File:Boris.jpg

Немцов Борис Ефимович (см. Путин убил Немцова), 2015, ^[1]

Nemtsov function

Family name Nemtsov is used as name of the Nemtsov function. The need to give the specific name to the special single-parametric 4th order polynomial had been revealed 2015.02.27, in the day, when Putin killed Nemtsov. To year 2025, no other scientific concept of that sad event is found. This makes the family name "Nemtsov" to be a memorial mark, label on the timeline of Human History. So, the image is used in article Nemtsov function. That article describes the special 4th order polynomial

\[ \mathrm{nem}_q(z)=x+z^3+qz^4 \]

Also, the image is used as Figure 13.10 at page 174 of book Superfunctions^[2].

The inverse function ArqNem is declared to be default inverse function for the Nemtsov function;

\[ \mathrm{ArqNem}_q=\mathrm{nem}_q^{-1} \]

functions nem and ArqNem are used to implement the superfunction SuNem, the abelfunction AuNem and the non-integer iterates of the Nemtsov function

\[ \mathrm{nem}_q^n(z)=\mathrm{SuNem}_q\big( n + \mathrm{AuNem}_q(z)\big) \]

in such a way that

\[ \mathrm{nem}_q^m\big(\mathrm{nem}_q^n(z)\big)=\mathrm{SuNem}_q^{m+n}(z) \]

Here, the numbers \(m\) and \(n\) have no need to be integer, they can be even complex; the function can be iterated complex number of times.

The Nemtsov function had been considered as an attempt to construct a real-homomorphic transfer function such that its superfunction, abelfunction cannot be implemented as special functions. That attempt was not successful: to year 2016, both functions SuNem and AuNem are implemented.

To year 2025, the consideration of the Nemtsov function remains the last attempts to construct a counter-example to limit range of validity of formalism of superfunctions.

However, the multiple attempts to construct such an example cannot substitute the formal proof of the conjecture below:

For any growing real-holomoprhic transfer function \(T\), there exist superfunction as real-holomorphic solution \(F\) of the transfer equation \[ F(z+1)=T(F(z)) \] valid at least in some vicinity of the positive part of the real axis.

Upon a construction of such a proof, the formula of the resulting theorem may slightly deviate from the euristic conjecture above.

Warning

The image is uploaded at TORI with Scientific goals.

This uploading should not be considered as an attempt to prolong the agony of the putin's Russia.
This uploading should not be considered as an attempt to boost the collapse of RF.
However Editor keeps his right to call things with their proper names, to give definitions to the fussy terms and euphemisms that may cause a confusion, to invent new objects and give them new names as soon as these objects become useful in description(s) of observed things, to construct scientific models and to compare their predictions to a posteriori observations.

References

Keywords

«ArqNem», «AuNem», «Boris Nemtsov», «Moscovia», «Nembra», «Nemtsov bridge», «Nemtsov function», «Putin killed Nemtsov», «State terror», «SuNem», «Superfunctions», «Transferfunction»,

«Московия», «Немцов Борис Ефимович», «Немцов мост», «Путин убил Немцова»,