The Android Debug Bridge

Android logo by Google.

The following is primarily a note for myself, but perhaps it can be useful for others as well.

It turns out to be rather straightforward to obtain command-line access to an Android phone, also when it is not rooted. Namely, one can use ADB – the Android Debug Bridge, a client-server tool that is part of the Android SDK Platform-Tools package. It requires a working Java runtime environment and is easy to use, following the clear instructions on the ADB homepage.

Calculating an auto-convolution integral by Fourier transforms

Recently I came across a forum contribution [1] where the author describes how to use the unitarity of the Fourier transform on $L^2(\RR)$ to compute the definite integral
\label{eq:I}
I(t_0) \DEF \int_{-\infty}^{\infty}{\frac{\sin(\tau – t_0)}{(\tau – t_0)}\frac{\sin(\tau + t_0)}{(\tau + t_0)}\,d\tau},

where $t_0 \in \RR$ is a constant. In the comments it is also argued that one may alternatively use contour integration. I liked the article, but wondered whether the symmetry of the problem would perhaps admit a simpler approach. Here I give a third method that uses Fourier transforms and convolutions.

From offline LaTeX to online QuickLaTeX

For writing mathematics in WordPress using LaTeX I have been using Pavel Holoborodko’s nice QuickLaTeX plugin. It makes it very easy to convert offline LaTeX source code, possibly including custom macros, into (part of) a WordPress post. To reduce the effort a bit further, I wrote a tiny Python 3 script.

Saved by a pipe smoking penguin

In the late 1990s I used Linux for the first time. Back then, Slackware was one of a limited number of distributions on the market. Installation took very long and failed repeatedly. Partly this was due to my slow and unreliable internet connection, but my inexperience and incompetence were likely at least as detrimental to my progress. From what I remember I managed to set up X11 with the aid of a configuration script that asked me many questions to which I guessed most answers. I also found out how to make Linux talk to my external dial-up modem. No longer chained by evil Microsoft, I was very proud of myself.

Continuity of eigenvalues

As a simple corollary to the result from my previous post I would like to show you how to obtain continuous dependence of the eigenvalues of a matrix on its entries.

Continuity of polynomial roots

It was recently brought up how to show that the $n$ roots of a real or complex polynomial depend continuously on the polynomial’s coefficients. Although I have used this proposition numerous times, implicitly and explicitly, I realized that I never saw a proof of it.

Perhaps the most obvious approach would try to apply the Implicit Function Theorem but, as you may know or can easily check, such an attempt would only work for roots that are simple. Indeed, the very failure of the Implicit Function Theorem in case of non-simple roots is one of the subjects studied in local bifurcation theory. For an example, see this discussion of the Bogdanov-Takens bifurcation.

Returning to the original proposition, here is an elementary proof using only the Fundamental Theorem of Algebra and some simple estimates.

Laatste-wil-pil

Gisterenavond las ik op NU.nl en de website van dagblad Trouw dat het voor senioren mogelijk moet worden een eind aan hun leven te maken door inname van een “laatste-wil-pil”. Aldus is althans het streven van de Nederlandse Vereniging voor een Vrijwillig Levenseinde en de Coöperatie Laatste Wil, die hiervoor steun vinden bij Tweede Kamerlid Pia Dijkstra (D66). Zij schrijft momenteel aan een wetsvoorstel van dergelijke strekking. De doelgroep bestaat nadrukkelijk uit ouderen die volgens de huidige euthanasiewet niet in aanmerking komen voor hulp bij zelfdoding, maar wel hun leven willen beëindigen omdat “ze er zelf helemaal klaar mee zijn en er echt niets meer van kunnen verwachten.”
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