The Ryll-Nardzewski fixed-point theorem is a result in the field of functional analysis, specifically concerning fixed points in nonatomic convex sets in topological vector spaces. It generalizes certain fixed-point results, including the well-known Brouwer fixed-point theorem, to more general settings.
The Stewart–Walker lemma is a result in the field of differential geometry, particularly in the study of Riemannian manifolds. It is specifically related to the curvature of manifolds and provides conditions under which the curvature tensor can be expressed in terms of the metric tensor and its derivatives. The lemma is often invoked in the context of proving properties about space forms and the relationship between curvature and geometric structures on manifolds.
Wiener's lemma is a result in functional analysis and harmonic analysis, particularly related to the theory of Fourier series and the spaces of functions. It is named after Norbert Wiener, who contributed significantly to the field.
The Parrot's Theorem is a humorous and informal mathematical theorem that originated in a cartoon by mathematician and author Paul Erdős. The essence of the theorem is that if a parrot mimics the phrase "I am a math genius," then at least one person in the room will believe it. While not a formal theorem in the traditional sense, it serves to illustrate ideas about belief, perception, and the influence of authority or charisma in discussions, particularly in mathematics and academia.
A wireless mesh network is a type of network topology where multiple wireless devices (nodes) work together to create a flexible and self-organizing network. Unlike traditional networks that rely on a central router or access point, a mesh network allows each node to communicate with one another directly, extending the network's range and reliability.
Guy Henniart is a French mathematician known for his work in the fields of algebraic geometry and mathematical logic. He is particularly recognized for his contributions to model theory and the study of algebraic structures.
The term "difference" can refer to several concepts depending on the context. Here are a few common meanings: 1. **Mathematics**: In mathematics, the difference usually refers to the result of subtracting one number from another. For example, the difference between 8 and 3 is 5 (8 - 3 = 5). 2. **Comparative Analysis**: In a broader sense, difference can refer to the characteristics that distinguish one thing from another.
As of my last update in October 2023, The American Mathematical Monthly is a well-regarded journal published by the Mathematical Association of America (MAA). It features articles on mathematics that are accessible to a broad audience, including undergraduates, teachers, and professional mathematicians. The editorial board typically consists of mathematicians and educators who are experts in various areas of mathematics.
"Topics" is one of Aristotle's works in which he addresses the nature of dialectical reasoning and argumentation. In this text, Aristotle explores how to construct and evaluate arguments, focusing particularly on how to engage in reasoning about likely or probable conclusions rather than certain truths. The main purpose of "Topics" is to provide a systematic method for argumentation, particularly in the context of informal logic and debate.
esolangs.org/wiki/Y86 mentions:
One specification at: web.cse.ohio-state.edu/~reeves.92/CSE2421sp13/PracticeProblemsY86.pdf
In piping and plumbing, "gooseneck" refers to a type of pipe or fitting that has a specific curved shape resembling the neck of a goose. This design is typically characterized by a U-shaped or S-shaped bend, allowing for the transition of flow direction or elevation gain while maintaining a smooth flow path.
A Fermi gas is a theoretical model used in quantum mechanics to describe a collection of fermions, which are particles that follow Fermi-Dirac statistics. Fermions include particles such as electrons, protons, and neutrons, each of which obeys the Pauli exclusion principle. This principle states that no two fermions can occupy the same quantum state simultaneously.
A list of rogue waves refers to documented instances or types of rogue waves, which are large, unexpected, and suddenly appearing ocean waves that can be incredibly dangerous. These waves are often defined as waves that are at least twice the height of surrounding waves and can occur in deep water as well as coastal areas. Rogue waves are also sometimes referred to by other names, such as "freak waves," "king waves," or "monster waves.
The South Atlantic Gyre is a large system of circulating ocean currents located in the South Atlantic Ocean. It is part of the global ocean circulation system and plays a significant role in oceanic and atmospheric processes. The gyre is characterized by a clockwise rotation in the Southern Hemisphere and is primarily formed by the interaction of several major currents, including: 1. **Brazil Current**: This warm current flows southward along the eastern coast of South America.
A Hefner lamp is a type of measurement device used to determine the luminosity or brightness of a light source, specifically in terms of its equivalent light output. Named after the physicist Robert Hefner, the lamp is used primarily in the field of photometry, which is the science of measuring visible light in terms of its perceived brightness to the human eye. The Hefner lamp contains a specific type of candle that provides a consistent and reproducible light output.
Pitch in music refers to the perceived frequency of a sound, which determines how high or low a note sounds. It is a fundamental characteristic of musical notes and is crucial for the creation of melodies and harmonies. Pitch is typically measured in Hertz (Hz), which represents the number of vibrations or cycles per second. For example, the standard pitch for the note A4 (the A above middle C) is set at 440 Hz.
Samarium-neodymium dating is a radiometric dating method used to determine the age of rocks and minerals, particularly those containing rare earth elements. This technique is based on the decay of the isotope samarium-147 (Sm) to neodymium-143 (Nd). Here's how it works: 1. **Decay Process**: Samarium-147 has a half-life of about 106 billion years.
Pediatric radiology is a specialized branch of medicine that focuses on the imaging and diagnosis of diseases and conditions in infants, children, and adolescents. It involves the use of various imaging techniques, including: 1. **X-rays**: Used to visualize the bones and detect fractures, infections, or congenital conditions. 2. **Ultrasound**: A non-invasive method that uses sound waves to create images of soft tissues and organs.
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





