The Madelung Equations are a set of equations proposed by Erwin Madelung in 1926 to describe a more physical interpretation of the Schrödinger Equation. Notably, Madelung's analysis resulted in a set ...

Abstract: Conflict resolution, particularly through effective priority assignment and right-of-way negotiation, is a critical factor in maximizing intersection throughput and minimizing vehicle ...

Abstract: In this work, we propose a complex-valued neural operator (CV-NeuralOp) based on graph neural networks (GNNs) to solve 2-D wave equations. Inspired by Green’s function method for solving ...

In this tutorial, we demonstrate how to construct an automated Knowledge Graph (KG) pipeline using LangGraph and NetworkX. The pipeline simulates a sequence of intelligent agents that collaboratively ...

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 mathematician has uncovered a way of answering some of algebra's oldest problems. University of New South Wales Honorary Professor Norman Wildberger, has revealed a potentially game-changing ...

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 ...

Scientists are using machine learning to find new treatments among thousands of old medicines. Scientists are using machine learning to find new treatments among thousands of old medicines. Joseph ...

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 ...

Introduction: Fractional diffusion equations offer an effective means of describing transport phenomena exhibiting abnormal diffusion pat-terns, often eluding traditional diffusion models. Methods: We ...