GraphBLAS is a specification for a set of building blocks for graph computations that leverage linear algebra techniques. It provides a standardized API that allows developers to use graph algorithms and operations in a way that is efficient, scalable, and easily integrable with existing software. The key features of GraphBLAS include: 1. **Matrix Representation**: Graphs can be represented as matrices, where the adjacency matrix signifies connections between nodes (vertices) in a graph.
Incomplete Cholesky factorization is a numerical method used to approximate the Cholesky decomposition of a symmetric positive definite matrix. The traditional Cholesky factorization decomposes a matrix \( A \) into the product of a lower triangular matrix \( L \) and its transpose \( L^T \) (i.e., \( A = LL^T \)).
Julia is a high-level, high-performance programming language primarily designed for numerical and scientific computing. It was created to address the need for a language that combines the performance of low-level languages, like C and Fortran, with the easy syntax and usability of high-level languages like Python and R. Here are some key features and aspects of Julia: 1. **Performance**: Julia is designed for speed and can often match or exceed the performance of C.
The Kaczmarz method, also known as the Kaczmarz algorithm or the algebraic reconstruction technique, is an iterative method used for solving systems of linear equations. It was developed by the Polish mathematician Simon Kaczmarz in 1937 and is particularly useful for large, sparse systems.
The Kreiss matrix theorem is a fundamental result in the theory of abstract differential equations, particularly in the context of the stability and asymptotic behavior of linear systems described by linear differential equations. The theorem is named after H. Kreiss, who introduced it. In essence, the Kreiss matrix theorem provides a criterion for determining whether a set of linear operators (or matrices) generates a strongly continuous semigroup of operators.
In the Book of Revelation, the number seven holds significant symbolic meaning and is used frequently throughout the text. It represents completeness, perfection, or divine order within the context of God's plan. Here are some key instances of the number seven in Revelation: 1. **Seven Churches**: Revelation addresses seven churches in Asia Minor (modern-day Turkey) in chapters 2 and 3. Each church receives specific messages, reflecting both commendations and admonitions.
The Flemish Region, also known simply as Flanders, is one of the three regions of Belgium, alongside the Walloon Region and the Brussels-Capital Region. Flanders is located in the northern part of the country and is predominantly Dutch-speaking. Here are some key points about the Flemish Region: 1. **Geography**: Flanders includes the provinces of East Flanders, West Flanders, Antwerp, Brabant, and Limburg.
Denmark is a Scandinavian country located in Northern Europe. It consists of the Jutland Peninsula and an archipelago of more than 400 islands, the largest of which include Zealand, Funen, and North Jutland. The country is bordered to the south by Germany and is surrounded by water, with the North Sea to the west and the Baltic Sea to the east.
Slovakia is a landlocked country located in Central Europe. It shares borders with several countries: to the north, it borders Poland; to the east, Ukraine; to the south, Hungary; and to the west, Austria and the Czech Republic. The country has a diverse landscape that includes mountains, forests, and rivers, with the Carpathian Mountains running through its northern region.
Brandenburg can refer to several related concepts: 1. **Geographical Region**: Brandenburg is a federal state (Bundesland) in northeastern Germany. It surrounds but does not include the capital city of Berlin. The state is known for its scenic landscapes, including lakes, forests, and historic towns.
The term "Great Plain" typically refers to the Great Plains, a vast region that stretches across North America, primarily in the United States and Canada. This area is characterized by its flat terrain, grasslands, and agricultural potential. It extends from Canada in the north down to Texas in the south, encompassing states like Montana, Wyoming, Colorado, Nebraska, Kansas, Oklahoma, and the Dakotas. "North" in this context could refer to various entities depending on the subject.
The East Midlands is a region in England, located in the central part of the country. It includes several counties, specifically Derbyshire, Leicestershire, Lincolnshire, Northamptonshire, Nottinghamshire, and Rutland. The East Midlands is known for its diverse landscape, which includes the Peak District, parts of the Fens, and rural countryside, as well as urban areas with significant cities such as Nottingham, Leicester, and Derby.
North West England is one of the nine official regions of England. It is located in the northwestern part of the country and includes a diverse landscape, comprising urban areas, rural countryside, and coastal regions. The region is known for its rich industrial heritage, cultural diversity, and natural beauty.
Eastern Slovenia, known as Vzhodna Slovenija in Slovenian, is a region that encompasses the eastern part of the country of Slovenia. This area is characterized by its diverse geography, which includes valleys, hills, and rivers. It is known for its rich cultural heritage, historical sites, and natural beauty, including parts of the picturesque Pohorje mountain range and the picturesque Drava River.
The West Midlands is a metropolitan county located in the central part of England. It was created in 1974 and includes several urban areas, notably the city of Birmingham, which is the largest city in the region and the second-largest in the UK after London. The West Midlands region also contains other major towns and cities, such as Coventry, Wolverhampton, Walsall, and Dudley.
Yorkshire and the Humber is one of the nine official regions of England. It is located in the northern part of the country and is known for its distinct cultural heritage, natural landscapes, and economic significance. The region encompasses the historic county of Yorkshire and the Humber estuary, which is a significant inland river system that flows into the North Sea. The region includes several key cities and towns, most notably: - **Leeds**: The largest city and a major cultural and economic center.
Cantabria is an autonomous community located in the northern region of Spain. It is bordered by the Bay of Biscay to the north, the autonomous community of the Basque Country to the east, and the regions of Castile and León to the south and west. The capital of Cantabria is Santander, which is also a significant port city.
Northwest Italy is a geographical region of Italy that includes several key areas known for their diverse landscapes, rich history, and cultural significance. The region typically encompasses the following regions: 1. **Liguria**: Known for its stunning coastline, including the famous Cinque Terre and the cities of Genoa and Sanremo. Liguria is characterized by its picturesque seaside villages and mountainous terrain.
In Slovakia, the Nomenclature of Territorial Units for Statistics (NUTS) classification is used to define regions for statistical purposes. The NUTS 2 level comprises eight statistical regions, which are as follows: 1. **Bratislavský kraj** (Bratislava Region) - the capital and most urbanized region. 2. **Trnavský kraj** (Trnava Region) - located to the north of Bratislava.
Burgenland is a federal state (Bundesland) in Austria, located in the eastern part of the country. It is bordered by Hungary to the east and has a diverse landscape that includes flat plains, rolling hills, and vineyards. The region is known for its wine production, particularly white wines, and is home to the Neusiedler See, a large lake that attracts tourists and supports various recreational activities.
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





