A triangular matrix ring is a specific type of matrix ring made up of upper or lower triangular matrices over a given ring. More formally, let's define it in a bit more detail. ### Definition: 1. **Triangular Matrices**: - An **upper triangular matrix** is a square matrix where all entries below the main diagonal are zero.
As of my last knowledge update in October 2021, there is no widely recognized figure or concept specifically known as "Mikhail Sadovsky." It's possible that this name could refer to a private individual, a fictional character, or perhaps someone who has gained prominence after my last knowledge update.
As of my last update in October 2023, there isn't a widely recognized figure or concept known as "Ivan Bardin" in popular culture, history, or academia. It's possible that he could be a private individual, a character in a niche work, or a reference that has emerged after my last update.
Alexander Shlyakhter is not a widely recognized public figure in mainstream discourse or media, so there may be limited information available depending on context. If you are referring to a specific individual, it could pertain to various fields such as science, art, politics, or other areas, but without more context, it's difficult to provide a precise answer.
Mikhail Lukin is a renowned physicist known for his work in the fields of quantum optics, quantum information, and condensed matter physics. He is a professor at Harvard University and has made significant contributions to the development of technologies related to quantum computing, quantum communication, and the understanding of quantum systems. Lukin's research often focuses on the interaction between light and matter at the quantum level, which has implications for the development of new quantum technologies.
Vitaly Efimov is a prominent Russian-American mathematician known for his contributions to several areas of mathematics, particularly in topology, differential topology, and mathematical physics. He is renowned for his work on the topology of manifolds and the development of new insights into the structure of higher-dimensional spaces. Efimov's work has had significant implications in various fields, including theoretical physics, where topological concepts are applied to problems concerning the nature of space and time.
Vladimir Veksler is a prominent Russian physicist, best known for his contributions to the field of particle physics and accelerator technology. He played a significant role in the development of synchrotron radiation and is recognized for introducing the concept of "synchronous" particles in accelerators, which led to the development of various technologies in high-energy physics.
"What Wondrous Love Is This" is a traditional American hymn that dates back to the 19th century. It is often associated with the shape note singing tradition, which was a popular method of musical education in the United States, particularly in the Southern regions. The hymn expresses themes of love, sacrifice, and redemption, centering on the love of Christ and His atonement for humanity's sins.
The East Texas Musical Convention is an annual event that celebrates and showcases traditional music, particularly focusing on shape note singing, which is a unique style of musical notation that facilitates participatory singing. Held in East Texas, this convention typically features a gathering of singers, musicians, and attendees who come together for a weekend of music, fellowship, and learning. Participants often sing from hymns or other songs that are commonly associated with shape note practices.
Seaborn McDaniel Denson is a notable figure, primarily recognized as a civil rights attorney and advocate. He is involved in various legal efforts aimed at promoting social justice and equality. While specific details about his career, including significant cases or projects, may vary, he is often associated with work that addresses issues related to civil rights, discrimination, and social advocacy.
SUNMOS (Sun Microsystems Multi Operating System) is a distributed operating system developed by Sun Microsystems in the late 1980s and early 1990s. It was designed for networked systems and aimed to facilitate resource sharing and communication between computers. SUNMOS is notable for its use in supporting a variety of hardware configurations and providing a platform for distributed computing environments. It included features that allowed multiple users and applications to access shared resources efficiently.
Salvador Dalí was a prominent Spanish surrealist artist known for his striking and eccentric works. His paintings often incorporate bizarre imagery and dream-like scenes, reflecting his unique imagination and technical skill. Here are some of his most notable works: 1. **The Persistence of Memory (1931)** - Perhaps his most famous painting, it features melting clocks draped over a surreal landscape, exploring themes of time and reality.
The Morohashi Museum of Modern Art, located in the city of Eiheiji in Fukui Prefecture, Japan, is an art museum that focuses on modern and contemporary art. Established in the late 20th century, it serves as a cultural institution dedicated to promoting the appreciation of modern art. The museum's collection includes works by Japanese and international artists, and it regularly hosts exhibitions, educational programs, and events to engage the public with contemporary art and artists.
Ernest K. Warburton is a physicist known for his contributions to the field of condensed matter physics, particularly in the area of semiconductor physics and nanotechnology. His work has involved researching the electronic properties of materials, as well as exploring the fundamental physics of quantum structures. Warburton has been associated with various academic institutions and has published numerous papers in scientific journals, contributing to the advancement of knowledge in his field.
Capella is an open-source model-based systems engineering tool developed by the Eclipse Foundation. It is designed to help engineers manage complex systems and facilitate the design, analysis, and validation of system architectures. Capella offers a modeling environment that supports the Arcadia method, which is a structured approach for managing system requirements, architecture, and verification.
Salvador Dalí was a prominent Spanish surrealist painter known for his eccentric and imaginative artworks. While he is best known for his paintings, his influence extended beyond visual arts to various forms of creative expression, including dance. Dalí had a fascination with movement and the human form, which often manifested in his work. He collaborated with several artists and choreographers to integrate his surrealist visions into performances.
Bremsstrahlung is a German term that translates to "braking radiation." It refers to the electromagnetic radiation emitted when charged particles, such as electrons, are accelerated or decelerated, particularly when they pass near atomic nuclei. This process occurs because the change in the velocity of the charged particle results in the emission of energy in the form of radiation, typically X-rays.
As of my last knowledge update in October 2021, Sandhawk may refer to different things depending on the context. It could be: 1. **A Vehicle or Equipment**: In some cases, "Sandhawk" could refer to a specific model of a vehicle or equipment, especially in off-road or outdoor contexts.
Sandia Base, formally known as Sandia Army Base, is a military installation located in Albuquerque, New Mexico. It is associated with the United States Army and serves various defense and research purposes. The base is closely linked with the nearby Sandia National Laboratories, which is a key center for research and development in nuclear weaponry, national security, and advanced technology.

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