My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum

LinkBack Thread Tools Display Modes
September 25th, 2015, 08:00 AM   #1
Banned Camp
Joined: Dec 2012

Posts: 1,028
Thanks: 24

More Complicate modulus algebra

As told in an old post, I figured was possible to rise with my sum several results:

- the first I show are Powers in N, than in Q than in R,

- But now I've little time to play with what I already know is possible to do:

More Complicate Modulus Algebra:

Is again a modified Sum, like my Step Sum but instead to make Fix Step 1/K, 2/K..... till A or else... we have a

New Variable Step Sum: so we now move ahead the index "y" following a known, complicate as we want, y= f(X)...

For example is possible to rise each result of the integer of type A(X)= X*(2X-1) = 2X^2-X

If we use this new Variable Step Sum where the index y = F(X):

y=2X-1 (so y= odds just...)

where uppercase X is 1,2,3,4,5,..... so the index y is

y1=2*X1-1 = 1
y2=2*X2-1 = 3

So for example we have the variable step sum:

$\displaystyle P= 2A^2-A = \sum_{X=1 ; y=2X-1}^{X=A} 2y-1 $

That is A000384, as just a simple trick as example...

Changing the function F(X) that generate the index y is possible to make very complex m-clocks..

One just little more complicate, for example, give use the A140676:

$\displaystyle A(n) = (A140676) = \sum_{X=1 ; x=3X+1}^{X=n} 2x-1 $


(A140676)= 0, 7, 20, 39, 64, 95, 132, 175, 224, 279, 340, 407, 480, 559, 64

... in some minutes of play I found A143941 where

A(n) = n*(1 + 6*n + 2*n^2)/3


So now you have an instrument that can generate billions of sequence... by the interaction of 2 simple gear.

...But you can add more and more complicate gear till you want !

So I let you digest this n-th Idiosincratic notation (where I probably find a way to let it more clear), and you can thanks to 2 days of Flu with a Laptop in the hands and silence in the emplty sweet home ...

complicatemodulus is offline  
September 27th, 2015, 08:29 AM   #2
Banned Camp
Joined: Dec 2012

Posts: 1,028
Thanks: 24

I call:



I try with

F(X) = (sin(X))^2

F(x) = 2x-1

and joining the points I've back a sort of A.M. signal....

It works just with liner CARRIER terms, so in a squares field, since with bigger power the Carrier fell the "signal" Down or push it to diverge.

That is what I've in my as an explanation why in our square driven real world wave can exist, and while cubic or more power effect will just let our wave fell down or diverge...

That, of course, is just a thought....

Last edited by complicatemodulus; September 27th, 2015 at 08:32 AM.
complicatemodulus is offline  
September 27th, 2015, 10:53 PM   #3
Banned Camp
Joined: Dec 2012

Posts: 1,028
Thanks: 24

This trick stinks lot...

X= 1/10,,,, p/10

Modulator: x= (sin(x)^2)

Carrier: 2x-1

Here the result: Modulator max /min are at same abscissa of the SUM zeros...

complicatemodulus is offline  
September 28th, 2015, 10:23 AM   #4
Banned Camp
Joined: Dec 2012

Posts: 1,028
Thanks: 24

Last picture here just to show the power of simple modulator (sin dependent) / carrier (here n=3 rational develope) functions:

As told the cubic carrier let the the SUM go +/- infinite.

It looks of course like "random" distribution, like another most famous, but it is not...

A most known Riemann work seems has influence also here...

But I stop dreaming and I return to reality since I've to understand better how to use this trick to have what I want...

complicatemodulus is offline  

  My Math Forum > College Math Forum > Number Theory

algebra, complicate, modulus

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
COMPLICATE MODULUS ALGEBRA, STEP SUM AND N-TH PROBLEMS:s complicatemodulus Number Theory 173 October 25th, 2014 11:48 PM
Modulus problem need help debumathur Real Analysis 1 June 4th, 2013 09:38 AM
Modulus bilano99 Calculus 2 March 15th, 2013 12:48 PM
Modulus Problem julian21 Number Theory 1 March 23rd, 2010 08:27 PM
Modulus Help Hemi08 Abstract Algebra 1 August 20th, 2009 07:54 PM

Copyright © 2018 My Math Forum. All rights reserved.