The Bateman transform, named after the mathematician H. Bateman, is a mathematical technique used in the context of solving certain types of integral transforms and differential equations. It is particularly useful in simplifying the computation of integrals that involve exponentials, polynomials, and special functions. The Bateman transform can be applied to the analysis of systems in physics, engineering, and applied mathematics, especially in areas such as signal processing and control theory.
Murray Gell-Mann by Ciro Santilli 40 Updated 2025-07-16
The way this dude speaks. He exhales incredible intelligence!!!
In the interviews you can see that he pronounces names in all languages amazingly, making acute effort to do so, to the point of being notable. His passion for linguistics is actually mentioned on Genius: Richard Feynman and Modern Physics by James Gleick (1994).
Maybe this obsession is partly due to his name which no English speaking person knows how to pronounce from the writing.
This passion also led in part for his names to some physics terminology he worked on winning out over alternatives by his collaborators, most notably in the case of the naming of the quark.
  • Google Maps download offline maps. This works very reliably, you can select the area you want to download. The only downside is that Google maps can't reliably show a route offline, and it does not contain national cycle route routes. Or those features are impossible for a software engineer to get working after trying for about 2 hours.
  • OpenStreetMap on browser with cycling layer: www.openstreetmap.org/#map=5/49.582/1.934&layers=C This is the best visualization of cycling routes I've found so far, contains both National Cycle Network and National Byway and a few others, and they are shown extremely clearly. But as a website it doesn't reliably work offline
  • the OsmAnd app for Android is the best offline free-ish OpenStreetMap viewer I've found so far. You only have to pay after reaching 5 region downloads, and it is very cheap if you want to do so. The cycle route view is not amazing, the routes are not so clearly marked and mixed with very similarly colored big roads, but with a bit of effort you can make them out. No routing though
  • I've heard Komoot can keep a predefined route (possibly auto planed) reliably offline, but haven't used it myself. I was not able to see National Cycle Route clearly marked anywhere on it
Some of the contributions are subjectively self evaluated based on:
  • How many significant lines changed (no indentation changes, moves, mass refactoring, trivial tests, etc.):
    0only trivial changes
    1< 20
    2< 150
    3
    150
  • How hard it was to make it. 4 algorithmic lines are harder than 100 web development/documentation lines.
Polonium by Ciro Santilli 40 Updated 2025-07-16
Discovered by Marie Curie, published July 1999.
As Ciro has rambled infinitely at Section "University", the school system is hugely inefficient and a waste of time for everyone involved.
Instead, just use Section "OurBigBook.com" instead.
Motor vehicle emissions refer to the pollutants released into the air from vehicles powered by gasoline, diesel, and other fuels. These emissions can include a variety of harmful compounds, such as carbon monoxide, nitrogen oxides, particulate matter, volatile organic compounds, and hydrocarbons. Exposure to these pollutants has been the focus of numerous studies due to their potential health impacts, especially for vulnerable populations such as pregnant women and their developing fetuses.
Copper is a widely used metal in heat exchangers due to its excellent thermal conductivity, resistance to corrosion, and antimicrobial properties. Here are some key points regarding the use of copper in heat exchangers: 1. **Thermal Conductivity**: Copper has one of the highest thermal conductivities of any commercially available metal, which makes it very effective at transferring heat. This property allows for efficient heat exchange between fluids.
AE Ursae Majoris is a binary star system located in the constellation Ursa Major. It consists of two stars that are close together in terms of their distance from Earth, making the system an interesting target for astronomical observation. The primary star is a focal point for researchers due to its classification as a variable star, specifically a type of AP star, which exhibits variations in luminosity.
Helium storage and conservation refer to the practices and technologies used to manage, store, and preserve helium, a finite and non-renewable resource that is crucial for various applications, such as in scientific research, medical technologies (like MRI machines), and high-tech industries (such as semiconductors and aerospace). ### Helium Storage 1.
Polyadic space is a concept in the field of mathematical logic and set theory, specifically relating to the study of algebras and their generalizations. It generally refers to structures that generalize the idea of a relational or functional space by considering relations or functions that can take multiple arguments (or "ary" inputs), hence the prefix "polyad-.
In topology, "open" and "closed" maps are concepts that describe certain properties of functions between topological spaces. Here's a brief explanation of each term: ### Open Maps A function \( f: X \rightarrow Y \) between two topological spaces is called an **open map** if it takes open sets in \( X \) to open sets in \( Y \).
The Katětov–Tong insertion theorem is a result in the field of topology, particularly in the area of set-theoretic topology. It deals with the properties of certain types of topological spaces, specifically separable metric spaces. The theorem is named after mathematicians František Katětov and David Tong.

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 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    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.
  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