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A point process is a probabilistic model for random scatterings of points on some space X often assumed to be a subset of R^d for some d. Oftentimes, point processes describe ...

Calabi-Yau spaces are important in string theory, where one model posits the geometry of the universe to consist of a ten-dimensional space of the form M×V, where M is a four ...

A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine consists of a ...

The term discrete percolation is used to describe models of percolation theory whose media are discrete sets like sets of regular lattice points (e.g., bond percolation and ...

Let phi(x_1,...,x_m) be an L_(exp) formula, where L_(exp)=L union {e^x} and L is the language of ordered rings L={+,-,·,<,0,1}. Then there exist n>=m and f_1,...,f_s in ...

A semialgebraic set is a subset of R^n which is a finite Boolean combination of sets of the form {x^_=(x_1,...,x_n):f(x^_)>0} and {x^_:g(x^_)=0}, where f and g are ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

The theorem of Möbius tetrads, also simply called Möbius's theorem by Baker (1925, p. 18), may be stated as follows. Let P_1, P_2, P_3, and P_4 be four arbitrary points in a ...

A logical system which possesses an explicitly stated set of axioms from which theorems can be derived.

A class of processes which attempt to round off a domain and simplify its theory by adjoining elements.