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A point p on a regular surface M in R^3 is said to be parabolic if the Gaussian curvature K(p)=0 but S(p)!=0 (where S is the shape operator), or equivalently, exactly one of ...

A catastrophe which can occur for four control factors and two behavior axes. The parabolic umbilic catastrophe is given by the unfolding ...

Let F(nu) and G(nu) be the Fourier transforms of f(t) and g(t), respectively. Then int_(-infty)^inftyf(t)g^_(t)dt ...

A metric defined by d(z,w)=sup{|ln[(u(z))/(u(w))]|:u in H^+}, where H^+ denotes the positive harmonic functions on a domain. The part metric is invariant under conformal maps ...

Let A be a C^*-algebra, then an element u in A is called a partial isometry if uu^*u=u.

An apodization function similar to the Bartlett function.

I((chi_s^2)/(sqrt(2(k-1))),(k-3)/2)=(Gamma(1/2chi_s^2,(k-1)/2))/(Gamma((k-1)/2)), where Gamma(x) is the gamma function.

The Pell-Lucas polynomials Q(x) are the w-polynomials generated by the Lucas polynomial sequence using the generator p(x)=2x, q(x)=1. The first few are Q_1(x) = 2x (1) Q_2(x) ...

Since (2a)/(a+b)=(2ab)/((a+b)b), (1) it follows that a/((a+b)/2)=((2ab)/(a+b))/b, (2) so a/A=H/b, (3) where A and H are the arithmetic mean and harmonic mean of a and b. This ...

The interval (generally, the smallest interval) over which the values of a periodic function recur. Functions may have one or more periods over time and in space.