SMT solvers, or Satisfiability Modulo Theories solvers, are tools designed to determine the satisfiability of logical formulas with respect to specific theories. They extend the capabilities of traditional SAT solvers, which deal only with propositional logic, by incorporating more complex theories such as: 1. **Arithmetic**: Integers, reals, etc. 2. **Bit-vectors**: Operations on sequences of bits.
Masyu is a type of logic puzzle that typically appears on puzzle websites and in puzzle books. The objective of Masyu is to draw a single loop through a grid, following certain rules indicated by special circles within the grid. Here are the basic rules of Masyu: 1. **Loop Structure**: The loop must be a continuous, non-intersecting path that forms a closed loop.
MAX-3SAT is an optimization problem that is a specific case of the broader boolean satisfiability problem (SAT). In MAX-3SAT, given a boolean formula in conjunctive normal form (CNF), the goal is to determine the maximum number of clauses that can be satisfied by any assignment of truth values to the variables.
"ER = EPR" is a conjecture in theoretical physics that connects two seemingly different concepts: wormholes (denoted by ER, after the physicists Einstein and Rosen) and quantum entanglement (denoted by EPR, after Einstein, Podolsky, and Rosen). The idea was proposed by the physicist Juan Maldacena in a paper published in 2013.
Hilbert's twelfth problem, proposed by the mathematician David Hilbert in 1900, is concerned with the theory of functions with respect to algebraic number fields and involves the study of the so-called "absolutely abelian extensions" of these fields. More specifically, the problem asks for a systematic method to construct all the abelian extensions of a given number field using explicit functions, particularly through the use of modular forms.
The Nagata–Biran conjecture is a conjecture in the field of symplectic geometry and Hamiltonian dynamics. It was formulated by the mathematicians Masahiro Nagata and Michael Biran. The conjecture relates to the properties of symplectic manifolds, particularly concerning the existence of certain types of Lagrangian submanifolds.
Ismail Mustafa al-Falaki (also known as Ismail al-Falaki) is a notable figure in the field of astronomy. He was an Ottoman Turkish astronomer and mathematician, known for his contributions to the study of astronomy during the late 19th and early 20th centuries. Al-Falaki is particularly recognized for his work in the modernization of astronomy in the Ottoman Empire, including the establishment of observatories and the introduction of western advances in astronomical techniques.
The Kerala School of Mathematics, located in Kozhikode, India, is an institution focused on the study and promotion of mathematics. Established to honor the rich tradition of mathematics in Kerala, especially during the medieval period, it aims to advance mathematical research, education, and outreach. The Kerala School is known for its significant contributions to various branches of mathematics, particularly in the development of techniques in calculus and infinite series, as well as advancements in astronomical and trigonometric calculations.
Japanese logicians refer to scholars, philosophers, and mathematicians from Japan who have made significant contributions to the field of logic, both in traditional and contemporary contexts. Over the centuries, Japan has developed its own unique approaches to logic, influenced by indigenous philosophical traditions as well as Western thought. ### Historical Context - **Traditional Japanese Logic**: The study of logic in Japan can be traced back to the influence of Buddhism and Confucianism. Buddhist philosophy included seminal discussions on reasoning and argumentation.
"Mathematicians from Tokyo" is not a commonly recognized term or specific title associated with a particular group or work in mathematics. However, it may refer to several possible interpretations: 1. **Prominent Mathematicians from Tokyo**: The city of Tokyo, Japan, is home to many notable mathematicians and researchers who have made significant contributions to various fields in mathematics.
Motoko Kotani is a character from the popular anime and manga series "Ghost in the Shell," created by Masamune Shirow. She is one of the primary protagonists in the franchise, particularly known for her role in "Ghost in the Shell: Stand Alone Complex." Kotani is a skilled cybernetic law enforcement officer in a future world where technology integrates with daily life, and she is often depicted as a highly capable leader within the Public Security Section 9.
Tomoyuki Arakawa is a Japanese artist and filmmaker known for his work in animation and visual arts. He may also be associated with various media projects or collaborations within the animation industry. However, specific information about his works or contributions might not be widely available, as he may not be a mainstream figure.
SNO+ (SNO Plus) is a neutrino experiment that is an upgrade of the original Sudbury Neutrino Observatory (SNO) in Canada. The SNO experiment primarily aimed to study neutrinos produced by the fusion reactions in the Sun, providing crucial insights into solar physics and neutrino properties.
Sergey Kiriyenko is a prominent Russian politician and businessman. He has held various high-ranking positions in the Russian government and has played a significant role in the country's political landscape. Kiriyenko served as the Prime Minister of Russia briefly in 1998 during a period of economic turmoil. Following his tenure as Prime Minister, he has held various roles in government and business, including positions related to energy and technology.
Novaya Zemlya is an archipelago located in the Arctic Ocean in northern Russia. It is situated north of the Russian mainland, separating the Barents Sea to the west from the Kara Sea to the east. The archipelago consists of two main islands, Severny (Northern) and Yuzhny (Southern), along with numerous smaller islands. Novaya Zemlya is known for its remote and harsh Arctic climate, characterized by long, extremely cold winters and short, cool summers.
Rocky Flats National Wildlife Refuge is a protected area located near Arvada and Westminster, Colorado, just northwest of Denver. Established in 2007, the refuge encompasses approximately 5,237 acres and aims to provide habitat for a variety of wildlife, including many species of birds, mammals, and other native animals and plants. The site was formerly home to the Rocky Flats Plant, which was a nuclear weapons production facility until its closure in 1992.
The School of Physics and Astronomy at the University of Edinburgh is a department dedicated to the study and research of physics and related fields. It is part of one of the leading research universities in the UK, known for its high academic standards and contributions to science. The school offers a range of undergraduate and postgraduate programs in physics, astronomy, and related disciplines, providing students with a solid foundation in both theoretical and experimental physics.
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





