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In spherical coordinates, the scale factors are h_r=1, h_theta=rsinphi, h_phi=r, and the separation functions are f_1(r)=r^2, f_2(theta)=1, f_3(phi)=sinphi, giving a Stäckel ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

A d-dimensional discrete percolation model on a regular point lattice L=L^d is said to be oriented if L is an oriented lattice. One common such model takes place on the ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthonormal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

For every even dimension 2n, the symplectic group Sp(2n) is the group of 2n×2n matrices which preserve a nondegenerate antisymmetric bilinear form omega, i.e., a symplectic ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

A cylindrical segment, sometimes also called a truncated cylinder, is the solid cut from a circular cylinder by two (or more) planes. If there are two cutting planes, one ...

A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, ...