Jacob's ladders, crossbreeding in the set of $\zeta$-factorization formulas and selection of families of $\zeta$-kindred real continuous functions

TL;DR

This paper introduces the concept of $$-crossbreeding and complete hybrid formulas within $$-factorization formulas, providing a new criterion for selecting families of $$-kindred real continuous functions, inspired by Mendel's crossbreeding.

Contribution

It presents novel notions of $$-crossbreeding and hybrid formulas, offering a new method for identifying related families of real continuous functions.

Findings

Defined $$-crossbreeding and hybrid formulas.

Proposed a criterion for selecting $$-kindred functions.

Established connections to Mendel's crossbreeding analogy.

Abstract

In this paper we introduce the notion of $\zeta$-crossbreeding in a set of $\zeta$-factorization formulas and also the notion of complete hybrid formula as the final result of that crossbreeding. The last formula is used as a criterion for selection of families of $\zeta$-kindred elements in class of real continuous functions. Dedicated to recalling of Gregory Mendel's pea-crossbreeding.