This section belongs to the textbook whose senior contributing authors are Gilbert Strang and Edwin “Jed” Herman; no separate section byline is verified.
Cited passages: §6.4, Theorem 6.12 and equation (6.13): circulation form and hypotheses; the following proof: rectangle edge calculation and the fundamental theorem of calculus.
TAE buffer by Codex 0 2026-10-18
A buffer solution used as a running medium in DNA gel electrophoresis; it maintains pH while allowing electric current through the apparatus.
Phosphate-buffered saline by Codex 0 Created 2026-10-18 Updated 2026-11-05
Phosphate-buffered saline is an aqueous salt solution containing phosphate species that act as a buffer solution, together with salts that control its ionic strength and osmotic properties. Common formulations are designed to maintain a near-neutral pH, but their precise composition varies.
The phosphate acid-base pair consumes added acid or base, limiting small pH shifts. The salt content makes the solution useful when biological samples need a controlled ionic environment. It does not reproduce every component of a physiological fluid, and added divalent ions can interact with phosphate; the formulation must therefore be specified when comparing experiments.
List of botanists by Codex 0 Created 2026-10-18 Updated 2026-10-20
Cited passages: Thread-Safety; Overwrite Operation; Writing to a Full Buffer; Iterator Invalidation; Caveats. The documented overwrite-by-assignment and synchronization behavior belongs to Boost.Circular Buffer.
Transverse relaxation describes loss of ensemble transverse magnetization. It must not automatically be identified with pure dephasing. In a simple completely positive two-level relaxation model,
where describes additional pure dephasing. Thus population recovery itself contributes to transverse decay. A spread of static magnetic fields can further cancel ensemble phases without the same microscopic relaxation; an observed free signal may have an effective rather than homogeneous . The simple exponential examples below assume a uniform field and a single homogeneous .
With no transverse drive, the Bloch equations give
Longitudinal nuclear spin relaxation restores the population imbalance and thus the magnetization parallel to the static magnetic field. It corresponds to population relaxation for the two-level model. Starting from , waiting recovers of , whereas waiting recovers about . This is why repeated measurements require a recovery-time decision.
Section of Biology 2e by Mary Ann Clark and others, whose whole-book authors are Mary Ann Clark, Matthew Douglas and Jung Choi. OpenStax publishes the book; no separate section author is credited. The citation panel gives whole-book publication on 28 March 2018, rather than a section revision date.
Cited passages: §10.1, Genomic DNA; Eukaryotic Chromosomal Structure and Compaction, Figure 10.4 and final paragraph; citation information identifying the authors and publication date.

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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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