There is an additional problem in that many of the maps in chaos studies (e.g., the baker's transformation) have purely mathematical origins rather than being derived from some more complex model for a target system.
The abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way, while retaining their essential structural aspects.
The examples below range from purely descriptive (A) which rely on a clinical impression, through hierarchical methods (B) which are mathematical in origin but requires a supplementary clinical judgment, to the very mathematical methods (C) which rely on the acceptance of a pre-specified statistical model.
The title refers to a stunning mathematical conclusion whose origin is something of a mystery.
The log file was then converted to a classic stress-strain curve, and values for the basic mechanical properties strength, rigidity, and work to fracture were obtained using a mathematical software package (Origin version 7.5; OriginLab Corp., Northampton, MA).
Thus, many mathematical recreations of early origin that have reappeared from time to time in new dress seem to have survived chiefly because they appeal to man's sense of curiosity or mystery.
For all the talk of Tensor Processing Units, the key innovations in AI are mathematical and software in origin, before hardware performance optimization.
A mathematical proof of the origin of the problem is proposed.
It was indeed attended by, among others, a large group of mathematical scientists of Turkish origin not only from Turkey, but also from elsewhere.
