In this paper, we show that for several second-order partial differential equations \begin{align*}L[u] &= A(x,y)u_{xx} + 2B(x,y)u_{xy} + C(x,y)u_{yy} + D(x,y)u_x + E(x,y)u_y \\ &= \lambda_nu\end{align ...

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

Let Φ(z) = ∑∞ 0 βjz j have radius of convergence $r (0 < r < \infty)$ and no singularities other than poles on the circle |z| = r. A complete solution is ...

A mathematician at Carnegie Mellon University has developed an easier way to solve quadratic equations. The mathematician hopes this method will help students avoid memorizing obtuse formulas. His ...