A **strongly connected component** (SCC) is a concept from graph theory, specifically in the study of directed graphs (digraphs). In a directed graph, a strongly connected component is defined as a maximal subgraph in which every pair of vertices is reachable from each other.
**St-connectivity** refers to a concept in graph theory, particularly in the context of directed and undirected graphs. It concerns whether there is a path between two specific vertices in a graph, typically denoted as vertex **S** and vertex **T**: 1. **In Undirected Graphs**: A graph is said to be **st-connected** if there exists a path between vertices **S** and **T**.
The Random Surfing Model is a mathematical framework used primarily to understand and analyze the behavior of users navigating through a network, often in the context of the internet or web pages. The model simulates the process of users randomly selecting links to traverse from one node (or webpage) to another, emulating how individuals may navigate through a vast network.
The New Digraph Reconstruction Conjecture is a conjecture in graph theory, specifically concerning directed graphs (digraphs). It builds upon the classical Reconstruction Conjecture concerning simple (undirected) graphs. The classical Reconstruction Conjecture posits that a graph with at least three vertices can be uniquely reconstructed (up to isomorphism) from the collection of its vertex-deleted subgraphs.
The Lucchesi–Younger theorem is a result in the field of combinatorial optimization, particularly related to the study of directed graphs and their networks. The theorem states that for any directed acyclic graph (DAG), there exists a way to assign capacities to the edges of the graph such that the maximum flow from a designated source node to a designated sink node can be achieved by the flow through a certain subset of the edges.
A Kautz graph is a type of directed graph that is used in combinatorial design and graph theory. It is defined by a specific set of parameters that determine its structure. The Kautz graph \( K(n, k) \) is constructed using two parameters: \( n \) and \( k \).
A Directed Acyclic Graph (DAG) is a type of graph that has the following characteristics: 1. **Directed**: The edges in the graph have a direction, meaning that they point from one vertex (or node) to another. This is often represented with arrows on the edges.
As of my last knowledge update in October 2023, "Dijoin" does not refer to a widely recognized concept, product, or service in popular culture, technology, or other fields. It’s possible that it could be a term that has emerged in a specific niche or context after that date, or it might refer to a smaller-scale or localized project or organization.
As of my last knowledge update in October 2023, "Dicut" does not refer to a widely recognized concept, product, or term in common usage. It's possible that it could refer to a brand, a specific project, or a term used in a niche context that has emerged more recently.
A **dependency graph** is a directed graph that represents dependencies between a set of items, where nodes represent the items and directed edges indicate a dependency from one item to another. In other words, if item A has a directed edge to item B, it means that A depends on B, or A cannot be completed until B has been completed.
Aczel's anti-foundation axiom is an alternative to the standard foundation axiom in set theory, which states that every non-empty set must contain an element that is disjoint from itself. The foundation axiom helps to avoid certain paradoxes and ensures that sets are constructed in a well-defined manner, typically preventing sets from containing themselves directly or indirectly. Aczel's anti-foundation axiom, on the other hand, allows for the existence of "non-well-founded" sets.
A Directed Acyclic Graph (DAG) is a type of graph that has two main characteristics: 1. **Directed**: This means that the edges (connections) between the nodes (vertices) have a direction. In other words, if there is a directed edge from node A to node B, this implies a one-way relationship, indicating that A influences B, or A precedes B in some context.
Causal diagrams are graphical representations used to illustrate relationships between variables in a system, helping to clarify the causal structures and interactions among them. They serve as a tool in fields such as statistics, epidemiology, social sciences, and causal inference to model and understand causal relationships. There are a few key types of causal diagrams: 1. **Directed Acyclic Graphs (DAGs)**: These are the most common form of causal diagrams.
Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of one component to the total number of moles of all components in the mixture.
Mass fraction in chemistry refers to the ratio of the mass of a particular component of a mixture to the total mass of the mixture. It is a way to express the concentration of a component in a solution or a mixture.
The Zeldovich number, often denoted as \( Z \), is a dimensionless quantity used in the field of combustion and thermal analysis. It is particularly relevant in the study of gas-phase chemical reactions and the dynamics of combustion processes. The Zeldovich number is defined as the ratio of the characteristic time scale of heat release to the characteristic time scale of thermal diffusion.
The term "West number" can refer to different concepts depending on the context, but it is most commonly associated with a mathematical concept or a specific function within various fields. In mathematics, it might not be a widely recognized term, and it could refer to different things depending on the area of study (like statistics, graph theory, etc.).
The Weinberg angle, also known as the weak mixing angle or the electroweak mixing angle, is a fundamental parameter in the electroweak theory, a critical component of the Standard Model of particle physics. It quantifies the mixing between the electromagnetic force and the weak nuclear force, which are unified at high energies. Specifically, the Weinberg angle (\(\theta_W\)) determines the relationship between the electric charge and the weak isospin of particles.
The Weber number (We) is a dimensionless quantity used in fluid mechanics to estimate the relative importance of inertial forces to surface tension forces in a flowing fluid. It is particularly useful in the study of interfaces, such as between liquids or between a liquid and a gas, where surface tension plays a significant role.
The Van 't Hoff factor, denoted as \( i \), is a measure of the effect of solute particles on colligative properties of solutions. It quantifies the number of particles into which a solute dissociates in solution. The concept is especially important in understanding how electrolytes and non-volatile solutes affect properties such as boiling point elevation, freezing point depression, osmotic pressure, and vapor pressure lowering.

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