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The subset {0} of a ring. It trivially fulfils the definition of ideal since it is a group (specifically, the zero group), and it is closed under multiplication by any ...

The zero product property asserts that, for elements a and b, ab=0=>a=0 or b=0. This property is especially relevant when considering algebraic structures because, e.g., ...

The partial differential equation ((partial^2)/(partialt^2)-(partial^2)/(partialx^2))((u_(xy))/u)+2(u^2)_(xt)=0.

The de Grey-Haugstrup graphs are two 6-chromatic graphs on 47 and 48 vertices that are unit-distance in 3 dimensions (de Grey and Haugstrup 2020).

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...

A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...