Synopsis:

This post writes down several theorems and remarks for research purposes.

Theorem A:

There exists an equation in \( \mathbb{R} \):

\( \mathcal{C}_k \cdot \mathcal{F}_k(x) = \iiint_{D} G_k(x) \, dx \).

And thus the following equation of a tensor \( \mathcal{C} \):

\( \mathcal{C}_k = \pm \frac{\iiint_{D} G_k(x) \, dx}{\mathcal{F}_k(x)} \).

Where \( \forall \mathcal{C}_k, \mathcal{F}_k, \mathcal{G}_k(x) \in \mathbb{C} \). And \( \forall x \in \mathbb{R}. \)