Mizugadro, pentation, Book

[tommy1729]

Happy year 2015! I have several news.

Same to you.
Nice to have you back here.

1. I could not recover my previous institute site at tori.ils.uec.ac.jp
But now I have clone at http://mizugadro.mydns.jp/t
Is it seen from other countries?

I have trouble with all links that start with " mizugadro " .
But not Always ?
A restart (F5) or restart the computer helps.

Maybe its my safety settings or so ...

2. I have constructed the natural pentation (superfunction of tetration):
http://mizugadro.mydns.jp/t/index.php/Pentation
http://article.sciencepublishinggroup.co...306.14.pdf
http://www.ils.uec.ac.jp/~dima/PAPERS/2014acker.pdf
http://mizugadro.mydns.jp/PAPERS/2014acker.pdf
D.Kouznetsov. Evaluation of holomorphic ackermanns. Applied and Computational Mathematics. Vol. 3, No. 6, 2014, pp. 307-314.

Im still reading those.

From an academic / career viewpoint these may be good papers.

But I feel the lack of complete explaination and motivation , at least in what I read -at first sight -.

For instance many methods of computation depend on a good " guess " ( I wonder if things can start from the " fake functions " but thats going offtopic ) and then I see things such as (say)

f(z) = 1.23515 log(d).

So natural questions are : what is 1.23515 ?

Does it has a closed form ? How was it computed ? Do you mean 1.23515... ? What is the property of this number ; does the iteration only work if 1.23515 log(d) < f(z) < 1.23516 log(d) ?

How did you find that solution ?
Does the iterate then work for all initial values of z , or do we have a fractal zone where it works ?

Are you talking about bases smaller then eta only in your formula ?
Cant we just rewrite 1.23515 by 1.2 and get the same result ?

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I prefer color wheel graphs ...

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3. I have Book about Superfunctions in Russian:
http://mizugadro.mydns.jp/t/index.php/Суперфункции
https://www.morebooks.de/store/ru/book/С...59-56202-0
http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf
http://mizugadro.mydns.jp/BOOK/202.pd
I am working on the English version and I hope to finish it this year.
If Henryk submits, en fin, our review article "Bunch", I shall be glad to cite it.

4. I need someone to criticise my activity. So, the feedback should be greatly appreciated.

I hope my criticism does not upset you.

At first sight it seems you have 2 topics :

pentation

" Tania functions "

For pentation see the comment above + Why the focus on L and exp(kz) ?

I do not know much about Tania functions or the related physics , but I like the idea of naming functions after girls ??

Tania seems like a sister of Lambert.
Apart from the physics and the identity in the table , does Tania serve another purpose ?

MAYBE you said this before but why did you choose - assuming choice !? - pentation to be periodic ?


Welcome back

regards

tommy1729