Abstract: Control of underactuated mechanical systems via energy shaping is a well-established, robust design technique. Unfortunately, its application is often stymied by the need to solve partial ...

Abstract: There are some quasi-tridiagonal system of linear equations arising from numerical simulations, and some solving algorithms encounter great challenge on solving quasi-tridiagonal system of ...

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, ...

Master the Toolkit of AI and Machine Learning. Mathematics for Machine Learning and Data Science is a beginner-friendly Specialization where you’ll learn the fundamental mathematics toolkit of machine ...

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

Stochastic dynamical systems arise in many scientific fields, such as asset prices in financial markets, neural activity in ...

Collaboration feels like a human challenge but behaves like a system. Systems thinking resolves this paradox by revealing how ...

Jenny Quinn, executive director of the Seattle Universal Math Museum, shows off a solved Fibonacci sequence puzzle. (GeekWire ...

This study offers a valuable theoretical framework for quantifying molecular transport across interfaces between coexisting liquid phases, emphasizing interfacial resistance as a central factor ...

A mathematical brain teaser challenges people to solve the matchstick equation in just two moves. The puzzle uses matchsticks to create an equation that shows 3 + 3 = 8 and instructs viewers to make ...

Systems thinking is the discipline of seeing problems as part of an interconnected whole, not isolated events. It forces us ...

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 ...