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The solution u(x,y)=int_0^xdxiint_1^yR(xi,eta;x,y)f(xi,eta)deta, where R(x,y;xieta) is the Riemann function of the linear Goursat problem with characteristics phi=psi=0 ...

The method for solving the Goursat problem and Cauchy problem for linear hyperbolic partial differential equations using a Riemann function.

A transformation consisting of rotations and translations which leaves a given arrangement unchanged.

A negative number multiplied by another negative number gives a positive number.

The set of "critical values" of a map u:R^n->R^n of map class C^1 has Lebesgue measure 0 in R^n.

A local-ringed space which is locally isomorphic to an affine scheme.

For R[z]>0, where J_nu(z) is a Bessel function of the first kind.

The symbol ; given special meanings in several mathematics contexts, the most common of which is the covariant derivative.

The distance a point moves due to shear divided by the perpendicular distance of a point from the invariant line.

The Japanese variant of the game of chess. Shogi is played on a 9×9 uncheckered board, and each player begins with 20 pieces: one king, one rook, one bishop, two gold ...