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 ...

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, ...

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 ...

Despite being the most abundant element in the universe, making cheap, clean hydrogen here on Earth has been a surprisingly tough nut to crack. “Hydrogen has always been plagued with a couple problems ...

Calcea Johnson (right), currently studying environmental engineering at Louisiana State University, published the new study with her high school classmate, Ne'Kiya Jackson (left), now a student in ...

Calcea Johnson and Ne'Kiya Jackson, who surprised the math world when they produced innovative solutions to a 2,000-year-old puzzle, wowed the math world again when they presented several new ways of ...

In their peer-reviewed work, Calcea Johnson and Ne'Kiya Jackson present five new ways of proving Pythagoras' Theorem via trigonometry. They also detail a new method for finding proofs that yield at ...

Two years ago, a couple of high school classmates each composed a mathematical marvel, a trigonometric proof of the Pythagorean theorem. Now, they’re unveiling 10 more. For over 2,000 years, such ...

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News. A high school ...

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 ...