Let $\Omega = \Omega_1 \times \cdots \times \Omega_n (n > 1)$ be a product of n Brelot harmonic spaces each of which has a bounded potential, and let K be a compact subset of Ω. Then, K is an n-polar ...

This is a preview. Log in through your library . Abstract It is shown that there exist $2n + 1$ real valued, continuous functions $\phi_0,\ldots, \phi_{2n}$ defined on $\mathbf{R}^n$ such that every ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

The benchmark tests show that the noise-free realization of QA can significantly outperform state-of-the-art classical algorithms. Quantum annealing (QA) is a cutting-edge algorithm that leverages the ...

The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky ...