Google will deprecate practice problem structured data in January and clarifies Dataset markup is only for Dataset Search. Book actions remain supported. Practice problem markup is being deprecated ...

Our research proves a conjecture from string theory asserting the vanishing of a specific convolution sum arising in the 4-graviton scattering amplitude in 10-dimensional type IIB string theory. The ...

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 ...

When the digital revolution first hit classrooms in the early 2010s—and more schools began issuing laptops or tablets to students for individual use—online learning seemed to promise a faster, easier ...

2025 marked a historic year in mathematics. Researchers solved a major case of Hilbert’s ambitious sixth problem, proved a sweeping new theorem about hyperbolic surfaces, and settled the longstanding ...

ABSTRACT: The quaternion linear canonical transform (QLCT) is defined in this paper, with proofs given for its reversibility property, its linear property, its odd-even invariant property and ...

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 ...

Complex organizational problems and chaos are silent killers of productivity and innovation. In today’s fractured work environment, they are more prevalent than ever. Political transitions, ...

Automating mathematical reasoning has long been a goal in artificial intelligence, with formal frameworks like Lean 4, Isabelle, and Coq playing a significant role. These frameworks enable users to ...

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.