zettaparsec

(astronomy) An astronomical unit of distance equal to 10²¹ parsecs.


ronnaparsec

(astronomy) An astronomical unit of distance equal to 10²⁷ parsecs.


quettaparsec

(astronomy) An astronomical unit of distance equal to 10³⁰ parsecs.


centimate

en-verb

centimate (third-person singular simple present centimates, present participle centimating, simple past and past participle centimated)

centimates (present singular third-person)
centimating (participle present)
centimated (participle past)
centimated (past)

Follows from decimate and quintate according to Latin-derived numerical prefixes (see centi-).

If independent samples are needed, it is useful to decimate (take one element every 10) or centimate (one in 100) the chain (known as thinning).

2015, Stefano Andreon, Brian Weaver, Bayesian Methods for the Physical Sciences, page 16:

(statistics) To take a sub-sample of a sample so as to include in the sub-sample one out of every hundred (i.e. 1%) of the original sample.


cryptocollectible

But at their core, all cryptocollectible projects are rooted deeply in internet culture. The name and spirit of CryptoPunks comes from cypherpunks, a name first given to an early '90s group cum mailing list that focused on ideas like the intersection of cryptography, privacy technology, philosophy and computer science.

2018 January 7, Jessica Klein, “The world of cryptocollectibles like CryptoKitties looks like the internet's early days”, in Salon.com, archived from the original on 2023-05-16:

NBA Top Shot, a partnership between the N.B.A. and the blockchain company Dapper Labs that turns basketball highlight videos into unique cryptocollectibles, has $230 million in sales since 2019.

2021 March 24, Kevin Roose, “Buy This NFT Column on the Blockchain!”, in The New York Times, New York, N.Y.: The New York Times Company, →ISSN, →OCLC, archived from the original on 2023-07-27:

A digital collectible item traded using cryptocurrency, so that the blockchain contains proof that one really owns that item.


fiatsplain

fiatsplain (third-person singular simple present fiatsplains, present participle fiatsplaining, simple past and past participle fiatsplained)

fiatsplains (present singular third-person)
fiatsplaining (participle present)
fiatsplained (participle past)
fiatsplained (past)

If you have ever had the displeasure of learning economics while in university or simply have had a pompous sheep fiatsplain to you why a sound money standard can never work you've likely had a professor or the fiatsplainer blame the gold standard for the Great Depression.

2021 December 2, Marty Bent, “They Haven't Been Teaching Monetary History Accurately”, in Bitcoin Magazine:

(informal, derogatory) To criticize bitcoin and other cryptocurrencies in a condescending manner, often by nocoiners.


fiatsplainer

(informal, derogatory) A person who criticizes cryptocurrency while defending fiat money.


cryptowealthy

en-adj

cryptowealthy (comparative more cryptowealthy, superlative most cryptowealthy)

more cryptowealthy (comparative)
most cryptowealthy (superlative)

There’s a common paranoia among the crypto-wealthy that they’ll be targeted and robbed since there’s no bank securing the money, so many are obsessively secretive.

2018 January 13, Nellie Bowles, “Everyone Is Getting Hilariously Rich and You’re Not”, in The New York Times:

While that could lead to cooperative arrangements of mutual assistance, it could also give the cryptowealthy all of the power and none of the limits of a liberal democratic society.

2018, Kevin Werbach, “Connecting the Legal and the Technical”, in The Blockchain and the New Architecture of Trust, Cambridge, MA: MIT Press, →ISBN, page 219:

“[…] one of the reasons for that is that there are a lot more people who’ve made their money in crypto and they tend to be younger,” Hyslop said. “They self-identify as crypto-wealthy; some who were bidding in the last slae realized for the first time that they could actually buy meteorites, and they were extremely enthusiastic.”

2022 February 13, James Tarmy, “Meteorite Market: Crypto has helped finance buyers willing to pay thousands”, in The Philadelphia Inquirer, volume 193, number 258, page H3:

For quotations using this term, see Citations:cryptowealthy.

(cryptocurrencies) Having acquired significant wealth in the cryptocurrency market.


postcompose

en-verb

postcompose (third-person singular simple present postcomposes, present participle postcomposing, simple past and past participle postcomposed)

postcomposes (present singular third-person)
postcomposing (participle present)
postcomposed (participle past)
postcomposed (past)

If we postcompose the embedding ɩ with a dilation by a factor of t, the algebraic growth Γ will obviously not change but the group will be generated by loops of length λ(tɩL) = tλ (ɩL), implying that Γ_T(#P_(g1)( tɩ, T ) ) → ∞ as t→ 0.

2022, Helmut Hofer, Alberto Abbondandolo, Urs Frauenfelder, Symplectic Geometry, page 64:

(transitive, mathematics) To apply (an operation) after another operation has occurred.


clustering coefficient

en-noun

clustering coefficient (plural clustering coefficients)

(graph theory) A quantitative measure of how often the nodes of a graph cluster together, defined as the ratio of the number of links among the nodes to the maximum possible number of links.


elementary cellular automaton

elementary cellular automaton (plural elementary cellular automata or elementary cellular automatons)

elementary cellular automata (plural)
elementary cellular automatons (plural)

(cellular automata) A one-dimensional, two-state cellular automaton in which a cell's state in the next generation depends only on its current state and the states of its two immediate neighbours.


block cellular automaton

block cellular automaton (plural block cellular automata or block cellular automatons)

block cellular automata (plural)
block cellular automatons (plural)

(cellular automata) A cellular automaton in which the grid is divided into distinct blocks in a uniform pattern, with the blocks being shifted by a certain number of cells in each generation, and each block serving as the neighborhood for all cells contained within it.


partitioning cellular automaton

partitioning cellular automaton (plural partitioning cellular automata or partitioning cellular automatons)

partitioning cellular automata (plural)
partitioning cellular automatons (plural)

block cellular automaton
block cellular automaton

(cellular automata) A block cellular automaton.


Margolus neighborhood

Margolus neighborhood (plural Margolus neighborhoods)

For Norman Margolus, Canadian-American cellular automatist

In addition to Moore, Von Neuman and Margolus neighborhoods, the spatial, temporal (phase) and user connector extensions of CAM-PC provide for a large number of different neighborhoods. In this sense, a simple neighborhood is actually a selection of up to 16 of the 50 to 100 signals (depending on what you count) that are available.

1992 March 16, CAM-PC Support Staff, “CAM, CAM-6, CAM\PC boards.”, in comp.theory.cell-automata (Usenet):

Another thing which seems to work very well is embodied in the Margolus neighborhood, for which different rules are operative at different points in the lattice, and even at different times.

1992 March 30, Harold V. McIntosh, “1) What kind of tilings? 2) CAM family.”, in comp.theory.cell-automata (Usenet):

For any one interested in CA's in general or in simulations that require the conservatin laws of the Margolus neighborhood in particular I've managed to devise a method for duplicating all the properties of the Margolus neighborhood without the paritioning and without the block rules.

2003 March 15, fiziwig, “New formulation of the Margolus neighborhood”, in comp.theory.cell-automata (Usenet):

(cellular automata) A block cellular automaton neighborhood consisting of a two-by-two square of cells which shifts one cell diagonally each generation.


lightweight spaceship

lightweight spaceship (plural lightweight spaceships)

To begin with and to be complete, I will list the original spaceships. These are the glider, the lightweight spaceship (LWSS), middleweight spaceship (MWSS), and the heavyweight spaceship (HWSS). These were all found very soon after Life was invented by Conway.

1992 August 13, David Bell, “Spaceships in Conway's Life (Part 1)”, in comp.theory.cell-automata (Usenet):

It's a reaction between a glider and a lightweight spaceship spark, nondestructive to the spaceship (so it can be used in puffers):

1994 May 14, Paul Callahan, “Louis Howell's question of block clearing in life (simple solution)”, in comp.theory.cell-automata (Usenet):

The usual non-glider suspects from Conway's Life (lightweight, middleweight, and heavyweight spaceships) all fail here due to central 7-neighbor OFF cells.

2008 May 31, Dave Greene, “Life: B37/S23 - A Chaotic Universe.”, in comp.theory.cell-automata (Usenet):

(cellular automata) A particular orthogonal spaceship in Conway's Game of Life, and the smallest such example.


LWSS

For example, two gliders can produce another glider, and three gliders can produce a LWSS or MWSS or a HWSS.

the simple "gliders" work perfectly fine, but the LWSS spaceship works great until the 15th generation when a singular pixel gets misplaced and the entire structure collapses.

1992 August 23, Albert Schnezer, “Programming Life in Tpascal”, in comp.theory.cell-automata (Usenet):

It begins with the period-20 spaceship that consists of a p20 puffer stabilized by a third lwss; this is the basis for the standard p20 forward and backward rakes.

1994 December 7, Paul Callahan, “Program to search for collisions in Conway's Life (C code)”, in comp.theory.cell-automata (Usenet):

lightweight spaceship
lightweight spaceship#English

(cellular automata) Initialism of lightweight spaceship.


middleweight spaceship

middleweight spaceship (plural middleweight spaceships)

The trailing middleweight spaceships convert the spark into a pair of pi-heptominos, which start the line of blinkers burning again, while leaving behind a pair of blocks.

1996 December 16, Dean Hickerson, “What is his name ?”, in comp.theory.cell-automata (Usenet):

(cellular automata) A particular orthogonal spaceship in Conway's Game of Life, and the second smallest such example.


R-pentomino

(geometry) A particular five-square polyomino.

I came up with an implementation of an algorithm on my Sparcstation 1 that does all 1103 generations of the R-pentomino, including the gliders, in 1.3 seconds (no display), and runs o.....o. ..o...o. ..o..o.o .o.o.... (a pattern by Wainright recommended to me by Gosper) out to 10,000 generations in 45 seconds (again, without display).

1990 January 15, Paul Dietz, “Gosper's Algorithm for Life”, in comp.theory.cell-automata (Usenet):

I've finisher debugging the code, and it works -- that is to say, its final configuration for the R-pentomino is the same as the one in my books. (It's my guess that the R-p will find any bug in any life program, no matter how obscure.)

1990 June 8, Robert Herrell, “Life without bounds”, in comp.theory.cell-automata (Usenet):

This explosive collision is "perturbed" by the permanent parts of the reflector so that at generation 242, the destroyed block is restored, a glider is released in the reverse direction, an r-pentomino is produced some distance from the stage, and a beehive is left in an awkward position close to the block.

1996 November 19, Paul Callahan, “Glider reflector in Life”, in comp.theory.cell-automata (Usenet):

(cellular automata) The methuselah based on this polyomino that, in Conway's Game of Life, has a lifespan of 1,103 generations.


B-heptomino

Perturbations of its reaction also reproduce it in different generations. This might be tamed someday to form glider guns or puffers, as the B-heptomino in Life has been.

1994 May 7, David Bell, “HighLife - An Interesting Variant of Life (part 3/3)”, in comp.theory.cell-automata (Usenet):

Actually, the period 30 "queen bee" shuttle seems irreparable, as it contains several instances of the Ship neighborhood duriod its cycle. It's the period 46 b-heptomino shuttle that can be stabilized with clocks.

1994 May 11, Paul Callahan, “HighLife - An Interesting Variant of Life (part 3/3)”, in comp.theory.cell-automata (Usenet):

In B37/S23, it goes symmetrical after 10 ticks, and produces a familiar pair of B-heptominoes after 23 ticks (the next generation after this can be found in the rotor of a standard B3/S23 p46 oscillator):

2008 June 25, Dave Greene, “Life: B37/S23 - A Chaotic Universe.”, in comp.theory.cell-automata (Usenet):

(cellular automata) A particular seven-cell methuselah in Conway's Game of Life.


pi-heptomino

A growing spaceship which uses the pi-heptomino.

1993 March 16, David Bell, “Life program (part 14/18)”, in comp.theory.cell-automata (Usenet):

It does include a pseudo-spaceship based on the Pi-heptomino (pseudo because it needs some classic spaceships in front, and so the middle gets longer and longer.

1995 March 30, John Harper, “Life - has anybody found....”, in comp.theory.cell-automata (Usenet):

1) gliders on paths *adjacent* to the six annihilating paths produce a pi-heptomino and consequent large explosion -- and there's no way to place blocks on nearby lanes to catch those gliders, because they'd interact messily with gliders on some of the original six glider paths;

2005 February 23, Dave Greene, “exist glider gun able of reconstruction in Life?”, in comp.theory.cell-automata (Usenet):

(cellular automata) A particular symmetric seven-cell methuselah in Conway's Game of Life.


Chinese restaurant process

Chinese restaurant process (plural Chinese restaurant processes)

The restaurant analogy first appeared in a 1985 write-up by David Aldous, where it was attributed to Jim Pitman (who additionally credits Lester Dubins).

(probability theory) A discrete-time stochastic process, analogous to seating customers at tables in a restaurant, such that, at time n, the n customers have been partitioned among m ≤ n tables (or blocks of a partition). It has applications in population genetics, linguistic analysis, and image recognition.


Padovan sequence

(mathematics) The integer sequence P(n) defined by the initial values P(0)=P(1)=P(2)=1 and the recurrence relation P(n)=P(n-2)+P(n-3)..


pattern word

(cryptography) A word in which some letter appears more than once, useful in solving a cryptogram.


pebbler

(graph theory) One who or that which places pebbles at the vertex of a graph, according to certain rules; see pebble game.


Generation Zedder

Generation Zedder (plural Generation Zedders)

On a high wall in the corner of Social Chain’s Manchester office, with a look of serene exasperation, Jesus Christ looks down on the sea of millennials and Generation Zedders (or whatever the dominant term is for the under-20s this month) tapping out tweets and social media stories.

2018 January 14, Simon Parkin, “Inside Britain’s meme factory”, in The Observer, page 17:

So we’re still not online as moving day approaches and it’s looking like our new digs won’t be digital right away. I break it to Youngest Child, a Generation Zedder raised by the interweb, that we may be temporarily off-grid.

2019 September 28, Janet Christie, “Youngest solves the no wi-fi issue in our new home: Mum’s the word”, in The Scotsman, page 8:

Linguistic experts say young people – Generation Zedders, so those in their early 20s and teens – have got a thing about full stops at the end of text messages.

2020 September 1, Nicola Whitfield, “Sorry, kids, the full stop is here to stay. Period.”, in News24, archived from the original on 2020-10-27:

Imagine showing this programme to someone currently in their teens and saying: “There you go, sonny. That’s what you Generation Zedders are missing out on. Jealous?”

2020 November 6, Mike Ward, “Annie’s a punk shocker”, in Daily Express, page 39:

So: congratulations millennials and Generation Zedders: we did it! We finally have our before and after, the one we will be experts on when it comes to passing wisdom on to our anticipated grand-younglings and beyond. For ours is the kingdom of Covid-19 and its aftermath in an increasingly totalitarian world, amen.

2021 January 1, “What a spectacular year 2020 has been; we have Covid to thank for it”, in The East African, Nation Media Group:

Cord cutting is becoming a thing in the United States as Generation ‘Zedders’ and Millennials ditch free-to-air and cable broadcasters to consume all their media, including sport, through streaming apps on their various devices.

2021 July 1, Ashley Browne, “Tell ’em they’re streaming”, in AFL Record, page 102:

Research shows that only 14 per cent of Generation Zedders have enough spare cash to weather rising prices, compared to 52 per cent of Millennials (in their 30s), 64 per cent of Generation X (in their 40s and 50s), which probably includes your parents, and 60 per cent of Baby Boomers (the post-war generation now in their 60s).

2022 February 28, Michael Kennedy, “How much longer can our finances stand these spiralling rises?”, in The Irish News, archived from the original on 2022-02-28:

We have become hopelessly entangled in our ability to express ourselves clearly over fundamental matters of biology. Younger people, Generation Zedders, have a pragmatic view of these matters. They all know who they are and are not fussed by new definitions, and neither should the older generations.

2022 June 1, Harvey Fewings, “Generational Change: Fundamental to the Human Story”, in The LOCAL News, number 7, page 8, columns 3–4:

Back in the 80s he [Ben Elton] was one of the angry young things of alternative comedy, but this time he was hosting up-and-coming acts. ‘It just goes to show that Boomers and Generation Zedders can get on after all!’

2023 May 27, Cole Moreton, Ray Burmiston, “I had to tell my kids never to Google me!: He’s just won a BAFTA and is about to star in a West End musical. Quite a turnaround, admits Ben Elton, the motormouth comic whose career went spectacularly off-key…”, in Daily Mail, page 4:


Zer

Boomers and Xers were told to stay silent, but millennials and Zers were encouraged to speak up. The millennials and some of these Zers who have grown up and joined our teaching force were raised in a model that put them at the center of the family circle, which helps explain why millennial and Gen Z teachers would want more interaction with authority figures.

2022, Mark White, 5-Gen Leadership: Leading 5 Generations in Schools in the 2020s, Corwin Press, SAGE Publishing, →ISBN:

Learning from the past is not the same as living in the past. Learning from the past is the only way one can truly live either progressively or conservatively in the present, whatever one’s preference might be. But don’t expect Millennials and Zers to believe such a tale.

2022 June 22, Robert Shinkoskey, “Ancient technology for today”, in Wabash Plain Dealer, page A7:

The percentage of people who are interested in extreme sports is rising, and most of these people belong to the age groups of Millennials and Zers, who already seek out glamping.

2023, Alastair M. Morrison, Dimitrios Buhalis, editors, Routledge Handbook of Trends and Issues in Global Tourism Supply and Demand, Routledge, →ISBN:


balayaged

(mathematics) Of a harmonic function: reconstructed by the balayage method.


quettagram

The arrival of the new prefixes means the Earth can now be said to weigh six ronnagrams, and Jupiter about two quettagrams.

2022 November 18, Ian Sample, “Earth weighs in at six ronnagrams as new prefixes picked for big and small”, in The Guardian:

(metrology) An SI unit of mass equal to 10³⁰ grams. Symbol: Qg


rontogram

The arrival of the new prefixes means the Earth can now be said to weigh six ronnagrams, and Jupiter about two quettagrams. An electron weighs about a rontogram, and a single bit of data stored on a mobile phone adds about 10 quectograms to its mass.

(metrology) An SI unit of mass equal to 10⁻²⁷ grams. Symbol: rg


quectogram

(metrology) An SI unit of mass equal to 10⁻³⁰ grams. Symbol: qg


synthetic geometry

Coordinate term: analytic geometry

(mathematics) Geometry without the use of coordinates, relying instead on proofs derived from axioms.


Verlet integration

Named after Loup Verlet, who rediscovered the algorithm in the 1960s.

(mathematics) A numerical method used to integrate Newton's equations of motion, frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics.


Euler's number

Named after Swiss mathematician Leonhard Euler (1707–1783), who did, however, not discover it, although he likely gave the constant its modern symbol e.

(mathematics) The mathematical constant e, the base of the natural logarithm; an irrational, transcendental number approximately equal to 2.71828.

Euler's constant
Euler's number
Leonhard Euler


pigpen cipher

(cryptography) A geometric simple substitution cipher, which exchanges letters for symbols which are fragments of a grid.


Darboux's theorem

differential geometry
differential geometry

(differential geometry) A theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. One of its many consequences is that any two symplectic manifolds of the same dimension are locally symplectomorphic to one another.


narcissistic number

narcissistic number (plural narcissistic numbers)

(number theory) A number that, in a given base, is the sum of its own digits each raised to the power of the number of digits.


Armstrong number

Armstrong number (plural Armstrong numbers)


multihypergraph

From multi- + hypergraph. Compare multigraph.

(graph theory) A set V (whose elements are called vertices or nodes), taken together with a multiset E, each of whose elements (called an edge or hyperedge) is a subset of V.


paraboloid of revolution

paraboloid of revolution (plural paraboloids of revolution)

surface of revolution
surface of revolution

(geometry) A surface of revolution formed by revolving a parabola around its axis.


artificial immune system

artificial immune system (plural artificial immune systems)

(machine learning) Any of a class of computationally intelligent, rule-based machine learning systems inspired by the principles and processes of the vertebrate immune system.


pseudoperiod

LL-Q1860 (eng)-Flame, not lame-pseudoperiod.wav

(mathematics) A solution function that is not technically periodic, but nevertheless displays repetitive behavior.


digraphoid

Blend of directed + graphoid, after digraph (“directed graph”). Coined by American mathematician George J. Minty in a 1966 article.

coinage

We now wish to consider what part of the theory of directed graphs can be built up in the wider context of graphoids/matroids. To this end, we shall introduce the concepts of digraphoid (short for “directed graphoid”) and orientable graphoid. […] A digraphoid is a structure consisting of: (1º) a graphoid, and (2º) a partitioning of each circuit and cocircuit of the graphoid, each being partitioned into two sets; this partitioning is to satisfy the axiom: […]

[1966, George J. Minty, “On the Axiomatic Foundations of the Theories of Directed Linear Graphs, Electrical Networks and Network-Programming”, in Journal of Mathematics and Mechanics, volume 15, number 3, →JSTOR, pages 506–507:

(combinatorics) A dual pair of regular matroids.


riffle shuffle

(mathematics) A permutation that models the outcome of a riffle shuffle; the operation of dividing an ordered set into two equal subsets and then alternately listing sequences of elements from each subset that have a common specified length.


shuffle product

en-noun

shuffle product (plural shuffle products)

(mathematics) The sum of all ways of interlacing of words on some set in Hopf algebra.


unsteckered

From un- + German Stecker (“plug”) + -ed.

(cryptography) unprocessed by a plugboard.


steckered

(cryptography) Processed by a plugboard.


antidifferentiate

en-verb

antidifferentiate (third-person singular simple present antidifferentiates, present participle antidifferentiating, simple past and past participle antidifferentiated)

antidifferentiates (present singular third-person)
antidifferentiating (participle present)
antidifferentiated (participle past)
antidifferentiated (past)

LL-Q1860 (eng)-Flame, not lame-antidifferentiate.wav

Back-formation from antidifferentiation, equivalent to anti- + differentiate.

If you are asked to antidifferentiate a rational function, use Partial Fractions.

(Can we date this quote?), Dave Rusin, “How to antidifferentiate”, in Department of Mathematics, University of Texas at Austin:

(mathematics, calculus) To find the antiderivative of a function.


z-test

(statistics) Any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution.


LRL

Coordinate term: URL

(medicine, statistics) Initialism of lower reference limit.


spatial locale

(topology) A locale which originates from a topological space.


strictification

(mathematics, category theory) ??Replacement of coherent isomorphisms by equalities.


arithmetico-harmonic

harmonic progression
harmonic progression

(mathematics) Relating to both arithmetic and harmonic progressions.


well-quasi-ordering

(mathematics) A preorder where every infinite sequence has an infinite increasing subsequence.


Turing pattern

Introduced by English mathematician Alan Turing in a 1952 paper titled The Chemical Basis of Morphogenesis.

(biology, mathematics) A pattern, found in nature, that arises naturally and autonomously from a homogeneous, uniform state, through instability.


quettameter

We welcome ronnagrams and quettameters into the likes of kilograms and millimeters.

2022 November 20, Agence France-Presse, “Say hello to quettameters: Scientists decide on new metric prefixes”, in Daily Sabah:


quettametre

(metrology) An SI unit of length equal to 10³⁰ meters. Symbol: Qm


superpolylogarithmic

The polylogarithmic bound on g is necessary. To see this, let f(x) = Σxᵢ, and let g(x) be |x|/2 (or any other superpolylogarithmic threshold).

2003, Jiri Wiedermann, Peter van Emde Boas, Mogens Nielsen, Automata, Languages and Programming: 26th International Colloquium, ICALP'99, Prague, Czech Republic, July 11-15, 1999 Proceedings (page 152)

Lindzey noticed that it is possible to speed-up several graph algorithms using switching to a lower number of edges - he obtained up to superpolylogarithmic speed-ups of algorithms for diameter, transitive closure, bipartite maximum matching and general maximum matching.

2016, Thang N. Dinh, My T. Thai, Computing and Combinatorics: 22nd International Conference, COCOON 2016, Ho Chi Minh City, Vietnam, August 2-4, 2016, Proceedings (page 169)

(mathematics) growing faster than any polynomial but slower than any exponential function.


concavifiability

We establish this characteristic of concavifiability for continuous functions whose domain is an arbitrary geodesic metric space.

2017, Connell, Chris and Rasmusen, Eric B., “Concavifying the Quasiconcave”, in Journal of Convex Analysis, volume 24, number 4, page 1239:

(mathematics) Capability of being concavified (being made concave).


convexifiability

The results of this paper, once one makes the obvious modifications, apply equally well to the analogous question of convexifiability.

2017, Connell, Chris and Rasmusen, Eric B., “Concavifying the Quasiconcave”, in Journal of Convex Analysis, volume 24, number 4, page 1240:

(mathematics) Capability of being convexified (being made convex).


convexifiable

(mathematics) Capable of being convexified (being made convex).


concavifiable

(mathematics) Capable of being concavified (being made concave).


versed cosine

trigonometric function
trigonometric function

(trigonometry) The trigonometric function 1 + cos(x).


quater-imaginary

(mathematics) Of or relating to a nonstandard numeral system using the imaginary number 2i (= √–4) as its base.


Stone-Čech compactification

en-noun

Stone-Čech compactification (countable and uncountable, plural Stone-Čech compactifications)

Named after Marshall Stone and Eduard Čech, who wrote on the topic in 1937.

A technique for constructing a universal map from a topological space to a compact Hausdorff space.

The space obtained by using this technique.


Čech-Stone compactification

Čech-Stone compactification (countable and uncountable, plural Čech-Stone compactifications)

Stone-Čech compactification
Stone-Čech compactification#English

Alternative form of Stone-Čech compactification


Tychonoff space

Tychonoff space (plural Tychonoff spaces)

Named after Andrey Nikolayevich Tychonoff.

(mathematics) Any completely regular topological space that is also a Hausdorff space.


Stone's representation theorem

(mathematics) A theorem stating that every Boolean algebra is isomorphic to a certain field of sets.


forward echo

forward echo (countable and uncountable, plural forward echoes)


rail fence cipher

rail fence cipher (plural rail fence ciphers)

(cryptography) A transposition cipher in which the plain text is written in a zigzag fashion diagonally up and down on successive "rails" of an imaginary fence, and then the characters are read off in rows to obtain the ciphertext.


Rabin fingerprint

Rabin fingerprint (plural Rabin fingerprints)

Named after Israeli mathematician Michael O. Rabin (1931–).

named-after

We use a 40 bit fingerprint function, based on Rabin fingerprints [7], enhanced to behave as a random permutation.

1997 September 1, Andrei Z. Broder, Steven C. Glassman, Mark S. Manasse, Geoffrey Zweig, “Syntactic clustering of the Web”, in Computer Networks and ISDN Systems (Papers from the Sixth International World Wide Web Conference), volume 29, number 8, →DOI, →ISSN, pages 1157–1166:

(mathematics) A fingerprint using polynomials over a finite field.


Zipfian distribution

en-noun

Zipfian distribution (plural Zipfian distributions)

A Zipfian distribution occurs when some values appear much more often than others. When you diagram it on a graph with logarithm scales on both axes, you get a straight line (see Figure 12.1).

2010, Joe Celko, Joe Celko's Analytics and OLAP in SQL, Elsevier, →ISBN, page 108:

probability distribution
probability distribution

(mathematical statistics) A discrete probability distribution whose rank-frequency distribution is an inverse power law relation.


interesting number paradox

the interesting number paradox (canonical)

(mathematics) A humorous paradox arising from the attempt to classify every natural number as either "interesting" or "uninteresting". If there exists a non-empty set of uninteresting natural numbers, there must be a smallest uninteresting number, but this number is paradoxically interesting because it is the smallest uninteresting number.


infinite hotel paradox

(set theory) A thought experiment illustrating a counterintuitive property of infinite sets, showing that a fully occupied hotel with infinitely many rooms may still accommodate any number of additional guests.


Legendre's constant

(mathematics) A mathematical constant occurring in a formula to approximate the behavior of the prime-counting function π(x), originally chosen to be 1.08366 but now known to be exactly 1.


Ramanujan's sum

Ramanujan's sum (plural Ramanujan's sums)

Vinogradov's theorem
Vinogradov's theorem

(number theory) A function, usually denoted c_q(n), of two positive integer variables q and n, defined by the formula c_q(n)=∑_(1<a≤q atop (a,q)=1)e^(2πi tfrac aqn),, where (a, q) = 1 means that a only takes on values coprime to q. It is used in the proof of Vinogradov's theorem.


Abel-Ruffini theorem

Named after Paolo Ruffini, who made an incomplete proof in 1799, and Niels Henrik Abel, who provided a proof in 1824.

(mathematics) A theorem stating that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients.


Abel's impossibility theorem

Abel-Ruffini theorem
Abel-Ruffini theorem#English

(mathematics) Synonym of Abel-Ruffini theorem


autohomeomorphism

(mathematics) Synonym of self-homeomorphism


half-mile

These trains in the course of their day's work often travel a distance little less than that from London to Glasgow, stopping and starting every half-mile.

1951 January, “The Inner Circle and its Rolling Stock”, in Railway Magazine, page 61:

They were greeted with applause, medals and the skirl of bagpipes from our lone piper - a sound some told us encouraged tired legs for the last half-mile as the pipes could be heard on the mountain.

2024 August 7, Paul Bigland, “'3 Peaks by Rail': ain't no mountain high enough”, in RAIL, number 1015, page 51:

Half of a statute mile, a measurement of 880 yards, or 2,640 feet, or 804.672 metres.


central tendency

central tendency (plural central tendencies)

Central tendency describes a single number that aims to give you a sense of the most representative value in your data. In other words, if you were to choose one number that would best represent all the numbers on a variable in your data set, this would be it.

2013, Donncha Hanna, Martin Dempster, Psychology Statistics For Dummies, John Wiley & Sons, →ISBN, page 54:

(statistics) A central or typical value for a probability distribution.


semiminor axis

Coordinate term: semimajor axis

(geometry) Half of the minor axis of a circle or ellipse.

demi-petit axe

half of the major axis of a circle or ellipse


Vinogradov's theorem

Named after Ivan Matveyevich Vinogradov, who proved it in the 1930s.

Goldbach's weak conjecture
Goldbach's weak conjecture

(number theory) A result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers; a weaker form of Goldbach's weak conjecture.


Ramanujan summation

Invented by the mathematician Srinivasa Ramanujan.

(mathematics) A technique for assigning a value to an infinite divergent series, not summation in the traditional sense, but having useful mathematical properties.


Darboux's formula

(mathematics) A formula for summing infinite series by using integrals or evaluating integrals using infinite series.


Euler-Maclaurin formula

Discovered independently by Leonhard Euler and Colin Maclaurin around 1735.

(mathematics) A formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus.


Christoffel-Darboux formula

the Christoffel-Darboux formula (canonical)

Named after Elwin Bruno Christoffel and Jean Gaston Darboux.

(mathematics) An identity for a sequence of orthogonal polynomials: ∑ⱼ₌₀ⁿ(f_j(x)f_j(y))/(h_j)=(k_n)/(h_nk_n+1)(f_n(y)f_n+1(x)-f_n+1(y)f_n(x))/(x-y) where fⱼ(x) is the jth term of a set of orthogonal polynomials of squared norm hⱼ and leading coefficient kⱼ.


schizophrenic number

schizophrenic number (plural schizophrenic numbers)

(mathematics) An irrational number with persistent patterns in its decimal expansion that give it the appearance of a rational number.


exceptional zero

exceptional zero (plural exceptional zeros)


Landau-Siegel zero

Landau-Siegel zero (plural Landau-Siegel zeros)


vampire number

(mathematics) A composite natural number with an even number of digits that can be factored into two natural numbers (called "fangs") each with half as many digits as the original number, and where the two factors contain precisely all the digits of the original number, in any order, counting multiplicity.


sad number

(mathematics) Any number that is not a happy number.


happy number

13 is a happy number because 1² + 3² is 10, and 1² + 0² is 1.

(mathematics) Any number that eventually reaches 1 after some number of iterations of replacing each of its digits by the sum of that digit's squares.


umbral calculus

(mathematics, historical) An area of study around the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to "prove" them.


Pidduck polynomial

Pidduck polynomial (plural Pidduck polynomials)

(mathematics) Any of a group of polynomials sₙ(x) given by the generating function displaystyle ∑ₙ(s_n(x))/(n!)tⁿ=((1+t)/(1-t))ˣ(1-t)⁻¹.


Narumi polynomial

Narumi polynomial (plural Narumi polynomials)

(mathematics) Any of a group of polynomials sₙ(x) given by the generating function displaystyle ∑s_n(x)tⁿ/n!=(t/(log (1+t)))ᵃ(1+t)ˣ.


superproperty

For our second principle we need the concept of superproperty. If (P) is a property of infinite dimensional Banach spaces, e.g. reflexivity, cotype, etc. we say that the infinite dimensional Banach space E has super (P) if any infinite dimensional Banach space F, F#92;hookrightarrowE, has property (P). If (P) = super (P), i.e. if a Banach space has super (P) if and only if it has (P) we call (P) a superproperty.

1999, Seán Dineen, “Polynomials”, in Complex Analysis on Infinite Dimensional Spaces (Springer Monographs in Mathematics), London: Springer, →ISBN, page 56:

(functional analysis) A property of an infinite dimensional Banach space E such that for any infinite dimensional Banach space F, F↪E, has that same property.


Tupper's self-referential formula

Defined (but not given this name) by Jeff Tupper.

(mathematics) An inequality that visually represents itself when graphed at a specific location in the (x, y) plane.


Tits group

exceptional isomorphism
exceptional isomorphism

(group theory) A finite simple group of order 2¹¹ · 3³ · 5² · 13 = 17,971,200. It is the only simple group that is a derivative of a group of Lie type that is not strictly a group of Lie type in any series due to exceptional isomorphism.


group of Lie type

group of Lie type (plural groups of Lie type)

Named for their close relationship with the (infinite) Lie groups, since a compact Lie group may be viewed as the rational points of a reductive linear algebraic group over the field of real numbers.

(group theory) Usually, a finite group that is closely related to the group of rational points of a reductive linear algebraic group with values in a finite field.


Tits building

Named after Jacques Tits, who introduced them.

(mathematics) A combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces.


Hurwiczian

en-adj

Hurwiczian (comparative more Hurwiczian, superlative most Hurwiczian)

more Hurwiczian (comparative)
most Hurwiczian (superlative)

(economics, mathematics) Of or relating to Leonid Hurwicz (1917-2008), Polish-American economist and mathematician.


Mojette transform

en-noun

Mojette transform (plural Mojette transforms)

(geometry) A discrete and exact version of the Radon transform, using only additions and subtractions, and having applications in medical tomography, cryptography, etc.


Radon transform

Radon transform (plural Radon transforms)

(mathematics) An integral transform which takes a function defined on the plane to a function defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line.


Landau's problems

Listed by Edmund Landau at the International Congress of Mathematicians in 1912.

Goldbach's conjecture
Goldbach's conjecture

twin prime conjecture
twin prime conjecture

Legendre's conjecture
Legendre's conjecture

(mathematics) Four basic unsolved problems about prime numbers: (i) is Goldbach's conjecture true?; (ii) is the twin prime conjecture true?; (iii) is Legendre's conjecture true?; (iv) are there infinitely many primes p such that p − 1 is a perfect square?


Legendre's conjecture

(number theory) A conjecture stating that there is a prime number between n² and (n+1)² for every positive integer n.


twin prime conjecture

(number theory) A conjecture stating that there are infinitely many twin primes.


Bernoulli umbra

Bernoulli umbra (plural Bernoulli umbrae)

(mathematics) In umbral calculus, a kind of umbra corresponding to the Bernoulli numbers.


Hardy field

Named after the English mathematician G. H. Hardy.

(mathematics) A field consisting of germs of real-valued functions at infinity that are closed under differentiation.


Levi-Civita field

Levi-Civita field (plural Levi-Civita fields)

(mathematics) A non-Archimedean ordered field whose every member a can be constructed as a formal series of the form a=∑_(q∈ℚ)a_qε^q, where a_q are real numbers, ℚ is the set of rational numbers, and ε is to be interpreted as a fixed positive infinitesimal.


lune of Hippocrates

lune of Hippocrates (plural lunes of Hippocrates)

(geometry) A lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.


potato paradox

potato paradox (plural potato paradoxes)

(economics): In reference to the 1845 Irish famine, when potatoes became expensive. It has been argued that poorer families, who habitually ate more potatoes, ended up having to consume even more of them, since the higher prices made it even harder to afford any other goods.

(mathematics) A calculation having a counterintuitive result: "Fred brings home 100 kg of potatoes, which consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight?" The surprising answer is 50 kg.


Quine-Putnam indispensability argument

en-prop

the Quine-Putnam indispensability argument

Named after the philosophers Willard Quine and Hilary Putnam.

(philosophy, mathematics) An argument for the existence of abstract mathematical objects such as numbers and sets, based on the fact that they are indispensable to the best scientific theories.


Suzuki group

(mathematics) Any of an infinite family of groups of Lie type, denoted by Sz(2²ⁿ⁺¹), ²B₂(2²ⁿ⁺¹), Suz(2²ⁿ⁺¹), or G(2²ⁿ⁺¹), that are simple for n ≥ 1.


midpoint theorem

A theorem stating that if the midpoints of two sides of a triangle are connected, the resulting line segment will be parallel to the third side and have half of its length.

A theorem stating that the midpoints of parallel chords in a conic are located on a common line.


hectohedron

en-noun

hectohedron (plural hectohedra or hectohedrons)

hectohedra (plural)
hectohedrons (plural)

LL-Q1860 (eng)-Flame, not lame-hectohedron.wav

For quotations using this term, see Citations:hectohedron.

(rare, geometry) A polyhedron with one hundred faces.


Moser's worm problem

Formulated by the Austrian-Canadian mathematician Leo Moser in 1966.

(geometry) An unsolved problem asking for the region of smallest area that can accommodate every plane curve of length 1, i.e. the curve can be rotated and translated to fit inside the region (which in some variations of the problem is restricted to be convex).


intercept theorem

(geometry) An important elementary theorem about the ratios of various line segments that are created if two rays with a common starting-point are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles.


moving sofa problem

(mathematics) A two-dimensional idealization of furniture-moving problems, asking for the rigid two-dimensional shape of largest area that can be maneuvered through an L-shaped planar region with legs of unit width.


sofa constant

(mathematics) The area that is the solution to the moving sofa problem.


Brocard circle

Named after Henri Brocard (1845–1922), French mathematician.

(geometry) A circle that passes through the circumcenter and symmedian of a given triangle, and is centered at the midpoint of the line segment joining them.


Bessel's correction

(statistics) The use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, where n is the number of observations in a sample. This corrects the bias in the estimation of the population variance and partially corrects the bias in the estimation of the population standard deviation, but often also increases the mean squared error in these estimations.


Japanese theorem

A theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle.


Lévy hierarchy

Zermelo-Fraenkel set theory
Zermelo-Fraenkel set theory

(set theory, logic) A hierarchy of formulas in the formal language of the Zermelo-Fraenkel set theory. Its first level contains only formulas with no unbounded quantifiers and is denoted by Δ₀=Σ₀=Π₀. Subsequent levels are given by finding a formula in prenex normal form which is provably equivalent over ZFC, and counting the number of changes of quantifiers.


few-shot

No additional prompts for getting the responses were used, i.e. the data was created with a basic prompt in a zero-shot scenario. This is in contrast to the benchmarks by OpenAI, who used an engineered prompt in a few-shot scenario to guide the generation of essays.

2023 October 30, Herbold et al., “A large-scale comparison of human-written versus ChatGPT-generated essays”, in Scientific Reports, volume 13, page 4:

(machine learning, attributive) A machine learning paradigm where a model is trained on a very small amount of data, typically less than that required for traditional machine learning approaches.


Kleene fixed-point theorem

the Kleene fixed-point theorem (canonical)

Named after American mathematician Stephen Cole Kleene.

(mathematics) Suppose (L,⊑) is a directed-complete partial order with a least element, and let f:L→L be a Scott-continuous (and therefore monotone) function. Then f has a least fixed point, which is the supremum of the ascending Kleene chain of f.


accumulated thermal unit

accumulated thermal unit (plural accumulated thermal units)

A unit of measurement describing the cumulative effect of temperature over time, such that 1 ATU is equal to 1 degree Celsius for one day.


Scott continuity

Named after the mathematician Dana Scott.

(mathematics) The property of being Scott-continuous.


Scott-continuous

partially ordered set
partially ordered set#English

(mathematics) Given two partially ordered sets P and Q, a function f: P → Q between them is Scott-continuous if it preserves all directed suprema.


Scott-open

(mathematics) Of a subset O of a partially ordered set P: such that it is an upper set and is inaccessible by directed joins, i.e. all directed sets D with supremum in O have non-empty intersection with O.


Scott topology

Scott topology (plural Scott topologies)

(mathematics) A topology on a partially ordered set, consisting of the Scott-open subsets of that set.


proompt

An alteration of prompt, possibly on the pattern of coom, influenced by the 4chan -oomer suffix for forming Wojak names and derogatory agent nouns.
In modern usage, the misspelling is deliberate, but accidental errors can be found much before the widespread adoption of AI.

It’s no wonder Proompt engineers get payed^([sic]) so much. The difference in output in ChatGPT when combined with automations can mean millions for companies.

this guy is really taking proompt engineering to the next level

We will all either become proompters or the people who create the proompt tools 😉

2023 April 13, jmeintjesn, Katalon Community:

proompt: wukong pops into xaiotian’s apartment one night as a wholesome surprise only to find him drunk because he was stressed

2023 January 13, Fics Written in the Stars, Tumblr:


proompt

en-verb

proompt (third-person singular simple present proompts, present participle proompting, simple past and past participle proompted)

proompts (present singular third-person)
proompting (participle present)
proompted (participle past)
proompted (past)

I like image proompting, but I don't always have a bot idea for every image I make.

2023 July 8, crikeymcdoodle, “CRIKEY'S COOMBOT CORNER”, in Rentry:

That’s why you proompt the AI to give you more specific ideas.

2023 May 23, foodman54, “Introducing GameIdeaGenerator: Unleash Your Creativity in Roblox!”, in Roblox Developer Forum:

"Catastrophic Forgetting" is a well researched topic in GAN and diffusion models, where the more training you perform, it "forgets" prior training: this is most visible in some of the lower quality ""finetunes"" floating around, where the model output reliably reflects a certain style, but contains very little flexibility to produce anything but standing/leaning cowboy shots of medium bust girls facing the camera. I'm not sure that this could ever be "beaten" (and if so, it would be by some research team at harvard, not some rando trying to proompt the biggest horkiest tiddies on their 3090) ..^([sic])

2023 February 8, bury_she, “Custom huge dohonkerbonkeros diffusion model v(-1) (Patreon)”, in Kemono:

(humorous, machine learning) To prompt; to write a prompt for an AI model.


Varignon parallelogram

en-noun

Varignon parallelogram (plural Varignon parallelograms)

(geometry) The parallelogram involved in Varignon's theorem, whose corners are the midpoints of the sides of an arbitrary quadrilateral.


antimedian

(graph theory) A function that maximizes the sum of distances to a set of nodes in a graph.


Budan's theorem

The theorem was published in 1807 by François Budan de Boislaurent.

(mathematics) A theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number.


VQ

vector quantization
w:Vector quantization

(signal processing) Initialism of vector quantization.


Nihilist cipher

Nihilist cipher (plural Nihilist ciphers)

The cipher was originally used by Russian Nihilists in the 1880s to organise terrorism against the tsarist regime.

(cryptography, historical) A symmetric cipher in which a Polybius square using a mixed alphabet is used to convert both the plain text and a keyword to a series of two-digit numbers, which are then summed in the normal way to get the ciphertext, with the key numbers repeated as required; (by extension) any of several improved algorithms based on this.


Wallace line

Named after William Wallace, who published the concept in 1799.


Simson line

Named after Robert Simson, though it had been published prior to his work.

(geometry) Given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P.


w.p.

(mathematics) Abbreviation of with probability.


Dunning-Krugerrand

Blend of Dunning-Kruger effect + Krugerrand.


light paper

WENN Digital, the company licensing Kodak's name to do an initial coin offering, sent emails to prospective investors Thursday with a link to a "light paper" detailing its plan for KodakCoin.

2018 March 18, Lily Katz, “Kodak's Crypto Coin Might Not Be a Security ... Or It Might Be”, in Bloomberg, New York, N.Y.: Bloomberg L.P., →ISSN, →OCLC, archived from the original on 2023-12-17:

There are many ICOs in our data sample that provide only the lightpaper version of their whitepaper. The lengthiest whitepaper in our data sample exhibits almost 300 pages, whereas the shortest one is just a single page lightpaper.

2023 March, Niranjan Sapkota, Klaus Grobys, “Fear sells: On the sentiment deceptions and fundraising success of initial coin offerings”, in Journal of International Financial Markets, Institutions and Money, volume 83, Amsterdam: Elsevier, →DOI, →ISSN, →OCLC, page 5:

(chiefly cryptocurrencies) A short white paper; a brief factual report detailing a new product or technology.


mainnet

Although 1G ~ 3G Blockchain technologies are all composed of independent mainnets, certain problems remain unresolved. For example, at present, information or data generated by each Blockchain cannot be exchanged with another Blockchain as mentioned earlier, and some immediate problems should be addressed to ensure a safer and more efficient exchange of data between the Blockchain platforms.

2020 October 27, Seong-Kyu Kim, Jun-Ho Huh, “Autochain platform: expert automatic algorithm Blockchain technology for house rental dApp image application model”, in EURASIP Journal on Image and Video Processing, volume 47, Berlin, Heidelberg: SpringerOpen, →DOI, →ISSN, →OCLC, page 2:

(cryptocurrencies) A large and established network of servers able to facilitate cryptocurrency transactions.


testnet

Though realistic experimental setups such as testnets aim to address these challenges to a degree, properly testing and evaluating such systems remains a challenging endeavour.

2023, Martijn de Vos, Georgy Ishmaev, Johan Pouwelse, Stefanie Roos, “A Deployment-First Methodology to Mechanism Design and Refinement in Distributed Systems”, in 2023 IEEE International Conference on Pervasive Computing and Communications Workshops and other Affiliated Events (PerCom Workshops), Atlanta, G.A.: IEEE, →DOI, →ISBN, page 472, column 1:

(cryptocurrencies) A network of servers able to facilitate cryptocurrency transactions, created for the purpose of testing or experimentation.


Pisano period

Named after Leonardo Bigollo Pisano a.k.a. Fibonacci (c. 1170 – c. 1240–1250).

(number theory) The period (of repetition) of the sequence of Fibonacci numbers reduced modulo a given natural number (≥1); it can be considered to be a function π(n) where n is the modulus of reduction (see modular arithmetic) and the function returns the period (of the reduced Fibonacci sequence) corresponding to that given modulus.


lemniscate of Gerono

en-noun

lemniscate of Gerono (plural lemniscates of Gerono)

(mathematics) A Lissajous curve in which one axis vibrates twice as fast as the other, producing a curve which crosses itself in the middle.


AFSOC

(mathematics) Initialism of assume for sake of contradiction.


incorporated place

incorporated place (plural incorporated places)

Coordinate term: unincorporated place

(US, demography) A type of governmental area incorporated under state law and having legally prescribed powers and functions.


rheonomy

Attributed to Boltzmann. By surface analysis, rheo- + -nomy.

(mathematics, sciences, uncommon) The state of a mechanical system whose whose equations of constraints contain time as an explicit variable.


scleronomy

(mathematics, very rare) A mechanical system whose constraint equations do not explicitly contain or are not dependent upon time.


quadratize

en-verb

quadratize (third-person singular simple present quadratizes, present participle quadratizing, simple past and past participle quadratized)

quadratizes (present singular third-person)
quadratizing (participle present)
quadratized (participle past)
quadratized (past)

(mathematics) To approximate a system with a quadratic system.


quadratization

From quadratic + -ization or quadratize + -ation.

(mathematics) An approximation of a system obtained by quadratizing it.


subproper

An object can have several subproper centers or none at all. Figure 2 shows the proper center and some subproper centers for the letter E.

1987, Journal of the Optical Society of America, page 1795:

The author establishes some basic properties and two surjectivity theorems for subproper operators.

1988, Reviews in Global Analysis, 1980-86, page 344:

Obviously, each perfect mapping is a proper mapping, each proper mapping is a subproper mapping and each subproper mapping is a compact-covering mapping.

2016, Shou Lin, Ziqiu Yun, Generalized Metric Spaces and Mappings, page 101:

(mathematics) Having some of the key characteristics of the proper property (which ones depend on the type of proper property).


Wiener-Hopf method

Developed by Norbert Wiener and Eberhard Hopf.

partial differential equation
partial differential equation

(mathematics) A technique for solving systems of integral equations, with wider use in solving two-dimensional partial differential equations with mixed boundary conditions on the same boundary. It works by exploiting the complex-analytical properties of transformed functions.


Lindley equation

Introduced by English statistician Dennis Lindley.

(probability theory) A discrete-time stochastic process Aₙ where n takes integer values and A_(n + 1) = max(0, Aₙ + Bₙ). It is useful in queueing theory.


Abel's irreducibility theorem

(mathematics) A field theory result asserting that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x).


Abel's theorem

(mathematics, algebra) A theorem that relates a limit of a power series to the sum of its coefficients.


Abel's identity

ordinary differential equation
ordinary differential equation

differential equation
differential equation

(mathematics) An equation expressing the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation.


Abel's formula

(mathematics) Synonym of Abel's identity


Liouville's formula

Named after the French mathematician Joseph Liouville.

(mathematics) An equation, a generalization of Abel's identity, that expresses the determinant of a square-matrix solution of a first-order system of homogeneous linear differential equations in terms of the sum of the diagonal coefficients of the system.


Abel-Jacobi-Liouville identity

the Abel-Jacobi-Liouville identity (canonical)

Liouville's formula
Liouville's formula#English

(mathematics) Synonym of Liouville's formula


Abel's summation formula

analytic number theory
analytic number theory

(mathematics) A formula used in analytic number theory and the study of special functions to compute series.


Abel-Jacobi map

en-noun

Abel-Jacobi map (plural Abel-Jacobi maps)

(mathematics) A construction of algebraic geometry that relates an algebraic curve to its Jacobian variety.


Abel-Plana formula

Discovered independently by Niels Henrik Abel (1823) and Giovanni Antonio Amedeo Plana (1820).

(mathematics) A summation formula stating that ∑ₙ₌₀ ᪲f(a+n)=∫ₐ ᪲f(x)dx+(f(a))/2+∫₀ ᪲(f(a-ix)-f(a+ix))/(i(e^(2πx)-1))dx.


folium of Descartes

(geometry) An algebraic curve defined by the implicit equation x³+y³-3axy=0.


pseudoform

LL-Q1860 (eng)-Flame, not lame-pseudoform.wav

(mathematics) A pseudodifferential form.


dynamic inconsistency

(economics, game theory) A situation in which a decision maker's preferences change over time in such a way that a preference can become inconsistent at another point in time.


computational humor

computational linguistics
computational linguistics

artificial intelligence
artificial intelligence

(computational linguistics) A field within computational linguistics and artificial intelligence that leverages computers for research on humor.


time derivative

time derivative (plural time derivatives)

(mathematics, calculus) A derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function.


block time

block time (countable and uncountable, plural block times)

(cryptocurrencies) The average time it takes for the network to generate one extra block in the blockchain.


Briggs logarithm

Briggs logarithm (plural Briggs logarithms)

After Henry Briggs (mathematician), English mathematician who pioneered its use.

common logarithm
common logarithm#English

(mathematics) Synonym of common logarithm


foundation model

foundation model (plural foundation models)

(computational linguistics) An AI model trained on comprehensive data, enabling its application across various use cases such as chatbots and generative AI.


generation time

generation time (plural generation times)

(demography) The average time between two consecutive generations in the lineages of a population.


randomized polynomial time

randomized polynomial time (countable and uncountable, plural randomized polynomial times)

(mathematics, computer science) The complexity class of problems for which a probabilistic Turing machine exists with certain properties.


time hierarchy theorem

(mathematics, computer science) A theorem that demonstrates that allowing Turing machines additional computation time strictly increases the class of languages that they can decide.


semiperfect number

semiperfect number (plural semiperfect numbers)

(mathematics) A number which is the sum of some, or all, of its proper divisors.


proper divisor

20 is a divisor of 20 itself, but not a proper divisor.

(mathematics) A divisor of a number which is not the number itself.


pseudoperfect

en-adj

pseudoperfect (comparative more pseudoperfect, superlative most pseudoperfect)

more pseudoperfect (comparative)
most pseudoperfect (superlative)

The number 18 is pseudoperfect, because 3 + 6 + 9 = 18.

(mathematics) Of a number, having proper divisors, some or all of which sum to the number itself.


forty weepy weepy

From a message whose plaintext began fortyweepyyweepy: German fort (“forth”), short for Fortsetzung (“continuation”) + weep, typewriter code for 23:30, the time of the previous message. Enigma machines had no number keys, so the letter y marked the letters to be interpreted as numbers.

(cryptography, historical) Cryptanalysis of an Enigma message which was a continuation of a previous message sent at a known time.


spatial computing

Apple insists that its $3,500 Vision Pro ski goggles, which officially debuted Friday, is not virtual reality but “spatial computing.” One problem: No one agrees on the definition of spatial computing. Ask 10 people in technology and you might get 12 different answers. What Apple calls a spatial computer, some technologists call “mixed reality” — or possibly “augmented reality,” “holographic computing,” “the metaverse” or “XR,” which some people say is shorthand for “extended reality.” […] “Even I can’t get my head on straight of what things mean all of the time,” said Alex Coulombe, co-founder of Agile Lens, which calls itself an XR company. Coulombe started to tell me that spatial computing and XR are the same — but changed his mind midsentence. […] What is spatial computing, anyway? I’m going to define it as an immersive video feed of the physical world plus the internet. […] Some experts instead use spatial computing as a catchall term for a range of technologies, including 3D images, virtual reality and smartphone games such as “Pokémon Go.”

2024 February 2, Shira Ovide, “Apple's Vision Pro is 'spatial computing.' Nobody knows what it means”, in Washington Post, retrieved 2024-02-02:

extended reality
extended reality#English


passive attack

(cryptography) An attack in which the cryptanalyst cannot interact with any of the parties involved, attempting to break the system solely based upon observed data such as ciphertext.


fuzzyism

(mathematics, rare) Of a state or condition pertaining to fuzzy math.


pyramidoidal

pyramidoidal (comparative more pyramidoidal, superlative most pyramidoidal)

more pyramidoidal (comparative)
most pyramidoidal (superlative)

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Cohen-Macaulay

Named for Irvin Cohen and Francis Sowerby Macaulay, who proved unmixedness results for specific classes of rings, which Cohen-Macaulay rings generalize.

(commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension.

(commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself.

(commutative algebra, of a module M over a noetherian ring) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.

(commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself.


spatial computer

en-noun

spatial computer (plural spatial computers)

Any of various devices that enable or are planned to enable spatial computing, including wearables (e.g., headsets, glasses, wristwatches), implants within the human body, and embeds within infrastructure.


Krull dimension

Named for Wolfgang Krull, for his work on the height of finitely generated ideals of noetherian rings. The term dimension is from the correspondence between the geometric dimension of an affine variety and the Krull dimension of its coordinate ring.

(commutative algebra, of a commutative ring) The supremum of the lengths of all chains of prime ideals.


codepth

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(commutative algebra, of a finitely generated module over a local ring) The Krull dimension minus the depth.


rocket equation

The equation for how much delta-v a rocket produces: Δv = vₑ ln(m₀/m₁); where Δv is delta-v, vₑ is effective exhaust velocity, ln is the natural log function, m₀ is initial mass of the rocket, and m₁ is final mass of the rocket.


Chebyshev's bias

The phenomenon that most of the time, there are more prime numbers of the form 4k + 3 than of the form 4k + 1 up to n.

The phenomenon that if a is a quadratic residue modulo q and b is a quadratic nonresidue modulo q, then π(x;b,q)>π(x;a,q) occurs more often than not


discrete time

discrete time (countable and uncountable, plural discrete times)

Coordinate term: continuous time

(mathematics, mathematical dynamics) A framework which views values of variables as occurring at distinct, separate points in time, or equivalently as being unchanged throughout each nonzero region of time.


continuous time

continuous time (countable and uncountable, plural continuous times)

Coordinate term: discrete time

(mathematics, mathematical dynamics) A framework which views variables as having a particular value only for an infinitesimally short amount of time.


integrally closed

(commutative algebra, of an integral domain) Equal to its own integral closure in its field of fractions; equivalently, containing all integral elements of its field of fractions.


scaled copy

(design, mathematics) A copy of a figure in which every length in the original is multiplied by the same scale factor.


Turing instability

(biology, mathematics) The property of a nonlinear reaction-diffusion system in which a steady state that is stable in the corresponding nonspatial system is able to, under certain parameter constraints, become unstable in the spatial system containing a particular wavelength.


Buffon's needle problem

(mathematics, probability theory) An experiment that determines the probability that a needle, when dropped, will lie across a line between two parallel strips of wood, each of the same width; often used used to estimate π.


SNN

spiking neural network
spiking neural network#English

(machine learning) Initialism of spiking neural network.


Stone-Weierstrass theorem

the Stone-Weierstrass theorem (canonical)

Named after Marshall H. Stone and Karl Weierstrass.

Weierstrass approximation theorem
Weierstrass approximation theorem

(mathematics) A generalization of the Weierstrass approximation theorem.


computational complexity theory

computational complexity theory (countable and uncountable, plural computational complexity theories)

computational complexity theories (plural)

(mathematics, computer science) A theory focusing on classifying computational problems according to their resource usage, and relating these classes to each other.


Weierstrass point

Weierstrass point (plural Weierstrass points)

Riemann-Roch theorem
Riemann-Roch theorem

(mathematics) A point P on a nonsingular algebraic curve C defined over the complex numbers, such that there are more functions on C, with their poles restricted to P only, than would be predicted by the Riemann-Roch theorem.


Weierstrass gap

Weierstrass gap (plural Weierstrass gaps)

(mathematics) Given a Weierstrass point P, a value of k such that no function on C has exactly a k-fold pole at P only.


SOFM

self-organizing feature map
self-organizing feature map#English

(machine learning) Initialism of self-organizing feature map.


Kohonen map

Introduced by the Finnish professor Teuvo Kohonen in the 1980s.

self-organizing map
self-organizing map#English

(machine learning) Synonym of self-organizing map


Kohonen network

Kohonen network (plural Kohonen networks)


self-organizing map

self-organizing map (plural self-organizing maps)

(machine learning) A kind of artificial neural network trained using competitive learning rather than error correction, and producing a low-dimensional (typically two-dimensional) representation of a higher-dimensional data set while preserving the topological structure of the data.


shoelace formula

So called because the constant cross-multiplying for the coordinates making up the polygon is analogous to the threading of shoelaces.

Cartesian coordinate
Cartesian coordinate

(mathematics) An algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane.


surveyor's formula

shoelace formula
shoelace formula#English

(mathematics) Synonym of shoelace formula


Conway criterion

Named for the English mathematician John Horton Conway.

(mathematics) A rule for determining whether a prototile will tile the plane.


GMAC

Galois Message Authentication Code
w:Galois Message Authentication Code

(cryptography) Acronym of Galois Message Authentication Code.


time evolution

time evolution (countable and uncountable, plural time evolutions)

(mathematics, physics) The change of state caused by the passage of time, applicable to systems with an internal state.


Moufang plane

(geometry) A type of projective plane whose every line is a translation line.


Pappus's hexagon theorem

Attributed to the Ancient Greek mathematician Pappus of Alexandria (c. 290–c. 350 AD).

(geometry) A theorem valid for projective planes over any field, stating that, given one set of collinear points A,B,C, and another set of collinear points a,b,c,, the intersection points X,Y,Z of line pairs Ab and aB,Ac and aC,Bc and bC are collinear, lying on the "Pappus line". These three points are the points of intersection of the "opposite" sides of the hexagon AbCaBc.


Chatty G

/t͡ʃætiː ˈd͡ʒiː/

Clipping of ChatGPT (separated into two words) + -y.

Generative AI is advancing at a fast pace and quickly finding a place within education. Tools such as ChatGPT (or Chatty G as the kids say) continue to dominate conversations in education as these technologies are explored and developed.

[2024 February 5, Tamika Worrell, “Generative AI in the classroom risks further threatening Indigenous inclusion in schools”, in The Conversation, archived from the original on 2024-02-09:


prompt crafting

Apparently appeared at about the same time as prompt engineering, the two terms being interchangeable.

Guiding students in assessing AI-generated content instills discernment, while prompt crafting elicits original thinking.

2022, Sean Doyle, “Chapter 6: Augmenting Intelligence with Generative AI”, in Julia Nyberg, Jessica A. Manzone, editors, Practices That Promote Innovation for Talented Students, IGI Global, page 139:

2022, M. L. Ronn, Indie Author Confidential 11: Secrets No One Will Tell You About Being a Writer, Author Level Up, unnumbered page,
Non-artists don't want to go through the trouble of learning the nuances of prompt crafting, so they will rely on other people to do it, creating a new cottage industry […] .

2023, Jason Brownlee, Adrian Tam, Matthew Mayo, Abid Ali Awan, Kanwal Mehreen, Maximizing Productivity with ChatGPT, MachineLearningMastery.com, eBook, page 33,
One way to improve your prompt crafting is to get ChatGPT involved.

When GPT-4 was tested by medical experts from Microsoft without any specialized prompt crafting, it exceeded the passing score on USMLE by over 20 points and outperformed earlier general-purpose models (GPT-3.5) as well as models specifically fine-tuned on medical knowledge (Med-PaLM, a prompt-tuned version of Flan-PaLM 540B) [13].

2023, Aravind Kumaresan, Lorna Udan, Shazad Ashaf, “Potential Role of ChatGPT in Healthcare in the Prevention and Management of Non-communicable Diseases”, in Lorna Uden, I-Hsien Ting, editors, Knowledge Management in Organisations: 17th International Conference, KMO 2023, Proceedings, Springer, page 432:

prompt engineering
prompt engineering#English

(artificial intelligence, technology, neologism) Synonym of prompt engineering


negaternary

(mathematics) In the base of negative 3.


negaquaternary

(mathematics) In the base of negative 4.


myriahedron

myriahedron (plural myriahedrons or myriahedra)

myriahedrons (plural)
myriahedra (plural)

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For quotations using this term, see Citations:myriahedron.

(geometry) A polyhedron with 10,000 faces.


uniformizing parameter

uniformizing parameter (plural uniformizing parameters)

(commutative algebra) An element of a discrete valuation ring which generates the unique maximal ideal.


tesseracted

(mathematics, uncommon) Raised to the fourth power.


hitting time

hitting time (countable and uncountable, plural hitting times)

(mathematics, stochastic process) The first moment in time in which a given process "hits" a given subset of the state space.


first exit time

first exit time (countable and uncountable, plural first exit times)

(mathematics, stochastic process) From A, the first hit time for S \ A, the complement of A in S.


first return time

first return time (countable and uncountable, plural first return times)

(mathematics, stochastic process)The first hit time for the singleton set {X₀(ω)}, which is usually a given deterministic element of the state space, such as the origin of the coordinate system.


Ramseyan

en-adj

Ramseyan (comparative more Ramseyan, superlative most Ramseyan)

more Ramseyan (comparative)
most Ramseyan (superlative)

Ramseyan taxation

(economics, mathematics, philosophy) Of or relating to Frank Ramsey (1903-1930), British economist, mathematician, and philosopher.


kisrhombille

(geometry, rare) A uniform tiling of rhombic faces divided by central points into four triangles.


undecahedron

en-noun

undecahedron (plural undecahedrons or undecahedra)

undecahedrons (plural)
undecahedra (plural)

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(geometry) A polyhedron with eleven faces.


hexagonal number

hexagonal number (plural hexagonal numbers)

(mathematics) The number of dots in a figure made up of partially overlapping dotted regular hexagons (6k dots arranged into a regular hexagon) of perimeter 6k for k = 1 ... n which grow out of a common vertex (and two shared or partially shared sides); a.k.a. “cornered hexagonal number”; H_n+1=6Δₙ-n²+1 where Δₙ denotes the nᵗʰ triangular number.

(mathematics) The number of dots in a figure made up of regular dotted hexagons (of perimeter 6k for k = 1 ... n) arranged concentrically around an extra dot at their common center; a.k.a. “centered hexagonal number”; H_n+1=1+6Δₙ.


trivariant

independent variable
independent variable

(mathematics) Having three independent variables.


Achilles number

Achilles number (plural Achilles numbers)

Coined by Henry Bottomley after Achilles, a hero of the Trojan War.

(mathematics) An integer that is a powerful number but not a perfect power.


pentacontahedron

pentacontahedron (plural pentacontahedrons or pentacontahedra)

pentacontahedrons (plural)
pentacontahedra (plural)

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From Ancient Greek πεντήκοντα (pentḗkonta) + -hedron.

suffix

(geometry) A polyhedron with fifty faces.


zequals

Coined in 2013 by English author Rob Eastaway, from equals. Eastaway wrote that "the Z is for Zeroes, and also for the ZigZagness of the symbol".

Zequals is a fun way of ruthlessly rounding numbers so that every number you deal with becomes simple. Using Zequals, whenever you encounter a number, you immediately round it to a single digit followed by zeroes (if it's bigger than ten).

2016, Rob Eastaway, Mike Askew, Maths on the Go: 101 Fun Ways to Play with Maths, page 31:

(mathematics, rare) A technique for simplifying mental approximations by reducing each number to one significant figure followed by zeroes.


zequals

Using Zequals, whenever you encounter a number, you immediately round it to a single digit followed by zeroes (if it's bigger than ten). So for example: 18 zequals 20. 142 zequals 100. 2.3 zequals 2.

(mathematics, rare) Is equal to, after performing such a reduction.


powerful number

en-noun

powerful number (plural powerful numbers)

(mathematics) A positive integer m such that for every prime number p dividing m, p² also divides m. Equivalently, it is the product of a square and a cube.


squareful

(mathematics) Synonym of powerful (“being a powerful number”)


equinormality

(statistics) Having a normal distribution and equal variance.


connecting homomorphism

connecting homomorphism (plural connecting homomorphisms)

(homological algebra) The homomorphism constructed by the snake lemma, leading to a particular exact sequence of kernels and cokernels.

(algebraic topology) Such a homomorphism in the context of exact sequences of chain complexes, leading to a long exact sequence of homology groups.


Napier's constant

Named after Scottish landowner, mathematician, physicist, and astronomer John Napier (1550–1617), who did, however, not discover it, although natural logarithms (discovered by him) have this number as their base.


monohedron

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This is a reflection of the fact that the monohedron collapses asymptotically to a line (along the w₁-axis) when T -> Tₜ (t -> 0) (Widom, 1975c).

1972, Cyril Domb, M. S. Green, Joel Louis Lebowitz, Phase Transitions and Critical Phenomena - Volume 9, page 112:

(geometry) A solid figure with a single continuous surface (face) and no edges, such as a torus or spheroid.


ladder operator

ladder operator (plural ladder operators)

(linear algebra) An operator that either increases or decreases the eigenvalue of another operator.


skeletoid

By proposition 6.5.4, X is a skeletoid and hence an absorber by theorem 6.5.1.

1988, J. van Mill, Infinite-Dimensional Topology: Prerequisites and Introduction, page 285:

Skeletoids and absorbers play an important role in infinite-dimensional topology. The existence and uniqueness of skeletoids (and absorbers) with respect to certain collections allow ^([sic]) one to study completely metrizable infinite-dimensional manifolds by using the technique of compact manifolds, incomplete manifolds by those of complete ones and so on.

2020, Howard Cook, Continua: With the Houston Problem Book, page 70:

(topology) A structure that captures the essential topological information of a space.


mixed alphabet

(cryptography) The mapping from plaintext to ciphertext characters in a substitution cipher, when it is not merely a shift or reversal but an arbitrary reordering.


silver ratio

(geometry) The irrational number (approximately 2.414), which is equal to the sum of its own reciprocal and two. It equals one plus the square root of two (1 + √).


search space

(mathematics, computing) The set of all possible points of an optimization problem that satisfy the problem's targets or goals.


anchoring effect

anchoring effect (plural anchoring effects)

A psychological phenomenon wherein a previous appraisal has its range determined by communication of a previous reference point.


squaregraph

(graph theory) a type of undirected graph that can be drawn in the plane in such a way that every bounded face is a quadrilateral and every vertex with three or fewer neighbors is incident to an unbounded face.


duocylindrical

en-adj

duocylindrical (comparative more duocylindrical, superlative most duocylindrical)

more duocylindrical (comparative)
most duocylindrical (superlative)

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(geometry) Of or pertaining to a 4-dimensional object having the shape of a duocylinder.


vicious circle principle

the vicious circle principle (canonical)

(mathematics) The rule (no longer widely accepted) that no mathematical object or property may be introduced by a definition that depends on the object or property itself.


time term

(mathematics, physics) A term of an equation in which the main variable is time (symbolized as t).


head

From each word's initial letter forming SOHCAHTOA.

Another high school teacher told me that he uses a similar acrostic, but his is as follows: Some Old Hippie Caught Another Hippie Tripping On Acid.

2003 March 5, “Mnemonic Devices” (chapter 9), in Marcia L. Tate, editor, Worksheets Don't Grow Dendrites, SAGE Publications, →ISBN, archived from the original on 2024-03-20, page 93:

"It's easier with a mnemonic," Molly says. "Like… Some Old Hippie Caught Another Hippie Tripping On Acid—"

2015 December 1, Eric Lindstrom, chapter 23, in Not If I See You First, Little, Brown Books For Young Readers, →ISBN, archived from the original on 2024-03-19:

[…] I thought my mastery of sines, cosines, and tangents—Some Old Hippie Caught Another Hippie Tripping On Acid—might elevate me to another level of intellectual superiority in my high school; […]

2022 September, Jill Christman, “The Googly Eye”, in If This Were Fiction, archived from the original on 2024-03-20, page 92:

trigonometric function
trigonometric function#English

(trigonometry, humorous) A mnemonic used to help people remember the different trigonometric functions: sine is opposite over hypotenuse; cosine is adjacent over hypotenuse; and tangent is opposite over adjacent.


tricategorical

(mathematics) Of or pertaining to a tricategory.


scalar-valued

Consider the set of Riemann-integrable functions on #91;a,b#93; as a vector space over #92;mathbb#58;Template#58;R, where addition and scaling is defined pointwise. Then #92;int#95;aᵇ is a scalar-valued function.

mathematical analysis
mathematical analysis

(mathematical analysis, of a function on a vector space V over a field K) Taking values in K; having codomain K.


faithfully flat

(algebraic geometry, of a morphism of schemes) Flat and surjective.


one-size-fits-most

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Synonym of one-size-fits-all (“designed to be worn with comfort by people with a wide range of sizes”).


sheaf theory

en-noun

sheaf theory (countable and uncountable, plural sheaf theories)

(mathematics, uncountable) That field of modern mathematics that studies sheaves (“abstract constructs in topology”).


IPD

IPD (countable and uncountable, plural IPDs)

iterated prisoner's dilemma
iterated prisoner's dilemma#English

(game theory) Initialism of iterated prisoner's dilemma.

(statistics) Initialism of individual participant data.


distinguished open set

distinguished open set (plural distinguished open sets)

(algebraic geometry) A particularly basic kind of set, generalizing the notion of the compliment of a hypersurface, originating in the study of algebraic varieties but in modern mathematics also extending to the setting of affine schemes. Formally: (in the context of affine or projective varieties) the compliment of the zero locus of a polynomial in affine or projective space; (in scheme theory) the subset of prime ideals of a commutative ring which do not contain some element of the ring.


zero locus

(algebraic geometry, of a polynomial, or, more generally, a function) The set of points (usually in affine or projective space, but more generally in the domain of the function) where the given polynomial (or function) takes the value zero.


vanishing locus

(algebraic geometry) Synonym of zero locus.


affine scheme

locally ringed space
locally ringed space

(algebraic geometry) An abstract, geometric object in mathematics which generalizes the notion of an affine variety qua domain of a commutative ring of polynomial functions: a space which is the result of a particular construction beginning with an arbitrary commutative ring whereby elements of the ring can be thought of as functions on the space; a space which can be constructed in such a way. Formally: the spectrum of a commutative ring; a locally ringed space isomorphic to the spectrum of a commutative ring.


structure sheaf

structure sheaf (plural structure sheaves)

(sheaf theory, algebraic geometry) The sheaf associated to a ringed space.


finitely generated

From the study of generators. The motivation for calling topologies satisfying sense 1.5 "finitely generated" is that any topology satisfies sense 1.5 if and only if it is coherent with its finite subspaces. Thus, metaphorically, it is "generated" by them. The category-theoretic senses were created to generalize those of abstract algebra, and so were named identically.

(algebra) In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

(most generally, category theory, of an object X in a locally small category 𝒞 that admits filtered colimits of monomorphism) Such that the functor operatorname Hom_( mathcal )C(X,·) preserves those filtered colimits of monomorphisms.

(less generally, but still covering most cases outside pure category theory, of an object X in a concrete category) Being a quotient object of a free object over a finite set, i.e. being the target of a regular epimorphism from an object which is free on a finite set.

less generally; but still covering most cases outside pure category theory; less generally; but still covering most cases outside pure category theory

(abstract algebra, of a group-like structure: a group, module, ring, monoid, etc.) Having a finite set of generators, i.e. having a finite set of elements from which all other elements can be created in finitely many steps under the permitted operations (viz. the group operation for groups, addition and scalar multiplication for modules, addition and multiplication for rings, etc.)

(ring theory, of a (left) ideal in a ring R) Finitely generated as a (left) module over R.

(of a space) Equipped with an Alexandrov topology (i.e. one where the intersection of every family of open sets is open).


locally small

(category theory, of a category) Such that the hom class between any two objects is a set (and not a proper class).


hom class

(category theory) A (possibly empty) class composed of the morphisms from A to B, where A and B are objects in some category, denoted operatorname Hom(A,B).


B-sheaf

(sheaf theory, algebraic geometry) A kind of partial, simpler to describe sheaf which can be extended into a sheaf (and which is, in a technical sense, equivalent to that sheaf). For a formal definition, see B-sheaf on Wikipedia.Wikipedia.


approximation theory

(mathematics) The study of how functions can best be approximated with simpler functions, and how the errors introduced in this way can be quantitatively characterized.


quasi-isomorphism

(homological algebra, of a (co)chain map) Which induces isomorphisms of the (co)homology groups.


formal sum

(mathematics) An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.

(algebra) An element of a free abelian group or vector space regarded as a sum of basis elements.

(of a series) A sum of an infinite sequence of numbers considered as an indeterminate object, in the sense of being subject to certain algebraic manipulations but not necessarily convergent.


associated prime

associated prime (plural associated primes)

(algebra, of a module M over a ring R) A ideal of R which is the annihilator of some prime submodule of M.

(commutative algebra) If the ring R is commutative, equivalently: A prime ideal of R which is the annihilator of some element of M.


endorelation

(mathematics, order theory) A binary relation between a set and itself.


model theory

(mathematics) The study of the relationship between formal theories and their models.


semiset

(set theory) In set theory, a semiset is a proper class that is a subclass of a set.


trajectoid

/tɹəˈd͡ʒɛk.tɔɪd/

Here, we develop an algorithm to design such bodies—which we call ‘trajectoids’—and then validate these designs experimentally by three-dimensionally printing the computed shapes and tracking their rolling paths, including those that close onto themselves such that the body’s centre of mass moves intermittently uphill.

2023, Sobolev, Y.I.Dong, R.Tlusty, Tet al., “Solid-body trajectoids shaped to roll along desired pathways”, in Nature, volume 620, pages 310–315:

(mathematics) A solid shape that traces a periodic trajectory when rolled down a slope.


induction hypothesis

induction hypothesis (plural induction hypotheses)

(mathematics) A statement which might be true for any natural number. In mathematical induction, such a statement is proven true for all natural numbers by first proving it for the base case and then proving that each case implies the next.


inductive hypothesis

inductive hypothesis (plural inductive hypotheses)

induction hypothesis
induction hypothesis#English

(mathematics) Synonym of induction hypothesis


prime subring

The image of the homomorphism ℤ→ R is called the prime subring of R. Clearly ch(R) = 0 ⟷ the prime subring of R is isomorphic to ℤ.

2006, Shreeram Shankar Abhyankar, The Algebraic Structure of Crossed Products, World Scientific, page 21:

The image of the morphism f_A is the prime subring of A. The prime subring is either isomorphic to the ring ℤ or isomorphic to the ring ℤ/nℤ for some n > 0.

2013, Michel Broué, Some Topics in Algebra: An Advanced Undergraduate Course at PKU, Springer Science & Business Media, page 10:

(algebra, ring theory, of a (unital) ring R) The image of the natural homomorphism from ℤ into R, which is the unique homomorphism mapping 1_ℤ to 1_R. Equivalently, the intersection of all subrings of R.


lower bound

Coordinate term: upper bound

(mathematics) A value that is less than or equal to every element of a given set of values.

lower boundary lower bound upper boundary


upper bound

Coordinate term: lower bound

(mathematics) A value that is greater than or equal to every element of a given set of values.

upper boundary upper bound lower boundary


Bézout domain

So-called because such domains satisfy Bézout's identity, in turn named after Étienne Bézout.

(algebra, ring theory) An integral domain in which the sum of two principal ideals is also a principal ideal.


lie above

en-verb

lie above (third-person singular simple present lies above, present participle lying above, simple past lay above, past participle lain above)

lies above (present singular third-person)
lying above (participle present)
lay above (past)
lain above (participle past)

If p₁, p ∈ Spec(A) with p₁ ⊂ p, and if q₁ ∈ Spec(B) lies above p₁, then there exists q ∈ Spec(B) which lies above p and such that q₁ ⊂ q.

2007, Meinolf Geck, Group Representation Theory, EPFL Press, page 199:

(algebra, ring theory) Synonym of lie over.


discrete valuation ring

en-noun

discrete valuation ring (plural discrete valuation rings)

principal ideal domain
principal ideal domain

(algebra, ring theory) A local principal ideal domain whose unique maximal ideal is not the zero ideal.


zero ideal

(algebra, ring theory, of a ring) The ideal containing only the element zero.


comaximal

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Two proper ideals I and J of R are said to be comaximal (or I is comaximal to J) if I + J = R.

2001, László Fuchs, Luigi Salce, Modules over Non-Noetherian Domains, American Mathematical Society, page 3:

(algebra, ring theory, of two ideals) Synonym of coprime.


Lambert W function

Lambert W function (plural Lambert W functions)

Named after Johann Lambert, who considered a related problem in 1758.

exponential function
exponential function

(mathematics) A multivalued function, namely the branches of the converse relation of the function f(w) = weʷ, where w is any complex number and eʷ is the exponential function.


sequentially compact

(topology, of a topological space) Such that every sequence in the space has a convergent subsequence. In a metric space, this is equivalent to being compact (sense 4.1).

jonokompakti

topology: every sequence in the space has a convergent subsequence


password wallet

password wallet (plural password wallets)

I believe Mozilla 5 (to be released as Netscape 6) also has a password "wallet" feature. Not sure about other vendors.

2000 March 16, Peter W, “allowing directory access for authorized users”, in comp.infosystems.www.servers.unix (Usenet):

Instead, the individual passwords are generated algorithmically from the master password and the sites’ names. As an advantage compared with a password wallet, nothing at all needs to be stored on the client machines. As a disadvantage, there is no easy way to change the master password.

2007, Max Hailperin, Operating Systems and Middleware: Supporting Controlled Interaction, Thomson Course Technology, page 405:

The two main things to remember with a password wallet is to have a very secure unique password or passphrase to access the wallet, and keep a secure record of the password or passphrase,[…]

2017, Graham Day, Security in the Digital World: For the home user, parent, consumer and home office, Walter de Gruyter GmbH, page 111:

He showed Gemma the files to read and unlocked his password wallet. "The password wallet isn't very secure." "More secure than my physical diary which I'm sure has been checked.[…]"

2017, Ray McCarthy, The Solar Alliance, Corvids Press, page 154:

The user must have access to the password wallet whenever she needs a password.

2018, Matt Bishop, Computer Security: Art and Science, Pearson Education, page 523:

In this section, we adapt our OTP wallet construction to the proof-of-stake setting (the password wallet can also be adapted likewise).

2023, Shin'ichiro Matsuo, Lewis Gudgeon, Ariah Klages-Mundt, Daniel Perez Hernandez, Sam Werner, Thomas Haines, Aleksander Essex, Andrea Bracciali, Massimiliano Sala, editors, Financial Cryptography and Data Security. FC 2022 International Workshops: CoDecFin, DeFi, Voting, WTSC, Grenada, May 6, 2022, Revised Selected Papers, Springer International Publishing, page 632:

(computing, cryptography) An application or mechanism which stores someone's passwords by encryption.


RLAIF

Coined by American artificial intelligence company Anthropic in 2022.

coinage

Reinforcement learning from human feedback (RLHF) has proven effective in aligning large language models (LLMs) with human preferences. However, gathering high-quality human preference labels can be a time-consuming and expensive endeavor. RL from AI Feedback (RLAIF), introduced by Bai et al., offers a promising alternative that leverages a powerful off-the-shelf LLM to generate preferences in lieu of human annotators.

2023, “RLAIF: Scaling Reinforcement Learning from Human Feedback with AI Feedback”, in Arxiv:

a prime hurdle lies in gathering high-quality human preference labels. This is where reinforcement learning from human feedback with AI feedback (RLAIF) comes into the picture, a novel framework by Google Research to train models with reduced reliance on human intervention.

2023 October 6, Tasmia Ansari, “Reinforcement Learning Craves Less Human, More AI”, in Analytics India Magazine:

reinforcement learning
reinforcement learning#English

(machine learning) Initialism of reinforcement learning from AI feedback.


fade time

en-noun

fade time (countable and uncountable, plural fade times)

The annual fade time is three times that occurring in a heavy fading month when the climate is average.

2006, Roger L. Freeman, Radio System Design for Telecommunications, page 31:

The fractional fade time (also called the probability of fade) describes the percentage of time the irradiance of the received wave is below some given threshold value.

2014, Arun K. Majumdar, Advanced Free Space Optics (FSO): A Systems Approach:

The mean fade time decreases with increasing elevation and fade threshold.

2016, Murat Uysal, Carlo Capsoni, Zabih Ghassemlooy, Optical Wireless Communications: An Emerging Technology, page 95:

Figure 4.12 of [8] shows that on the same path from which the data in Fig. 4.11 of [8] was derived, for fade depth deeper than about 20 dB, the fade time decreases by a factor of about 10 for a 10 dB increase in fade depth.

2021, Douglas H Morais, 5G and Beyond Wireless Transport Technologies, page 62:

(signal processing) The time during which a wireless signal is too faint to be accurately received.


GFT

GFT (countable and uncountable, plural GFTs)

From Atari's official website and blog, coined in 2022.

A GFT is a surprise, limited edition, gift-wrapped NFTs designed to delight – on any occasion.

2022 January 27, “Atari is celebrating it’s 50th anniversary with giftable NFTs”, in New Musical Express:

Purchasers can either keep their GFT for themselves, or alternatively, and as their title suggests, they can gift the suspense-filled digital asset to a friend.

2022 February 1, “Atari Combine NFTs with Loot Boxes in New ‘GFT’ Collection”, in NFT Plaza:

(cryptocurrencies, technology, neologism) Initialism of gift-fungible token.


quasi-projective

From quasi- + projective, the sense being that projective varieties are closed subsets of projective space while quasi-projective varieties are only required to be locally closed, a strictly weaker condition. The second, scheme-theoretic sense generalizes the first.

(algebraic geometry, of a variety) Locally closed with respect to the Zariski topology on projective n-space; isomorphic to such a set.

(algebraic geometry, of a scheme) Comprising an open subscheme of a projective scheme


time-use survey

time-use survey (plural time-use surveys)

(economics, statistics) A statistical survey which aims to report data, on average, on the manners and ways of people spending their time.


time-space grid

time-space grid (plural time-space grids)

(sciences, statistics) The combination of a geographical area divided into equal sectors and a regular time interval.


time-ordered

(physics, mathematics) Of a definition, presenting information in a specific chronological order, starting from the earliest event or concept and moving forward in a sequential manner.


time-frequency analysis

electrical engineering
electrical engineering

time-frequency representation
time-frequency representation

(electrical engineering, signal processing) A technique that studies a signal in both the time and frequency domains simultaneously, using various time-frequency representations.


time-frequency representation

time-frequency representation (countable and uncountable, plural time-frequency representations)

(electrical engineering, signal processing) A view of a signal, taken to be a function of time, represented over both time and frequency.


time integration

differential equation
differential equation

(mathematics, calculus) A numerical method for solving differential equations that describes the manner in which a system changes over time.