Gerhard Ringel (1924–2017) was an accomplished Austrian mathematician known primarily for his contributions to topology and combinatorial mathematics. He is particularly noted for his work in the field of graph theory and has made significant contributions to the study of maps on surfaces, as well as the development of concepts related to the colorability of graphs. Ringel is also recognized for the Ringel-Youngs theorem and had collaborations that further enriched the field of mathematical research.
Hansjoachim Walther is a German mathematician known for his contributions to various areas of mathematics, particularly in functional analysis and differential equations. His work often focuses on the theoretical aspects of these fields.
Irene Sciriha is a prominent Maltese academic and researcher known for her work in the fields of education and technology. She has held various academic positions and has contributed to the development of educational programs and policies in Malta and beyond. Her research often focuses on topics related to educational technology, digital learning, and innovative teaching methods.
Jeanette McLeod does not appear to be a widely recognized figure based on the information available up to October 2023. It's possible she could be a private individual, a lesser-known artist, academic, or a character in a story, but without more context, it's difficult to provide detailed information.
As of my last update, Kristina Vušković does not appear to be a widely recognized public figure, celebrity, or topic in mainstream discussions. If she has gained prominence or relevance after October 2023, I wouldn't have that information.
Bloch space, often denoted as \( \mathcal{B} \), is a functional space that arises in complex analysis, particularly in the study of holomorphic functions defined on the unit disk. It is named after the mathematician Franz Bloch.
The Kramers–Kronig relations are a set of equations in the field of complex analysis and are widely used in physics, particularly in optics and electrical engineering. They provide a mathematical relationship between the real and imaginary parts of a complex function that is analytic in the upper half-plane.
Infinite compositions of analytic functions refer to the repeated application of a function while allowing for an infinite number of iterations. Given a sequence of analytic functions \( f_1, f_2, f_3, \ldots \), one considers the composition: \[ f(z) = f_1(f_2(f_3(\ldots f_n(z) \ldots))) \] In the case of infinite compositions, we extend this idea to an infinite number of functions.
A Hessian polyhedron, in the context of optimization and convex analysis, refers to a geometric representation of the feasible region or a set defined through linear inequalities in n-dimensional space, specifically associated with the Hessian matrix of a function. The Hessian matrix is a square matrix that consists of second-order partial derivatives of a scalar-valued function. It provides information about the local curvature of the function.
Line Integral Convolution (LIC) is a technique used in computer graphics and visualization to generate vector field visualizations. It creates a texture that represents the direction and magnitude of a vector field, often seen in the contexts of fluid dynamics and flow visualization. ### Concept: The key idea behind LIC is to use the properties of a vector field to create a convoluted image that conveys the underlying flow information.
Logarithmic form is a way of expressing exponentiation in terms of logarithms. The logarithm of a number is the exponent to which a specified base must be raised to produce that number.
A movable singularity, also known as a "removable singularity," typically refers to a point in a complex function where the function is not defined, but can be made analytic (i.e., smooth and differentiable) by appropriately defining or modifying the function at that point.
A **planar Riemann surface** is a one-dimensional complex manifold that can be viewed as a two-dimensional real surface in \(\mathbb{R}^3\). More specifically, it is a type of Riemann surface that can be embedded in the complex plane \(\mathbb{C}\). ### Key Features: 1. **Complex Structure**: A Riemann surface is equipped with a structure that allows for complex variable analysis.
In the context of engineering, mathematics, and particularly control theory and complex analysis, the "right half-plane" refers to the set of complex numbers that have a positive real part.
In mathematics, particularly in functional analysis and operator theory, the Schur class refers to a class of bounded analytic functions with values in the open unit disk. More formally, the Schur class consists of functions that are holomorphic on the open unit disk and map to the unit disk itself.
The Schwarz triangle function, often denoted as \( S(x) \), is a mathematical function that is primarily defined on the interval \([0, 1]\) and is known for its interesting properties and applications in analysis and number theory, particularly in the study of functions of bounded variation and generalized functions. The function is constructed through an iterative process involving the "triangulation" of the unit interval.
The Calabi conjecture is a significant result in differential geometry, particularly in the study of Kähler manifolds. Formulated by Eugenio Calabi in the 1950s, the conjecture addresses the existence of Kähler metrics with special properties on certain compact complex manifolds. Specifically, the conjecture states that for a given compact Kähler manifold with a vanishing first Chern class, there exists a unique Kähler metric in each Kähler class that is Ricci-flat.
A Calabi–Eckmann manifold is a type of complex manifold that is constructed as a special case of a more general theory involving complex and symplectic geometry. Specifically, Calabi–Eckmann manifolds are a class of compact Kähler manifolds that serve as examples of non-Kähler, simply-connected manifolds with rich geometric structures.
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





