A **local diffeomorphism** is a mathematical concept from differential geometry that describes a type of smooth map between two differentiable manifolds (or smooth manifolds).
An amenable Banach algebra is a specific type of Banach algebra that possesses a certain property related to its representations and, intuitively speaking, its "size" or "complexity." The concept of amenability can be traced back to the theory of groups, but it has been extended to abstract algebraic structures such as Banach algebras.
BK-space generally refers to a specific type of topological space in the context of topology and functional analysis. The term "BK-space" often denotes a **Banach-Knaster space**, which is a certain type of topological vector space that can be endowed with the properties of completeness and other characteristics typical to Banach spaces.
Borchers algebra refers to a mathematical framework introduced by Daniel Borchers in the context of quantum field theory. It arises notably in the study of algebraic quantum field theory (AQFT), where the focus is on the algebraic structures that underpin quantum fields and their interactions. In Borchers algebra, one typically deals with specific types of algebras constructed from the observables of a quantum field theory. These observables are collections of operators associated with physical measurements.
The Cramér–Wold theorem is a result in probability theory that provides a characterization of multivariate normal distributions. It states that a random vector follows a multivariate normal distribution if and only if every linear combination of its components is normally distributed. More formally, let \( X = (X_1, X_2, \ldots, X_n) \) be a random vector in \( \mathbb{R}^n \).
The Cohen–Hewitt factorization theorem is an important result in the field of functional analysis, particularly in the study of commutative Banach algebras and holomorphic functions. The theorem essentially deals with the factorization of elements in certain algebras, specifically those elements that have a suitable structure, such as being the spectrum of a compact space.
The Eberlein–Šmulian theorem is a result in functional analysis that characterizes weak*-compactness in the dual space of a Banach space. Specifically, it provides a criterion for when a subset of the dual space \( X^* \) (the space of continuous linear functionals on a Banach space \( X \)) is weak*-compact.
An enveloping von Neumann algebra is a concept from the field of functional analysis, specifically in the context of operator algebras. To understand this concept, we first need to clarify what a von Neumann algebra is. A **von Neumann algebra** is a *-subalgebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator.
The Fifth-order Korteweg–De Vries (KdV) equation is a mathematical model that extends the classical KdV equation, which is used to describe shallow water waves and other dispersive wave phenomena.
Friedrichs's inequality is a fundamental result in the field of functional analysis and partial differential equations. It provides a way to control the norm of a function in a Sobolev space by the norm of its gradient. Specifically, it is often used in the context of Sobolev spaces \( W^{1,p} \) and \( L^p \) spaces.
The Mandelbox is a type of fractal, specifically a 3D fractal that is an extension of the Mandelbrot set. It was discovered by artist and mathematician Bert Wang. The Mandelbox fractal is generated using a combination of simple transformations and complex mathematical rules, primarily involving iterations of mathematical functions. The structure of the Mandelbox is notable for its intricate, self-similar shapes and the depth of detail that can be found within it, which can be zoomed into indefinitely.
Jean Favard is a French mathematician known for his work in the field of analysis, particularly for his contributions to the theory of functions of several variables, including the Favard theorem related to set functions and measures. He has also made impacts in various areas of real analysis and topology.
The Pansu derivative is a concept from the field of geometric measure theory and analysis on metric spaces, particularly related to the study of Lipschitz maps and differentiability in the context of differentiable structures on metric spaces. It is named after Pierre Pansu, who introduced the idea while investigating the behavior of Lipschitz functions on certain types of spaces, especially in relation to their geometry.
The Sarason interpolation theorem is a result in complex analysis related to the theory of functional spaces, particularly in the context of the Hardy space \( H^2 \). It provides a criterion for the existence of an analytic function that interpolates a given sequence of points in the unit disk, subject to certain conditions.
The Szász–Mirakjan–Kantorovich operator is a mathematical operator used in approximation theory, particularly in the context of approximating functions using linear positive operators. This operator is a generalization of the Szász operator, which itself is a well-known tool for function approximation.
Andreas Seeger can refer to different individuals or contexts depending on the area of discussion. Without specific context, it's challenging to pinpoint exactly who you are referring to. 1. **Academia**: There may be academics or researchers with the name Andreas Seeger who have made contributions to their respective fields. 2. **Sports**: There could be athletes or coaches with that name. 3. **Popular Culture**: It could also refer to a public figure or celebrity.
Value distribution theory is a branch of complex analysis that focuses on understanding how holomorphic functions distribute their values in the complex plane. This theory is primarily concerned with the behavior of meromorphic functions (functions that are holomorphic except at a discrete set of poles) and their relationship with their value sets, particularly in terms of how often certain values are attained.
Ervin Feldheim is a prominent physicist known for his research in the fields of condensed matter physics and materials science. He has contributed to our understanding of various physical phenomena and has published numerous papers in scientific literature.
Isaac Jacob Schoenberg (1915–2006) was a notable mathematician known primarily for his work in the fields of functional analysis and numerical analysis. He made significant contributions to applied mathematics, particularly in the areas of interpolation and approximation theory. Schoenberg is often recognized for his development of the so-called Schoenberg splines. In addition, Schoenberg's work extended to various applications in engineering and numerical methods, which have had a lasting impact on the field.
Norair Arakelian could refer to a person, but without additional context, it is difficult to determine exactly who you are referring to. There might be multiple individuals with that name, and they may have various professions or roles.
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





