Abstract: In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters.

Large language models (LLMs) have astounded the world with their capabilities, yet they remain plagued by unpredictability and hallucinations – confidently outputting incorrect information. In ...

Back in 1971, the late physicist Stephen Hawking made an intriguing prediction: The total surface area of a black hole cannot decrease, only increase or remain stable. So if two black holes combine, ...

Researchers celebrate 10th anniversary of gravitational wave discovery, announce verification of a Hawking theorem. Two black holes spiral together and violently merge in this simulation of an event ...

Stephen Hawking’s 50-year-old theorem on how black holes merge together has been successfully tested thanks to huge advances in gravitational wave astronomy, which helped astronomers catch the waves ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...

This deceptively simple math problem has stumped mathematicians for almost 300 years! Donald Trump floats move to new state New Mexico fire victims await payments. A FEMA director got his. Disney ...

Convolution is a remarkable property of the Fourier transform, often cited in the literature as the “faltung theorem”. Convolution is a remarkable property of the Fourier transform, often cited in the ...

A windowed sinc function can implement a low-pass filter, and a two-dimensional convolutional filter can blur or sharpen images. In part 3 of this series, we introduced a low-pass filter based on the ...