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The mean square displacement (MSD) of a set of N displacements x_n is given by <|x|^2>=sum_(k=1)^N|x_k|^2. It arises particularly in Brownian motion and random walk problems. ...

A nonuniform rational B-spline surface of degree (p,q) is defined by ...

Am octagonal prims is a prism composed of octagonal faces. The regular right octagonal prism of unit edge length has surface area and volume S = 4(3+sqrt(2)) (1) V = ...

A octagrammic prism is a prism formed by two regular octagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

The pentagonal cupola is Johnson solid J_5. Its faces consist of 5 equilateral triangles, 5 squares, 1 pentagon, and one decagon. The surface area and volume of the ...

An attractive compound can be constructed of 6 pentagonal prisms having unit edge lengths, as illustrated above. A net for the solid is illustrated above, where s_1 = ...

A 1-form omega=sum_(i=1)^na_i(x)dx_i such that omega=0.

A proper subset S^' of a set S, denoted S^' subset S, is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is ...

V=100(Q_3-Q_1)/(Q_3+Q_1), where Q_1 and Q_3 are the first and third quartiles and Q_3-Q_1 is the interquartile range.

A queue is a special kind of list in which elements may only be removed from the bottom by a pop action or added to the top using a push action. Examples of queues include ...