"Trill" in music refers to a specific vocal technique commonly used in various genres, particularly in hip-hop and R&B. It is characterized by the rapid alternation between two pitches, creating a rapid, fluttering sound. The term combines "true" and "real," reflecting a sense of authenticity and genuine expression in the music.
The \( p \)-adic exponential function is an important concept in \( p \)-adic analysis, which is a branch of mathematics that deals with \( p \)-adic numbers. The \( p \)-adic numbers are a system of numbers that extend the rational numbers and provide a different perspective on number theory and algebra.
"A History of Folding in Mathematics" is not a specific title of a well-known book or article, but the topic it refers to relates to the mathematical study of folding, which intersects with various areas such as geometry, topology, and computational mathematics. The concept of folding can be explored in several contexts. For instance: 1. **Origami**: The mathematical study of origami has gained significance over the years.
The Big-Little-Big Lemma is a result in number theory, particularly in the area of prime number theory and additive combinatorics. This lemma typically relates to the distribution of primes and the structure of integer sequences. The lemma asserts that if we have a prime p that divides a certain expression involving integers, and if we also have a prime q not dividing the same primes, then we can draw conclusions about the divisibility or arithmetic properties of sequences or sums involving these primes.
Kawasaki's theorem is a result in the field of differential geometry, particularly concerning Riemannian geometry and the construction of Riemannian manifolds. It specifically deals with the conditions under which a certain type of surface can be isometrically immersed in Euclidean space.
The Schwarz lantern is a geometric object that serves as a counterexample in the field of topology and differential geometry. It demonstrates that certain intuitively reasonable assumptions about the properties of manifolds cannot be universally applied. Specifically, the Schwarz lantern is constructed to show that it is possible to have a collection of regions in a compact manifold, each of which can be continuously deformable to a simpler shape, that do not yield a manifold with the desired topological properties when combined.
Origamics is a creative field that combines origami, the art of paper folding, with principles of engineering, mathematics, and design to create complex and innovative structures. The term "origamics" is often used to describe the study and application of foldable and deployable structures that can transform from a compact state to a larger, functional form.
A random permutation is a rearrangement of a finite sequence of elements where each possible arrangement is equally likely. In other words, if you have a set of \( n \) distinct elements, a random permutation is one of the \( n! \) (n factorial) possible orderings of those elements chosen uniformly at random. For example, consider the set of elements \( \{1, 2, 3\} \).
Allocative efficiency is an economic concept that occurs when resources are distributed in such a way that maximizes the total benefit received by all members of society. In other words, it refers to a situation where the quantity of each good or service produced is exactly what consumers want to consume, reflecting the highest utility or satisfaction. Allocative efficiency is achieved when the price of a good or service is equal to the marginal cost of producing it.
Acceleration is a vector quantity that measures the rate of change of velocity of an object over time. It indicates how quickly an object is speeding up, slowing down, or changing direction.
John S. Toll could refer to a notable figure in academia or science, specifically John S. Toll, an American physicist and former president of the University of Maryland, who is known for his contributions to education and research. He served as a president of the university from 1987 to 1998 and played a significant role in its development. If you are referring to a different context or aspect regarding John S.
A **permutation group** is a mathematical structure consisting of a set of permutations that can be combined in a way that satisfies the properties of a group. Specifically, if you have a set \( X \), a permutation is a bijective function that rearranges the elements of \( X \). The collection of all possible permutations of a finite set \( X \) of size \( n \) is called the symmetric group, denoted as \( S_n \).
Jordan A. Goodman is a notable figure, often recognized for his contributions in academia or business. However, without further context, it is challenging to specify which Jordan A. Goodman you are referring to, as there may be multiple individuals with that name. If you are asking about a specific area of expertise, such as a particular discipline in academia or a role within a company, could you please provide more details?
As of my last knowledge update in October 2021, there isn't a widely recognized public figure or entity by the name "Oliver Buchmueller." He may be a private individual or a professional who is not well-known in the public domain.
Stefan Ulmer is a physicist known for his research in the fields of particle physics and fundamental physics, particularly in the study of antimatter and precision measurements. He has contributed to experiments involving antihydrogen, studies of the properties of antimatter, and tests of fundamental symmetries in physics. Ulmer has been associated with significant projects, including those at CERN and other research institutions, focusing on understanding the differences and similarities between matter and antimatter.
The 15 Puzzle, also known as the sliding puzzle, is a classic sliding puzzle that consists of a frame divided into a 4x4 grid of 16 square tiles. The tiles are numbered from 1 to 15, with one empty space that allows the tiles to slide to rearrange them.
Phonocentrism is a philosophical and linguistic concept that prioritizes spoken language over written language. The term arises from the critique of the traditional Western metaphysical idea that speech is the primary and most authentic form of communication. This view tends to value the immediacy and perceived authenticity of oral communication over the more mediated and artificial nature of written language. The concept has been notably discussed by philosopher Jacques Derrida, particularly in his deconstruction of language and meaning.
Landau's function typically refers to concepts or mathematical functions related to Landau's theory in various fields, particularly in physics and mathematics. One prominent example involves Landau's theory of phase transitions, where critical phenomena are studied. In statistical physics, Landau's theory often introduces a free energy functional expressed in terms of order parameters, which are quantities that describe the different phases of a system.
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





