westinghouse notes (like https://www.nrc.gov/reading-rm/basic-ref/students/for-educators/04.pdf) and nuclear engineering books like Lamarsh, and technical reports like the licensing for the EPR in the US (https://www.nrc.gov/reactors/new-reactors/large-lwr/design-cert/epr/reports) that together cover the technology, but I was interested in finding a resource that covers all aspects and is at a level adequate to undergraduate students.
Edit: Googling it, it seems that there is a new two volume book about PWRs
"The Technology of Pressurized Water Reactors
From the Nautilus to the EPR" S. Marguet
https://link.springer.com/book/10.1007/978-3-030-86638-9
I'll try to find it.
Reading about medieval history, one finds the fame of Muslim and Jew doctors, compared to the Northern European ones. But, did they deserve it? In what ways were those doctors better? What diseases did they cure?
Let's assume a prime p, like p = 41, and I want to make the table of modular multiplicative inverses mod 41, by hand. I can do that (and it is a fun way to pass the time), by combining several methods.
For instance
1/1 = 1, obviously
1/(-1) = -1, that means that 1/40 = 40
For 2 I apply that
2*21 = 42 = 1, so 1/2 = 21 and 1/21 = 2
changing signs
1/39 = 20 and 1/20 = 39
The fact that 42 = 2*21 = 3*14 = 6*7 gives us also
1/3 = 14, 1/14 = 3, 1/38 = 27, 1/27 = 38
1/6 = 7, 1/7 = 6, 1/35 = 34, 1/34 = 35
For n = 5, I use that
5*8 = 40 = -1
so
5*(-8) = 1 ---> 1/5 = 33, 1/33 = 5, 1/8 = 36, 1/36 = 8
For n = 9
1/9 = 1/3*1/3 = 14*14 = (3*5 - 1)*14 = 5*(3*14) - 14 = 5 - 14 = -9 = 32
and 1/32 = 9
and so on.
But my question is, is there a systematic and easy way to find inverses by hand, that for a prime < 50 doesn't involve numbers larger than 50?