Computational complexity of matrix multiplicationIn theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central subroutine in theoretical and numerical algorithms for numerical linear algebra and optimization, so finding the right amount of time it should take is of major practical relevance. Directly applying the mathematical definition of matrix multiplication gives an algorithm that requires n3 field operations to multiply two n × n matrices over that field (Θ(n3) in big O notation).
Sci-HubSci-Hub is a shadow library website that provides free access to millions of research papers, without regard to copyright, by bypassing publishers' paywalls in various ways. It does not provide access to books. Sci-Hub was founded in Kazakhstan by Alexandra Elbakyan in 2011, in response to the high cost of research papers behind paywalls (see Serials crisis). The site is extensively used worldwide. In September 2019, the site's operator(s) said that it served approximately 400,000 requests per day.
EquationIn mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
Russian invasion of UkraineOn 24 February 2022, in an escalation of the Russo-Ukrainian War which began in 2014. The invasion has killed tens of thousands on both sides. Russian forces have been responsible for mass civilian casualties and for torturing captured Ukrainian soldiers. By June 2022, about 8 million Ukrainians had been internally displaced. More than 8.2 million had fled the country by May 2023, becoming Europe's largest refugee crisis since World War II. Extensive environmental damage, widely described as ecocide, contributed to food crises worldwide.
