Search Results for ""

Two functions f(x) and g(x) are orthogonal over the interval a<=x<=b with weighting function w(x) if <f(x)|g(x)>=int_a^bf(x)g(x)w(x)dx=0. (1) If, in addition, ...

A pair of functions phi_i(x) and phi_j(x) are orthonormal if they are orthogonal and each normalized so that int_a^b[phi_i(x)]^2w(x)dx = 1 (1) int_a^b[phi_j(x)]^2w(x)dx = 1. ...

The variation of a function which exhibits slope changes, also called the saltus of a function. A series may also oscillate, causing it not to converge.

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

If f(x) is a monotonically increasing integrable function on [a,b] with f(b)<=0, then if g is a real function integrable on [a,b], ...

A fixed point of a linear transformation for which the rescaled variables satisfy (delta-alpha)^2+4betagamma=0.

A partial differential equation of second-order, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called parabolic if the matrix Z=[A B; B C] (2) ...

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 ...