A third class of applications is branching process constructions which are used to gain greater understanding of other mathematical structures, such as critical phenomena in percolation.
Any topos may be conceived as possible "universe of discourse" in which mathematical assertions may be interpreted and mathematical constructions may be performed.
Some new methods are motivated by mathematical constructions such as tree metrics, while the rest employ tree concepts which work well in practice.
The device of associating mechanical properties with the fields, which up to this point had appeared merely as convenient mathematical constructions, has even greater implications when conservation of energy is considered.
Jacob de Gelder (1765-1848) a mathematical ideologist proposed a geometric construction which gives π correct to 6 decimal places.
But then no contact at all is made with the concepts that figure in meaning explanations, which have to do with our cognitive capacities, such as those of effecting mathematical constructions or those of understanding, learning, and using a language.
We found differences in the mathematical construction of these two criteria which made it difficult to decide which of them is better suited for selecting the most relevant rupture-repair episodes in the analyzed curves.
"But they are not purely mathematical constructions, either".
The natural numbers are mental constructions, the real numbers are mental constructions, proofs and theorems are mental constructions, mathematical meaning is a mental construction… Mathematical constructions are produced by the ideal mathematician, i.e., abstraction is made from contingent, physical limitations of the real life mathematician.
Evaluating several dispersal functions was necessary because these mathematical constructions behave differently across dispersal distances.
