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In mathematics, the Bernoulli numbers B_n are a sequence of rational numbers which occur frequently in number theory. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function.

The values of the first 20 Bernoulli numbers are given in the adjacent table. Two conventions are used in the literature, denoted here by ${\displaystyle B_{n}^{-{}}}$ and ${\displaystyle B_{n}^{+{}}}$; they differ only for n = 1, where ${\displaystyle B_{1}^{-{}}=-1/2}$ and ${\displaystyle B_{1}^{+{}}=+1/2}$. For every odd n > 1, B_n = 0. For every even n > 0, B_n is negative if n is divisible by 4 and positive otherwise. The Bernoulli numbers are special values of the Bernoulli polynomials ${\displaystyle B_{n}(x)}$, with ${\displaystyle B_{n}^{-{}}=B_{n}(0)}$ and ${\displaystyle B_{n}^{+}=B_{n}(1)}$ (Weisstein 2016).

The Bernoulli numbers were discovered around the same time by the Swiss mathematician Jacob Bernoulli, after whom they are named, and independently by Japanese mathematician Seki Kōwa. Seki's discovery was posthumously published in 1712 (Selin 1997, p. 891; Smith & Mikami 1914, p. 108) in his work Katsuyo Sampo; Bernoulli's, also posthumously, in his Ars Conjectandi of 1713. Ada Lovelace's note G on the Analytical Engine from 1842 describes an algorithm for generating Bernoulli numbers with Babbage's machine (Menabrea 1842, Note G). As a result, the Bernoulli numbers have the distinction of being the subject of the first published complex computer program.

An Atlas of Fantasy, compiled by Jeremiah Benjamin Post, was originally published in 1973 by Mirage Press and revised for a 1979 edition by Ballantine Books. The 1979 edition dropped twelve maps from the first edition and added fourteen new ones. It also included an introduction by Lester del Rey.

To remain of manageable size, the Atlas excludes advertising maps, cartograms, most disproportionate maps, and alternate history ("might have been") maps, focusing instead on imaginary lands derived from literary sources. It purposefully omits "one-to-one" maps such as Thomas Hardy's Wessex (which merely renames places in southwest England), but includes Barsetshire and Yoknapatawpha County, which are evidently considered to be sufficiently fictionalized. The emphasis is on science fiction and fantasy, though Post suggests there exist enough mystery fiction maps to someday create The Detectives' Handy Pocket Atlas. Other maps were omitted due to permission costs or reproduction quality.

The maps are reproduced from many sources, and an Index of Artists is included.

Wireworld is a cellular automaton first proposed by Brian Silverman in 1987, as part of his program Phantom Fish Tank. It subsequently became more widely known as a result of an article in the "Computer Recreations" column of Scientific American. Wireworld is particularly suited to simulating transistors, and Wireworld is Turing-complete.

Closed-eye hallucinations and closed-eye visualizations (CEV) are a distinct class of hallucination. These types of hallucinations generally only occur when one's eyes are closed or when one is in a darkened room. They can be a form of phosphene. Some people report closed-eye hallucinations under the influence of psychedelics. These are reportedly of a different nature than the "open-eye" hallucinations of the same compounds. Similar hallucinations that occur due to loss of vision are called visual release hallucinations.

In Western art history, Mise en abyme (French pronunciation: ​[miz ɑ̃n‿abim]; also mise en abîme) is a formal technique of placing a copy of an image within itself, often in a way that suggests an infinitely recurring sequence. In film theory and literary theory, it refers to the technique of inserting a story within a story. The term is derived from heraldry and literally means "placed into abyss". It was first appropriated for modern criticism by the French author André Gide.

A common sense of the phrase is the visual experience of standing between two mirrors, seeing as a result an infinite reproduction of one's image. Another is the Droste effect, in which a picture appears within itself, in a place where a similar picture would realistically be expected to appear. That is named after the 1904 Droste cocoa package, which depicts a woman holding a tray bearing a Droste cocoa package, which bears a smaller version of her image.

Norway is not a member state of the European Union (EU). However, it is associated with the Union through its membership in agreements in the European Economic Area (EEA) established in 1994, and by virtue of being a founding member of the European Free Trade Association (EFTA) which was founded in 1960, one of the two historically dominant western European trade blocs. Norway had considered joining the European Community and the European Union twice, but opted to decline following referendums in 1972 and 1994.

GOES-3, known as GOES-C before becoming operational, is an American geostationary weather and communications satellite. It was originally built for the National Oceanic and Atmospheric Administration as part of the Geostationary Operational Environmental Satellite system, and was launched in June 1978. It is positioned in geostationary orbit, from where it was initially used for weather forecasting in the United States. Since ceasing to function as a weather satellite in 1989, it has been used as a communications satellite, and has spent over thirty-eight years in operation. GOES-3 was decommissioned 29 June 2016 at the CSTARS facility in Miami, Florida.

GOES-3 was built by Ford Aerospace, and is based on the satellite bus developed for the SMS programme. At launch it had a mass of 627 kilograms (1,382 lb).

The McCollough effect is a phenomenon of human visual perception in which colorless gratings appear colored contingent on the orientation of the gratings. It is an aftereffect requiring a period of induction to produce it. For example, if someone alternately looks at a red horizontal grating and a green vertical grating for a few minutes, a black-and-white horizontal grating will then look greenish and a black-and-white vertical grating will then look pinkish. The effect is remarkable because, where time-elapse testing is employed, it has been reported to last up to 2.8 months.

The effect was discovered by American psychologist Celeste McCollough in 1965.

Spiegelman's Monster is the name given to an RNA chain of only 218 nucleotides that is able to be reproduced by the RNA replication enzyme RNA-dependent RNA polymerase, also called RNA replicase. It is named after its creator, Sol Spiegelman, of the University of Illinois at Urbana-Champaign who first described it in 1965.