Lebesgue's Number Lemma is a fundamental result in real analysis, particularly in the context of uniform continuity and compactness. It is often used in the field of topology and forms an important part of the theory of measure and integration. The lemma states the following: Let \( \mathcal{U} \) be an open cover of a compact metric space \( X \).
Leland John Haworth was an American businessman and philanthropist known for his contributions to various industries and community initiatives. However, information about him may be limited or less well-known compared to other figures.
In algebra, a lemma is a proven statement or proposition that is used as a stepping stone to demonstrate a larger theorem or more complex result. Lemmas are often simpler and more specific than theorems, providing necessary support or foundational results that help prove more significant mathematical claims. The main characteristics of a lemma include: 1. **Supporting Role**: Lemmas are not typically the main focus of mathematical work; rather, they support the development of more substantial results (theorems).
Léon Brillouin (1889–1969) was a French physicist and a prominent figure in the field of condensed matter physics. He is best known for his contributions to the understanding of crystal dynamics and the theory of phonons, which are quantized modes of vibrations in a crystal lattice. One of his key contributions was the Brillouin zone concept, which is used in solid-state physics to describe the periodicity of the energy states of electrons in a crystalline solid.
Leon Cooper is an American physicist known for his contributions to the field of condensed matter physics. He is particularly famous for his work on superconductivity and the BCS theory, which he developed alongside John Bardeen and Robert Schrieffer in 1957. This theory explains how certain materials can exhibit zero electrical resistance at very low temperatures.
The Copa Libertadores is an annual club football (soccer) tournament organized by the South American Football Confederation (CONMEBOL). Established in 1960, it is one of the most prestigious tournaments in club football in South America, comparable to the UEFA Champions League in Europe. The tournament features the top club teams from various South American countries, including Brazil, Argentina, Chile, Colombia, Uruguay, Paraguay, and others.
The Lewandowski-Kurowicka-Joe (L-K-J) distribution is a family of multivariate distributions that is used to model dependence structures among random variables. It is particularly useful in the context of copulas, which are functions that describe the dependence between random variables while allowing for flexibility in their marginal distributions. The L-K-J distribution is a specific type of copula that is defined on the unit simplex.
The lightest supersymmetric particle (LSP) is a concept from supersymmetry (SUSY), a theoretical framework in particle physics that extends the Standard Model. In SUSY, every Standard Model particle has a superpartner with differing spin characteristics.
The Linear Transform Model in the context of MRI (Magnetic Resonance Imaging) generally refers to mathematical models used for image acquisition, reconstruction, and processing. MRI employs complex physical principles of nuclear magnetic resonance to generate images of the inside of the body. The Linear Transform Model specifically deals with how the raw data (often called k-space data) is transformed into the final images and how various linear transformations can be employed to enhance image quality or reconstruct images from the acquired data.
Linguistic anthropology is a subfield of anthropology that studies the relationship between language and culture. It explores how language influences social life, shapes cultural identities, and reflects societal structures. Linguistic anthropologists examine various aspects of language, including its use in different contexts, its role in shaping thought and perception, and how it varies across different cultures and communities.
Linn F. Mollenauer is a notable figure in the field of optics and photonics, particularly known for his contributions to fiber optics and nonlinear optics. He has worked extensively on optical communication techniques and has authored numerous research papers in these areas. Mollenauer's work has played a significant role in advancing the technology that underpins fiber optic communication systems, which are crucial for modern telecommunications infrastructure.
The Lin–Tsien equation is a mathematical formula that is used in the field of fluid mechanics and aerodynamics. It describes the relationship between pressure and temperature variations in a compressible flow, particularly in the study of shock waves and expansions in gases. The equation helps to analyze the behavior of gases under varying conditions of temperature and pressure, which is particularly important in the design and analysis of aircraft, rockets, and other systems involving high-speed flows.
A "List of artillery" typically refers to a compilation or catalog of different types of artillery pieces used throughout history. Artillery refers to large-caliber guns used in warfare on land, such as cannons, howitzers, mortars, and rocket artillery, among others. The list may be categorized by various criteria, including: 1. **Type of Artillery**: - **Cannons**: Traditional artillery pieces, often used for direct fire.
The Balkans are home to a diverse range of flora, including many endemic plants that are unique to this region. The term "endemic" refers to species that are native to a particular geographic area and not found naturally anywhere else. The Balkan Peninsula's varied climate and topography contribute to its rich biodiversity. Some notable genera and species of Balkan endemic plants include: 1. **Adenocarpus decorticans** - A shrub or small tree endemic to parts of the Balkans.
Michael Jordan, widely regarded as one of the greatest basketball players of all time, has an extensive list of career achievements. Here are some of his most notable accomplishments: ### Individual Awards 1. **6× NBA Champion** (1991–1993, 1996–1998) 2. **5× NBA Most Valuable Player (MVP)** (1988, 1991, 1992, 1996, 1998) 3.
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





