Abstract: Nonlinear equation systems are ubiquitous in a variety of fields, and how to tackle them has drawn much attention, especially dynamic ones. As a particular class of recurrent neural network, ...

NonlinearSystems.jl is a Julia package for solving nonlinear systems of equations and nonlinear least squares. It renovates well-trusted solution algorithms with highly performant and extensible ...

The program runs each method 100 times to measure average execution time and compares the performance against expected computational complexity. Cramer's Rule computes each variable xᵢ as the ratio ...

Abstract: This article investigates a class of systems of nonlinear equations (SNEs). Three distributed neurodynamic models (DNMs), namely a two-layer model (DNM-I) and two single-layer models (DNM-II ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

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 ...

Masaki Kashiwara has won the 2025 Abel prize, sometimes called the Nobel prize of mathematics, for his work on algebraic analysis. Kashiwara, a professor at Kyoto University, Japan, received the award ...

I’ve been out of school a long time (I mean a long time), yet I think I’m still pretty good at basic math. I’m always able to figure out whether a “bargain buy” at the supermarket is actually a ...

Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. Population balance equation (PBE) models have the potential to automate many ...

Dr. Kevin M. Passino was my doctoral research adviser at the Ohio State University, where I did my PhD. As a control systems researcher, I have long felt that control systems – and systems science in ...

A "drone detection system" is being deployed to New York after a series of mysterious drones were spotted flying over parts of the East Coast in recent weeks. The sightings have been reported in New ...

Apple's release of iOS 18.1 builds on the groundbreaking features of iOS 18, offering users new capabilities and fixes. Among the best updates in iOS 18 is the enhanced Messages app, which now lets ...