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The partial differential equation u_t=u_(xxxxx)+5/2u_(xxx)u+(25)/4u_(xx)u_x+5/4u^2u_x.

The partial differential equation u_t+del ^4u+del ^2u+1/2|del u|^2=0, where del ^2 is the Laplacian, del ^4 is the biharmonic operator, and del is the gradient.

A function that has a natural boundary.

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

The numbers B_(n,k)(1!,2!,3!,...)=(n-1; k-1)(n!)/(k!), where B_(n,k) is a Bell polynomial.

Whittaker and Watson (1990, pp. 539-540) write Lamé's differential equation for ellipsoidal harmonics of the first kind of the four types as ...

The system of partial differential equations U_t=U·U_(xx)+U·LambdaU.

A self-adjoint elliptic differential operator defined somewhat technically as Delta=ddelta+deltad, where d is the exterior derivative and d and delta are adjoint to each ...

A law in (2-valued) logic which states there is no third alternative to truth or falsehood. In other words, for any statement A, either A or not-A must be true and the other ...

Let alpha(x) be a monotone increasing function and define an interval I=(x_1,x_2). Then define the nonnegative function U(I)=alpha(x_2)-alpha(x_1). The Lebesgue integral with ...