A quick look at PostgreSQL's compliance notes: www.postgresql.org/docs/13/features.html shows the complete utter mess that this standard is. Multiple compliance levels that no one fully implements and optional features everywhere.
This section is about functions that operates on arbitrary sets.
Analogous to what the Euler-Lagrange equation is to Lagrangian mechanics, Hamilton's equations give the equations of motion from a given input Hamiltonian:So once you have the Hamiltonian, you can write down this system of partial differential equations which can then be numerically solved.
IDEs are absolutely essential for developing complex software.
The funny thing is that you don't notice this until someone shows it to you. But once you see it, there is not turning back, just like Steve Jobs customers don't know what they want quote.
Unfortunately, after the Fall of Eclipse (archive), the IDE landscape in 2019 is horrible and split between:
Programmers of the world: unite! Focus on one IDE, and make it work for all languages and all build systems. Give it all the features that Eclipse has, but none of the bugginess. Work with top project to make sure the IDE works for all top projects.
Projects of the world: support one IDE, with in-tree configuration. Complex integration is often required between the IDE and the build system, and successful projects must to that once for all developers. Either do this, or watch you complex project wither away.
Build tool maintainers: make it possible for IDEs to support your tool! E.g., implement JSON Compilation Database output so that IDEs can read the exact compiler commands from that, in order to automatically determine how files should be parsed! Or better, just use libllvm in your IDE itself as the main parser.
Ciro is evaluating some IDEs at: github.com/cirosantilli/ide-test-projects
Mean Absolute Error (MAE) is a common metric used to evaluate the performance of regression models. It measures the average magnitude of the errors in a set of predictions, without considering their direction (i.e., it takes the absolute values of the errors).
The term "spin representation" is commonly used in the context of quantum mechanics and refers to a mathematical framework for describing the intrinsic angular momentum (spin) of quantum particles. Spin is a fundamental property of quantum particles like electrons, protons, neutrons, and other elementary and composite particles. ### Key Elements of Spin Representation: 1. **Quantum States**: Spin states are represented as vectors in a Hilbert space.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact