Application of the Fourier method to very general linear hyperbolic Cauchy problems having nonsmooth initial data is considered, both theoretically and computationally. In the absence of smoothing, ...

Super-resolution (SR) fluorescence microscopy, through the use of fluorescent probes and specific excitation and emission procedures, surpasses the diffraction limit of resolution (200~300 nm) that ...

Stochastic control problems in finance often involve complex controls at discrete times. As a result, numerically solving such problems using, for example, methods based on partial differential or ...

Recently, a research team led by Prof. GAO Minguang and Associate Prof. LI Xiangxian from Hefei Institutes of Physical Science (HFIPS), Chinese Academy of Sciences (CAS), has developed a spectral ...

Nyström's method with the trapezoidal rule, and the Fourier method, produce the same approximation to the solution of an integral equation at the collocation points ...

We provide a bound for the error committed when using a Fourier method to price European options, when the underlying follows an exponential Lévy dynamic. The price ...

A new study finds that a 200-year-old technique called Fourier analysis can reveal crucial information about how the form of artificial intelligence called deep neural networks (DNN) learn to perform ...

Microsoft Office Excel contains a data analysis add-in that allows to to perform a Fourier analysis of a series of numbers. So named for the French mathematician who developed the analytic technique ...