A graph is said to be **well-covered** if all of its maximal independent sets are of the same size. An independent set of a graph is a set of vertices no two of which are adjacent. A maximal independent set is an independent set that cannot be extended by including any adjacent vertex.
Convolution power is a concept used primarily in the field of probability theory and signal processing. It refers to the repeated application of the convolution operation to a probability distribution or a function. The convolution of two functions (or distributions) combines them into a new function that reflects the overlap of their values, effectively creating a new distribution that represents the sum of independent random variables, for example.
A monotonic function is a function that is either entirely non-increasing or non-decreasing throughout its domain.
The uniform norm, also known as the supremum norm or infinity norm, is a type of norm used to measure the size or length of functions or vectors. It is particularly important in functional analysis and is often applied in the context of continuous functions.
Ware Tetralogy, also known as Warkany Syndrome, is a rare genetic disorder that typically consists of a group of four congenital malformations. While the term "tetralogy" suggests a collection of four specific abnormalities, it may refer to a variety of presentations depending on the underlying genetic cause and the specific types of defects involved.
The Void Cube is a type of mechanical puzzle similar to the Rubik's Cube, designed to challenge a solver's spatial reasoning and problem-solving skills. Unlike traditional Rubik's Cubes, which have colored stickers on each face, the Void Cube features a unique design where certain pieces are missing or have holes. This creates a more complex challenge because the lack of certain visual cues can make it harder to determine the positions of the colors or patterns that would typically guide a solver in solving the puzzle.
Mirror blocks, commonly referred to in the context of puzzles, are three-dimensional twisty puzzles that exhibit reflective symmetry. These puzzles are typically constructed in a way that each block has different dimensions, creating an asymmetric shape that can add complexity to the solving process. One well-known variant is the "Mirror Cube" (also known as the "Mirror Block" or "Bump Cube").
As of my last knowledge update in October 2023, "Phoebe Carlo" does not refer to a widely recognized term, person, or concept in public discourse, literature, or media. It's possible that it could refer to a character in a story, a lesser-known individual, or a new development that emerged after my last update.
NYC Mesh is a community-driven initiative aimed at providing free and open wireless broadband internet access in New York City. It is a grassroots network that relies on volunteers to build a decentralized mesh network, connecting residents and community organizations, especially in underserved areas that may lack reliable internet service. The project operates on the principle that internet access is a fundamental right and seeks to empower communities by giving them control over their own connectivity.
The Duhem-Quine thesis is a philosophical concept that addresses the challenges of testing scientific theories. It originates from the ideas of two philosophers, Pierre Duhem and Willard Van Orman Quine. The thesis highlights the idea that it is impossible to test a scientific hypothesis in isolation because empirical observations are always influenced by various interconnected assumptions and auxiliary hypotheses.
In computer programming, a **function** is a self-contained block of code that performs a specific task. Functions can take input in the form of parameters, execute a sequence of statements, and often return a result. They are a fundamental concept in programming and are used to organize code, promote reusability, and improve readability. Here are some key aspects of functions: 1. **Definition**: Functions are defined using a specific syntax that varies by programming language.
Proof by contrapositive is a method of mathematical proof used to establish the truth of a conditional statement. A conditional statement is typically of the form "If \( P \), then \( Q \)", which can be written symbolically as \( P \implies Q \). The contrapositive of this statement is "If not \( Q \), then not \( P \)", symbolically expressed as \( \neg Q \implies \neg P \).
"Set Theory: An Introduction to Independence Proofs" typically refers to a specific area of study within mathematical set theory, focusing on the concepts of independence and proofs related to it. While I can't provide a specific book or text with that exact title, here's a general overview of what such a work might cover: 1. **Basic Set Theory**: The book would likely start with foundational concepts in set theory, including sets, subsets, the power set, relations, and functions.
The Mathematics Educator is a peer-reviewed academic journal that focuses on research and practice in the field of mathematics education. It typically includes articles that cover various aspects of teaching and learning mathematics at different educational levels, from elementary to higher education. The journal aims to improve mathematics education by sharing empirical research, theoretical analyses, and practical insights that can inform teaching practices and curriculum development.
A performative utterance is a statement that performs an action rather than merely describing a state of affairs. The term comes from the work of philosopher J.L. Austin, particularly in his book "How to Do Things with Words," where he argues that certain statements, typically found in speech acts, do not just convey information but actually enact an action by the very act of saying them.
The cosmological constant, denoted by the symbol \( \Lambda \), is a term introduced by Albert Einstein in his equations of general relativity. It represents a constant energy density filling space homogeneously, and it has significant implications for the dynamics of the universe. 1. **Historical Context**: Einstein originally introduced the cosmological constant in 1917 while formulating his theory of general relativity.
The term "E6B" can refer to several different things depending on the context: 1. **E6B Flight Computer**: This is a mechanical or electronic device used by pilots for flight planning and navigation. It helps in calculations for various flight parameters such as groundspeed, wind correction, fuel consumption, and altitude. The E6B flight computer is commonly used for calculating headings and distances during flight, assisting in navigation and ensuring safe travel.
The "ripple effect" is a term used to describe how an event or action can create a series of consequences that spread outward, much like the ripples that form when a stone is dropped into water. The initial action can have both direct and indirect impacts on various individuals, groups, or systems, influencing them in ways that might not be immediately apparent.
The classical limit is a concept in physics that refers to the behavior of quantum systems as they transition to classical systems, typically as certain parameters approach appropriate limits. It describes the conditions under which quantum mechanical systems can be approximated by classical mechanics. Here are a few key points about the classical limit: 1. **Planck's Constant**: One of the most important factors in the classical limit is Planck's constant (h).
Criticism of science encompasses various perspectives and concerns raised about the practices, methodologies, assumptions, implications, and impacts of scientific inquiry. Here are some key areas where criticism can occur: 1. **Methodological Limitations**: Critics may argue that scientific methods can be limited by biases, such as selection bias, confirmation bias, or funding biases. The reproducibility crisis, where many studies cannot be replicated, has also highlighted potential flaws in scientific methods and practices.

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