## Fourier integrals vanishing on large circles

When evaluating contour integrals, it is often of interest to prove that Fourier-type integrals vanish on large enough semicircles (see the figure). This holds under the following condition: Theorem. Suppose that $$f(z)=O(|z|^{-a}), \quad a>0$$ for in the upper half-plane. Then for any $$\lambda > 0$$ we have $$\int_{\gamma_R} f(z)\mathrm{e}^{i\lambda z} \rightarrow 0, \quad R\to+\infty,$$ where …

## Modern Bibliography Management

A solid bibliography database is vital for every research project, yet building it is considered an ugly manual task by many – particularly by old-school researchers. But this does not have to be painful if we use modern toolkit. The following features appear particularly important: collaborative work (sharing etc) extraction magic (online search, automated record …

## Performance drawbacks of Tensorflow Datasets

Tensorflow, the popular framework for machine-learning, recommends its new dataset API for preprocessing and serving data. It supports useful tricks, such as caching data in memory, prefetching in parallel threads and others described in tutorials. Still, Tensorflow has issues with slow data slicing, so the dataset API may actually do harm in setups where computations …