Hilbert's second problemIn mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that the arithmetic is consistent – free of any internal contradictions. Hilbert stated that the axioms he considered for arithmetic were the ones given in , which include a second order completeness axiom. In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new light on the problem. Some feel that Gödel's theorems give a negative solution to the problem, while others consider Gentzen's proof as a partial positive solution.
Ajax (programming)Ajax (also AJAX ˈeɪdʒæks; short for "asynchronous JavaScript and XML") is a set of web development techniques that uses various web technologies on the client-side to create asynchronous web applications. With Ajax, web applications can send and retrieve data from a server asynchronously (in the background) without interfering with the display and behaviour of the existing page. By decoupling the data interchange layer from the presentation layer, Ajax allows web pages and, by extension, web applications, to change content dynamically without the need to reload the entire page.
E-commerce payment systemAn e-commerce payment system (or an electronic payment system) facilitates the acceptance of electronic payment for offline transfer, also known as a subcomponent of electronic data interchange (EDI), e-commerce payment systems have become increasingly popular due to the widespread use of the internet-based shopping and banking. Credit cards remain the most common forms of payment for e-commerce transactions. As of 2008, in North America, almost 90% of online retail transactions were made with this payment type.
Gentzen's consistency proofGentzen's consistency proof is a result of proof theory in mathematical logic, published by Gerhard Gentzen in 1936. It shows that the Peano axioms of first-order arithmetic do not contain a contradiction (i.e. are "consistent"), as long as a certain other system used in the proof does not contain any contradictions either. This other system, today called "primitive recursive arithmetic with the additional principle of quantifier-free transfinite induction up to the ordinal ε0", is neither weaker nor stronger than the system of Peano axioms.
Nuclear power in the United KingdomNuclear power in the United Kingdom generated 16.1% of the country's electricity in 2020. , the UK has 9 operational nuclear reactors at five locations (8 advanced gas-cooled reactors (AGR) and one pressurised water reactor (PWR)), producing 5.9 GWe. It also has nuclear reprocessing plants at Sellafield and the Tails Management Facility (TMF) operated by Urenco in Capenhurst. The United Kingdom established the world's first civil nuclear programme, opening a nuclear power station, Calder Hall at Windscale, England, in 1956.
Hilbert's programIn mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early 1920s, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent.
Apache CassandraCassandra is a free and open-source, distributed, wide-column store, NoSQL database management system designed to handle large amounts of data across many commodity servers, providing high availability with no single point of failure. Cassandra offers support for clusters spanning multiple datacenters, with asynchronous masterless replication allowing low latency operations for all clients. Cassandra was designed to implement a combination of Amazon's Dynamo distributed storage and replication techniques combined with Google's Bigtable data and storage engine model.
Online datingOnline dating, also known as Internet dating, Virtual dating, or Mobile app dating, is a method used by people with a goal of searching for and interacting with potential romantic or sexual partners, via the internet. An online dating service is a company that promotes and provides specific mechanisms for the practice of online dating, generally in the form of dedicated websites or software applications accessible on personal computers or mobile devices connected to the internet.
Decay theoryThe Decay theory is a theory that proposes that memory fades due to the mere passage of time. Information is therefore less available for later retrieval as time passes and memory, as well as memory strength, wears away. When an individual learns something new, a neurochemical "memory trace" is created. However, over time this trace slowly disintegrates. Actively rehearsing information is believed to be a major factor counteracting this temporal decline.
Payment systemA payment system is any system used to settle financial transactions through the transfer of monetary value. This includes the institutions, payment instruments such as payment cards, people, rules, procedures, standards, and technologies that make its exchange possible. A common type of payment system, called an operational network, links bank accounts and provides for monetary exchange using bank deposits. Some payment systems also include credit mechanisms, which are essentially a different aspect of payment.
