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The apodization function A(x)=(1-(x^2)/(a^2))^2. Its full width at half maximum is sqrt(4-2sqrt(2))a. Its instrument function is ...

A map f:X-->Y is called constant with constant value y if f(x)=y for all x in X, i.e., if all elements of X are sent to same element y of Y.

A hypergeometric function in which one parameter changes by +1 or -1 is said to be contiguous. There are 26 functions contiguous to _2F_1(a,b;c;x) taking one pair at a time. ...

The space of continuously differentiable functions is denoted C^1, and corresponds to the k=1 case of a C-k function.

Contracting tensors lambda with nu in the Bianchi identities R_(lambdamunukappa;eta)+R_(lambdamuetanu;kappa)+R_(lambdamukappaeta;nu)=0 (1) gives ...

The apodization function A(x)=cos((pix)/(2a)). Its full width at half maximum is 4a/3. Its instrument function is I(k)=(4acos(2piak))/(pi(1-16a^2k^2)), which has a maximum of ...

Let f*g denote the cross-correlation of functions f(t) and g(t). Then f*g = int_(-infty)^inftyf^_(tau)g(t+tau)dtau (1) = ...

A number taken to the power 3 is said to be cubed, so x^3 is called "x cubed." This terminology derives from the fact that the volume of a cube of edge length x is given by ...

Let gamma(t) be a smooth curve in a manifold M from x to y with gamma(0)=x and gamma(1)=y. Then gamma^'(t) in T_(gamma(t)), where T_x is the tangent space of M at x. The ...

A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve x^3-y^2=0, which ...