Macroscopic traffic flow models are used to describe and analyze the flow of traffic on a larger scale, often at the level of road networks or regions rather than individual vehicles. These models treat traffic as a continuous fluid rather than focusing on individual vehicles, and they typically use aggregate quantities such as traffic density, flow (the number of vehicles passing a point per unit time), and average velocity.
The Press–Schechter formalism is a theoretical framework used in cosmology to describe the formation of structure in the universe, particularly the statistical properties of dark matter halos and galaxy formation. Developed by SLAC physicists William H. Press and Paul Schechter in 1974, this formalism provides a way to estimate the number density and mass distribution of bound systems, like galaxies and clusters of galaxies, from the primordial density fluctuations in the universe.
CLIC3 (Chloride Intracellular Ion Channel 3) is a protein that belongs to the CLIC (Chloride Intracellular Ion Channel) family of proteins. These proteins are involved in various cellular processes, including the regulation of ion transport across cell membranes. CLIC3 is known to function as an ion channel that facilitates the transport of chloride ions and may also have roles in cell signaling and maintaining cellular homeostasis.
Mirror symmetry is a concept in string theory and algebraic geometry that primarily relates to the duality between certain types of Calabi-Yau manifolds. It originated from the study of string compactifications, particularly in the context of Type IIA and Type IIB string theories.
Schröder's equation is a functional equation that is often associated with the study of fixed points and dynamical systems. Specifically, it is used to describe a relationship for transformations that exhibits a form of self-similarity. In one common form, Schröder's equation can be expressed as: \[ f(\lambda x) = \lambda f(x) \] for some constant \(\lambda > 0\).
The Yang–Mills equations are a set of partial differential equations that describe the behavior of gauge fields in the context of gauge theory, which is a fundamental aspect of modern theoretical physics. Named after physicists Chen-Ning Yang and Robert Mills, who formulated them in 1954, these equations generalize Maxwell's equations of electromagnetism to non-Abelian gauge groups, which are groups that do not necessarily commute.
"Knowledge space" can refer to different concepts depending on the context in which it is used. Here are some of the common interpretations: 1. **Ontology and Knowledge Representation**: In fields like artificial intelligence and knowledge management, a knowledge space refers to a structured representation of knowledge. This can include concepts, categories, and the relationships between them, often organized in a way that facilitates understanding and inference.
The theory of conjoint measurement is a mathematical framework used to understand and quantify preferences, particularly in the context of decision-making processes where multiple attributes are considered. It originated in the field of psychophysics and operational research, and it has applications in economics, social sciences, marketing, and various areas of management. ### Key Concepts: 1. **Attributes and Levels**: In a typical conjoint analysis, choices are characterized by a set of attributes, each of which may have different levels.
The Norwegian Mathematical Society (Den Norske Matematiske Forening) is a professional organization in Norway that aims to promote the advancement, dissemination, and application of mathematics. Founded in 1875, it serves as a platform for mathematicians, researchers, teachers, and students to engage with one another and with the broader community. The society organizes various activities, including conferences, seminars, and workshops, to foster collaboration and the sharing of knowledge in the field of mathematics.
Richard Samworth is a statistician known for his contributions to the fields of statistical learning and high-dimensional statistics. He has published significant research on topics such as nonparametric statistics, graphical models, and model selection. His work often focuses on developing statistical methods for analyzing complex data structures, particularly in areas where traditional methods may struggle due to high dimensionality or the presence of dependencies among variables.
William Kruskal was a prominent American statistician known for his contributions to statistical theory and methodology. He played a significant role in developing non-parametric statistics, particularly through the Kruskal-Wallis test, which is used for comparing three or more independent samples. Kruskal was also involved in other areas of statistics, including multivariate analysis and the analysis of variance. His work has had a considerable impact on the field, and he has been recognized for his contributions throughout his career.
John Greig is a mathematician known for his contributions to the field of mathematics, particularly in areas such as combinatorics and number theory. His work often involves studying mathematical structures and their applications. However, it appears that he may not be as widely recognized in the mathematical community compared to other prominent mathematicians.
Michael J. D. Powell is a prominent figure in the field of optimization and applied mathematics. He is known for his significant contributions to numerical optimization, particularly in derivative-free optimization and methods for solving nonlinear optimization problems. He has authored numerous papers and has been involved in the development of algorithms that are widely used in scientific and engineering applications. Powell is also noted for his work on the "Powell's method," a specific algorithm for multidimensional optimization that does not require gradient information.
"Murderous Maths" is a popular series of children's books authored by British writer and mathematician Kjartan Poskitt. The series is designed to make mathematics engaging and accessible for young readers, often utilizing humor, illustrations, and engaging storytelling to explain mathematical concepts. Each book in the series covers different aspects of mathematics, from basic arithmetic to more advanced topics like geometry and probability.
"The Annotated Turing" is a book by Charles Petzold that provides a detailed exploration of Alan Turing's groundbreaking 1936 paper "On Computable Numbers, with an Application to the Entscheidungsproblem." This paper is considered foundational in the field of computer science and introduces the concept of the Turing machine, which is a theoretical model of computation that helps in understanding the limits of what can be computed.
"Advances in Mathematics" is a peer-reviewed scientific journal that publishes original research articles in all areas of mathematics. It is well-known for featuring high-quality papers that contribute to various fields, including algebra, geometry, topology, analysis, and applied mathematics. The journal aims to present significant new results, techniques, and perspectives in mathematics. The journal has a strong reputation and is widely cited in the mathematical community.
Self-dealing is a term used primarily in the context of finance, law, and governance, referring to a situation where a person in a position of authority or trust uses their role to benefit themselves personally, rather than acting in the best interest of the organization or individuals they are meant to serve. This behavior is often seen in contexts such as corporate governance, fiduciary duties, and nonprofit organizations.
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