In category theory, an injective object is a specific type of object that satisfies a particular property in terms of homomorphisms (morphisms) between objects in a category.
An in-place algorithm is a type of algorithm that requires a small and constant amount of extra space for its operations, aside from the space needed to store the input. This means that the algorithm transforms the input data without needing to create a copy of it or requiring additional data structures that scale with the input size. ### Characteristics of In-Place Algorithms: 1. **Space Efficiency**: They use only a fixed amount of extra space (e.g.
An **integrally closed domain** is a type of integral domain in which every element that is integral over the domain is already an element of the domain itself. To understand this concept, let's break it down: 1. **Integral Domain**: An integral domain is a commutative ring with no zero divisors and a multiplicative identity (usually denoted as 1). It also has the property that it is non-trivial (the ring is not the zero ring).
Fazle Hussain could refer to a specific individual, but there isn't widely available information on a person by that name in public knowledge as of my last training cut-off in October 2023.
Invasion percolation is a model used in statistical physics and materials science to study the behavior of fluid or other substances infiltrating a porous medium. It is particularly applicable in the analysis of how interfaces between different phases evolve and how materials break or disengage under stress. ### Key Features of Invasion Percolation: 1. **Lattice Representation**: Invasion percolation is often modeled on a lattice or grid, where each site or bond can be occupied or vacant.
Pinned article: ourbigbook/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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . 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. 
- 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