The term "bitangent" can have different meanings depending on the context—mathematics, graphics, or computer science. Here are a couple of interpretations: 1. **Mathematics and Geometry**: In the context of curves, a bitangent is a line that is tangent to a curve at two distinct points. This concept often comes up in the study of curves and surfaces, where you may analyze the properties of tangential lines to understand the behavior of the curve.
A fibered manifold is a type of manifold that is structured in such a way that it can be viewed as a "fiber bundle" over another manifold. More formally, a fibered manifold can be described in terms of a fibration, which is a particular kind of mapping between manifolds. To clarify, let’s break down the concept: 1. **Base Manifold**: A manifold \( B \) that serves as the "base" space for the fibration.
The term "symmetry set" can refer to different concepts depending on the context in which it is used. Here are a few interpretations: 1. **Geometry and Mathematics**: In geometry, a symmetry set may refer to a set of transformations (such as rotations, reflections, and translations) that leave an object unchanged or invariant. For example, the symmetry set of a square includes rotations by 0°, 90°, 180°,270° and reflections across its axes of symmetry.
Tetrad formalism, also known as the vierbein formalism in the context of General Relativity, is a mathematical framework used to describe the geometry of spacetime. It plays a crucial role in formulating theories of gravity and field theories in curved spacetime. In the tetrad formalism, the geometry of spacetime is described using a set of four vector fields called tetrads (or vierbeins in 4 dimensions).
S/2004 S 4 is a natural satellite, or moon, of Saturn. It was discovered in 2004 and is part of a group of small moons known as the "S/2004 S" series, which are characterized by their small size and irregular shapes. The designation "S" indicates that it is a moon of Saturn, and the numbers denote the year of discovery and its order of discovery among Saturn's moons in that year.
KCNMB1 (Potassium Calcium-Activated Channel Subfamily M Beta Member 1) is a gene that encodes a protein involved in the regulation of potassium ion channels. Specifically, it is known to be a regulatory beta subunit for a class of calcium-activated potassium (BK) channels, which play a crucial role in various physiological processes such as smooth muscle contraction, neuronal signaling, and cardiac function.
Wei Ji Ma is a prominent figure in the field of cognitive neuroscience, particularly known for his work on decision-making and perception. As a researcher and educator, he focuses on how perception and cognition interact, especially in the context of decision-making under uncertainty. His work often employs experimental methods, including behavioral studies and neuroimaging techniques, to explore these themes. In addition to his research, Wei Ji Ma is involved in teaching and mentoring students in cognitive neuroscience and related fields.
S/2004 S 6 is a designation for a natural satellite (moon) of Saturn. It was discovered in 2004 and is one of the many small moons orbiting the planet. Like many of Saturn's other small moons, S/2004 S 6 is irregularly shaped and has a relatively small diameter. The designation follows a standard naming convention, where "S" refers to Saturn, and the numbers indicate the order of discovery.
A CM-field, short for "Complex Multiplication field," is a type of number field that is significant in algebraic number theory, particularly in the study of elliptic curves and modular forms. More specifically, a CM-field is an imaginary quadratic field \(K\) that arises from the theory of elliptic curves with complex multiplication by a certain ring of integers.
Beverley McKeon is a professor and researcher known for her work in the field of engineering, particularly in the areas of fluid mechanics and heat transfer.
A conoid is a three-dimensional geometric shape that resembles a cone but has a more complex structure. It is typically defined as a surface generated by moving a straight line, which is called a generator, along a predetermined path while maintaining a constant distance from a fixed point or axis. More formally, a conoid can be described mathematically in several ways, but one of the common forms is defined using a parameterization in Cartesian coordinates.
Lexicographic code, often referred to in the context of coding theory and combinatorial generation, is a method of ordering or defining sequences or strings based on a lexicographic (dictionary-like) sorting order. It's primarily used in various fields such as computer science, information theory, and combinatorics for organizing data or generating combinations.
Edgar Krahn is not widely recognized in a global context or in popular knowledge databases. It's possible that he may refer to a lesser-known individual or a character from a specific context, but without additional information, it’s challenging to provide a precise answer. If "Edgar Krahn" pertains to a specific field such as literature, science, or entertainment, or if there are more details about his contributions or relevance, please provide that context for a more accurate response.
A hydraulic jump is a phenomenon in fluid dynamics that occurs when a high-velocity liquid flow transitions to a lower-velocity flow, resulting in a sudden change in water depth. This often happens in open channel flow systems, such as rivers or irrigation channels, where a fast-moving stream of fluid encounters an obstruction or change in elevation.
A hypertree is a concept used in the field of graph theory and databases, particularly in the context of data management and semantic databases. It is a generalization of the concept of a tree, where the usual restrictions on the structure of trees are relaxed. In a standard tree, each node has one parent (except for the root), and there are specific, hierarchical relationships among nodes.
In topology, a **Hausdorff gap** (or just **gap**) is a concept relating to the structure of certain topological spaces, specifically in relation to the properties of sequences or nets in those spaces. A Hausdorff gap is often associated with the concept of a *Hausdorff space*, which is a topological space where any two distinct points can be separated by neighborhoods.
The number 6 is a natural number that follows 5 and precedes 7. It is an integer and is often used in various mathematical contexts. In addition, 6 can represent different concepts depending on the context, such as: - In mathematics, it is an even number and has properties like being a perfect number (the sum of its divisors excluding itself equals the number). - In science, 6 is the atomic number of carbon, an essential element for life.
An integer is a whole number that can be positive, negative, or zero. Integers do not include fractions, decimals, or any non-whole numeric values. The set of integers is typically represented by the symbol **ℤ** and includes numbers such as: - Positive integers: 1, 2, 3, ... - Zero: 0 - Negative integers: -1, -2, -3, ...
Knot operations refer to methods used in the field of knot theory, a branch of topology in mathematics that studies the properties and classifications of knots. A knot is defined as a closed loop in three-dimensional space that does not intersect itself, akin to a tangled piece of string. Knot operations are techniques that allow mathematicians to manipulate these knots to study their properties, relationships, and classifications.
Photon upconversion is a process in which lower-energy photons (such as infrared or near-infrared light) are absorbed and the energy is combined to emit higher-energy photons (often in the visible range). This phenomenon can occur in certain materials, often referred to as upconverters, which can convert multiple low-energy photons into a single higher-energy photon through various mechanisms.
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





