The original version of this story appeared in Quanta Magazine. If you want to solve a tricky problem, it often helps to get organized. You might, for example, break the problem into pieces and tackle ...

ABSTRACT: In this paper, we consider the model updating problem of the undamped vibroacoustic system with no spill-over (MUP-UVA), which is to update the original system to a new system such that some ...

Abstract: In this study, we introduce numerical methods for discretizing continuous-time linear-quadratic optimal control problems (LQ-OCPs). The discretization of continuous-time LQ-OCPs is ...

The nation relies on cyber systems for commerce, critical infrastructure, national security, and most facets of daily life. However, the growing scale and complexity of cyber technologies–coupled with ...

Forbes contributors publish independent expert analyses and insights. John Hall covers entrepreneurial topics that help companies grow. Many attributes go into strong leadership, such as having a ...

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 UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

A team of quantum computer researchers at quantum computer maker D-Wave, working with an international team of physicists and engineers, is claiming that its latest quantum processor has been used to ...

If you want to accentuate the importance of a problem, it seems sensible to explain how prevalent it is. Lots of people are at risk of Alzheimer’s disease. Lots of women carry a gene that makes them ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

This study presents an (ε, μ)−uniform numerical method for a two-parameter singularly perturbed time-delayed parabolic problems. The proposed approach is based on a fitted operator finite difference ...