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The space B of a fiber bundle given by the map f:E->B, where E is the total space of the fiber bundle.

A subset X subset Y is said to be bicollared in Y if there exists an embedding b:X×[-1,1]->Y such that b(x,0)=x when x in X. The map b or its image is then said to be the ...

A metric space X is boundedly compact if all closed bounded subsets of X are compact. Every boundedly compact metric space is complete. (This is a generalization of the ...

The function given by CK_n(x)=cos(nxcos^(-1)x), where n is an integer and -1<x<1.

A change of basis is the transformation of coordinate-based vector and operator representations in a given vector space from one vector basis representation to another.

In the plane, a closed curve is a curve with no endpoints and which completely encloses an area.

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...

Functions which can be expressed in terms of Legendre functions of the first and second kinds. See Abramowitz and Stegun (1972, p. 337). P_(-1/2+ip)(costheta) = (1) = ...

The mathematical study of how to manipulate the parameters affecting the behavior of a system to produce the desired or optimal outcome.

Attractive compounds can be constructed from the cube 3-compounds and their octahedron 3-compound duals. One is illustrated above. This compound will be implemented in a ...