A formal manifold is a concept from the field of mathematics, particularly in differential geometry and algebraic geometry. It is primarily used in the study of smooth manifolds and formal schemes. In essence, a formal manifold is a "manifold" that is equipped with a formal structure allowing for the study of its infinitesimal properties without relying on the usual notions of topology or smoothness. Instead, it utilizes a local coordinate system that behaves much like a formal power series.
A Higgs bundle is a mathematical structure that arises in the study of geometry and mathematical physics, particularly in the context of gauge theory and string theory. It consists of a vector bundle equipped with a differential form, called a Higgs field, that satisfies certain conditions. More specifically, a Higgs bundle can be described as follows: 1. **Vector Bundle**: You start with a vector bundle \( E \) over a complex algebraic or differentiable manifold \( X \).
The Homotopy Excision Theorem is an important result in algebraic topology that deals with the behavior of homotopy groups under certain conditions related to pairs of spaces. In essence, it allows us to conclude that if two spaces are homotopy equivalent, then certain derived spaces (like certain subspaces and their complements) retain these equivalences within homotopy categories.
The Pinewood Derby is a racing event for Cub Scouts, where participants design and build small wooden cars from a block of wood, typically a pine block. The cars are usually around 5 ounces in weight and must meet specific size and weight regulations set by the scouting organization. Participants start with a basic kit that includes a block of wood, plastic wheels, and metal axles. They can then carve, paint, and customize their cars to create unique designs.
In geometry, scaling refers to the process of resizing an object by a certain factor. This involves changing the dimensions of the object uniformly (maintaining the shape) or non-uniformly (changing shape) while preserving the proportions of the object. The factor by which the object is scaled is called the scale factor. When scaling is uniform, every linear dimension of the object (length, width, height) is multiplied by the same scale factor.
Choro-Q, also known as Q-Pop or Choro-Q Cars, is a line of small, toy cars that originated in Japan. The toys feature a unique design with a distinctive "popping" action characterized by a spring-loaded mechanism.
"Crusader 101" could refer to a variety of topics depending on the context, including historical studies, educational programs, gaming, or specific organizations. One possible interpretation is that it relates to a beginner's course or introduction to the historical Crusades, which were a series of religious wars during the medieval period, particularly focused on the Holy Land.
Mini-Z refers to a brand of small-scale radio-controlled (RC) cars produced by the Japanese company Kyosho. These cars are typically 1/27th scale and are known for their performance, detail, and advanced technology. Mini-Z cars are popular among hobbyists and are often used for racing on small tracks, both indoor and outdoor.
Tamiya Radio Controlled Nitro Vehicles refer to a range of remote-controlled cars, trucks, and other vehicles produced by Tamiya, a well-known Japanese manufacturer of plastic model kits and radio-controlled models. Nitro vehicles are powered by small internal combustion engines that run on a special nitromethane-based fuel, offering a different experience compared to electric-powered RC vehicles. Tamiya is recognized for its high-quality products, attention to detail, and innovative designs.
Transport law is a branch of law that governs the movement of people and goods from one location to another. It encompasses a wide range of legal principles, regulations, and frameworks that apply to various modes of transportation, including: 1. **Land Transport**: This includes laws related to road traffic, railways, and the liabilities associated with transporting goods and passengers by land.
In computing, particularly in the context of peer-to-peer (P2P) file sharing networks and torrenting, a "leecher" refers to a user who downloads files from other users but does not share or upload those files back to the network. This term is often used to describe individuals who take advantage of the resources made available by "seeders," who are users that upload and share files.
The Gummel-Poon model is a semiconductor device modeling framework, primarily used for the simulation of bipolar junction transistors (BJTs) and some MOSFET characteristics. It was developed by the physicists Gummel and Poon in the 1970s and has become a foundational element in circuit simulation tools.
Accessible transportation refers to transportation systems and services designed to accommodate individuals with disabilities, including those with mobility, sensory, cognitive, and other impairments. The goal of accessible transportation is to ensure that all individuals can travel safely, efficiently, and with dignity, regardless of their abilities. Key features of accessible transportation may include: 1. **Accessible Vehicles:** Buses, trains, and taxis equipped with features like wheelchair ramps, lifts, and designated spaces for passengers with disabilities.
Intermodal transport refers to the use of two or more different modes of transportation to move goods from one location to another. This approach combines multiple forms of transportation—such as trucks, trains, ships, or airplanes—within a single, seamless transport chain. Key features of intermodal transport include: 1. **Containerization**: Goods are typically loaded into standardized containers that can be easily transferred between different modes of transport without needing to unpack the contents.
Lemoine's problem, named after the French mathematician Georges Lemoine, is a conjecture in number theory concerning the representation of odd integers as sums of prime numbers. Specifically, the conjecture posits that every odd integer greater than 5 can be expressed as the sum of an odd prime and an even semiprime (a product of two primes, where at least one of the primes is 2).
The 85th percentile speed is a measurement used in traffic engineering and transportation studies to indicate the speed at which 85% of vehicles are traveling at or below on a particular stretch of road at a given time. In essence, it is a statistical measure that helps identify the speed at which most drivers are comfortable driving without feeling the need to speed. To calculate the 85th percentile speed, traffic speed data is collected from a specified site over a certain period.
Travel refers to the act of moving from one place to another, typically over a distance that requires some form of transportation. It can encompass a variety of purposes, including: 1. **Leisure**: Traveling for enjoyment, relaxation, and exploration, such as vacations or excursions. 2. **Business**: Traveling for work-related purposes, including meetings, conferences, and other professional engagements.
Transport in culture refers to the ways in which transportation systems, technologies, and practices influence and shape cultural dynamics within societies. It encompasses various dimensions, including: 1. **Cultural Exchange**: Transport facilitates the movement of people and goods, enabling the exchange of ideas, traditions, and customs among different cultures. This can lead to cultural blending and the emergence of new social practices. 2. **Regional Identity**: Different modes of transport can contribute to regional identities.
Transport safety refers to the measures, practices, regulations, and technologies designed to ensure the safe movement of people and goods across various modes of transportation, including road, rail, air, and maritime. The objective of transport safety is to minimize the risk of accidents, injuries, and fatalities while promoting an efficient and reliable transportation system. Key components of transport safety include: 1. **Regulations and Standards**: Governments and international organizations establish laws, regulations, and standards to ensure safety in transportation.
Transport terminology refers to the specialized vocabulary and terms used within the field of transportation and logistics. It encompasses a wide range of concepts, practices, and modes of transport, addressing everything from the movement of goods and passengers to the infrastructure supporting these systems. Here are some key areas within transport terminology: 1. **Modes of Transport**: - **Road Transport**: Vehicles such as cars, trucks, and buses that travel on roads.

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