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A generalization of Schröter's formula.

A common mechanism which generates singularities from smooth initial conditions.

For a smooth harmonic map u:M->N, where del is the gradient, Ric is the Ricci curvature tensor, and Riem is the Riemann tensor.

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

For homogeneous polynomials P and Q of degree m and n, then sqrt((m!n!)/((m+n)!))[P]_2[Q]_2<=[P·Q]_2<=[P]_2[Q]_2, where [P·Q]_2 is the Bombieri norm.

The system of partial differential equations u_t = b·v_x (1) b_(xt) = u_(xx)b+axv_x-2vx(vxb). (2)

The partial differential equation (1-u_t^2)u_(xx)+2u_xu_tu_(xt)-(1+u_x^2)u_(tt)=0.

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

A bounded left approximate identity for a normed algebra A is a bounded net {e_alpha}_(alpha in I) with the property lim_(alpha)e_alphaa=a for a in A. Bounded right and ...

The function Pi_(a,b)(x)=H(x-a)-H(x-b) which is equal to 1 for a<=x<=b and 0 otherwise. Here H(x) is the Heaviside step function. The special case Pi_(-1/2,1/2)(x) gives the ...