Look for the leftmost and rightmost points of the graph. If the graph extends indefinitely to the left or right, the domain includes negative or positive infinity, respectively. Note any breaks or ...

At the 2024 International Mathematical Olympiad (IMO), one competitor did so well that it would have been awarded the Silver ...

A new paper shows ChatGPT-5 emerging as a tool that helps scientists test ideas, navigate literature and refine experiments ...

THE role of the chief financial officer (CFO) has evolved significantly over the past years. Traditionally defined as the one responsible for the financial activities of an entire business, the role ...

This paper describes the eccentricity, amplitude, phase shift, angular momentum, polarization, radial path, and orbital energy of two-body orbital mechanics simultaneously, and then presents a wave ...

Exponential functions, characterized by their consistent multiplicative growth or decline, play a pivotal role in modeling diverse real-world phenomena. Understanding whether a given exponential ...

If you’ve ever looked at the growth trajectory of companies like HubSpot, Canva, or Slack and wondered how they did it, you ...

Revise how to work out equivalent ratios and simplify ratios by dividing both sides by the highest common factor. Test yourself with practice questions and a game. NEW: Ratio and fractions, and ...

Video-based anomaly detection in urban surveillance faces a fundamental challenge: scale-projective ambiguity. This occurs when objects of different physical sizes appear identical in camera images ...

Abstract: The simulation of a free-space optical (FSO) communication channel in the presence of strong turbulence typically requires the generation of channel states with a K or gamma–gamma ...

What began with a focus on weather forecasting has evolved toward addressing errors in scientific modeling. In the collaborative environment of the Penn State Institute for Computational and Data ...