Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit contraction (special homotopy equivalence) from the ...

Nilpotent adjacency matrix methods have proven useful for counting self-avoiding walks (paths, trails, cycles, and circuits) in finite graphs. In the current work, these ...

The implantation of an intraocular lens following cataract surgery has become the standard method of correcting residual refraction following cataract surgery. The ...

Sometimes in calculus, it is useful to see the x, y, and z axes in a 3D plot. This notebook illustrates a method for placing a coordinate axis set in the middle of a 3D plot ...

A simple and fast method for computing the exact distribution of the ranked-set sample sign test statistic is suggested. The proposed technique works even for very large ...

The method of analytic continuation is used to formulate a condition that is equivalent to the Riemann hypothesis on the zeros of the zeta function. Numerical experiments to ...

A fast new method for tropospheric delay predictions is discussed. It uses Mathematica for critical functional fits to refractivity profiles, and a critical closed-form ...

This notebook discusses methods of solving the simple pendulum equation. It is the first in a series of notebooks showing how Mathematica can be used to find exact power ...

This notebook is the first in an instructional series which shows how Mathematica may be used to solve ordinary differential equations (with and without the use of DSolve). ...

This example shows how a one- and a two-dimensional function can be approximated in machine learning framework using various supervised learning methods, including SOM, ...