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.

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 ...

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 ...

In a new peer-reviewed study, Ne'Kiya Jackson and Calcea Johnson outlined 10 ways to solve the Pythagorean theorem using trigonometry, including a proof they discovered in high school. When you ...

Introduction: Improving the rationality and accuracy of classroom quality analysis is crucial in modern education. Traditional methods, such as questionnaires and manual recordings, are ...

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 ...

1 Mathematical Sciences Department, University of Mines and Technology, Tarkwa, Ghana. 2 Faculty of Science and Technology, University of Silesia in Katowice, Sosnowiec, Poland. The existence of an ...