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The term "Cartan algebra" has two meanings in mathematics, so care is needed in determining from context which meaning is intended. One meaning is a "Cartan subalgebra," ...

This theorem states that, for a partial differential equation involving a time derivative of order n, the solution is uniquely determined if time derivatives up to order n-1 ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

The idiosyncratic polynomial is the bivariate graph polynomial defined as the characteristic polynomial in x of A+y(J-I-A), where A is the adjacency matrix, J is the unit ...

Also known as metric entropy. Divide phase space into D-dimensional hypercubes of content epsilon^D. Let P_(i_0,...,i_n) be the probability that a trajectory is in hypercube ...

The Laplacian polynomial is the characteristic polynomial of the Laplacian matrix. The second smallest root of the Laplacian polynomial of a graph g (counting multiple values ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

The base 2 method of counting in which only the digits 0 and 1 are used. In this base, the number 1011 equals 1·2^0+1·2^1+0·2^2+1·2^3=11. This base is used in computers, ...

A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...