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dN^^+kappa_idr=0, where N^^ is the unit normal vector and kappa_i is one of the two principal curvatures.

For algebraic alpha |alpha-p/q|<1/(q^(2+epsilon)), with epsilon>0, has finitely many solutions. Klaus Roth received a Fields medal for this result.

The partial differential equation u_t+45u^2u_x+15u_xu_(xx)+15uu_(xxx)+u_(xxxxx)=0.

A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

Suppose f(x) is a function of x that is twice differentiable at a stationary point x_0. 1. If f^('')(x_0)>0, then f has a local minimum at x_0. 2. If f^('')(x_0)<0, then f ...

The Seiberg-Witten equations are D_Apsi = 0 (1) F_A^+ = -tau(psi,psi), (2) where tau is the sesquilinear map tau:W^+×W^+->Lambda^+ tensor C.

If a matrix A has a matrix of eigenvectors P that is not invertible (for example, the matrix [1 1; 0 1] has the noninvertible system of eigenvectors [1 0; 0 0]), then A does ...

A surface parameterized in variables u and v is called smooth if the tangent vectors in the u and v directions satisfy T_uxT_v!=0, where AxB is a cross product.

A solvable Lie group is a Lie group G which is connected and whose Lie algebra g is a solvable Lie algebra. That is, the Lie algebra commutator series ...

Let X and Y be topological spaces. Then their join is the factor space X*Y=(X×Y×I)/∼, (1) where ∼ is the equivalence relation (x,y,t)∼(x^',y^',t^')<=>{t=t^'=0 and x=x^'; or ; ...