The Maurer–Cartan form is a fundamental concept in the theory of Lie groups and differential geometry, particularly in the study of Lie group representations and the geometry of principal bundles. Given a Lie group \( G \), the Maurer–Cartan form is a differential 1-form on the Lie group that captures information about the group structure in terms of its tangent space.

A "moving frame" can refer to different concepts depending on the context, including mathematics, physics, and engineering. Here are a few interpretations: 1. **Mathematics (Differential Geometry)**: In the context of differential geometry, a moving frame is often used to describe a set of vectors that vary along a curve or surface.

In music, a "key" refers to the tonal center around which a piece of music is organized. It is defined by a specific scale that serves as the foundation for melodies and harmonies within a composition. Each key is typically associated with a specific note (the tonic) and a set of pitches that can be used in the music. Keys are categorized as major or minor: 1. **Major Key**: Associated with a bright and happy sound.

Their websites a bit shitty, clearly a non cohesive amalgamation of several different groups.

E.g. you have to create several separate accounts, and different regions have completely different accounts and websites.

The Europe replacement part website for example is clearly made by a third party called flex.com/ and has Flex written all over it, and the header of the home page has a slightly broken but very obviously broken CSS. And you can't create an account without a VAT number... and they confirmed by email that they don't sell to non-corporate entities without a VAT number. What a bullshit!

Datasheet: datasheets.raspberrypi.com/picow/pico-w-datasheet.pdf

Pinout: datasheets.raspberrypi.com/picow/PicoW-A4-Pinout.pdf

Natural pseudodistance is a concept used in mathematical biology and ecology, particularly in the study of population genetics and evolutionary theory. It is typically used to quantify the genetic differences or relationships between populations or individuals based on genetic data. In general, a pseudodistance is a metric that measures how "far apart" two entities are within a particular space or context, but it may not fulfill all the properties of a true distance metric (such as the triangle inequality).

This equation is a subcase of Equation "Schrödinger equation for a one dimensional particle" with $V(x)=x^2$.

We get the time-independent Schrödinger equation by substituting this $V$ into Equation "time-independent Schrödinger equation for a one dimensional particle":

Now, there are two ways to go about this.

The first is the stupid "here's a guess" + "hey this family of solutions forms a complete basis"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.

The second is the much celebrated ladder operator method.

Open source driver/hardware interface specification??? E.g. on Ubuntu, a large part of the nastiest UI breaking bugs Ciro Santilli encountered over the years have been GPU related. Do you think that is a coincidence??? E.g. ubuntu 21.10 does not wake up from suspend.

The Neovius surface refers to a specific type of mathematical surface that has properties useful in the study of differential geometry and topology. It is named after the Finnish mathematician A.F. Neovius, who studied the surface and its properties. The Neovius surface is typically characterized by its complex structure, including features like cusps and self-intersections, making it interesting from the perspectives of both geometry and mathematical physics.

Basically a synonym of Lorentz covariance?

Supergeometry is a branch of mathematics that extends the concepts of geometry to include both geometric structures and "supersymmetrical" objects, which involve odd or "fermionic" dimensions. It arises from the study of supersymmetry in theoretical physics, where it plays a crucial role in string theory and quantum field theory. In conventional geometry, one typically works with spaces that are defined by traditional notions of points and curves in even-dimensional Euclidean spaces.

Synthetic Differential Geometry (SDG) is a branch of mathematics that provides a framework for differential geometry using a synthetic or categorical approach, rather than relying on traditional set-theoretic and analytical foundations. This approach is particularly notable for its use of "infinitesimals," which are small quantities that can be treated algebraically in a way that is similar to how they are used in non-standard analysis.