Finsler geometry is a branch of differential geometry that generalizes the concepts of Riemannian geometry. While Riemannian geometry is based on the notion of a smoothly varying inner product that defines lengths and angles on tangent spaces of a manifold, Finsler geometry allows for a more general structure by using a norm on the tangent spaces that need not be derived from an inner product.
The ADHM construction, which stands for Atiyah-Drinfeld-Hitchin-Manin construction, is a mathematical framework used in theoretical physics and geometry, particularly in the study of instantons in gauge theory. It is a method for constructing solutions to the self-duality equations of gauge fields in four-dimensional Euclidean space, which are fundamental in the study of Yang-Mills theory.
The Atiyah Conjecture is a notable hypothesis in the fields of mathematics, specifically in algebraic topology and the theory of operator algebras. It was proposed by the British mathematician Michael Atiyah and concerns the relationship between topological invariants and K-theory. The conjecture primarily asserts that for a certain class of compact manifolds, the analytical and topological aspects of these manifolds are intimately related.
A Courant algebroid is a mathematical structure that arises in the study of differential geometry and mathematical physics, particularly in the context of higher structures in geometry and gauge theory. It is a generalization of a Lie algebroid and incorporates the notions of both a Lie algebroid and a symmetric bilinear pairing.
A nonlinear partial differential equation (PDE) is a type of equation that relates a function of multiple variables to its partial derivatives, where the relationship involves nonlinear terms. In contrast to linear PDEs, where the solution can be combined using superposition due to linearity, nonlinear PDEs can exhibit more complex behavior and often require different analytical and numerical methods for their solution.
A projective vector field is a concept that arises in the context of differential geometry and dynamical systems, particularly in relation to the study of vector fields defined on manifolds. In the simplest terms, a vector field on a manifold assigns a vector to each point on the manifold. A projective vector field is a special type of vector field that is defined up to a certain equivalence relation.
The Transversality Theorem is a concept from differential topology and differential geometry. It provides conditions under which the intersection of two submanifolds of a manifold is itself a submanifold. The theorem essentially deals with the idea of how two continuous maps, or more generally submanifolds, can intersect in a regular manner, giving rise to a well-defined structure.
The Whitney topology is a specific topology that can be defined on the space of smooth maps (or differential functions) between two smooth manifolds, typically denoted as \(C^\infty(M, N)\), where \(M\) and \(N\) are smooth manifolds. The Whitney topology can also refer to the topology on a space of curves in a manifold, particularly when discussing the space of embeddings of one manifold into another.
Topological degree theory is a branch of mathematics, particularly within the field of topology and functional analysis, that deals with the concept of the degree of a continuous mapping between topological spaces. It provides a way to classify the behavior of functions, particularly in terms of their zeros, and to establish the existence of solutions to certain types of equations.
Blackjack video games are electronic versions of the classic card game Blackjack, which is popular in casinos. These video games can be found in various formats, including standalone arcade-style machines, digital versions on computers, and applications for smartphones and tablets. They simulate the mechanics of traditional Blackjack, allowing players to bet and play against a computer dealer instead of human opponents.
The International Centre for Diffraction Data (ICDD) is a non-profit organization that serves the scientific community by providing a comprehensive database of diffraction data for crystalline materials. Founded in 1978, the ICDD focuses on the collection, organization, and dissemination of data related to X-ray, neutron, and electron diffraction. The ICDD is best known for its Powder Diffraction File (PDF), which is a critical resource for researchers in materials science, chemistry, mineralogy, and other fields.
Ultimate Card Games is typically a collection of various card games combined into one platform, often available as a video game or digital application. These collections can include classic games like Solitaire, Poker, Rummy, Hearts, and many others. The platform may offer features such as single-player modes, multiplayer options, various game rules, and customizable settings. In some contexts, Ultimate Card Games can also refer to specific titles created by developers, which aim to provide a comprehensive card gaming experience.
LCD crosstalk is a phenomenon that occurs in liquid crystal display (LCD) panels, particularly in those that use modern multi-layered technologies such as LCD screens with backlighting from LEDs. Crosstalk refers to the leakage of light from one pixel to adjacent pixels, which can cause blurring, ghosting, or double images in display content, especially during fast-moving scenes or when there are sharp edges between contrasting colors.
Encoding law generally refers to principles or rules that govern how information is transformed into a specific format for storage, transmission, or processing. While it’s not a term widely recognized in a particular field, it can intersect various areas such as: 1. **Information Theory**: In this context, encoding laws might refer to coding schemes used to efficiently represent data for storage or transmission.
The logarithmic number system is a numerical representation system that utilizes logarithms to express numbers. In this system, rather than representing a number by its direct value, it represents it by the logarithm of that value to a specific base. This approach can provide advantages in various fields, particularly in algorithms, computer science, and certain mathematical contexts.
A media processor is a specialized type of hardware or software designed to handle various media-related tasks, such as audio and video encoding, decoding, processing, and streaming. Media processors are commonly used in devices like smartphones, cameras, smart TVs, and gaming consoles to improve the efficiency and quality of media handling.
The Parks-McClellan algorithm, also known as the Remez exchange algorithm, is a widely used method for designing linear-phase finite impulse response (FIR) digital filters. It is particularly effective in designing filters with specified frequency response characteristics, such as low-pass, high-pass, band-pass, and band-stop filters. The algorithm minimizes the maximum error between the desired response and the actual response of the filter.
Virtual Acoustic Space (VAS) generally refers to a simulated environment that recreates a sound field, allowing users to experience spatial audio as if they were in a physical space. It is commonly used in various fields, including virtual reality (VR), gaming, film, music production, and audio research.
The term "relative canonical model" is not a standard concept in established fields like mathematics, computer science, or physics as of my last update in October 2021. However, it could refer to various interpretations depending on the context in which you encounter it. 1. **In Mathematics and Logic**: It could potentially relate to model theory, where a "canonical model" often refers to a specific model that serves as a standard or reference point for a particular theory.
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