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The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

The finite difference is the discrete analog of the derivative. The finite forward difference of a function f_p is defined as Deltaf_p=f_(p+1)-f_p, (1) and the finite ...

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

The Möbius-Kantor graph is the unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. Its unique canonical LCF notation is [5,-5]^8. The ...

The m×n rook graph (confusingly called the m×n grid by Brouwer et al. 1989, p. 440) and also sometimes known as a lattice graph (e.g., Brouwer) is the graph Cartesian product ...