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The 10.1.2 equation A^(10)=B^(10)+C^(10) (1) is a special case of Fermat's last theorem with n=10, and so has no solution. No 10.1.n solutions are known with n<13. A 10.1.13 ...

Toroidal functions are a class of functions also called ring functions that appear in systems having toroidal symmetry. Toroidal functions can be expressed in terms of the ...

Gives a lower bound for the inner product (Lu,u), where L is a linear elliptic real differential operator of order m, and u has compact support.

The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

Denote the nth derivative D^n and the n-fold integral D^(-n). Then D^(-1)f(t)=int_0^tf(xi)dxi. (1) Now, if the equation D^(-n)f(t)=1/((n-1)!)int_0^t(t-xi)^(n-1)f(xi)dxi (2) ...

A surface which a monkey can straddle with both legs and his tail. A simple Cartesian equation for such a surface is z=x(x^2-3y^2), (1) which can also be given by the ...

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

If a minimal surface is given by the equation z=f(x,y) and f has continuous first and second partial derivatives for all real x and y, then f is a plane.

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...