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 ...

Differentiation is process of finding the derivative, or rate of change, of a function. Derivative itself is defined by the limit of function's change divided by the function's argument change as ...

Pythagoras Theorem: The Pythagoras Theorem is a fundamental principle in geometry, attributed to the ancient Greek mathematician Pythagoras. This theorem establishes a relationship between the sides ...

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.

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 ...

Abstract: The quaternion windowed fractional Fourier transform (QWFRFT) is a generalized form of the quaternion fractional Fourier transform (QFRFT), it plays a crucial role in signal processing for ...

Convolution has a significant impact on many scientific disciplines, ranging from probability theory and harmonic analysis to information theory. Here, we introduce a framework to study quantum ...

Electroencephalogram (EEG) is a crucial and widely utilized technique in neuroscience research. In this paper, we introduce a novel graph neural network called the spatial-temporal graph attention ...

Two high school seniors have presented their proof of the Pythagorean theorem using trigonometry — which mathematicians thought to be impossible — at an American Mathematical Society meeting. When you ...