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A group or other algebraic object is called non-Abelian if the law of commutativity does not always hold, i.e., if the object is not Abelian. For example, the group of ...

A geometry in which Archimedes' axiom does not hold.

The star figure {9/3} composed of three equilateral triangles rotated at angles 0 degrees, 40 degrees, and 80 degrees. It has been called the star of Goliath by analogy with ...

A generalization of Student's t-distribution known as the noncentral Student's t-distribution is given by (1) where Gamma(z) is the gamma function and _1F_1(a;b;z) is a ...

A noncommutative ring R is a ring in which the law of multiplicative commutativity is not satisfied, i.e., a·b!=b·a for any two elements a,b in R. In such a case, the ...

Let gamma be a path in C, w=f(z), and theta and phi be the tangents to the curves gamma and f(gamma) at z_0 and w_0. If there is an N such that f^((N))(z_0) != 0 (1) ...

A ruled surface parameterization x(u,v)=b(u)+vg(u) is called noncylindrical if gxg^' is nowhere 0. A noncylindrical ruled surface always has a parameterization of the form ...

A function f(x) is said to be nondecreasing on an interval I if f(b)>=f(a) for all b>a, where a,b in I. Conversely, a function f(x) is said to be nonincreasing on an interval ...

A nonempty set is a set containing one or more elements. Any set other than the empty set emptyset is therefore a nonempty set. Nonempty sets are sometimes also called ...

If A=>!B and B=>!A (i.e., (A=>!B) ^ (B=>!A), where !A denotes NOT, => denotes implies, and ^ denotes AND), then A and B are said to be inequivalent, a relationship which is ...