Search Results for ""

The partial differential equation (u_t)/(u_x)=1/4(u_(xxx))/(u_x)-3/8(u_(xx)^2)/(u_x^2)+3/2(p(u))/(u_x^2), where p(u)=1/4(4u^3-g_2u-g_3). The special cases ...

Let E_n(f) be the error of the best uniform approximation to a real function f(x) on the interval [-1,1] by real polynomials of degree at most n. If alpha(x)=|x|, (1) then ...

Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. Whereas mathematics began merely as a calculational ...

A flow defined analogously to the Anosov diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

A property of X is said to hold almost everywhere if the set of points in X where this property fails is contained in a set that has measure zero.

A test for the convergence of Fourier series. Let phi_x(t)=f(x+t)+f(x-t)-2f(x), then if int_0^pi(|phi_x(t)|dt)/t is finite, the Fourier series converges to f(x) at x.

An alternative name for an associated Legendre polynomial.

The determinant G(f_1,f_2,...,f_n)=|intf_1^2dt intf_1f_2dt ... intf_1f_ndt; intf_2f_1dt intf_2^2dt ... intf_2f_ndt; | | ... |; intf_nf_1dt intf_nf_2dt ... intf_n^2dt|.

A square integrable function phi(t) is said to be normal if int[phi(t)]^2dt=1. However, the normal distribution function is also sometimes called "the normal function."

A conjecture that, as proved by Parshin (1968), implies the Mordell conjecture.