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The system of partial differential equations u_t+uu_x+vu_y=U_t+UU_x+mu/rhou_(yy) u_x+v_y=0.

The problem of forecasting future values X_(t+tau) (tau>0) of a weakly stationary process {X_t} from the known values X_s (s<=t).

A primary ideal is an ideal I such that if ab in I, then either a in I or b^m in I for some m>0. Prime ideals are always primary. A primary decomposition expresses any ideal ...

5((x^5)_infty^5)/((x)_infty^6)=sum_(m=0)^inftyP(5m+4)x^m, where (x)_infty is a q-Pochhammer symbol and P(n) is the partition function P.

A type of cusp as illustrated above for the curve x^4+x^2y^2-2x^2y-xy^2+y^2=0.

If the fourth moment mu_4!=0, then P(|x^_-mu_4|>=lambda)<=(mu_4+3(N-1)sigma^4)/(N^3lambda^4), where sigma^2 is the variance.

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.