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Tracing through the connections of a branchial graph gives rise to the notion of a kind of space in which states on different branches of history are laid out. In particular, ...

A set of positive integers S is called sum-free if the equation x+y=z has no solutions x, y, z in S. The probability that a random sum-free set S consists entirely of odd ...

Let g be a finite-dimensional Lie algebra over some field k. A subalgebra h of g is called a Cartan subalgebra if it is nilpotent and equal to its normalizer, which is the ...

Catalan's triangle is the number triangle 1 ; 1 1 ; 1 2 2 ; 1 3 5 5 ; 1 4 9 14 14 ; 1 5 14 28 42 42 ; 1 6 20 48 90 132 132 (1) (OEIS A009766) with entries given by ...

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

A notation used to describe curves. The fundamental principle of Clebsch-Aronhold notation states that if each of a number of forms be replaced by a power of a linear form in ...

The subset C of the Euclidean plane formed by the union of the x-axis, the line segment with interval [0,1] of the y-axis, and the sequence of segments with endpoints (1/n,0) ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

A topological space X such that for every closed subset C of X and every point x in X\C, there is a continuous function f:X->[0,1] such that f(x)=0 and f(C)={1}. This is the ...

The inversion of a convolution equation, i.e., the solution for f of an equation of the form f*g=h+epsilon, given g and h, where epsilon is the noise and * denotes the ...