On The Stability Of The Solar System

, 7 min read

Our solar system is not stable when considerung time ranges of several Gigayears. These are the results of simulations done by Laskar and Gastineau. 1. Nomenclature Notions for ellipses, see below figure: center M semi-minor axis b semi-major axis a (linear) eccentricity e, numerical eccentricity…

XHProf with NGINX

, 2 min read

XHProf is a PHP profiler. I had written on XHProf here: Profiling PHP Programs Profiling PHP Programs #2 XHProf was originally written by Facebook engineers. Even though it severely slows down your PHP program during execution, it is nevertheless a valuable tool to get an understanding, where…

Direct st-connectivity with few paths is in quantum logspace

, 36 min read

Authors: Roman Edenhofer and Simon Apers Université Paris Cité, CNRS, IRIF, Paris, France Abstract 1. Introduction and summary Counting few paths Unambiguity, Fewness and a language in $\mathsf{BQL}$ (maybe) not in $\mathsf{BPL}$ Conclusion and open questions 2. Space-bounded computation 2.1…

Replacing SSHGuard with 20 Lines of Perl Code

, 5 min read

SSHGuard is a software to block unwanted SSH login attempts. SSHGuard has a very remarkable architecture: it has a set of independent programs doing parsing, block-indication, and actual blocking. I wrote about this in Analysis And Usage of SSHGuard. SSHGuard 2.4.3 is about 100kLines of C and shell…

Slashdot Effect on a Single Page

, 2 min read

1. The post Hosting Static Content with GitLab was mentioned on Hacker News and this site experienced a heavy increase in accesses. Neither PHP, nor NGINX, nor the ISP experienced any problems. Nevertheless, I had never before seen such a stark rise in accesses to this website. The Slashdot effect…

Recursive Generation of Runge-Kutta Formulas

, 15 min read

1. Notation 2. Example Runge-Kutta methods 3. Local discretization error 4. Order condition 5. Power series expansion for global error 6. Cauchy product formula 7. Recursive calculation of the order condition Below text is based on the results in Peter Albrecht: "A New Theoretical Approach…

Hosting Static Content with GitHub

, 2 min read

I wrote about hosting static sites on various platforms: Hosting Static Content with surge.sh Hosting Static Content with now.sh, now.sh renamed themself to vercel.app Hosting Static Content with netlify.app Hosting Static Content with Cloudflare Hosting Static Content with Neocities Hosting…

Hosting Static Content with GitLab

, 2 min read

I wrote about hosting static sites on various platforms: Hosting Static Content with surge.sh Hosting Static Content with now.sh, now.sh renamed themself to vercel.app Hosting Static Content with netlify.app Hosting Static Content with Cloudflare Hosting Static Content with Neocities GitLab…

Das Fehlerverhalten zusammengesetzer linearer Mehrschrittformeln

, 57 min read

1. Konsistenz, Konsistenzordnung und Fehlerkonstanten 2. Die Anwendung linearer Mehrschrittverfahren bei DAE 3. Mehrere Charakterisierungen der Konsistenzordnung 4. Die erste Dahlquist-Barriere 5. Die zweite Dahlquist-Barriere 6. Annullierte Dominanz und Totalannullation 7. Das $n$-dimensionale…

Stabilitätsfunktionale und Semistabilitätsfunktionale

, 17 min read

1. Semistabilitätsfunktionale in Matrixdarstellung 2. Bemerkungen zum Spijkerschen Stabilitätsfunktional 1. Semistabilitätsfunktionale in Matrixdarstellung Mit Ausnahme der Booleschen Algebra wird keine Theorie in der Mathematik universeller benutzt als die lineare Algeba. Es gibt kaum eine…

Divergenz der Korrektoriteration: Theorie und Experimente

, 19 min read

1. Das modifizierte Newton-Verfahren und Spezialisierungen 2. Die Divergenzsätze von Hughes Hallett 3. Die Experimente von Byrne/Hindmarsh/Jackson/Brown Einer der ganz zentralen Bestandteile eines Programmes, basierend auf Verfahren mit impliziten Stufen, ist die Auflösung der…

Konvergenzresultate für feste Schrittweiten

, 58 min read

1. Einführung und grundlegende Begriffe 2. Die Lemmata von Gronwall 3. Notation und Darstellungssatz für Differenzengleichungen 4. Stabilitätsfunktionale für feste Schrittweiten 5. Projektorstabilitätsfunktionale 6. Nichtäquidistante Gitter 7. Die Eigenwerte gewisser tridiagonaler…

Lösung linearer Gleichungssysteme

, 23 min read

1. Konditionszahlen von Matrizen 2. Elementare Zeilen- und Spaltenoperationen 3. Die $LU$-Zerlegung 4. Die Gauß-Elimination Bei jedem Iterationsschritt eines Newton-Raphson-Verfahrens, bzw. bei jeder Aktualisierung der Iterationsmatrix beim Newton-Kantorovich Iterationsverfahren, fällt die…

Projektionsmatrix eines Raumes

, 6 min read

1. Projektor Sei eine lineare Mannigfaltigkeit ${\cal M}\subseteq\mathbb{C}^n$ aufgespannt durch die $s$ linear unabhängigen Vektoren $a_1,\ldots,a_s\in\mathbb{C}^n$. Sei $A=(a_1,\ldots,a_s)\in\mathbb{C}^{n\times s}$. Es gilt $$ % Mehrfache Indizes für Minoren: % #1: Anzahl der Indizes, #2:…

Turning 60 - Now What?

, 2 min read

I turned 60 this year. I had written a similar post ten years ago: Turning 50 - Now what? What has happened in the last ten years? The last time I wrote: I am married and have three children. All three children show interest in society and technology, and will likely find their way through life.…

Dark Mode on Website

, 6 min read

This blog offered to switch betwen light and dark mode. But this choice was not stored anywhere. So any page you clicked on, you had to choose dark mode again. Now I store this choice in localStorage on the client. While cookies could also be used for storing this choice, they are not needed for…

IGYRC5108-U: IBM Cobol Compiler Terminating

, 1 min read

I stumbled on below error message from the IBM COBOL compiler for mainframe: IGYRC5108-U COBOL COMPILER TERMINATING: UNCORRECTABLE PROGRAM INTERRUPT CONDITION. The COBOL program was not fully compiled but compilation stopped midway. Further messages from the compile run: PROGRAM CHECK,…

Member of 1MB club

, 1 min read

I am now a member of the 1MB club. The members must have websites with size below 1 MB. This new membership is not surprising as I am already a member of the two clubs: Member of 512KB club Member of 250KB club This 1MB club has 781 members as of today. Becoming member there is by using: git…

Performance Comparison of Wendt Website: WordPress vs. Simplified Saaze

, 4 min read

In the previous post Example Theme for Simplified Saaze: Wendt I demonstrated the transition from a website using WordPress to Simplified Saaze. This very blog, which you are reading right now, also uses Simplified Saaze. This post shows how much better performance-wise this transition was. The…

Example Theme for Simplified Saaze: Wendt

, 12 min read

Another theme for Simplified Saaze called "Wendt". You can inspect it here. It offers below features: Responsive with media breaks for large and small screens, and for printing. Top menu with submenus. Two column using CSS grid, "Holy Grail Layout". Multiple blogs: Each…