Re: TOMMY1729 STRIKES AGAIN !!! what ? g( g(x) ) = f(x) is too easy for you

timothy wrote:

timothy golden wrote:

I've only just found this thread Tommy.
I do like you choice.
In physics the second derivative is paramount and

g(g(x))
is alike somehow to the second derivative, if
not
in
reality than in some abstracted form. What makes
this
natural? That is a difficult question yet I do
feel
that you may be striking at a natural phenom.
There
are other puzzles such as self-action which are
difficult yet here you have a construction that
is
similar to self-action. The usage of functions
here
is challenging to square (chuckle) with reality.
You
have an extensible form with dynamics and so as
a
basis this construction is interesting.

-Tim

thank you :-)

i could even go a step further, yet then i dont
have
a closed form solution ... yet ( ;-) )

in science it is important to "mix" properties
since
this also occors in the real world by collision ,
wave interferance , reactions etc

"mixing" f(x) and g(x) is an operator based on two
functions.

and given this "mixing" operator , inverse mixing
can
be sometimes a hard thing , often leading to
differential equations ...

a mix could be for example integral [f(x)*g(x-y)]

differential equations with 2 functions.

etc.

however in general they include

1) classical calculus operators
2) a discrete version like cellular automaton ,
nice
but not defined for reals or fields , only
integers
or rings.

Wow. Thanks for the education. I do see that what you
have is substantial though I may not understand it
thoroughly.

I've just been pondering some operator theory and I
suggest that beyond an operator and an operand that
there might also be a construction of 'operation'
that will fit in nicely. Now functions contain just
an operator and an operand so this is somewhat a
functional analysis problem.
What qualities could be given to such a construction
are an open problem but one would hope that something
slim could generate interesting results.

-Tim

but dont expect to find the below in any books.

we have something in common

we dont do "book math"

dont expect to find tommy1729-math in the books, it usually aint there ...



and considering the history and subject
classification of math this makes sence...

however a logical thing has been overlooked.

you liked g(g(x)) = f(x)

if a process is defined by X_t = f[X_(t-1)]
(simple recursion)

where X_t is a state of x at time t.

then solving for a certain time requires things
like


g(g(x)) = f(x)

however the mix involved 2 functions which is
interaction of 2 things rather than
self-interaction
(with time only).

the operator "mix" or "FG" is defined as follows :

given A(x) and B(x)

( if i recall well ; this is an old idea and i
havent
worked on it for a while )

g-A-2 -> g(g(x))=A(x)
g-A-3 -> g(g(g(x)))=A(x)
g-A-4 -> g(g(g(g(x)))) = A(x)

...

g-B-2 -> g(g(x))=B(x)
g-B-3 -> g(g(g(x)))=B(x)
g-B-4 -> g(g(g(g(x)))) = B(x)

...

t1 = g-A-2(g-B-2)
t2 = g-A-3(g-B-3(g-A-3))
t3 = g-A-4(g-B-4(g-A-4(g-B-4)))
t4 = g-A-5(g-B-5(g-A-5(g-B-5(g-A-5)))
...

the A and B alternate indefinately

and tN has N+1 nestings.

if lim N -> oo tN converges

and there is no double-limit or several limits

then lim N -> oo of tN gives "FG"

"FG" can be considered an average.

an iterative average.

indeed "FG" [f(x);f(x)] = f(x)

it resembles fractals in a sence

yet im pretty sure you wont find this in the
books.

not even books on iterations.

an interative average seems logical for an
interaction between two states defined by
interations.

and despite most are descibed by differential
equations and statistical ones ; a morph to a
definition with iterations can usually be made.

finding a closed form solution for FG computations
is
in general a harder problem.

regards
tommy1729

it might be hard to write a program doing FG ...

as usual i only got a reply from you (or quasi ) , whereas the rest pretends this is below their math level or something ...

this is a big lie and im starting to get frustrated by it.

JSH is right about one thing , perhaps the only thing ;

all they have to do is ignore; to stop new math.

just ignore , thats all the community has to do.

and that is a discrease !!

my grades speak for themselves.

i pay taxes.

i pay for education.

i contribute on the internet.

really a discrease.

in some way you suffer the same way, yet on sci.math your polysignes are finally getting some attention , but getting into the " real world" ; society , education , the common known and accepted knowledge

that is still far away

if you have the time look at FG again, im convinced you will like it.

regards
tommy1729
.

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