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The Balaban index J is a graph index defined for a graph on n nodes, m edges, and c connected components by J=m/(gamma+1)sum_((i,j) in E(G))(D_iD_j)^(-1/2), where gamma=m-n+c ...

A barrel solid of revolution composed of parallel circular top and bottom with a common axis and a side formed by a smooth curve symmetrical about the midplane. The term also ...

The probability P(a,n) that n random arcs of angular size a cover the circumference of a circle completely (for a circle with unit circumference) is ...

Define S_n(x) = sum_(k=1)^(infty)(sin(kx))/(k^n) (1) C_n(x) = sum_(k=1)^(infty)(cos(kx))/(k^n), (2) then the Clausen functions are defined by ...

Let V be an n-dimensional linear space over a field K, and let Q be a quadratic form on V. A Clifford algebra is then defined over T(V)/I(Q), where T(V) is the tensor algebra ...

A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). For a right circular cone, let s be the slant height and R_1 ...

A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The ...

A curtate cycloid, sometimes also called a contracted cycloid, is the path traced out by a fixed point at a radius b<a, where a is the radius of a rolling circle. Curtate ...

Form a sequence from an alphabet of letters [1,n] such that there are no consecutive letters and no alternating subsequences of length greater than d. Then the sequence is a ...

A method of determining the maximum number of positive and negative real roots of a polynomial. For positive roots, start with the sign of the coefficient of the lowest (or ...