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🔗 Biography 🔗 Mathematics 🔗 Biography/science and academia 🔗 History of Science 🔗 India 🔗 India/Indian history workgroup 🔗 India/Tamil Nadu

Srinivasa Ramanujan FRS (; listen ; 22 December 1887 – 26 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Ramanujan had produced groundbreaking new theorems, including some that Hardy said had "defeated him and his colleagues completely", in addition to rediscovering recently proven but highly advanced results.

During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Nearly all his claims have now been proven correct. The Ramanujan Journal, a scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan, and his notebooks—containing summaries of his published and unpublished results—have been analyzed and studied for decades since his death as a source of new mathematical ideas. As late as 2011 and again in 2012, researchers continued to discover that mere comments in his writings about "simple properties" and "similar outputs" for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death. He became one of the youngest Fellows of the Royal Society and only the second Indian member, and the first Indian to be elected a Fellow of Trinity College, Cambridge. Of his original letters, Hardy stated that a single look was enough to show they could only have been written by a mathematician of the highest calibre, comparing Ramanujan to mathematical geniuses such as Euler and Jacobi.

In 1919, ill health—now believed to have been hepatic amoebiasis (a complication from episodes of dysentery many years previously)—compelled Ramanujan's return to India, where he died in 1920 at the age of 32. His last letters to Hardy, written in January 1920, show that he was still continuing to produce new mathematical ideas and theorems. His "lost notebook", containing discoveries from the last year of his life, caused great excitement among mathematicians when it was rediscovered in 1976.

A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess. "An equation for me has no meaning," he once said, "unless it expresses a thought of God."

🔗 Computing

A long-running debate in computer science known as the Protocol Wars occurred from the 1970s to the 1990s when engineers, organizations and nations became polarized over the issue of which communication protocol would result in the best and most robust computer networks. This culminated in the Internet–OSI Standards War in the late 1980s and early 1990s, which was ultimately "won" by the Internet protocol suite ("TCP/IP") by the mid-1990s and has since resulted in most other protocols disappearing.

The pioneers of packet switching technology built computer networks to research data communications in the early 1970s. As public data networks emerged in the mid to late 1970s, the debate about interface standards was described as a "battle for access standards". An international collaboration between several national postal, telegraph and telephone ("PTT") providers and commercial operators developed the X.25 standard in 1976, which was adopted on public networks providing global coverage. Several proprietary standards also emerged, most notably IBM's Systems Network Architecture.

The United States Department of Defense developed and tested TCP/IP during the 1970s in collaboration with universities and researchers in the United States, United Kingdom and France. IPv4 was released in 1981 and the DoD made it standard for all military computer networking. By 1984, an international reference model known as the OSI model had been agreed on, with which TCP/IP was not compatible. Many governments in Europe – particularly France, West Germany, the United Kingdom and the European Economic Community – and also the United States Department of Commerce mandated compliance with the OSI model and the US Department of Defense planned to transition away from TCP/IP to OSI.

Meanwhile, the development of a complete Internet protocol suite by 1989, and partnerships with the telecommunication and computer industry to incorporate TCP/IP software into various operating systems laid the foundation for the widespread adoption of TCP/IP as a comprehensive protocol suite. While OSI developed its networking standards in the late 1980s, TCP/IP came into widespread use on multi-vendor networks for internetworking and as the core component of the emerging Internet.

🔗 Radio 🔗 BBC 🔗 Radio/UK Radio

The Wartime Broadcasting Service is a service of the BBC that is intended to broadcast in the United Kingdom either after a nuclear attack or if conventional bombing destroyed regular BBC facilities in a conventional war.

🔗 United States 🔗 Biography 🔗 Virginia 🔗 Montana 🔗 United States/Wyoming

John Colter (c.1770–1775 – May 7, 1812 or November 22, 1813) was a member of the Lewis and Clark Expedition (1804–1806). Though party to one of the more famous expeditions in history, Colter is best remembered for explorations he made during the winter of 1807–1808, when he became the first known person of European descent to enter the region which later became Yellowstone National Park and to see the Teton Mountain Range. Colter spent months alone in the wilderness and is widely considered to be the first known mountain man.

🔗 Computing 🔗 Computing/Software 🔗 Computing/Free and open-source software 🔗 Linux

The X Window System (X11, or simply X) is a windowing system for bitmap displays, common on Unix-like operating systems.

X provides the basic framework for a GUI environment: drawing and moving windows on the display device and interacting with a mouse and keyboard. X does not mandate the user interface – this is handled by individual programs. As such, the visual styling of X-based environments varies greatly; different programs may present radically different interfaces.

X originated at the Project Athena at Massachusetts Institute of Technology (MIT) in 1984. The X protocol has been at version 11 (hence "X11") since September 1987. The X.Org Foundation leads the X project, with the current reference implementation, X.Org Server, available as free and open source software under the MIT License and similar permissive licenses.

🔗 Lists 🔗 Transport 🔗 Automobiles 🔗 Countries 🔗 Trucks

This article is a list of countries by the number of road motor vehicles per 1,000 inhabitants. This includes cars, vans, buses, and freight and other trucks; but excludes motorcycles and other two-wheelers.

China has the largest fleet of motor vehicles in the world in 2021, with 292 million cars, and in 2009 became the world's largest new car market as well. In 2011, a total of 80 million cars and commercial vehicles were built, led by China, with 18.4 million motor vehicles manufactured.

🔗 Business 🔗 Game theory

A Keynesian beauty contest is a concept developed by John Maynard Keynes and introduced in Chapter 12 of his work, The General Theory of Employment, Interest and Money (1936), to explain price fluctuations in equity markets.

🔗 Physics 🔗 History of Science

The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century to early 20th century classical physics that an ideal black body at thermal equilibrium would emit an unbounded quantity of energy as wavelength decreased into the ultraviolet range.^: 6–7 The term "ultraviolet catastrophe" was first used in 1911 by Paul Ehrenfest, but the concept originated with the 1900 statistical derivation of the Rayleigh–Jeans law.

The phrase refers to the fact that the empirically derived Rayleigh–Jeans law, which accurately predicted experimental results at large wavelengths, failed to do so for short wavelengths. (See the image for further elaboration.) As the theory diverged from empirical observations when these frequencies reached the ultraviolet region of the electromagnetic spectrum, there was a problem. This problem was later found to be due to a property of quanta as proposed by Max Planck: There could be no fraction of a discrete energy package already carrying minimal energy.

Since the first use of this term, it has also been used for other predictions of a similar nature, as in quantum electrodynamics and such cases as ultraviolet divergence.

🔗 Mathematics 🔗 Economics 🔗 Statistics 🔗 Sociology 🔗 Globalization

In economics, the Gini coefficient ( JEE-nee), sometimes called the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measurement of inequality. It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper Variability and Mutability (Italian: Variabilità e mutabilità).

The Gini coefficient measures the inequality among values of a frequency distribution (for example, levels of income). A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income). A Gini coefficient of one (or 100%) expresses maximal inequality among values (e.g., for a large number of people, where only one person has all the income or consumption, and all others have none, the Gini coefficient will be very nearly one). For larger groups, values close to one are very unlikely in practice. Given the normalization of both the cumulative population and the cumulative share of income used to calculate the Gini coefficient, the measure is not overly sensitive to the specifics of the income distribution, but rather only on how incomes vary relative to the other members of a population. The exception to this is in the redistribution of income resulting in a minimum income for all people. When the population is sorted, if their income distribution were to approximate a well-known function, then some representative values could be calculated.

The Gini coefficient was proposed by Gini as a measure of inequality of income or wealth. For OECD countries, in the late 20th century, considering the effect of taxes and transfer payments, the income Gini coefficient ranged between 0.24 and 0.49, with Slovenia being the lowest and Mexico the highest. African countries had the highest pre-tax Gini coefficients in 2008–2009, with South Africa the world's highest, variously estimated to be 0.63 to 0.7, although this figure drops to 0.52 after social assistance is taken into account, and drops again to 0.47 after taxation. The global income Gini coefficient in 2005 has been estimated to be between 0.61 and 0.68 by various sources.

There are some issues in interpreting a Gini coefficient. The same value may result from many different distribution curves. The demographic structure should be taken into account. Countries with an aging population, or with a baby boom, experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Scholars have devised over a dozen variants of the Gini coefficient.