Another very important matter is the identification as nearly as possible, not absolutely proved by mathematical demonstration, that the Lualaba is the Congo.
From basic physics, a detailed mathematical demonstration that the first modal damping ratio of a structure equipped with the MPD system is always larger than the first modal damping ratio of a structure equipped with the SPD system is provided here.
If we are only seeking an a priori proof of something (anything at all!), then why not rest content with a mathematical demonstration that there exists an even prime number?
Galileo, on the other hand, countered that the spots were on or near the surface of the Sun itself, and he supported his position with a series of meticulous observations and mathematical demonstrations that eventually convinced even his rival.
These results represent a direct demonstration that, as predicted by mathematical modeling, binding of BSP to albumin indeed results in a more homogeneous distribution of BSP within the liver acinus.
"This is the most convincing demonstration that I've ever seen of the armpit effect," said Dr. Wayne Getz, mathematical biologist at University of California, who has looked for the armpit effect in honeybees.
This means that most mathematical theorems are one thing A said of another C and that every mathematical demonstration has a middle term B which explains the connection between A and C. Aristotle provides several examples of such triads of terms in mathematics, e.g., two right angles-angles about a point-triangle, or right angle-half two right angles-angle in a semicircle.
Aquinas and the others who held to his view recognized that a demonstrable attribute in a natural thing would have to be a potentiality, though, of course, an actuality could be demonstrated in a mathematical demonstration, where efficient causation is not at issue, and an occurrent attribute can be shown to inhere in the subject necessarily and at every time.
It is absolutely decisive for the consistency of the argument that the necessity of the hypothesis is guaranteed by the fact that it already exists as a mathematical demonstration (by Euclid, Elements XIII, prop. 18, schol)., according to which there are only five regular ("Platonic" for the tradition) polyhedra.
However, the mathematical demonstration of the proposed index is based on a somewhat impractical hypothesis that considers impedance without resistive component.
Although reproducing that 2003 study is a useful demonstration that their model is applicable beyond slime molds, Döbereiner points out that from a mathematical standpoint, such a demonstration is somewhat redundant.
