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π Nelson Rules
Nelson rules are a method in process control of determining if some measured variable is out of control (unpredictable versus consistent). Rules, for detecting "out-of-control" or non-random conditions were first postulated by Walter A. Shewhart in the 1920s. The Nelson rules were first published in the October 1984 issue of the Journal of Quality Technology in an article by Lloyd S Nelson.
The rules are applied to a control chart on which the magnitude of some variable is plotted against time. The rules are based on the mean value and the standard deviation of the samples.
The above eight rules apply to a chart of a variable value.
A second chart, the moving range chart, can also be used but only with rules 1, 2, 3 and 4. Such a chart plots a graph of the maximum value - minimum value of N adjacent points against the time sample of the range.
An example moving range: if N = 3 and values are 1, 3, 5, 3, 3, 2, 4, 5 then the sets of adjacent points are (1,3,5) (3,5,3) (5,3,3) (3,3,2) (3,2,4) (2,4,5) resulting in moving range values of (5-1) (5-3) (5-3) (3-2) (4-2) (5-2) = 4, 2, 2, 1, 2, 3.
Applying these rules indicates when a potential "out of control" situation has arisen. However, there will always be some false alerts and the more rules applied the more will occur. For some processes, it may be beneficial to omit one or more rules. Equally there may be some missing alerts where some specific "out of control" situation is not detected. Empirically, the detection accuracy is good.
Discussed on
- "Nelson Rules" | 2015-07-31 | 219 Upvotes 40 Comments
π Uranium Glass
Uranium glass is glass which has had uranium, usually in oxide diuranate form, added to a glass mix before melting for coloration. The proportion usually varies from trace levels to about 2% uranium by weight, although some 20th-century pieces were made with up to 25% uranium.
Uranium glass was once made into tableware and household items, but fell out of widespread use when the availability of uranium to most industries was sharply curtailed during the Cold War in the 1940s to 1990s. Most such objects are now considered antiques or retro-era collectibles, although there has been a minor revival in art glassware. Otherwise, modern uranium glass is now mainly limited to small objects like beads or marbles as scientific or decorative novelties.
Discussed on
- "Uranium Glass" | 2021-10-23 | 104 Upvotes 74 Comments
- "Uranium Glass" | 2020-02-19 | 97 Upvotes 42 Comments
π List of mathematical symbols
This is a list of mathematical symbols used in all branches of mathematics to express a formula or to represent a constant.
A mathematical concept is independent of the symbol chosen to represent it. For many of the symbols below, the symbol is usually synonymous with the corresponding concept (ultimately an arbitrary choice made as a result of the cumulative history of mathematics), but in some situations, a different convention may be used. For example, depending on context, the triple bar "β‘" may represent congruence or a definition. However, in mathematical logic, numerical equality is sometimes represented by "β‘" instead of "=", with the latter representing equality of well-formed formulas. In short, convention dictates the meaning.
Each symbol is shown both in HTML, whose display depends on the browser's access to an appropriate font installed on the particular device, and typeset as an image using TeX.
Discussed on
- "List of mathematical symbols" | 2013-11-09 | 44 Upvotes 9 Comments
π Hashcash
Hashcash is a proof-of-work system used to limit email spam and denial-of-service attacks, and more recently has become known for its use in bitcoin (and other cryptocurrencies) as part of the mining algorithm. Hashcash was proposed in 1997 by Adam Back and described more formally in Back's 2002 paper "Hashcash - A Denial of Service Counter-Measure".
π Pierre Menard, Author of the Quixote
"Pierre Menard, Author of the Quixote" (original Spanish title: "Pierre Menard, autor del Quijote") is a short story by Argentine writer Jorge Luis Borges.
It originally appeared in Spanish in the Argentine journal Sur in May 1939. The Spanish-language original was first published in book form in Borges's 1941 collection El jardΓn de senderos que se bifurcan (The Garden of Forking Paths), which was included in his much-reprinted Ficciones (1944).
Discussed on
- "Pierre Menard, Author of the Quixote" | 2023-06-01 | 56 Upvotes 26 Comments
π Dane-Geld (Poem)
"Dane-geld" is a poem by British writer Rudyard Kipling (1865-1936). It relates to the unwisdom of paying "Danegeld", or what is nowadays called blackmail and protection money. The most famous lines are "once you have paid him the Danegeld/ You never get rid of the Dane."
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- "Dane-Geld (Poem)" | 2021-06-02 | 14 Upvotes 1 Comments
π The moving sofa problem
The moving sofa problem or sofa problem is a two-dimensional idealisation of real-life furniture-moving problems and asks for the rigid two-dimensional shape of largest area A that can be maneuvered through an L-shaped planar region with legs of unit width. The area A thus obtained is referred to as the sofa constant. The exact value of the sofa constant is an open problem.
Discussed on
- "The moving sofa problem" | 2018-07-13 | 215 Upvotes 51 Comments
- "Moving sofa problem" | 2016-12-28 | 38 Upvotes 5 Comments
π Long S
The long s (ΕΏ) is an archaic form of the lower case letter s. It replaced the single s, or the first s in a double s (e.g. "ΕΏinfulneΕΏs" for "sinfulness" and "ΕΏucceΕΏs" for "success"). The long s is the basis of the first half of the grapheme or the German alphabet ligature letter Γ, which is known as the Eszett. The modern letterform is known as the short, terminal, or round s.
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- "The Long S" | 2022-09-04 | 127 Upvotes 81 Comments
- "Long S" | 2019-12-03 | 98 Upvotes 38 Comments
- "Long S" | 2011-10-07 | 81 Upvotes 26 Comments
π MSX-DOS
MSX-DOS is a discontinued disk operating system developed by Microsoft for the 8-bit home computer standard MSX, and is a cross between MS-DOS v1.25 and CP/M-80Β v2.2.
Discussed on
- "MSX-DOS" | 2023-07-20 | 161 Upvotes 49 Comments
π A mathematical proof by an anonymous 4chan user
In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. While trivial superpermutations can simply be made up of every permutation concatenated together, superpermutations can also be shorter (except for the trivial case of n = 1) because overlap is allowed. For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations.
It has been shown that for 1 β€ n β€ 5, the smallest superpermutation on n symbols has length 1! + 2! + β¦ + n! (sequence A180632 in the OEIS). The first four smallest superpermutations have respective lengths 1, 3, 9, and 33, forming the strings 1, 121, 123121321, and 123412314231243121342132413214321. However, for n = 5, there are several smallest superpermutations having the length 153. One such superpermutation is shown below, while another of the same length can be obtained by switching all of the fours and fives in the second half of the string (after the bold 2):
12345123Β41523412Β53412354Β12314523Β14253142Β35142315Β42312453Β12435124Β31524312Β54312134Β52134251Β34215342Β13542132Β45132415Β32413524Β13254132Β14532143Β52143251Β432154321
For the cases of n > 5, a smallest superpermutation has not yet been proved nor a pattern to find them, but lower and upper bounds for them have been found.