Reachability is a term used in various fields, such as computer science, networking, and mathematics, and it generally refers to the ability to access or connect to a particular node, state, or point of interest in a system or network. 1. **In Computer Science**: Reachability often pertains to graph theory, where it refers to whether there exists a path from one node (or vertex) to another within a directed or undirected graph.
A K-tree (or K-ary tree) is a type of tree data structure in which each node can have at most K children. This means that each node can link to K different nodes or child nodes, making it suitable for various applications where a more extensive branching factor is desirable compared to binary trees (which have a maximum of two children per node).
The percolation threshold is a critical point in the study of percolation theory, which is a mathematical framework used to understand the connectivity of networks and similar structures. It refers to the minimum density or concentration of occupied sites (or edges) in a lattice or network at which a spanning cluster— a connected cluster that spans from one side of the structure to the other—first appears.
Szymanski's conjecture refers to a problem in the field of number theory, particularly concerning prime numbers. Specifically, it conjectures the existence of infinitely many primes of a certain form related to the sequence of prime numbers. The conjecture states that for any integer \( n \geq 1 \), there are infinitely many primes of the form \( p_k = k^2 + n \) for some positive integer \( k \).
Asymptotic distribution refers to the probability distribution that a sequence of random variables converges to as some parameter tends to infinity, often as the sample size increases. This concept is fundamental in statistics and probability theory, particularly in the context of statistical inference and large-sample approximations. In particular, asymptotic distributions are used to describe the behavior of estimators or test statistics when the sample size grows large.
The history of calculus is a fascinating evolution that spans several centuries, marked by significant contributions from various mathematicians across different cultures. Here’s an overview of its development: ### Ancient Foundations 1. **Ancient Civilizations**: Early ideas of calculus can be traced back to ancient civilizations, such as the Babylonians and Greeks. The method of exhaustion, used by mathematicians like Eudoxus and Archimedes, laid the groundwork for integration by approximating areas and volumes.
A Dirichlet space is a type of Hilbert space that arises in the study of Dirichlet forms and potential theory. These spaces have applications in various areas of analysis, including the theory of harmonic functions and partial differential equations. A Dirichlet space can be defined as follows: 1. **Function Space**: A Dirichlet space is typically formed from a collection of functions defined on a domain, often a subset of Euclidean space or a more general manifold.
Giuseppe Mingione is an Italian mathematician known for his contributions to the field of calculus of variations and partial differential equations. His work often involves the study of non-linear problems and weak solutions. Mingione has published numerous papers and has made significant advancements in understanding the regularity of solutions to certain types of variational problems. His research is influential in both theoretical mathematics and its applications in different scientific fields.
Jesse Douglas was an American mathematician known for his contributions to the field of mathematics, particularly in complex analysis and functional analysis. He is perhaps best known for being one of the winners of the first Clay Mathematics Institute's prize for solving the Riemann Hypothesis, although this claim is often confused with other mathematicians, as the Riemann Hypothesis remains unproven.
As of my last knowledge update in October 2023, there is no widely recognized entity, product, or concept specifically known as "Tristan Rivière." It might refer to a person, a business, a fictional character, or something else that has emerged after that date.
Ralph Lent Jeffery is not a widely recognized name in popular culture, literature, or other public domains as of my last update in October 2023. It's possible that he is a private individual or someone who has not gained significant media attention or acclaim.
Wolfgang Heinrich Johannes Fuchs is not a widely recognized public figure or term, and there does not appear to be significant information or context available about someone by that name in the usual sources. If you are referring to a specific individual, concept, or a character from a work of fiction, could you please provide more context or details? This will help me provide a more accurate response.
The Kervaire invariant is a concept in algebraic topology, specifically in the study of bordism theory and the classification of high-dimensional manifolds. It is named after the mathematician Michel Kervaire, who introduced it in the context of differentiable manifolds. More formally, the Kervaire invariant is a specific invariant associated with a smooth manifold, particularly focusing on the topology of the manifold's tangent bundle.
Static spacetime is a concept in general relativity that refers to a type of spacetime geometry that is both time-independent (static) and has a specific symmetry. More formally, a static spacetime is one where the gravitational field does not change over time and exhibits certain symmetries, particularly time translation symmetry and spatial symmetry. Key characteristics of static spacetimes include: 1. **Time Independence**: The metric tensor, which describes the geometry of spacetime, does not vary with time.
As of my last update in October 2023, Dario Graffi is not a widely recognized public figure or concept in mainstream media, literature, or academia. It’s possible that this name could refer to a person in a specific context (such as a local figure, artist, or professional) or might have emerged more recently.
The conformal anomaly, also known as the trace anomaly, is a phenomenon that occurs in certain quantum field theories (QFT) when a theory that is classically conformally invariant loses this symmetry at the quantum level. In simpler terms, while a classical theory may display conformal invariance under scale transformations (where distances are scaled by some factor without changing the shape), quantum effects can introduce terms that break this invariance.
Two-dimensional Conformal Field Theory (2D CFT) is a branch of theoretical physics that studies two-dimensional quantum field theories that are invariant under conformal transformations. These transformations include translations, rotations, dilations (scaling), and special conformal transformations, which preserve angles but not necessarily lengths. ### Key Features of 2D CFT: 1. **Conformal Symmetry**: In two dimensions, the conformal group is infinite-dimensional.
Intermittent rhythmic delta activity (IRDA) refers to a specific pattern observed on an electroencephalogram (EEG). It is characterized by rhythmic delta wave activity (0.5 to 4 Hz) that occurs intermittently, rather than continuously, and typically appears in one or more regions of the brain.
As of my last knowledge update in October 2021, there isn't a widely recognized concept, product, or term specifically named "Visual N1." It's possible that it could refer to a new technology, product, or concept that has emerged after that date. Alternatively, it could relate to a niche area within visual technology, graphics, or another field.
The invention of musical tunings is not attributed to a single inventor but rather evolved over centuries and across different cultures. Musical tuning systems, which determine the pitches of notes in relation to each other, have been developed by various civilizations. Here are some key contributions to the evolution of musical tunings: 1. **Ancient Civilizations**: Early musical tunings can be traced back to ancient civilizations such as the Mesopotamians, Egyptians, and Greeks. Pythagoras (c.

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 5. . 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.
  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