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A bitangent is a line that is tangent to a curve at two distinct points. Aa general plane quartic curve has 28 bitangents in the complex projective plane. However, as shown ...

A fundamental system of logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924). This mathematical discipline was ...

A special case of Apollonius' problem requiring the determination of a circle touching three mutually tangent circles (also called the kissing circles problem). There are two ...

In order to find integers x and y such that x^2=y^2 (mod n) (1) (a modified form of Fermat's factorization method), in which case there is a 50% chance that GCD(n,x-y) is a ...

A doubly stochastic matrix is a matrix A=(a_(ij)) such that a_(ij)>=0 and sum_(i)a_(ij)=sum_(j)a_(ij)=1 is some field for all i and j. In other words, both the matrix itself ...

A connected graph is said to be highly irregular if the neighbors of each vertex have distinct vertex degrees. Highly irregular graphs exist on all orders except 3, 5 and 7, ...

An isolated singularity is a singularity for which there exists a (small) real number epsilon such that there are no other singularities within a neighborhood of radius ...

An integer j(n) is called a jumping champion if j(n) is the most frequently occurring difference between consecutive primes <=n (Odlyzko et al. 1999). This term was coined by ...

Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...

A modified spherical Bessel function of the first kind (Abramowitz and Stegun 1972), also called a "spherical modified Bessel function of the first kind" (Arfken 1985), is ...