In the field of mathematical analysis, particularly in functional analysis and the theory of partial differential equations, the concepts of *test functions* and *distributions* (or generalized functions) are quite important. Here's an overview of both concepts and their relationship: ### Test Functions **Test functions** are smooth functions that have certain desirable properties, such as being infinitely differentiable and having compact support.
Witness-indistinguishable proofs are a concept in cryptography and zero-knowledge proofs. They are a type of interactive proof where the validity of a statement can be proven without revealing any specific information about the witness (or secret) used to prove the statement. ### Key Characteristics of Witness-Indistinguishable Proofs: 1. **Witness**: In the context of proofs, a witness is typically a solution or secret information that helps validate a statement.
Wolfgang Dahmen is a distinguished German mathematician known for his contributions to several areas of mathematics, including approximation theory, numerical analysis, and wavelet theory. He has made significant advancements in the mathematical foundations of wavelets and their applications in various fields, such as signal processing and data compression. Dahmen is also recognized for his work on splines, a type of piecewise polynomial function that is widely used in computer graphics, data fitting, and numerical mathematics.
In geometry, a lens is a shape formed by the intersection of two circular arcs. Specifically, it is the region bounded by two circles that overlap. The area enclosed by these arcs resembles the shape of a lens, which is the reason for its name. There are two main types of lenses: 1. **Convex Lens**: This occurs when both arcs are part of circles that are convex towards each other. The resulting lens shape bulges outward.
John von Neumann was a pioneering mathematician, physicist, computer scientist, and polymath whose contributions have inspired numerous concepts, theories, and entities. Here’s a list of notable things named after him: 1. **Von Neumann Architecture**: A computer architecture design model that outlines a system where a single memory space stores both data and instructions.
Projections onto convex sets is a mathematical concept often used in optimization, functional analysis, and convex geometry. The idea centers around finding a point in a convex set that is closest to a given point outside that set.
The Hilbert–Schmidt integral operator is a specific type of integral operator that arises in functional analysis and is connected to the theory of compact operators on Hilbert spaces. It is particularly important in the context of integral equations and various applications in mathematical physics and engineering. ### Definition Let \( K(x, y) \) be a measurable function defined on a product space \( [a, b] \times [a, b] \).
Shape Modeling International (SMI) is an annual academic conference focused on research in the field of shape modeling and related areas. It aims to bring together researchers, practitioners, and industry professionals to discuss advancements in the understanding, representation, and manipulation of shapes in various contexts, including computer graphics, computer-aided design (CAD), and geometric modeling.
WolframAlpha is a computational knowledge engine developed by Wolfram Research. Unlike traditional search engines that provide links to web pages, WolframAlpha is designed to generate specific answers and insights from a vast store of curated data, algorithms, and computational capabilities. It can answer factual queries by performing calculations, generating graphs, and providing detailed information across various domains, including mathematics, science, engineering, history, geography, and more.
MuMATH, which stands for "Multiple Use Mathematics," is a software tool designed for teaching and learning mathematics through interactive visualizations and simulations. It allows users, especially students, to explore mathematical concepts in a hands-on manner, facilitating a deeper understanding of complex topics. MuMATH is often utilized in educational settings to demonstrate various mathematical principles, including algebra, geometry, and calculus.
Mxparser is a lightweight and highly configurable mathematical expression parser and evaluator designed for Java and other programming languages. It allows users to parse, evaluate, and manipulate mathematical expressions represented as strings. Mxparser supports a wide range of mathematical functions, operators, and features, making it suitable for applications that require mathematical calculations, such as scientific computing, educational tools, and financial applications.
In the context of mathematics, particularly linear algebra and numerical analysis, a **convergent matrix** often refers to matrices that exhibit certain convergence properties under iterative processes. However, the term "convergent matrix" isn't a standard term broadly recognized like "convergent series" or "convergent sequence.
A **copositive matrix** is a special type of matrix that arises in the context of optimization and mathematical programming, particularly in the study of quadratic forms and convexity. A symmetric matrix \( A \) is said to be copositive if for any vector \( x \) in the non-negative orthant \( \mathbb{R}^n_+ \) (i.e.
The One-Child Policy was a population control policy instituted by the Chinese government in 1979 to curb the rapid population growth in the country. The policy restricted urban couples to having only one child, although there were some exceptions based on ethnicity, parental status, and other factors. In rural areas, families were often allowed to have a second child if the first was a girl, as a way to address cultural preferences for male heirs.
Reindeer, also known as caribou in North America, have a distribution that primarily spans the Arctic and Subarctic regions. Their populations are found across the northern parts of Europe, Asia, and North America. Here are some key points on their distribution: 1. **Habitat**: Reindeer are adapted to cold environments and are typically found in tundra, boreal forests, and alpine regions.
Reproductive rights refer to the legal rights and freedoms related to reproduction and reproductive health. These rights encompass a range of issues that affect individuals' ability to make informed choices about their reproductive lives. Key components of reproductive rights include: 1. **Access to Contraception**: The right to obtain and use contraceptives to prevent unwanted pregnancies. 2. **Abortion Rights**: The right to access safe and legal abortion services without facing discrimination, stigma, or undue restrictions.
Zero Population Growth (ZPG) refers to a statistical condition in which a population's size remains constant over time, meaning that the number of births is equal to the number of deaths, leading to no net growth. This concept is often used in discussions about sustainable development and environmental impact.
Optimized Consumer Intensity Analysis (OCIA) is a method used primarily in the context of market research, consumer behavior analysis, and business strategy. While the term may not be widely standardized across all industries, it generally relates to analyzing how intensely consumers engage with a product or brand, and it aims to optimize this engagement for better business outcomes.
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





