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The S distribution is defined in terms of its distribution function F(x) as the solution to the initial value problem (dF)/(dx)=alpha(F^g-F^h), where F(x_0)=F_0 (Savageau ...

A root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line ...

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...

A map u:M->N, between two compact Riemannian manifolds, is a harmonic map if it is a critical point for the energy functional int_M|du|^2dmu_M. The norm of the differential ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

A linkage with six rods which draws the inverse of a given curve. When a pencil is placed at P, the inverse is drawn at P^' (or vice versa). If a seventh rod (dashed) is ...

The set of fixed points which do not move as a knot is transformed into itself is not a knot. The conjecture was proved in 1978 (Morgan and Bass 1984). According to Morgan ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

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.