When last we saw [xoreaxeax], he had built a lens-less optical microscope that deduced the structure of a sample by recording ...

Harmonic analysis occupies a central position in modern mathematical analysis by providing the tools to express complex functions as superpositions of simpler sinusoidal components via the Fourier ...

Fourier analysis provides a powerful framework for decomposing functions into sums or integrals of sinusoidal components, thereby enabling the study of frequency content in signals. In tandem, ...

Over at Quanta Magazine [Shalma Wegsman] asks What Is the Fourier Transform? [Shalma] begins by telling you a little about Joseph Fourier, the French mathematician with an interest in heat propagation ...

Several bounds on the solutions and the pressure are obtained for regular solutions to the Navier-Stokes equations in two and three dimensions on the whole space. More precisely, we obtain L1 ...

A non-linear parametric model for brain activation detection by functional magnetic resonance imaging (FMRI) is proposed. The effects of a designed temporal stimulus on the FMRI signal at each brain ...

In less than 100 seconds, Carola-Bibiane Schönlieb of the University of Cambridge in the UK provides a basic definition of a Fourier transform. She explains how this mathematical tool was introduced ...