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 ...

We consider the problem of efficiently estimating multivariate densities and their modes for moderate dimensions and an abundance of data. We propose polynomial histograms to solve this estimation ...

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 ...

A mathematician has uncovered a way of answering some of algebra's oldest problems. University of New South Wales Honorary Professor Norman Wildberger, has revealed a potentially game-changing ...