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An affine tensor is a tensor that corresponds to certain allowable linear coordinate transformations, T:x^_^i=a^i_jx^j, where the determinant of a^i_j is nonzero. This ...

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, ...

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) ...

The functions theta_s(u) = (H(u))/(H^'(0)) (1) theta_d(u) = (Theta(u+K))/(Theta(k)) (2) theta_c(u) = (H(u))/(H(K)) (3) theta_n(u) = (Theta(u))/(Theta(0)), (4) where H(u) and ...

The algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other ...

A method for numerical solution of a second-order ordinary differential equation y^('')=f(x,y) first expounded by Gauss. It proceeds by introducing a function delta^(-2)f ...

If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...

The variable phi (also denoted am(u,k)) used in elliptic functions and elliptic integrals is called the amplitude (or Jacobi amplitude). It can be defined by phi = am(u,k) ...

A topology that is "potentially" a metric topology, in the sense that one can define a suitable metric that induces it. The word "potentially" here means that although the ...

Baud rate is a measure of the number of times per second a signal in a communications channel changes state. The state is usually voltage level, frequency, or phase angle.