Ram Prakash Bambah is likely a name that refers to an individual, but there isn't widely available public information on a person by that name as of my last knowledge update in October 2023. It’s possible that he may not be a widely recognized public figure or that he could be notable within certain specific circles or fields that are not broadly documented.
Reza Sadeghi is an Iranian mathematician recognized for his contributions to various areas of mathematics, particularly in the fields of analysis, particularly real analysis and partial differential equations. His work often involves the study of mathematical models and their applications in different scientific domains.
A 4-manifold is a topological space that locally resembles \(\mathbb{R}^4\) (four-dimensional Euclidean space) and is a type of manifolda fundamental concept in topology and differential geometry. Formally, a 4-manifold \(M\) is a space that is Hausdorff, second countable, and locally homeomorphic to \(\mathbb{R}^4\).
Sergei Ivanov is a mathematician known for his contributions to various fields within mathematics, particularly in the area of functional analysis and its applications. He has made significant contributions to the study of Banach spaces, operator theory, and related mathematical concepts. Ivanov may also be associated with certain academic institutions, where he conducted research, published papers, and engaged in teaching.
Steven Kerckhoff is a well-known figure in the field of cryptography, particularly recognized for his contributions to secure communication and encryption methods. He is best known for formulating Kerckhoffs's principle, which states that a cryptographic system should remain secure even if everything about the system, except for the secret key, is made public. This principle emphasizes the importance of the secrecy of the key rather than the secrecy of the algorithm itself.
Walter Whiteley is a prominent mathematician known for his contributions to the field of geometry, particularly in the area of algebraic geometry and its applications. He has worked on various topics, including the study of curves, surfaces, and their properties. Additionally, he has made significant contributions to mathematics education and has been involved in research related to mathematical thinking and pedagogy.
In geometry, a "sagitta" refers to the vertical distance from the midpoint of a chord of a circle to the arc itself. Essentially, it is the length of the line segment that is perpendicular to the chord and extends upward to meet the arc of the circle.
The term "normal fan" can have different meanings depending on the context. Here are a few possible interpretations: 1. **General Definition**: A "normal fan" could simply refer to a standard electric fan used for cooling or ventilation in homes or offices. These fans typically have blades that rotate to circulate air and are available in various types, such as ceiling fans, floor fans, and table fans.
The Axiom of Global Choice is a concept in set theory, specifically in the context of the foundations of mathematics. It can be understood as a generalization of the Axiom of Choice. The Axiom of Choice states that given a collection of non-empty sets, it is possible to select exactly one element from each set, even if there is no explicit rule for making the selection.
Slewing can refer to different concepts depending on the context, but generally, it involves a gradual change or shift in position or orientation. Here are a few contexts in which the term is commonly used: 1. **In Astronomy**: Slewing refers to the movement of a telescope or an astronomical instrument as it adjusts its position to track celestial objects. This is particularly important in tracking moving objects like planets, comets, and satellites.
In the context of differential geometry and topology, "maps of manifolds" typically refers to smooth or continuous functions that associate points from one manifold to another. Manifolds themselves are mathematical structures that generalize the concept of curves and surfaces to higher dimensions. They can be thought of as "locally Euclidean" spaces, meaning that around any point in a manifold, one can find a neighborhood that looks like Euclidean space.
The mapping class group is an important concept in the field of algebraic topology, particularly in the study of surfaces and their automorphisms. Specifically, it is the group of isotopy classes of orientation-preserving diffeomorphisms of a surface. Here's a more detailed explanation: 1. **Surface**: A surface is a two-dimensional manifold, which can be either compact (like a sphere, torus, or more complex shapes) or non-compact.
Alexander's trick is a technique used in topology, specifically in the study of continuous functions and compactness. It is primarily associated with the construction of continuous maps and the extension of functions. The trick is named after the mathematician James W. Alexander II and is often employed in scenarios where one needs to extend continuous functions from a subspace to a larger space.
The Blaschke selection theorem is a result in complex analysis and functional analysis concerning the behavior of sequences of Blaschke products, which are a type of analytic function associated with a sequence of points in the unit disk in the complex plane.
The Nielsen realization problem is a concept in the field of algebraic topology and group theory, specifically concerning the study of free groups and their automorphisms. More formally, it deals with the conditions under which a given group presentation can be realized as the fundamental group of a topological space, usually a certain type of surface or manifold.
A piecewise linear manifold is a type of topological space that is composed of a finite number of linear pieces or segments, which are pieced together in such a way that the overall structure preserves some properties of linearity.
Mori Dream Space is a conceptual space that embodies elements of Mori Girl aesthetics and culture. The "Mori Girl" style originated in Japan and is characterized by a whimsical, rustic, and nature-inspired look. This aesthetic often includes layered clothing, soft and flowing fabrics, and earthy colors, evoking a sense of tranquility and connection to nature.

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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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