The McMullen problem, posed by mathematician Curtis T. McMullen in the late 20th century, pertains to the study of hyperbolic 3-manifolds and their geometric structures. Specifically, it concerns the classification of certain types of 3-manifolds known as "hyperbolic 3-manifolds" and the conditions under which these manifolds can be represented as the complement of a knot in S³ (the 3-sphere).
The HNN extension, named after the mathematicians Graham Higman, B. H. Neumann, and Hanna Neumann, is a construction in group theory that allows the creation of new groups from existing ones. Specifically, an HNN extension is a type of group that is used to generalize the notion of groups with an additional structure, particularly when it comes to accommodating certain types of relations between groups.
A financial security system refers to a set of policies, regulations, and safety measures designed to protect individuals, businesses, and the overall economy from financial fraud, theft, and other risks. It encompasses various components including regulatory frameworks, insurance policies, risk management practices, and technological safeguards aimed at ensuring the integrity and stability of financial transactions and institutions.
Doubtnut is an educational technology platform primarily focused on helping students with their studies in subjects like mathematics and science. It provides a range of resources including video tutorials, interactive content, and problem-solving tools. One of the key features of Doubtnut is its ability to allow students to upload images of their doubts or questions, after which the platform provides solutions or explanations through its extensive database of educational content.
"Mathematics in Ancient Egypt: A Contextual History" is a scholarly work that explores the development and application of mathematical concepts in ancient Egyptian society. This book typically examines the historical, cultural, and practical contexts in which mathematics was used in ancient Egypt, shedding light on how it interacted with various aspects of life, including architecture, astronomy, trade, and daily activities.
Egyptian women physicists have made significant contributions to the field of physics, often overcoming societal challenges and gender barriers in pursuing their careers. Like many women in STEM (Science, Technology, Engineering, and Mathematics) fields, they have worked in various specializations within physics, including theoretical physics, experimental physics, astrophysics, and applied physics. Historically, women in Egypt, as in many parts of the world, faced obstacles in education and professional advancement.
Ferroelectricity is a property of certain materials that exhibit a spontaneous electric polarization that can be reoriented by an external electric field. This means that, unlike ordinary dielectric materials that only polarize in response to an applied electric field, ferroelectric materials can maintain a permanent electric polarization even when the external field is removed.
A Sachs subgraph is a concept from graph theory, specifically in the context of combinatorial structures and properties related to planar graphs. It refers to a type of subgraph that is constructed from a planar graph in such a way that certain conditions are met. In more detail, a Sachs subgraph is typically defined for a planar graph as a spanning subgraph that respects the original graph's facial structures in a certain way.
Fluid dynamics is the study of the behavior of fluids (liquids and gases) in motion. The equations that govern fluid dynamics describe how fluids flow and how they interact with forces and boundaries. The main equations governing fluid dynamics are derived from the principles of fluid mechanics and encompass several fundamental concepts, including conservation of mass, momentum, and energy. Here are the key equations in fluid dynamics: 1. **Continuity Equation**: This equation is based on the principle of conservation of mass.
Experimental particle physics is a branch of physics that investigates the fundamental constituents of matter and the forces that govern their interactions by conducting experiments. Unlike theoretical particle physics, which focuses on developing models and predictions based on mathematical frameworks, experimental particle physics involves the design, construction, and operation of experiments to test those theories and to discover new particles or phenomena.
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





