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9/25/2021 1:21 pm  #1211


Re: Free Association, Part 3

"We also walk dogs."  (obscure reference) https://cdn.boardhost.com/emoticons2/big-grin.png


"Those who can give up essential liberties in order to purchase a little extra security deserve neither liberty nor security." - Benjamin Franklin
"The object of life is not to be on the side of the majority, but to escape finding oneself in the ranks of the insane." - Marcus Aurelius
 

9/25/2021 5:12 pm  #1212


Re: Free Association, Part 3

Who let the dogs out?
 


It's a strange world.  Let's keep it that way.
 

9/26/2021 3:44 pm  #1213


Re: Free Association, Part 3

Who's on first


http://strengthofthehills.tripod.com/hanilanguageandculturepage/   

The date I joined the original board: 12/04/2002
 
     Thread Starter
 

9/26/2021 5:36 pm  #1214


Re: Free Association, Part 3

first come, first serve


"Those who can give up essential liberties in order to purchase a little extra security deserve neither liberty nor security." - Benjamin Franklin
"The object of life is not to be on the side of the majority, but to escape finding oneself in the ranks of the insane." - Marcus Aurelius
 

9/26/2021 5:39 pm  #1215


Re: Free Association, Part 3

queueing theory
 


It's a strange world.  Let's keep it that way.
 

9/26/2021 5:42 pm  #1216


Re: Free Association, Part 3

The steady state equations for the birth-and-death process, known as the balance equations, are as follows. Here =16.52px{\displaystyle P_{n}}https://wikimedia.org/api/rest_v1/media/math/render/svg/5949c8b1de44005a1af3a11188361f2a830842d1
 denotes the steady state probability to be in state n

https://wikimedia.org/api/rest_v1/media/math/render/svg/a7a4e5285814b8eea220253084ab8f82def8fba4

https://wikimedia.org/api/rest_v1/media/math/render/svg/a51aff4e76af68ff0f33d4e8df7880aadfae1a7e

https://wikimedia.org/api/rest_v1/media/math/render/svg/cd1372440063dca352ad00370fdd7720bb8fd791

The first two equations implyhttps://wikimedia.org/api/rest_v1/media/math/render/svg/cf82d5d7d9b0fa14ba1e64073b6b5a7f432980a2

and
https://wikimedia.org/api/rest_v1/media/math/render/svg/6b9b9b3bd4ab8f9ebf826b61279971b3e4544f5c

https://wikimedia.org/api/rest_v1/media/math/render/svg/8ee2356f827bb07544fdf7902347772ee10e86ca


By mathematical induction,
The condition   https://wikimedia.org/api/rest_v1/media/math/render/svg/a63e8bb72ee3619d1be086ac4fc83a86ab1e2ac1
  leads to: 
https://wikimedia.org/api/rest_v1/media/math/render/svg/f869a5079ca1fb0e336634309b65c1a10097aacd
w
which, together with the equation for https://wikimedia.org/api/rest_v1/media/math/render/svg/9ba2ba4672a730074e09f736217cd4dc797688c4
, fully describes the required steady state probabilities.


http://strengthofthehills.tripod.com/hanilanguageandculturepage/   

The date I joined the original board: 12/04/2002
 
     Thread Starter
 

9/26/2021 7:07 pm  #1217


Re: Free Association, Part 3

A Question of Balance


"Those who can give up essential liberties in order to purchase a little extra security deserve neither liberty nor security." - Benjamin Franklin
"The object of life is not to be on the side of the majority, but to escape finding oneself in the ranks of the insane." - Marcus Aurelius
 

9/26/2021 7:17 pm  #1218


Re: Free Association, Part 3

scales
 


It's a strange world.  Let's keep it that way.
 

9/26/2021 9:14 pm  #1219


Re: Free Association, Part 3

arias


http://strengthofthehills.tripod.com/hanilanguageandculturepage/   

The date I joined the original board: 12/04/2002
 
     Thread Starter
 

9/27/2021 12:30 pm  #1220


Re: Free Association, Part 3

Jimmy


One world -- or none
 

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