1. Summary of the problem and prerequisites This problem asks to show that a function $$ { f }$$ satisfying the following conditions belongs to the space of absolutely convergent Fourier series $$ { A ...

Our research proves a conjecture from string theory asserting the vanishing of a specific convolution sum arising in the 4-graviton scattering amplitude in 10-dimensional type IIB string theory. The ...

This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is ...

The Fourier Neural Operator (FNO) [1] is a neural operator with an integral kernel parameterized in Fourier space. This allows for an expressive and efficient architecture. Applications of the FNO ...

Physics-informed convolutional recurrent network (PhyCRNet) can solve partial differential equations without labeled data by encoding physics constraints into the loss function. However, the ...

remove-circle Internet Archive's in-browser video "theater" requires JavaScript to be enabled. It appears your browser does not have it turned on. Please see your ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Brain computer interaction (BCI) based on EEG can help patients with limb dyskinesia to carry out daily life and rehabilitation training. However, due to the low signal-to-noise ratio and large ...