See the article on rate distortion theory for a mathematical explanation of this threshold effect.

They developed the endogenous growth theory that includes a mathematical explanation of technological advancement.

I believe that we should continue to look for a mathematical explanation for stability.

This supplied a mathematical explanation for the apparent computational difficulty of finding optimal tours.

This process can be quite complex (see root mean square for a detailed mathematical explanation).

The patent also contains mathematical explanations regarding the inner state of his machine.

There are no mathematical explanations yet for life, love or consciousness.

Stevin's later patents were all based on mill technology, and he described his requests with mathematical explanations.

To find the elasticity of demand using the mathematical explanation of the total revenue test, it's necessary to use the following rule:

A mathematical explanation of the paradox, showing that it is not a contradiction in mathematics, was given by Skolem (1922).