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 …
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The problem of inverting the implicit function $$y=f(x)$$ in the form of power-series $$x = a + \sum_{k=1}^{\infty} b_k (y-f(a))^k$$ around a point of interest $x=a$, has a long history. Lagrange obtained a theoretical inversion formula [1]https://mathworld.wolfram.com/LagrangeInversionTheorem.html, yet efficient implementations are relatively recent [2]Brent, Richard P., and Hsiang T. Kung. “Fast algorithms for manipulating formal …
Azure Cloud is a popular work environment for many data scientists, yet many features remain poorly documented. This note shows how to monitor Azure experiments in a more handy and detailed way than through web or cl interface. The trick is to create a dashborad of experiments and their respective runs, up to a desired …
Poetry, a popular Python package manager, prefers to use keyring to manage passwords for private code repositories. Storing passwords in plain text is a secondary option, but may be needed in case of either issues in poetry itself or with keyring configuration (may not be properly installed, be locked etc). To disable the use of …
Often code tests are to be run on special demand, rather than in a CI/CD manner: for instance, they may be slow or work only in a local mode with protected data. This note shows how to declare code tests optional in pytest, the leading testing framework for Python. The article is inspired by the …
What to do when CircleCI reports are not informative enough on errors? Debug the failing environment live with SSH!
For data scientists, it is a must to prototype in multiple virtual environments which isolate different (and often very divergent) sets of Python packages. This can be achieved by linking one Jupyter installation with multiple Python environments. Use the command <code>which jupyter</code> to show the Jupyter location and <jupyter kernelspec list> to show available kernels, …
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 …
Ukrainian refugees see their currency hardly convertible at fair rates or even accepted. The lack of liquidity will also hit Ukraine’s government urgent expenses (medical supplies or weapons). The National Bank of Poland (NBP) offered a comprehensive financial package to address these problems. Firstly, it enabled the refugees to exchange the currency at a nearly …
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Following the Russia invasion on Ukraine an oil supply shock is expected and what is worse there may be no supply increase from OPEC+ . A way out is to cut the demand as advised by IEA. The proposed steps are quick-wins: easy to implement and reverse while having measurable and significant impact. The overall …
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