Audrey Terras is a mathematician known for her contributions to the fields of number theory and algebraic geometry. She has made significant contributions to the study of modular forms and has worked on topics related to the theory of automorphic forms, as well as mathematical research involving complex analysis and topology. Terras is also recognized for her work in mathematics education and outreach.
Mean sojourn time refers to the average amount of time that a system, individual, or process spends in a particular state before transitioning to another state. It is a concept commonly used in various fields such as queuing theory, operations research, and systems analysis. In the context of queuing systems, for instance, the mean sojourn time can represent the average time a customer spends in the system, which includes the time waiting in line as well as the time being served.
Techniques to get numerical approximations to numeric mathematical problems.
The entire field comes down to estimating the true values with a known error bound, and creating algorithms that make those error bounds asymptotically smaller.
Not the most beautiful field of pure mathematics, but fundamentally useful since we can't solve almost any useful equation without computers!
The solution visualizations can also provide valuable intuition however.
Important numerical analysis problems include solving:
All those dedicated applied mathematicians languages are a waste of society's time, Ciro Santilli sure applied mathematicians are capable of writing a few extra braces in exchange for a sane general purpose language, we should instead just invest in good libraries with fast C bindings for those languages like NumPy where needed, and powerful mainlined integrated development environments.
And when Ciro Santilli see the closed source ones like MATLAB being used, it makes him lose all hope on humanity. Why. As of 2020. Why? In the 1980s, maybe. But in the 2020s?
MATLAB Breaking Bad crossover
. Source. Each side is a sphere section. They don't have to have the same radius, they are still simple to understand with different radiuses.
The two things you have to have in mind that this does are:
- This is for example why you can use lenses to burn things with Sun rays, which are basically parallel.Conversely, if the input is a point light source at the focal length, it gets converted into parallel light.
- image formation: it converges all rays coming from a given source point to a single point image. This amplifies the signal, and forms an image at a plane.The source image can be far away, and the virtual image can be close to the lens. This is exactly what we need for a camera.
Used a lot in quantum mechanics, where the equations are really hard to solve. There's even a dedicated wiki page for it: en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics). Notably, Feynman diagrams are a way to represent perturbation calculations in quantum field theory.
Average number of steps until reaching a state of a Markov chain by
Ciro Santilli 40 Updated 2025-07-16
TODO how to calculate
Ryūjo Hori, also known as "Ryūjo Hori Hōjō," refers to an ancient Japanese carving technique primarily associated with the creation of intricate designs on lacquerware and other materials. The term "Ryūjo" means "dragon castle," and "Hori" means "to carve" or "to engrave." This technique is notable for its detailed and expressive designs, which often include motifs of dragons, flowers, and other elements from Japanese culture and folklore.
22.2 surround sound is a multi-channel audio format designed to provide an immersive sound experience, especially for film and multimedia applications. It expands on traditional surround sound formats by utilizing a large number of audio channels and speakers to create a more enveloping sound field. The configuration of 22.2 surround sound consists of: - **22 audio channels**: These channels include various placements for speakers around the listener. The usual arrangement includes speakers positioned at various heights and locations (e.g.
The RCA Type 77-A microphone is a well-regarded ribbon microphone that was introduced in the mid-20th century by RCA (Radio Corporation of America). It is part of a series of ribbon microphones that RCA produced, designed primarily for professional recording and broadcasting applications. Key characteristics of the RCA Type 77-A microphone include: 1. **Ribbon Element**: The Type 77-A features a bi-directional (figure-eight) pickup pattern that captures sound equally from the front and rear.
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






