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Let c=(c_1,...,c_n) be a point in C^n, then the open polydisk is defined by S={z:|z_j-c_j|<|z_j^0-c_j|} for j=1, ..., n.

The highest power in a univariate polynomial is known as its degree, or sometimes "order." For example, the polynomial P(x)=a_nx^n+...+a_2x^2+a_1x+a_0 is of degree n, denoted ...

The term used in physics and engineering for a harmonic function. Potential functions are extremely useful, for example, in electromagnetism, where they reduce the study of a ...

The power circles of a reference triangle are the three circles centered at the midpoints M_A, M_B, M_C of the sides of a reference triangle DeltaABC that pass through the ...

A unit in a ring is an element u such that there exists u^(-1) where u·u^(-1)=1.

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

The distance a point moves due to shear divided by the perpendicular distance of a point from the invariant line.

Consider (1) If the probability distribution is governed by a Markov process, then P_3(y_1,t_1;y_2,t_2|y_3,t_3) = P_2(y_2,t_2|y_3,t_3) (2) = P_2(y_2|y_3,t_3-t_2). (3) ...

A square grid is a grid formed by tiling the plane regularly with squares.