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The Wiener index W, denoted w (Wiener 1947) and also known as the "path number" or Wiener number (Plavšić et al. 1993), is a graph index defined for a graph on n nodes by ...

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).

A graph or directed graph together with a function which assigns a positive real number to each edge (Harary 1994, p. 52).

The Barth sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was ...

The Stieltjes integral is a generalization of the Riemann integral. Let f(x) and alpha(x) be real-valued bounded functions defined on a closed interval [a,b]. Take a ...

The term "wedge" has a number of different meanings in mathematics. It is sometimes used as another name for the caret symbol. The term also refers to the notation ( ^ ) used ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

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 ...

The triangle DeltaM_AM_BM_C formed by joining the midpoints of the sides of a triangle DeltaABC. The medial triangle is sometimes also called the auxiliary triangle (Dixon ...