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Given F_1(x,y,z,u,v,w) = 0 (1) F_2(x,y,z,u,v,w) = 0 (2) F_3(x,y,z,u,v,w) = 0, (3) if the determinantof the Jacobian |JF(u,v,w)|=|(partial(F_1,F_2,F_3))/(partial(u,v,w))|!=0, ...

Every finite-dimensional Lie algebra of characteristic p!=0 has a faithful finite-dimensional representation.

If f_1,...,f_m:R^n->R are exponential polynomials, then {x in R^n:f_1(x)=...f_n(x)=0} has finitely many connected components.

The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

The unit lower half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]<0}.

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

A nonuniform rational B-spline surface of degree (p,q) is defined by ...

The identities between the symmetric polynomials Pi_k(x_1,...,x_n) and the sums of kth powers of their variables S_k(x_1,...,x_n)=sum_(j=1)^nx_j^k. (1) The identities are ...