Abstract: LaSalle’s invariance principle is a commonly used extension of Lyapunov’s second method to study asymptotic stability of nonlinear systems. If the system can be written in polynomial form, ...

Abstract: Inhomogeneous linear ordinary differential equations (ODEs) and systems of ODEs can be solved in a variety of ways. However, hardware circuits that can perform the efficient analog ...

Re: “Too embarrassing to go downtown,” letter, Sept. 8. When I read letters like this I think about the expression “cutting ...

Sparse methods are primarily valuable for systems in which the number of non-zero entries is substantially less than the overall size of the matrix. Such situations are common in physical systems, ...

Can neural networks learn to solve partial differential equations (PDEs)? We investigate this question for two (systems of) PDEs, namely, the Poisson equation and the steady Navier–Stokes equations.

For centuries, astronomers have puzzled over the origins of one of the universe's oldest and densest stellar systems, known ...

Scientists are rethinking the universe’s deepest mysteries using numerical relativity, complex computer simulations of Einstein’s equations in extreme conditions. This method could help explore what ...

The latest episode of Project Runway Season 21 delivered a stunning twist that left everyone in shock. At the beginning of ...

Hamilton's rule, introduced in the 1960s, says that altruism—helping others at your own expense—can evolve when the benefits ...

The coordinates of the turning point and the equation of the line of symmetry can be found by writing the quadratic expression in completed square form. Find the equation of the line of symmetry and ...

An elimination tag team match to determine contenders to the WWE Women's Tag Team Championships is set for next week's "WWE ...

Learn how to simplify complex calculations and visualize data with an online graphing calculator. A graphing calculator is a handheld device or online tool designed to plot graphs, solve complex ...