[3]Wioletta Grzegorzewska, Brownian motion, [in:] 'Finite Formulae & Theories of Chance', Arc Publications, p. 41.
[2] Wioletta Grzegorzewska, The late feeding of bees, [in:] 'Finite Formulae & Theories of Chance', Arc Publications, p. 45.
Theoretical framework using thin ring theory provides formulae in terms of geometric and material parameters.
The knowledge spectrum spans from a complex reality (the source of experimental data and information gathered from observations and measurements) to high-level abstractions (e.g., theories, hypotheses, beliefs, concepts, formulae etc).
If quantifier-free formulae correspond to the "real" part of the mathematical theory, the first epsilon-theorem shows that ideal elements can be eliminated from proofs of real statements, provided the axioms are also real statements.
If the formulae given in this section are standard formulae taken from the literature, please supply references.
After all, the majority of the formulae productively involved in that dramatic progress were the wrong formulae from a modern point of view!
In this section, we present some formulae and examples to find the values of finite and infinite series in number theory as an application of Δ ℓ.
Δ ℓ 2 u ( k ) + f ( k, u ( k ) ) = 0, k ∈ [ a, ∞ ), a > 0. and we prove the condition for non existence of non-trivial solution where Δ ℓ u ( k ) = u ( k + ℓ ) − u ( k ) for ℓ > 0. Further we present some formulae and examples to find the values of finite and infinite series in number theory as application of Δ ℓ. MSC 39A12, 39A70, 47B39, 39B60.
These 3751 formulae account for 84-91% of the total magnitude of all formulae assigned per sample.
The NAL-R formula was selected because this formula is a relatively widely used method among linear prescriptive formulae [ 1].
