Ciro Santilli @cirosantilli 37

Topology is the plumbing of calculus.

The key concept of topology is a neighbourhood.

Just by havin the notion of neighbourhood, concepts such as limit and continuity can be defined without the need to specify a precise numerical value to the distance between two points with a metric.

As an example. consider the orthogonal group, which is also naturally a topological space. That group does not usually have a notion of distance defined for it by default. However, we can still talk about certain properties of it, e.g. that the orthogonal group is compact, and that the orthogonal group has two connected components.

He was a leading figure at the MIT Radiation Laboratory, and later he was head at the Columbia University laboratory that carried out the crucial Lamb-Retherford experiment and the anomalous magnetic dipole moment of the electron published at The Magnetic Moment of the Electron by Kusch and Foley (1948) using related techniques.

Previously on EdX: www.edx.org/learn/quantum-physics-mechanics/delft-university-of-technology-topology-in-condensed-matter-tying-quantum-knots "DelftX: Topology in Condensed Matter: Tying Quantum Knots".

But then they regained their sanity and put the source code on GitHub: github.com/topocm/topocm_content and is CC BY-SA.

Uses an ungodly combination of Jupyter notebooks and Pelican.

TODO where to find it: www.kaggle.com/general/50987

Cited on original Generative adversarial network paper: proceedings.neurips.cc/paper_files/paper/2014/file/5ca3e9b122f61f8f06494c97b1afccf3-Paper.pdf

TODO what is the standard compliant syntax?

PostgreSQL requires you to define a SQL stored procedure: stackoverflow.com/questions/28149494/is-it-possible-to-create-trigger-without-execute-procedure-in-postgresql Their syntax may be standard compliant, not sure about the EXECUTE part. Their docs: www.postgresql.org/docs/current/sql-createtrigger.html

SQLite does not support SQL stored procedures at all, so maybe that's why they can't be standard compliant here: stackoverflow.com/questions/3335162/creating-stored-procedure-in-sqlite

SQL:1999 11.38 covers "Trigger definition". The Abstract syntax tree starts with the CREATE TRIGGER and ends in:

This is defined at 13.5 "SQL procedure statement", but that is humongous and I'm not sure what it is at all.

The elliptic curve group of all elliptic curve over the rational numbers is always a finitely generated group.

The number of points may be either finite or infinite. But when infinite, it is still a finitely generated group.

For this reason, the rank of an elliptic curve over the rational numbers is always defined.

TODO example.

See form.

Analogous to a linear form, a multilinear form is a Multilinear map where the image is the underlying field of the vector space, e.g. ${\mathbb{R}}^{n_1}\times {\mathbb{R}}^{n_2}\times {\mathbb{R}}^{n_2}\to \mathbb{R}$.

There's a billion simple looking expressions which are not known to be transcendental numbers or not. It's cute simple to state but hard to prove at its best.

Open as of 2020:

Bibliography:

The co-founder's name, Toby Cubitt, is the mos awesome thing ever (Cubitt -> qubit). From UCL.

Funding:

Example: nodejs/sequelize/trigger_count.js

There is of course no built-in support for SQL TRIGGERs in Sequelize, but we can add our own: stackoverflow.com/questions/29716346/how-to-create-a-trigger-in-sequelize-nodejs/76215728#76215728

Maximum current that can flow across a Josephson junction, as can be directly seen from the Josephson equations.

Is a fixed characteristic value of the physical construction of the junction.