The Ohsawa–Takegoshi L² extension theorem is a significant result in complex analysis, particularly in the theory of several complex variables. It provides conditions under which holomorphic functions defined on a submanifold can be extended to a larger domain while retaining certain properties, such as being in the L² space. More precisely, the theorem addresses the problem of extending holomorphic functions that are square-integrable on certain subvarieties of complex manifolds.
Calculators are electronic or mechanical devices designed to perform mathematical calculations, ranging from basic arithmetic (addition, subtraction, multiplication, and division) to more complex operations such as trigonometry, logarithms, and calculus. There are several types of calculators, including: 1. **Basic Calculators**: Simple devices that handle basic arithmetic operations. 2. **Scientific Calculators**: These calculators can perform more advanced functions, including trigonometric calculations, exponentiation, and statistical operations.
Stochastic Portfolio Theory (SPT) is a mathematical framework used to analyze portfolio allocations and their performance in a probabilistic context. It combines elements of probability theory, stochastic processes, and financial modeling to understand how portfolios behave over time under uncertainty. The key aspects of SPT include: 1. **Stochastic Processes**: SPT treats asset prices and portfolio returns as stochastic processes, meaning they evolve randomly over time according to certain probabilistic rules.
The Universal Chord Theorem is a concept from geometry, specifically related to circles. It states that for any triangle inscribed in a circle (also known as a circumcircle), the perpendicular bisectors of its sides will intersect at a single point, which is the circumcenter of the triangle (the center of the circumcircle).
Straightedge can refer to a few different concepts, depending on the context: 1. **Tool**: In carpentry and various trades, a straightedge is a tool used to create straight lines or check the flatness of a surface. It is typically a long, flat piece of material, usually wood or metal, marked with measurement units and utilized for drawing or guiding cutting tools.
Mathematical tables are organized sets of numerical values or functions arranged in a systematic manner, often used to simplify calculations in mathematics and related fields. They serve as reference tools that provide quick access to answers for various mathematical queries without the need for complex calculations.
The Beevers–Lipson strip is a type of chemical test used to detect the presence of reducing sugars, such as glucose and fructose, in a solution. It is named after the chemists Sir William Beevers and M. Lipson, who introduced this method. The strip is coated with reagents that change color in the presence of reducing sugars when the sample comes into contact with it. The color change is typically used as an indicator of the concentration of reducing sugars in the sample.
A C-Thru Ruler typically refers to a type of transparent ruler, often made of plastic, that allows for clear visibility of the surface underneath it while making measurements. The name "C-Thru" suggests its see-through design, which is especially useful for precise alignment over drawings, graphs, or text. These rulers are commonly used in classrooms, design settings, engineering, and art because they help users take accurate measurements while maintaining a clear view of what they are working on.
A French curve is a template made from plastic or other materials, used in drafting and drawing to create smooth curves. It features a variety of curves along its edge, allowing artists, engineers, and designers to draw arcs and curves of different radii accurately. French curves are especially useful for freehand drawing and for creating complex shapes that cannot be easily achieved with a compass or straightedge. They are commonly used in technical drawing, illustration, and other fields requiring precise curvilinear designs.
Intergraph, now known as Hexagon Geospatial, is a company that specializes in geospatial software and technology. It provides solutions for geographic information systems (GIS), computer-aided design (CAD), and various applications in industries such as public safety, natural resources, utilities, and government. Intergraph's software helps organizations manage and visualize spatial data, enabling them to make informed decisions based on geographic information. Over time, Hexagon, a global provider of information technologies, acquired Intergraph.
The term "Integrator" can refer to several different concepts depending on the context in which it is used. Here are a few interpretations: 1. **Mathematics**: In mathematics, an "integrator" often refers to a function or operator that performs integration, which is the process of finding the integral of a function.
Cultural depictions of mathematicians often reflect a range of stereotypes, themes, and representations in literature, film, television, and other forms of art. These depictions can vary significantly from positive portrayals to negative stereotypes. Here are some common themes and characteristics associated with cultural depictions of mathematicians: 1. **The "Mad Scientist" Trope**: In some works, mathematicians are portrayed as eccentric geniuses, often obsessed with their work to the point of social awkwardness.
A tally stick is a historical accounting tool used primarily in England and other parts of Europe during the medieval period. Typically made from wood, a tally stick is a stick with notches carved into it to represent numbers or amounts. The most common use of tally sticks was for recording debts or financial transactions. The process of using a tally stick involved cutting the stick to a specific length and making notches on it to indicate amounts owed or other data.
As of my last knowledge update in October 2023, "Bullet Group" may refer to a few different entities or concepts depending on the context. It's important to clarify your question for accurate information, but potential interpretations include: 1. **Business or Corporate Entity**: There may be a company or organization called Bullet Group operating in various industries, such as marketing, technology, or logistics.
In geometry, a "tomahawk" typically refers to a shape or figure resembling the outline or silhouette of a tomahawk, which is a type of axe. However, there isn't a widely recognized geometric term specifically called "tomahawk" in classical geometry.
A list of equations typically refers to a compilation of mathematical statements that express the equality between two expressions. These equations can cover various fields such as algebra, calculus, physics, and more.
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . 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. - 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