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A short exact sequence of groups 0-->A-->B-->C-->0 (1) is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct ...

A two-dimensional map also called the Taylor-Greene-Chirikov map in some of the older literature and defined by I_(n+1) = I_n+Ksintheta_n (1) theta_(n+1) = theta_n+I_(n+1) ...

The transformation S[{a_n}_(n=0)^N] of a sequence {a_n}_(n=0)^N into a sequence {b_n}_(n=0)^N by the formula b_n=sum_(k=0)^NS(n,k)a_k, (1) where S(n,k) is a Stirling number ...

In logic, the term "homomorphism" is used in a manner similar to but a bit different from its usage in abstract algebra. The usage in logic is a special case of a "morphism" ...

An integer n such that 3n^3 contains three consecutive 3s in its decimal representation is called a super-3 number. The first few super-3 numbers are 261, 462, 471, 481, 558, ...

The supremum is the least upper bound of a set S, defined as a quantity M such that no member of the set exceeds M, but if epsilon is any positive quantity, however small, ...

The tangent numbers, also called a zag number, and given by T_n=(2^(2n)(2^(2n)-1)|B_(2n)|)/(2n), (1) where B_n is a Bernoulli number, are numbers that can be defined either ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...

The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...