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Zeration = inconsistant ?
#11
(10/02/2014, 10:58 PM)tommy1729 Wrote: It feels a bit strange ...
A so called new concept " zeration " being almost equivalent to max[a,b].

Max[a,b] does not seem so intresting as a function.
Max[12,100] = Max[13,100] = Max[91,100]
Nothing special.
...............
Also there is not much algebra or geometry about Max.
Max+ algebra being a big exception.
...............
Or ...
Finding addional must-have properties.
................
Im sure there are many nice algorithms that use max.
( even without max+ algebra )
Maybe one of those could help us out.
---
regards
tommy1729

Well, ... why not!

As a matter of fact 'Tropical Algebra' and 'Tropical Geometry' seem to use Max-Plus algebra, where the max operation such as:
c = a[max]b
is one of the basic operations. Together with:
d = a[+]b
they are used to build an 'Idempotent Semi-Ring'. Not a 'Field', because with [max] we cannot create a 'group' (-oo is the unity element, but there is no 'inverse element'), but a 'monoid'.

Nevertheless, the result of this formalism is extremely important, because a lot of successful applications from this new discipline are expected in fields such as the Petri-nets, machine scheduling, discrete event processes (DEP), industrial manufacturing systems, telecommunication networks, parallel processing, coding/decoding systems, traffic control and, last but not least, cellular automata (NKS). Amazing. We need to think about that.

Best regards.
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Messages In This Thread
Zeration = inconsistant ? - by tommy1729 - 10/01/2014, 08:40 AM
RE: Zeration = inconsistant ? - by MphLee - 10/01/2014, 11:27 AM
RE: Zeration = inconsistant ? - by GFR - 10/02/2014, 02:44 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 09:27 PM
RE: Zeration = inconsistant ? - by MphLee - 10/02/2014, 10:02 PM
RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 09:58 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 10:58 PM
RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:29 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:11 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/02/2014, 11:11 PM
RE: Zeration = inconsistant ? - by GFR - 10/03/2014, 11:39 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:12 PM
RE: Zeration = inconsistant ? - by MphLee - 10/03/2014, 09:20 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:32 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/03/2014, 09:41 PM
RE: Zeration = inconsistant ? - by GFR - 10/04/2014, 10:19 AM
RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 11:24 AM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 12:16 PM
RE: Zeration = inconsistant ? - by MphLee - 10/04/2014, 12:58 PM
RE: Zeration = inconsistant ? - by tommy1729 - 10/04/2014, 10:20 PM
RE: Zeration = inconsistant ? - by MphLee - 10/05/2014, 03:36 PM

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