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.
A finite potential well is a concept in quantum mechanics that describes a potential energy region in which a particle can exist with energy levels that are quantized. Unlike an infinite potential well, where the potential energy is infinitely high outside a certain region, a finite potential well has a finite depth and finite width.
The Hong–Ou–Mandel (HOM) effect is a phenomenon in quantum optics that describes the interference of indistinguishable single photons. It was first observed by physicists Claude Hong, Ming Wu Ou, and Leonard Mandel in 1987. The effect illustrates the unique behaviors of quantum particles, specifically bosons, such as photons.
Quantum suicide and immortality are thought experiments related to the interpretation of quantum mechanics, particularly the many-worlds interpretation (MWI). These concepts explore the implications of quantum mechanics on concepts of life, death, and consciousness. ### Quantum Suicide The thought experiment of quantum suicide was devised by physicist David Deutsch and is typically framed as a scenario involving an observer and a quantum event with two outcomes.
"G.I. Joe: The Rise of Cobra" is a 2009 action film directed by Stephen Sommers, based on the popular Hasbro toy line and the associated media franchise. The movie is a live-action adaptation that reimagines the classic G.I. Joe characters and storyline, blending elements of military action, sci-fi, and espionage. The plot revolves around an elite military unit known as G.I.
"The Mind of God" can refer to different concepts depending on context, including philosophical, theological, and scientific perspectives. Here are a few interpretations: 1. **Philosophical and Theological Perspective**: In theology, "The Mind of God" often refers to the nature and will of God, encompassing divine knowledge, intention, and understanding.
PhysMath Central was an online platform that focused on publishing open-access scientific research in the fields of physics and mathematics. It aimed to provide a venue for researchers to share their findings without the restrictions often associated with traditional publishing models. The platform allowed for the publication of various types of articles, including research papers, reviews, and more, and fostered collaboration and communication within the scientific community.
Back pressure is a term used in various fields, notably in engineering and fluid dynamics, to describe a situation where resistance or pressure within a system prevents or slows down the movement of fluids or gases. It can occur in different contexts, such as: 1. **Fluid Systems**: In pipelines or hydraulic systems, back pressure is the pressure exerted in the opposite direction of the flow. It can be caused by factors such as narrowing of pipes, obstructions, or changes in elevation.
Italy has had a vibrant technology and computing sector, and while several companies have succeeded, many have also become defunct over the years. Some notable defunct computer companies from Italy include: 1. **Olivetti**: Founded in 1908, Olivetti was known for its typewriters and later became a significant player in the computing industry with products like computers and software.
Wikirank.com is a website that provides analytics and ranking information for Wikipedia. It allows users to explore various metrics related to Wikipedia pages, such as page views, edits, and other engagement statistics. The site often visualizes data related to the popularity and activity of different Wikipedia articles, helping users understand trends and the most visited topics on the platform. Additionally, it may provide insights into the performance of Wikipedia in different languages and regions.
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





