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There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means ...

An irreducible representation of a group is a group representation that has no nontrivial invariant subspaces. For example, the orthogonal group O(n) has an irreducible ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

The word quantile has no fewer than two distinct meanings in probability. Specific elements x in the range of a variate X are called quantiles, and denoted x (Evans et al. ...

A public-key cryptography algorithm which uses prime factorization as the trapdoor one-way function. Define n=pq (1) for p and q primes. Also define a private key d and a ...

A real polynomial P is said to be stable if all its roots lie in the left half-plane. The term "stable" is used to describe such a polynomial because, in the theory of linear ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

The Kepler-Poinsot polyhedra are four regular polyhedra which, unlike the Platonic solids, contain intersecting facial planes. In addition, two of the four Kepler-Poinsot ...