The Brouwer Fixed-Point Theorem is a fundamental result in topology, specifically in the field of fixed-point theory. It states that any continuous function mapping a compact convex set to itself has at least one fixed point.
The Browder Fixed-Point Theorem is a result in functional analysis and topological fixed-point theory, named after the mathematician Felix Browder. This theorem extends the classical Brouwer Fixed-Point Theorem to more general contexts, particularly in infinite-dimensional spaces.
The Atiyah–Bott fixed-point theorem is a fundamental result in algebraic topology and differential geometry, developed by mathematicians Michael Atiyah and Raoul Bott in the context of the study of fixed points of smooth maps on manifolds.
Fluid thread breakup refers to the phenomenon where a continuous thread or filament of liquid (such as a stream of ink, paint, or other fluids) breaks into separate droplets. This process is crucial in various applications, including inkjet printing, spray painting, and fuel injection systems, where the effective atomization of liquids into fine droplets is necessary for efficient application and performance.
Nielsen theory, often associated with the work of mathematician and physicist Nielsen, primarily pertains to the field of topological and algebraic invariants in the context of knot theory and three-manifolds. One of the key contributions of Nielsen is his work on the concept of "Nielsen classes," which relate to the classification of covering spaces of surfaces and the study of fundamental groups.
The term "circumpolar" refers to areas or regions near the poles of a planet, typically the North Pole or South Pole. In the context of Earth, it describes features, phenomena, or celestial bodies that surround or are located around the poles.
"Inventing the Flat Earth" is a book written by Jeffrey Burton Russell, published in 1991. The book explores the historical misconceptions surrounding the belief that people in the Middle Ages thought the Earth was flat. Russell argues that this flat Earth myth is largely a modern fabrication, and he investigates how this misunderstanding developed over time. In the book, Russell discusses the views of various historical figures, examines ancient and medieval cosmology, and how the imagination regarding the shape of the Earth has evolved.
The Myth of the Flat Earth refers to a common misconception that, during the Middle Ages, people widely believed in a flat Earth and that this belief was only corrected by the work of scientists like Christopher Columbus and Galileo Galilei. In reality, the idea of a spherical Earth was well established among educated people in the ancient world, including the Greeks, and was further confirmed by various forms of evidence and observations.
Baryon number is a quantum number in particle physics that represents the total number of baryons in a system. Baryons are a class of subatomic particles that include protons and neutrons, which are the building blocks of atomic nuclei. The baryon number is defined as follows: - Each baryon (like protons and neutrons) has a baryon number of +1.
"Bottomness" is not a widely recognized term in a specific academic or professional context, but it may refer to various concepts depending on the context in which it is used. Here are a few interpretations: 1. **Philosophical Context**: It could describe a state of being at the bottom of a hierarchical structure or system, emphasizing themes like despair, depression, or existential reflection.
Weak isospin is a quantum number associated with the weak interaction, one of the four fundamental forces of nature responsible for processes like beta decay in atomic nuclei. It is a key concept in the electroweak theory, which unifies the electromagnetic force and the weak nuclear force. In the context of particle physics, weak isospin is analogous to the concept of isospin (or isotopic spin) used for strong interactions, but it is specifically related to the weak force.
Michiel Coignet (also known as Michiel de Coignet) was a Flemish astronomer and mathematician who lived during the late 16th and early 17th centuries. He is best known for his work in developing and promoting scientific instruments, particularly for astronomy, and his contributions to cartography and geodesy.
Rayleigh–Bénard convection is a fluid dynamics phenomenon that occurs in a horizontal layer of fluid (such as a liquid or gas) that is heated from below and cooled from above. This setup creates a temperature gradient, where the bottom layer of fluid becomes warmer and less dense, while the top layer remains cooler and denser. As the bottom fluid heats up, it becomes buoyant and begins to rise, while the cooler, denser fluid descends to take its place.
Richard Courant (1888–1972) was a prominent mathematician known for his contributions to various fields, including mathematical analysis, partial differential equations, and mathematical physics. He was one of the founding figures of modern applied mathematics and played a key role in the establishment of mathematical education in the United States, especially through his work at New York University.
Adhémar Jean Claude Barré de Saint-Venant (1797-1886) was a French engineer and mathematician known for his significant contributions to the fields of mechanics and fluid dynamics, particularly in the study of elasticity and the flow of fluids. He is best known for formulating the Saint-Venant's principle, which is a fundamental concept in structural engineering and elasticity theory.
Chung K. Law is a prominent figure in the field of mechanical engineering, particularly known for his contributions to the study of fluid mechanics, combustion, and thermodynamics. He is a professor at Princeton University and has been involved in research related to high-temperature gas dynamics, reactive flows, and the fundamentals of combustion. His work often involves both theoretical analysis and computational modeling.
Alexander Gorlov is a notable figure primarily associated with engineering and academia. He is best known for his work in the field of fluid dynamics, particularly for his contributions related to fluid mechanics and the design of advanced fluid systems. One of his significant contributions includes the development of the Gorlov helical turbine, which is a type of water turbine designed to be efficient in low-flow and low-head environments.
Amable Liñán is a prominent Spanish physicist known for his work in the field of astrophysics, fluid dynamics, and cosmology. As a researcher, he has contributed significantly to the understanding of various physical phenomena and has published numerous scientific papers. His work often involves theoretical approaches to complex scientific problems.
Andrea Prosperetti is an accomplished researcher and professor known for his work in the field of mechanical engineering and fluid dynamics. He has made significant contributions to various areas, including bubble dynamics, multiphase flows, and acoustics in fluids. Prosperetti has published numerous scientific papers, and his research often involves both theoretical and experimental approaches.
Andrei Monin is a well-known Russian-American scientist and professor, recognized primarily for his contributions to the field of fluid dynamics. His work has advanced the understanding of various fluid-related phenomena, and he has published extensively in the area. He is also involved in the field of turbulence and has made significant contributions to theoretical and computational fluid mechanics.
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





