Search Results for ""

The approximation of a piecewise monotonic function f by a polynomial with the same monotonicity. Such comonotonic approximations can always be accomplished with nth degree ...

If k is the elliptic modulus of an elliptic integral or elliptic function, then k^'=sqrt(1-k^2) (1) is called the complementary modulus. Complete elliptic integrals with ...

Define A^' to be the point (other than the polygon vertex A) where the triangle median through A meets the circumcircle of ABC, and define B^' and C^' similarly. Then the ...

If g is a continuous function g(x) in [a,b] for all x in [a,b], then g has a fixed point in [a,b]. This can be proven by supposing that g(a)>=a g(b)<=b (1) g(a)-a>=0 ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_7=f(x_7). Then Hardy's rule approximating the ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

An isogonal mapping is a transformation w=f(z) that preserves the magnitudes of local angles, but not their orientation. A few examples are illustrated above. A conformal ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

There exist lattices in n dimensions having hypersphere packing densities satisfying eta>=(zeta(n))/(2^(n-1)), where zeta(n) is the Riemann zeta function. However, the proof ...