The Kernighan-Lin algorithm is a heuristic method used for graph partitioning. Specifically, it is designed to minimize the edge cut of a graph when dividing the vertices into two disjoint subsets. This algorithm is particularly useful in areas such as VLSI design, network analysis, and clustering, where balancing the workload or minimizing communication cost between different parts of a system is important.
Aviezri Fraenkel is a notable figure in the field of mathematical logic, particularly known for his contributions to set theory and combinatorics. He is recognized for his work in the area of infinitary combinatorics and has published several influential papers on related topics. His research often intersects with various branches of mathematics, and he has been involved in teaching and mentoring students in these areas.
BreakMate is a type of coffee vending machine designed for workplaces, offering freshly brewed coffee and a variety of other beverages. It typically features a user-friendly interface that allows employees to customize their drinks, including options for coffee, tea, and other refreshment beverages. The machine is designed to enhance workplace productivity and employee satisfaction by providing quick and convenient access to quality beverages, reducing the need for employees to leave the office for coffee breaks.
A fortune teller machine is a themed, usually vintage-style electronic device that predicts the future, offers insights, or provides "fortunes" to users. These machines typically feature a mechanical or digital figure that appears to perform an act of fortune-telling. One of the most iconic types of fortune teller machines is the Zoltar machine, popularized by the movie "Big," where a robotic figure gives vague advice or readings based on user input or random selection.
In mathematics, particularly in the context of category theory, a "picture" is often used to refer to a diagram that visually represents mathematical concepts or structures, such as objects and morphisms in a category. These diagrams help convey relationships and properties intuitively. However, the term "picture" can also refer to specific visual representations or constructions in various fields of mathematics.
Tietze transformations are a method in topology used to extend a continuous function defined on a subspace of a topological space to the whole space.
"Gold to Go" refers to a unique vending machine concept that allows consumers to purchase gold in various forms, such as coins or small bars, using cash or credit cards. These machines are strategically placed in high-traffic areas, such as malls, airports, and luxury hotels. The idea is to make buying physical gold more accessible and convenient for the average consumer. The machines typically display current gold prices and offer a selection of products, often including items with various weights and designs.
An interactive kiosk is a stand-alone device that provides information and facilitates various services to users through touchscreens or other interactive interfaces. These kiosks are equipped with software and hardware that enable users to engage with the content presented. **Key features of interactive kiosks include:** 1. **User Interface:** Typically, they have touchscreens that allow users to navigate through options, make selections, and input information.
Cloud condensation nuclei (CCN) are tiny particles in the atmosphere that provide a surface for water vapor to condense upon, leading to the formation of clouds. When moist air rises and cools, the water vapor begins to condense into tiny droplets. However, for condensation to occur, there must be some surfaces or nuclei present on which the water vapor can condense. These surfaces are the cloud condensation nuclei.
A love tester machine is a novelty device typically found in amusement parks, fairs, or arcades. It's designed to measure the compatibility or romantic connection between two people, often through a playful or humorous mechanism. Users usually place their hands on sensors or input their names or other relevant information, and the machine provides a result that suggests a compatibility score or a "love percentage." The readings from these machines are not scientifically based and are meant purely for entertainment purposes.
Marvin's Marvelous Mechanical Museum is an eclectic attraction located in Farmington Hills, Michigan. Owned by Marvin Yagoda, this unique museum showcases a wide variety of mechanical and automated pieces, including vintage arcade games, animatronic figures, and unusual curiosities. The collection features numerous items that represent both the history of mechanical amusements and creative artwork, often highlighting the whimsical and bizarre aspects of entertainment.
Disk algebra is a concept that arises in the area of functional analysis, particularly in the study of function spaces and operator theory. Specifically, it refers to the algebra of holomorphic (analytic) functions defined on the open unit disk in the complex plane. The disk algebra, often denoted as \( A(D) \), consists of all continuous functions on the closed unit disk that are holomorphic in the interior of the disk.
A mutoscope is a type of motion picture device that was popular in the late 19th and early 20th centuries. It allows users to view a series of images in rapid succession to create the illusion of motion, similar to a flip book but with a mechanism that makes it easier to view animations. The mutoscope consists of a series of photographs mounted on a rotating drum.
The Gallai–Edmonds decomposition is a fundamental concept in graph theory, particularly in the study of matchings within bipartite graphs. It provides a structured way to analyze matchings and their properties, and it is named after mathematicians Claude Berge, who contributed to matching theory, and Laszlo Lovasz and others who contributed to its broader understanding.
The Albertson conjecture is a hypothesis in the field of graph theory, specifically concerning the coloring of graphs. Proposed by a mathematician named Michael Albertson in 1994, the conjecture deals with the chromatic number of certain types of graphs, particularly those that are constructed using specific rules or properties.
The Hopcroft–Karp algorithm is a classic algorithm used to find the maximum matching in a bipartite graph. A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set. The algorithm works in two main phases: 1. **BFS Phase**: It performs a breadth-first search (BFS) to find the shortest augmenting paths.
Iterative Deepening A* (IDA*) is an informed search algorithm that combines the benefits of depth-first search (DFS) and the A* search algorithm. It is particularly useful in scenarios where memory efficiency is a concern, as it does not need to store all nodes in memory like A* does. Instead, IDA* seeks to efficiently explore the search space while managing memory usage effectively.
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





