summation – What is the main difference between two results of apparently similar sums?

warning

    Sum[(a^2 + (b + n)^2)^(-1), {n, -Infinity, Infinity}]

given

$$ frac { pi sinh (2 pi a)} {a ( cosh (2 pi a) – cos (2 pi b))}} $$

while the sum

                    Sum[(a^2 + (b + 2 [Pi] n) ^ 2) ^ (- 1), {n, -Infinity, Infinity}

given

$$ begin {array} {cc}
{And
begin {array} {cc}
frac { coth left ( frac {a} {2} + frac {ib} {2} right) + coth left ( frac {a} {2} – frac {ib} {2 } right)} {4 a} & arg (b + ia) geq 0 \
frac { coth left ( frac {1} {2} (a + ib) right)} {4a} + frac { coth left ( frac {1} {2} (ai b) right)} {4 a} – frac {1} {2 a} & text {True} \
end {array}
\
end {array} $$

listing two different cases. What is the source of this?

Also, ask a condition on $ a $ to be real and positive

    Refine[Sum[(a^2 + (b + 2*[Pi] n) ^ 2) ^ (- 1), {n, -Infinity,
Infinite}], {Element[{a, b}, Reals], a> 0}]

do not get rid of "cases", as it should be (because then the imaginary part of $ (b + ia) $ always positive), the result remains exactly the same as above. Maybe I have not stated the assumptions on $ a $ correctly? I use Mathematica version 11.3.0.0.

Related to
What is the meaning of True in my result?

bitcoin – 51% attack – apparently very easy? Referring to CZ's "BTC rollback chain" – How to ensure that such a corruptible scenario can never happen so easily?

I was shocked to see binance CZ literally "canceling" the bitcoin chain by "calling" some favors of "friendly" Asian miners.

This one person could actually do it ??? I mean, are we all in a bubble, in a kind of utopia then, to think that the decentralization of the chain makes it "armored" and resistant to collusion on the part of the miners?

(1) This is a fundamental question: how do our brilliant bitcoin developers, highly respected and esteemed, explain such a situation in which only a handful of people's interests could be enough to attack with a 51% majority?

(2) Second, are there active debates on how to mitigate such a situation in the future? What technical aspects implemented in the BTC chain (or to be implemented) could be useful?

These huge mining farms are basically very disturbing. it's like a proof of stake, where the "richest" has the most power. And in the case of PoW mining, it's similar to the "biggest hardware" that has the most power.

we must try in a way to eliminate these easily corruptible scenarios, right?

In today's digital world, there are many examples of collusion involving even more than 1000 different people involved.

A handful of minor accomplices would be a piece of cake, right?

Thank you for having explained this problem. I sincerely hope that this will be picked up by our great developer community, or maybe I just do not understand anything.

So, apparently, Facebook is now putting the focus on the privacy of user data | Promotion Forum

Yesterday again, I found an article describing how Facebook was "Will start to worry and solve the privacy issues of usersI was quite surprised to see that.

Knowing Facebook and the number of scandals in which they have been involved in recent years, I will be aware of it. I think they will, but at the same time, I do not do it.

I hope Facebook really starts to care about privacy. I would love to use Facebook, but in their current position, it's a no-no for me. Again, I will keep an eye on them to see if they are doing what they promise (but I doubt it).

Do you believe that Facebook will start to worry about the privacy of users?

permissions – Windows 10 update 1803 has apparently revoked net stop and sc config access

Scenario:
The bandwidth on my network is rare, a batch script is bound on my desktop to end the gluttonous services, Windows Update and Broadcast Optimization being the most frequent hackers. Before the last update of Windows 10, this tool worked well, the main commands in question being

NET stop "Windows Update"
Net stop "Optimization of delivery"
Config SC DoSvc start = disabled
SC config wuauserv start = disabled

Attempts with cmd, Services or resmon: Previously, Windows canceled all changes to the startup type, so the script was a temporary fix. Now, however, Access is denied for all these commands, even when the script is "Run as Administrator". Even if I run the Services utility as an administrator, all options to change the startup type or stop services are dimmed. I did not check if I could terminate these services from the Resource Monitor utility. I found that I can take and of the arbitrary executables in System32, so if anyone knows which executables for WU and DO, this can also work.

Potential solution via the registry: From this question, I discovered that it was possible to change the startup type of these services in the registry. I found that in HKEY_LOCAL_MACHINE SYSTEM CurrentControlSet Services DoSvc and ~ wuauserv there is no beginning DWORD registry, as shown in the above question, but there are DWORD registers called Type in ~ % svc% TriggerInfo for DoSvc and wuauserv. Is the edition of these Type Do the registers have the desired effect? If not, what would be the register?

Should I install Gentoo?


Windows 10 Home Edition v. 1803

Is SiteDistrict worth its (apparently) high cost?

SiteDistrict is a web hosting company located in Oakland. They seem
specialize in WordPress sites.

Their price calculator on their main page uses horizontal sliders.
Examples:

– Sites: $ 25 each for one, $ 14 each for 10, $ 9 each for 50, etc.
– Disk space: 17 GB included, then $ 1 per GB per month
– Bandwidth: 83 GB included, then about 30 ยข per GB per month

These prices seem incredibly high, but maybe I'm
missing something. Does SiteDistrict offer good value for money?
money?