Modified Richardson iteration is a technique used to accelerate the convergence of iterative methods for the solution of problems, particularly in numerical linear algebra, such as solving systems of linear equations. The Richardson iteration method itself is based on the idea of correcting the current approximation of the solution to an equation by using a linear correction term.
The Luoshu Square, also known as the Luo Shu or the Lo Shu Square, is an ancient Chinese diagram that is associated with feng shui, numerology, and I Ching practices. It consists of a 3x3 grid where the numbers 1 to 9 are arranged in a specific order such that the sum of the numbers in each row, column, and diagonal equals 15.
Petosiris and Nechepso are figures from ancient Egyptian history, specifically related to the development of astrology and astronomy in the Hellenistic period. Petosiris was an Egyptian priest and astrologer, most noted for his works in the field of astrology during the 2nd century BCE. His writings reflect the integration of Egyptian religious practices with Greek philosophical thought, especially in the context of astrology.
Madeira is an archipelago located in the North Atlantic Ocean, southwest of Portugal. It is an autonomous region of Portugal and consists of several islands, the largest of which is Madeira Island itself, along with Porto Santo, Desertas Islands, and Selvagens Islands. Madeira is known for its stunning natural landscapes, including rugged mountains, lush forests, and a mild climate, which makes it a popular destination for tourists.
NUTS stands for "Nomenclature of Territorial Units for Statistics," which is a hierarchical system for dividing up the economic territory of the European Union and European Economic Area. In the context of the United Kingdom, the NUTS classification consists of multiple levels, with NUTS 1 being the highest level of regional classification. As of the most recent classifications, the NUTS 1 regions of the United Kingdom are: 1. **East Scotland** 2.
Transdanubia is a historical and geographical region located west of the Danube River in Hungary. It is known for its diverse landscapes, which include rolling hills, vineyards, and the picturesque Lake Balaton, the largest freshwater lake in Central Europe. The region features a mix of rural and urban areas, with cities like Székesfehérvár, Veszprém, and Pécs being notable centers.
NUTS, or the Nomenclature of Territorial Units for Statistics, is a hierarchical system for dividing up the economic territory of the European Union and the European Economic Area. The NUTS classification is used for collecting, developing, and analyzing the regional statistics of the EU.
Catalonia is an autonomous community in northeastern Spain, characterized by its distinct culture, history, and language, Catalan. It has its own parliament and government, which have varying degrees of legislative power. The capital of Catalonia is Barcelona, a major cultural and economic center known for its architecture, art, and vibrant lifestyle. Historically, Catalonia has a unique identity that dates back centuries, with its own language, customs, and traditions.
Melilla is a Spanish autonomous city located on the northern coast of Africa, bordering Morocco. It is one of two cities—along with Ceuta—that form part of Spain but are situated on the African continent. Melilla has a strategic location near the Mediterranean Sea and is separated from the Spanish mainland by the Mediterranean waters. The city has a rich history influenced by various cultures, including Berber, Spanish, and other Mediterranean civilizations.
Pays de la Loire is one of the regions of France, located in the western part of the country. It is bordered by the Atlantic Ocean to the west and is known for its diverse landscapes, which include coastal areas, river valleys, vineyards, and agricultural land. The region was officially created in 1956 and is named after the Loire River, which flows through it.
Middle Norrland is a region in Sweden that is part of the larger Norrland area, which encompasses the northern part of the country. Middle Norrland typically includes the provinces of Ångermanland, Medelpad, and parts of Jämtland. This region is known for its diverse landscapes, including forests, rivers, and mountains, as well as its rural communities and outdoor recreational opportunities.
Provence-Alpes-Côte d'Azur (PACA) is a region located in the southeastern part of France. It is known for its stunning landscapes, rich history, and diverse culture. The region is bordered by Italy to the east and the Mediterranean Sea to the south. It includes several major cities, with Marseille being the largest and the regional capital. Other notable cities in the region include Nice, Toulon, and Avignon.
Upper Normandy, known as "Haute-Normandie" in French, was an administrative region in northern France. It was formed in 1984 and included the departments of Seine-Maritime and Eure. The region was characterized by its historical significance, picturesque landscapes, and a mix of coastal and rural areas. Notable cities within Upper Normandy included Rouen, the capital, and Le Havre, a major port city.
Salzburg is a federal state (Bundesland) in Austria, located in the central part of the country. It is named after its capital, the city of Salzburg, which is famous for its baroque architecture and as the birthplace of the composer Wolfgang Amadeus Mozart. The state is known for its stunning alpine scenery, historic sites, and cultural heritage.
Východné Slovensko, or Eastern Slovakia, is a region in Slovakia located in the eastern part of the country. It is characterized by a diverse landscape that includes mountains, plains, and rivers. The region is known for its cultural heritage, historical sites, and natural beauty. Key cities in Východné Slovensko include: - **Košice:** The second-largest city in Slovakia and an important cultural and economic center.
Western Macedonia is a geographic region located in the northwestern part of Greece. It is one of the country's thirteen administrative regions and is known for its diverse landscapes, including mountains, lakes, and rivers. The region is characterized by its rich natural beauty, including the Pindus mountain range and Lake Prespa. The capital of Western Macedonia is Kozani, and other significant cities in the region include Grebne, Florina, and Kastoria.
Learned readers will ask themselves: so why use an unbalanced tree instead of balanced one, which offers better asymptotic times en.wikipedia.org/wiki/Self-balancing_binary_search_tree?
Addresses are now split as:
| directory (10 bits) | table (10 bits) | offset (12 bits) |Then:
- The top table is called a "directory of page tables".
cr3now points to the location on RAM of the page directory of the current process instead of page tables.Page directory entries are very similar to page table entries except that they point to the physical addresses of page tables instead of physical addresses of pages.Each directory entry also takes up 4 bytes, just like page entries, so that makes 4 KiB per process minimum.Page directory entries also contain a valid flag: if invalid, the OS does not allocate a page table for that entry, and saves memory.Each process has one and only one page directory associated to it (and pointed to bycr3), so it will contain at least2^10 = 1Kpage directory entries, much better than the minimum 1M entries required on a single-level scheme. - Second level entries are also called page tables like the single level scheme.Each page table has only
2^10 = 1Kpage table entries instead of2^20for the single paging scheme. - the offset is again not used for translation, it only gives the offset within a page
One reason for using 10 bits on the first two levels (and not, say,
12 | 8 | 12 ) is that each Page Table entry is 4 bytes long. Then the 2^10 entries of Page directories and Page Tables will fit nicely into 4Kb pages. This means that it faster and simpler to allocate and deallocate pages for that purpose. 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





