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Each Cartan matrix determines a unique semisimple complex Lie algebra via the Chevalley-Serre, sometimes called simply the "Serre relations." That is, if (A_(ij)) is a k×k ...

The functions describing the horizontal and vertical positions of a point on a circle as a function of angle (cosine and sine) and those functions derived from them: cotx = ...

A partially ordered set (or ordered set or poset for short) (L,<=) is called a complete lattice if every subset M of L has a least upper bound (supremum, supM) and a greatest ...

The composite number problem asks if for a given positive integer N there exist positive integers m and n such that N=mn. The complexity of the composite number problem was ...

The conchoid of de Sluze is the cubic curve first constructed by René de Sluze in 1662. It is given by the implicit equation (x-1)(x^2+y^2)=ax^2, (1) or the polar equation ...

Condorcet's jury theorem states that given a group of voters (a "jury") independently choosing by majority vote between a correct outcome with probability 0<=p<=1 and an ...

A statement is in conjunctive normal form if it is a conjunction (sequence of ANDs) consisting of one or more conjuncts, each of which is a disjunction (OR) of one or more ...

The winding number of a contour gamma about a point z_0, denoted n(gamma,z_0), is defined by n(gamma,z_0)=1/(2pii)∮_gamma(dz)/(z-z_0) and gives the number of times gamma ...

Defining p_0=2, p_n as the nth odd prime, and the nth prime gap as g_n=p_(n+1)-p_n, then the Cramér-Granville conjecture states that g_n<M(lnp_n)^2 for some constant M>1.

Cube point picking is the three-dimensional case of hypercube point picking. The average distance from a point picked at random inside a unit cube to the center is given by ...