biflecnode

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


bigenus

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(geometry) The second plurigenus P₂ of a surface.


binode

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

(geometry) A double point of a surface whose tangent cone consists of two different planes.


biregular

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

(geometry, of a map) Being a regular map with regular inverse.

(geometry, of two varieties) Having a biregular map from one to the other, i.e. isomorphic as abstract varieties.


biscribed

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a biscribed triangle

(geometry) Both circumscribed and inscribed, i.e. having vertices that lie on a curve and sides that are tangent to the curve.


bitangential

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(geometry) Meeting a curve at the tangency points of its bitangents.


Brianchon hexagon

en-noun

Brianchon hexagon (plural Brianchon hexagons)

Named after Charles Julien Brianchon (1783–1864).

(geometry) A nonplanar hexagon whose three diagonals meet.


Zeuthen-Segre invariant

Zeuthen-Segre invariant (plural Zeuthen-Segre invariants)

Introduced by Zeuthen (1871) and rediscovered by Corrado Segre (1896).

(geometry) A certain invariant of complex projective surfaces.


klafter

... for the purpose of working the machine, employed in raising water from the mines, and a tunnel of 300 klafters long, passing through a mountain, which serves as a road for foot-passengers, between Herrengrund and Altgebirg.

1818, Richard Bright, Travels from Vienna Through Lower Hungary: With Some Remarks on the State of Vienna During the Congress, in the Year 1814:

The building for the protection of the horses was erected on three sides of a square of 48 klafter, and was 12 klafter wide, making a structure 72 klafters long on each side, giving a covered space of 2,304 square klafter.

1874, W. P. Blake, Report on the Vienna Exposition, in the United States Congressional Serial Set, page 133

Ten or more families unite to dig a hole 20 to 30 klafters long and 3 to 4 wide, add to this excavation with a frame of driftwood,148 of which they also make the roof, and cover it with long dry grass or sod, which is held down with[…]

According to this instruction, one lot must be 75 to 100 klafters long and 12 to 15 klafters wide (1 klafter = 1[.]896 m). A house must be on the street line of a lot with its narrow side and the distance between houses should be at least[…]

2012 May 31, C. Mileto, F. Vegas, V. Cristini, Rammed Earth Conservation, CRC Press, →ISBN, page 84:

A unit of length formerly widely used in Central Europe, derived from the span of a man's outstretched arms, typically defined as six local feet (equivalent to a fathom) or about 1.8 meters.


asymptosy

(rare, dated, mathematics) The quality of being asymptotic.


orbiform

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(geometry) A plane for which the distance between the points of contact of two nonequal parallel tangents at a circle is the same everywhere.


subcascade

(mathematics, sciences) A cascade that originates from a member of another


antilocal

en-adj

antilocal (comparative more antilocal, superlative most antilocal)

more antilocal (comparative)
most antilocal (superlative)

an antilocal operator

(mathematics, not comparable) The property of a function or operator whereby, when applied to nonzero elements from any non-empty open subset of its domain, the function or operator yields a result outside of that non-empty subset.


BVP

(mathematics) Initialism of boundary value problem.


dummy variable

(statistics) A binary variable that takes a value of 0 or 1 to indicate which category an individual falls into.


sympercent

(statistics) A symmetric percentage difference (used to simplify the presentation of logarithmically transformed data)


S-shaped

S-shaped (comparative more S-shaped, superlative most S-shaped)

more S-shaped (comparative)
most S-shaped (superlative)

an S-shaped hook

A-shaped - B-shaped - C-shaped - D-shaped - E-shaped - F-shaped - G-shaped - H-shaped - I-shaped - J-shaped - K-shaped - L-shaped - M-shaped - N-shaped - O-shaped - P-shaped - Q-shaped - R-shaped - S-shaped - T-shaped - U-shaped - V-shaped - W-shaped - X-shaped - Y-shaped - Z-shaped


treelikeness

(mathematics) The condition of being treelike


hypercylindrical

hypercylindrical (comparative more hypercylindrical, superlative most hypercylindrical)

more hypercylindrical (comparative)
most hypercylindrical (superlative)


hypergroupoid

(mathematics) A hyperstructure with a hyperoperation.


hyperalgebra

(mathematics) The formal group ring of a formal group law.


isodual

an isodual lattice

(mathematics) geometrically congruent to its dual


hypernumber

(mathematics) A kind of number more complex than a hypercomplex number.


surcomplex

(mathematics) Of or relating to any number of the form a+bi, where a and b are surreal numbers.


surreal number

Coined by Donald Knuth in his 1974 novelette Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. The concept had been developed by British mathematician John Conway for his game theoretic research of the board game go. Conway had simply called them numbers, but subsequently adopted Knuth's term and used it in his 1976 book On Numbers and Games.

Conway's construction of surreal numbers relies on the use of transfinite induction.

Conway's approach was to build numbers from scratch using a construction inspired by his game theory research; the resulting class of surreal numbers proved much larger than the class of real numbers.

1986, Harry Gonshor, “An Introduction to the Theory of Surreal Numbers”, in Paperback, Cambridge University Press, published 1987, →ISBN:

• A surreal number X=(X_L,X_R) consists of two sets X_L and X_R of surreal numbers, such that no element from X_L is greater than any element from X_R.
• A surreal number Y=(Y_L,Y_R) is greater than another surreal number X=(X_L,X_R), X<Y, if and only if
− there is no x∈X_L such that Y<x, and
− there is no y∈Y_R such that y<X.

2012, Fredrik Nordvall Forsberg, Anton Setzer, A Finite Axiomatisation of Inductive-Inductive Definitions, Ulrich Berger, Hannes Diener, Peter Schuster, Monika Seisenberger (editors), Logic, Construction, Computation, Ontos Verlag, page 263, The class² of surreal numbers is defined inductively, together with an order relation on surreal numbers wich is also defined inductively

Here we shall follow Conway's exposition rather closely. Let L and R be two sets of numbers. Assume that no member of L is greater than or equal to any member of R. Then #92;#123;L#92;vertR#92;#125; is a surreal number. All surreal numbers are constructed in this fashion.

2018, Steven G. Krantz, Essentials of Mathematical Thinking, Taylor & Francis (Chapman & Hall/CRC Press), page 247:

(mathematics) Any element of a field equivalent to the real numbers augmented with infinite and infinitesimal numbers (respectively larger and smaller (in absolute value) than any positive real number).

Donald Knuth
John Horton Conway
On Numbers and Games
surreal number

nombre surréel

element of an extension of the real numbers that includes infinite numbers and infinitesimals


tessarine

(mathematics) A hypercomplex number of the form t=w+xi+yj+zk, w,x,y,z∈ℝ where ij=ji=k, i²=-1, j²=+1.


diagonality

en-noun

diagonality (countable and uncountable, plural diagonalities)

(mathematics) The condition of being diagonal


causal set

(mathematics, physics) A set of spacetimes that have a causality relationship


semibounded

(mathematics) Having either an upper or a lower bound, but not both


quasisimple

(mathematics, of a group) Being a perfect central extension of a simple group S.


left eigenvalue

left eigenvalue (plural left eigenvalues)

(linear algebra) An eigenvalue corresponding to the left transform of a given linear operator; i.e. λ such that urm A=uλ.


right eigenvalue

right eigenvalue (plural right eigenvalues)

(linear algebra) An eigenvalue corresponding to the right transform of a given linear operator; i.e. λ such that rm Au=λu.


proper value

1961 [Oxford University Press], Sterling K. Berberian, Introduction to Hilbert Space, American Mathematical Society (AMS Chelsea), 1999, Reprint, page 178,
In this terminology, Theorem 1 asserts that every non-zero proper value of a CC-operator has finite multiplicity. This result is not always helpful, for there exist CC-operators having no proper values at all:

Thus any proper value of AA* is a proper value of A*A.

1962, A. R. Amir-Moéz, A. L. Fass, Elements of Linear Space, Pergamon Press, page 134:

– the proper values of L;
– for each proper value α of L|Eᶜ and proper value β of L|Eᵘ, the proper value α/β — from the assumptions it follows that this latter collection of proper values consists of contracting proper values only.

2010, F. Takens, A Vanderbauwhede, Local invariant manifolds and normal forms, H. Broer, F. Takens, B. Hasselblatt (editors), Handbook of Dynamical Systems, Volume 3, Elsevier (North-Holland), page 106, The proper values of this linear mapping are


left eigenvector

left eigenvector (plural left eigenvectors)

(linear algebra) An eigenvector corresponding to the left transform of a given linear operator; i.e. u such that urm A=uλ.


right eigenvector

right eigenvector (plural right eigenvectors)

(linear algebra) An eigenvector corresponding to the right transform of a given linear operator; i.e. u such that rm Au=λu.


integral transform

integral transform (plural integral transforms)

(Tf)(u)=∫ limits _(t_1)K(t,u),f(t),dt

(mathematics) Any transform of the form:


operational calculus

(calculus) The study of calculus from the perspective of the theory of operators.


fractional calculus

fractional calculus (countable and uncountable, plural fractional calculi)

2000, Carl F. Lorenzo, Tom T. Hartley, Initialized Fractional Calculus, NASA, NASA/TP—2000-209943, page 12,
The paper presents the definition sets required for initialized fractional calculi. Two underlying bases have been used, the Riemann-Liouville based fractional calculus and the Grünwald based functional calculus (by reference).

One of the major advantages of fractional calculus is that it can be considered as a superset of integer-order calculus. Thus fractional calculus has the potential to accomplish what integer-order calculus cannot. We believe that many of the great future developments will come from the applications of fractional calculus to different fields.

2007, J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado, editors, Advances in Fractional Calculus, Springer, page xii:

This chapter presents a number of functions that have been found to be useful in providing solutions to the problems of fractional calculus. […]The Mittag-Leffler function is the basis function to functional calculus, as the exponential function is to the integer-order calculus.

2008, Shantanu Das, Functional Fractional Calculus for System Identification and Controls, Springer, page 19:

mathematical analysis
mathematical analysis

(mathematical analysis, uncountable) The branch of mathematics that studies generalisations of calculus to allow noninteger (i.e., real or complex) powers of the differentiation operator D and the integration operator J; (countable) any one of said generalisations of calculus.


Lickorish-Wallace theorem

The theorem was proved independently in the early 1960s by W. B. R. Lickorish and Andrew H. Wallace.

(mathematics) The theorem that any closed, orientable, connected 3-manifold may be obtained by performing Dehn surgery on a framed link in the 3-sphere with ±1 surgery coefficients, and that each component of the link can be assumed to be unknotted.


totative

Euler's totient function φ(n) counts the number of totatives of n.

(mathematics) A positive integer that is smaller than or equal to, and coprime to, another given positive integer.


associativeness

(mathematics) The condition of being associative


thirteener

From thirteen + -er (suffix denoting people characterized by something, or people or things to which certain measurements or numbers apply).

affix

oner · twoer · fiver · sixer · Sevener · niner · tenner · elevener · twelver · fourteener · fifteener · sixteener · hundreder · thousander · twenty-five-thousander

Boomers played cassettes in their cars and popularized FM radio. Thirteeners love their compact disks. Today's electronics industry is abuzz with talk of the new digital technology that awaits Millennial teenagers.

1991, William Strauss, Neil Howe, “The Past as Prologue”, in Generations: The History of America’s Future, 1584 to 2069, New York, N.Y.: William Morrow and Company, →ISBN, part III (The Future), page 352:

Raise the tough issues and questions that Thirteeners struggle with in the real world. […] The speaker should be transparent about his or her own life struggles and problems. This creates credibility and helps Thirteeners identify their own problems.

1995, Kevin Graham Ford, with Jim Denney, “How to Reach Us, Part 2: Process Evangelism”, in Jesus for a New Generation: Putting the Gospel in the Language of Xers, Downers Grove, Ill.: InterVarsity Press, →ISBN, page 205:

(dated) A member of the 13th Gen; a Generation Xer or Gen-Xer.

Upon their return from Ireland, vvhere they collected ſome thirteeners for vvhich they had not given the intrinſic value, ſhillings, they made their appearance at Tenby, in Pembrokeſhire, on a pretended tour of pleaſure.

1782, Genuine Memoirs of the Lives of George and Joseph Weston, who were Executed September 3d. 1782. The First for Forgery; the Latter for Shooting at John Davis, and Wounding Him in Cock-Lane: […], 4th edition, London: […] John Walker, […], →OCLC, pages 9–10:

["]A gintleman once said to me: 'Here, Pat, yer sowl, you look hungry. Here's a thirteener for yez; go and get drunk wid it.' Och, no, your honour, he wasn't an Irish gentleman; it was afther mocking me he was, God save him." […] On my asking the boy if he felt hurt at the mockery, he answered, slily, with all his air of simplicity, "Sure, thin, wasn't there the shillin'! For it was a shillin' he gave me, glory be to God. No, I niver heard it called a thirteener before, but mother has.["]

1851, Henry Mayhew, “Of the Street-seller of Crackers and Detonating Balls”, in London Labour and the London Poor; […], volume I (The London Street-folk. Book the First.), London: [George Woodfall], →OCLC, page 434, column 1:

[T]he woman banged a shilling down upon the table, crying, "Arrah, my honey, with this thirteener, won't I sit in the gallery, and won't your Royal Grace give me a curtsey—and won't I give your Royal Highness a howl and a hiss into the bargain!"

1877 October, [Henry Barton Baker], “Our Old Actors. Mrs. [Dorothea] Jordan.”, in Temple Bar: A London Magazine for Town and Country Readers, volume LI, London: Richard Bentley & Son, […]; New York, N.Y.: Willmer and Rogers; Paris: Galignani, →OCLC, page 182:

(numismatics, dated) A coin worth thirteenpence, especially an Irish shilling (as contrasted with a British shilling which was worth twelvepence).

There are six summits in Colorado above thirteen thousand feet named "Grizzly." Four of them are in the highest two hundred summits. This one was once rated a Fourteener, but new surveys demoted it so that it is now the highest Thirteener.

1992, Mike Garratt, Bob Martin, “Grizzly Peak (13,988 feet), Garfield Peak (13,780 feet)”, in Colorado’s High Thirteeners (A Climbing & Hiking Guide), 3rd edition, Boulder, Colo.: Johnson Books, →ISBN, page 38:

Few who venture into this region know that the area is a superb place to go after thirteener ski descents.

2020, Ben Conners, Brian Miller, “Cronin Peak—Northeast Face”, in Climbing and Skiing Colorado’s Mountains: Over 50 Select Ski Descents, 2nd edition, Lanham, Md.: Falcon Guides, Rowman & Littlefield Publishing Group, →ISBN, page 169:

(US, climbing) A mountain rising to more than 13,000 feet (about 4,000 metres) but less than 14,000 feet above mean sea level.

kolmetoista tuhatta korkea vuori

mountain rising to more than 13,000 feet but less than 14,000 feet above mean sea level


anabelian

From an- (“not”) + abelian (“commutative”); coined to imply a nuancedly stronger condition than "merely" noncommutative (see an-).

We end up this section with the following remarks, both for the sake of completeness, but mostly because of the relevance of the facts we want to mention for the anabelian phenomena.

2000, Florian Pop, “Alterations and Birational Anabelian Geometry”, in H. Hauser, J. Lipman, F. Oort, A. Quirós, editors, Resolution of Singularities, Birkhäuser, page 522:

We will formulate Grothendieck's anabelian conjectures in a more general context later, after having presented the basic facts about ́etale fundamental groups.

2012, Florian Pop, “Lectures on anabelian phenomena in geometry and arithmetic”, in John Coates, Minhyong Kim, Florian Pop, Mohamed Saïdi, Peter Schneider, editors, Non-abelian Fundamental Groups and Iwasawa Theory, Cambridge University Press, page 5:

But the interplay between those two parts remains mysterious and is at the source of some of the most standard conjectures about fundamental groups such as anabelian conjectures or the section conjecture.

2013, Anna Cadoret, “Galois Categories”, in Pierre Dèbes, Michel Emsalem, Matthieu Romagny, A. Muhammed Uludağ, editors, Arithmetic and Geometry Around Galois Theory, Springer (Birkhäuser), page 172:

algebraic fundamental group
algebraic fundamental group

(mathematics, algebraic geometry, arithmetic geometry) Of or relating to anabelian geometry, a proposed theory describing the way the algebraic fundamental group G of an algebraic variety (or some related geometric object) V determines how V can be mapped into another geometric object W, under the assumption that G is very far from being an abelian group, in a sense to be made more precise.


Hodge theory

partial differential equation
partial differential equation

(mathematics) One aspect of the study of differential forms of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M.


subdistribution

en-noun

subdistribution (countable and uncountable, plural subdistributions)

(statistics, countable) A subset of a distribution.


abc conjecture

From the names of the variables a, b, and c. The conjecture was proposed in 1985.

1985, Paul Vojta, Appendix, Serge Lang, Introduction to Arakelov Theory, Springer, 1988 Softcover, page 156,
Finally in §5 we give one application to the curve X⁴ + Y⁴ = Z⁴, showing that the height inequalities for the curve imply the asymptotic Fermat conjecture and a weak form of the Masser-Oesterlé abc''' conjecture.

The abc''' conjecture may well replace the Fermat theorem for the future generation of mathematicians.

2004, Sergei K. Lando, R.V. Gamkrelidze, V.A. Vassiliev, Graphs on Surfaces and Their Applications, Springer, page 137:

To prove or disprove the abc'''-conjecture would be an important contribution to number theory.[…]Langevin ([236], [237]) proved that the abc'''-conjecture implies the Erdős-Woods conjecture with k = 3 except perhaps a finite number of counter examples.

2006, Pei-Chu Hu, Chung-Chun Yang, Value Distribution Theory Related to Number Theory, Springer (Birkhäuser), page 233:

The abc'''-conjecture of Masser and Oesterle is a typical example of a simple statement that can be used to unify and motivate many results in number theory, which otherwise would be scattered statements without a common link.

2007, Enrico Bombieri, Walter Gubler, Heights in Diophantine Geometry, Cambridge University Press, page 401:

(number theory) Given coprime positive integers a, b and c, such that a + b = c, and d the radical of abc (the product of its distinct prime factors), the conjecture that d is usually not much smaller than c (in other words, that if a and b are divisible by large powers of primes, then c usually is not).


blockchain

From block + chain, from earlier “block chain”. In the 2008 Bitcoin paper block and chain are used separately; the concept is referred to as “chain of hash-based proof-of-work” or “chain of digital signatures”.

By the way, mobile wallets differ from most software wallets in that they don't download the entire Bitcoin blockchain with every transaction. (Many software wallets do, interestingly.) Because the blockchain is a file several gigabytes in size, this would eat up a ton of mobile bandwidth and probably cause your mobile provider to either enact overage charges or just plain cancel your account. In addition, your mobile phone probably doesn't have enough onboard storage to host the entire […]

2014, Michael R. Miller, The Ultimate Guide to Bitcoin, Que Publishing, →ISBN, page 93:

[…] blockchain is arguably the most important innovation introduced by Bitcoin. It is the missing link that makes distributed peer-to-peer digital currencies possible. The blockchain is in essence a distributed database holding all the Bitcoin transactions since the beginning (January 3, 2009) and a method to secure this database. The blockchain keeps a secure list of all the transactions. However, there are relevant questions, such as whether a particular transaction output is spendable, that […]

2014, Pedro Franco, Understanding Bitcoin: Cryptography, Engineering and Economics, John Wiley & Sons, →ISBN, page 95:

A shared record of past transactions in a distributed network, typically used for cryptocurrency.


cryptocurrency

cryptocurrency (countable and uncountable, plural cryptocurrencies)

Bitcoin was the first decentralized cryptocurrency.

As secure Internet payment systems develop, of course, betting will become easier. And if some form of digital cash—crypto-currency that can be exchanged like cash via the Internet—really does take hold, betting will be even easier still.

1995 July 26, Daniel Akst, “Info Highway May Convert Your PC Into a Gambling Mecca”, in Los Angeles Times:

Then there is bitcoin, the cryptocurrency that has been skyrocketing in value lately. Bitcoin is basically virtual cash — anonymous, untraceable currency stuffed into a mobile wallet.

2013 November 17, Nick Bilton, “Disruptions: A Digital Underworld Cloaked in Anonymity”, in New York Times:

The US chip-maker Nvidia has said cryptocurrencies do not “bring anything useful for society” despite the company’s powerful processors selling in huge quantities to the sector.

2023 March 26, Alex Hern, quoting Michael Kagan, “Cryptocurrencies add nothing useful to society, says chip-maker Nvidia”, in The Guardian, →ISSN:

As alleged in the Indictment filed on January 9, 2023, EISENBERG engaged in a scheme to fraudulently obtain approximately $110 million worth of cryptocurrency from the cryptocurrency exchange Mango Markets and its customers and achieved this objective by artificially manipulating the price of certain perpetual futures contracts.

2023 February 2, U.S. Attorney's Office, Southern District of New York, “Alleged Perpetrator Of $100 Million Crypto Market Manipulation Scheme To Make Initial Appearance In The Southern District Of New York”, in justice.gov, sourced from justice.gov:

According to Recorded Future’s research, the regime considers cryptocurrency theft a significant revenue source, primarily funding military and weapons programs.

2023 November 30, Alessandro Mascellino, “North Korean Hackers Amass $3bn in Cryptocurrency Heists”, in (Please provide the book title or journal name):

A digital currency based on a cryptographic system, usually having no central issuing or regulating authority.


altcoin

Sure, like all the other altcoins, Dogecoin offers some variability, like a theoretical max of 100 billion versus 21 million, and a different proof-of-work algorithm, but we’re reaching Furby levels of ridiculousness here.

2013, sdjf, “Dogecoin ~ internet meme dog coin.”, in uk.politics.misc (Usenet):

Altcoins use either Scrypt or SHA256 encryption algorithm, because the 'project forks' are from either Litecoin or Bitcoin. […] A few crypto economists believed that Altcoins is contributed ^([sic]) to a diverse crypto commodities marketplace, which is good.

2013, John Davidson, The Digital Coin Revolution - Crypto Currency - How to Make Money Online, JD-Biz Corp Publishing, →ISBN:

Indeed, after a week of existence, Dogecoin is already the 24th most valuable altcoin, with a total market value of $1,621,559 based on the exchange CoinedUp, though it might be worth even more elsewhere.

2013, John Stevenson, Dogecoin - Bitcoin's poor cousin?, page 18:

MASTERCOIN […] An altcoin invented by J. R. Willett. According to the Website, “The Master Protocol facilitates the creation and trading of smart properties and user currencies as well as other types of smart contracts. […]”

2014, Deborah Gonzalez, Managing Online Risk: Apps, Mobile, and Social Media Security, Butterworth-Heinemann, →ISBN, page 199:

Most altcoins follow the bitcoin model of having a finite ultimate supply of coins.

2014 June 13, Black Market Cryptocurrencies, page 47:

(cryptocurrencies) A cryptocurrency other than bitcoin.


satoshi

Named after Satoshi Nakamoto, the pseudonymous designer of Bitcoin, from Japanese さとし (Satoshi), nominalization of the classical adjective 聡し (satoshi), modern 聡い (satoi, “clever, smart, sharp”).

A hundred-millionth (10⁻⁸) of a bitcoin; the same as 10 nanocoins (nBTC) or 10⁻⁸ BTC.


nullspace

(mathematics) The kernel of a linear map between two vector spaces or two modules.


subvector

(mathematics) A subset of a vector (ordered tuple, or member of a vector space)


algebraization

algebraization (countable and uncountable, plural algebraizations)

(mathematics) conversion to algebraic form


supersquare

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

(mathematics) The equivalent of a Latin square in greater than two dimensions


powerstructure

(mathematics) An analog of a power set in the context of mathematical structuralism.


ellipsoid of revolution

ellipsoid of revolution (plural ellipsoids of revolution)

An ellipsoid of revolution may be either prolate or oblate.

(geometry) A spheroid; a solid of revolution generated by rotating an ellipse about one of its axes.


sociable number

sociable number (plural sociable numbers)

The numbers in the sequence <1264460, 1547860, 1727636, 1305184> are sociable numbers.

(number theory) Any of a sequence of numbers having the property that the sum of the divisors of each, excluding itself, is equal to the next number in the sequence; in the case of the last number of the sequence, the sum of the divisors, excluding that number, is equal to the first number of the sequence.


method of indivisibles

(mathematics, obsolete) An old kind of calculus in which lines were considered as made up of an infinite number of points; surfaces, as made up of an infinite number of lines; and volumes, as made up of an infinite number of surfaces.


spherical excess

(geometry) The amount by which the sum of the three angles of a spherical triangle exceeds two right angles. The spherical excess is proportional to the area of the triangle.


duplication of the cube

duplication of the cube (usually uncountable, plural duplications of the cube)

(mathematics) The operation of finding a cube having a volume which is double that of a given cube.


wellfounded

(mathematics) Alternative form of well-founded


prewellordering

(mathematics, set theory) A binary relation that is transitive, total, and well-founded.


Riemann sphere

Named after German mathematician Bernhard Riemann.

We use #92;hat#123;#92;Complex#125;#92;times (resp. #92;Complex) to denote the subset #92;#123;z#92;in#92;hat#92;Complex#58;z#92;ne 0#92;#125; (resp. #92;#123;z#92;in#92;hat#92;Complex#58;z#92;ne#92;infty#92;#125;) in the Riemann sphere #92;hat#92;Complex.

2002, Wenhua Zhao, “Some Generalizations of Genus Zero Two-Dimensional Conformal Field Theory”, in Stephen Berman, Paul Fendley, Yi-Zhi Huang, Kailash Misra, Brian Parshall, editors, Recent Developments in Infinite-dimensional Lie Algebras and Conformal Field Theory, American Mathematical Society, page 306:

(topology, complex analysis) The complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended with a single idealised point at infinity and consequently homeomorphic to a sphere in 3-dimensional Euclidean space.

1967 [Prentice-Hall], Richard A. Silverman, Introductory Complex Analysis, Dover, 1972, page 22,
Every circle γ on the Riemann sphere Σ which does not go through a given point P^*∈Σ divides Σ into two parts, such that one part contains P^* and the other does not.

In order to visualize the point at infinity, we consider the Riemann sphere that has radius 1#47;2 and is tangent to the complex plane at the origin (see Figure 1.8). We call the point of contact the south pole (denoted by S) and the point diametrically opposite S the north pole (denoted by N). Let z be an arbitrary point in the complex plane, represented by the point P. We draw the line PN which intersects the Riemann sphere at the unique point P', distinct from N. Conversely, to each point P' on the sphere, other than the north pole N, we draw the line P'N which cuts uniquely one point P in the complex plane. Clearly, there exists a one-to-one correspondence between points on the Riemann sphere, except N, and all the finite points on the complex plane. We assign the north pole N as the point at infinity. With such an assignment, we then establish a one-to-one correspondence between all the points on the Riemann sphere and all the points in the extended complex plane. This correspondence is known as the stereographic projection.

2002, Yue Kuen Kwok, Applied Complex Variables for Scientists and Engineers, Cambridge University Press, page 27:

We find that many mathematicians, even those who specialize in complex analysis and conformal geometry, are not familiar with the inversive distance between pairs of circles in the Riemann sphere.

2003, Philip L. Bowers, Monica K. Hurdal, “Planar Conformal Mappings of Piecewise Flat Surfaces”, in Hans-Christian Hege, Konrad Polthier, editors, Visualization and Mathematics III, Springer, page 6:

extended complex plane
extended complex plane

extended complex numbers
extended complex numbers

(topology, complex analysis) The 2-sphere embedded in Euclidean three-dimensional space and often represented as a unit sphere, regarded as a homeomorphic representation of the extended complex plane and thus the extended complex numbers.

complex projective line

differently constructed set homeomorphic to the Riemann sphere


Riemann integral

Riemann integral (plural Riemann integrals)

Named after Bernhard Riemann, a German mathematician.

(mathematical analysis) A type of integral whose computation involves dividing the interval of integration into smaller sub-intervals, summing sample values of the integrand inside those sub-intervals multiplied by their lengths, and letting the number of sub-intervals tend to infinity.


logocyclic curve

logocyclic curve (plural logocyclic curves)


strophoid

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(geometry) The locus of a point that has a certain relationship with a given curve


autokey

(cryptography) Being a cipher that incorporates the plaintext into the key.


googolgon

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(geometry) A polygon with a googol number of sides (virtually indistinguishable from a circle)


maquila

From Spanish maquila, from Andalusian Arabic مَكِيلَة (makíla), from Arabic مَكِيلَة (makīla, “measured”). In reference to factories, via Spanish clipping of maquiladora, from maquilar (“to assemble”) + -adora (“-ator: forming agent nouns”), from maquilar's original sense of taking a toll of grain. Also understood as a clipping within English.

Synonym of medio, half-celemin, a traditional Spanish unit of dry measure equivalent to about 2.3 L.


ultraparallel

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(geometry, of lines in hyperbolic geometry) Sharing a common perpendicular.


boat conformation

boat conformation (plural boat conformations)

(organic chemistry) an unstable chemical conformation of a six-member single bonded carbon ring such as cyclohexane


newton metre

A standard unit of torque or (rarely) energy, symbol N m or N·m.


nonconcordant

(mathematics) not preserving the sign; of opposite sign or zero


non-Archimedean

Archimedean property
Archimedean property

(mathematics, of an ordered field) Not having the Archimedean property: containing infinite elements, i.e. elements which are larger than any result of adding 1 to itself any finite number of times.

(mathematics, of a metric) Meeting the requirements to be an ultrametric.


Minkowski inequality

(mathematics) An inequality that establishes that the Lp spaces are normed vector spaces.


bagplot

From bag + plot, introduced in 1999 by Peter Rousseeuw, Ida Ruts and John Tukey.

(statistics) A method for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot.

John Tukey
Peter Rousseeuw
R (programming language)
bagplot


abuse of notation

abuse of notation (usually uncountable, plural abuses of notation)

(mathematics) The use of a mathematical notation in a way that is not formally correct but seems likely to simplify the exposition or suggest the correct intuition.


debigulate

en-verb

debigulate (third-person singular simple present debigulates, present participle debigulating, simple past and past participle debigulated)

debigulates (present singular third-person)
debigulating (participle present)
debigulated (participle past)
debigulated (past)

Back-formation from Debigulator, itself from de- + big + -ule + -ate + -or, a fictional shrink ray featured in the 1996 episode "Treehouse of Horror VII" of the American animated television series The Simpsons.

> think moe will get his ears enlarged 2.27.00?
No, he'll get them debigulated.

2000 February 27, Ben Mann, “Re: X'tapolapocetl (Quetzelsacatanango?)”, in alt.tv.simpsons (Usenet):

2002 October 22, Ed, “Button to enlarge or debigulate size of text?”, in netscape.public.mozilla.wishlist (Usenet):

Does debigulating a table first delete blank rows? (I don't know if blank rows are always at the end or not.)

2008 May 13, Ron Newcomb, “I7: Dynamic Tables extension for Glulx”, in rec.arts.int-fiction (Usenet):

(rare, humorous) To reduce or shrink; to make or become smaller.


minimoon

Coordinate term: quasi-satellite

This photo of Earth's newest minimoon was taken by the 8-meter Gemini North telescope on Hawaii's Maunakea.

2020 March 4, Theresa Machemer, “Earth's New Mini-Moon Is Leaving Soon”, in Smithsonian Magazine, archived from the original on 2022-08-20:

Earth has only had two minimoons on record – one in February 2020 and the other in 2006.

2020 September 22, Stacy Liberatore, “Earth is set to capture a minimoon in October that may stay until May 2021 – but some experts say the object could be man-made space junk”, in The Daily Mail, archived from the original on 2021-07-26:

These included a rare 'minimoon' named 2020 CD3, a tiny asteroid less than 3 metres in diameter that had been temporarily captured by Earth's gravity. The minimoon broke away from Earth's pull last April.

2021 March 11, Alexandra Witze, “Record number of asteroids seen whizzing past Earth in 2020”, in Nature, archived from the original on 2022-09-09:

(astronomy) A small asteroid captured by the Earth's gravity and temporarily acting as a second moon of Earth.


Cartesian closed category

en-noun

Cartesian closed category (plural Cartesian closed categories)

Named after René Descartes (1596–1650), French philosopher, mathematician, and scientist, whose formulation of analytic geometry gave rise to the concept of Cartesian product, which was later generalized to the notion of categorical product.

In any event, Lambek showed that every typed lambda-theory gives a cartesian closed category — and conversely, every cartesian closed category gives a typed lambda-theory. This discovery led to a rich line of research blending category theory and computer science.

2009 February 3, John C. Baez with Mike Stay, Physics, Topology, Logic and Computation: A Rosetta Stone, page 54:

(category theory) A category which has a terminal object and which for every two objects A and B has a product A × B and an exponential object Bᴬ.

Cartesian closed category
René Descartes


bicartesian closed category

bicartesian closed category (plural bicartesian closed categories)

Cartesian closed category
Cartesian closed category

(category theory) A Cartesian closed category which also has an initial object and such that for any pair of objects, A and B, in the category, the category has another object which is their coproduct, A∐B.


Rolle's theorem

Named after French mathematician Michel Rolle (1652–1719), although his 1691 proof covered only the case of polynomial functions and did not use the methods of differential calculus.

(calculus) The theorem that any real-valued differentiable function that attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. In mathematical terms, if f:ℝ→ℝ is differentiable on (a,b) and f(a)=f(b) then ∃c∈(a,b):f'(c)=0.

teorema di Rolle

theorem that a differentiable function with points of equal value must have a point of zero slope between them


R-module

(algebra) The monoid action of a ring R on an abelian group.


isoconic

(mathematics, of precessional motion) Describing the same cone.


closed curve

(topology) A map from the circle, S¹, to a topological space.^((McLarty, p. 4))


balanced category

balanced category (plural balanced categories)

(category theory) A category in which every bimorphism is an isomorphism.


bimorphism

(category theory) A morphism which is both a monomorphism and an epimorphism.


zero object

(category theory) An object which is both an initial object and a terminal object.


generalized element

generalized element (plural generalized elements)

Thinking of x∈_AB as a generalized element, for any f:B→C, we may write f(x) for the composite f∘x. In this notation the first domain–codomain axiom reads as follows: for any x∈_AB and f:B→C there is a well-defined f(x)∈_AC; that is, at each stage A, f takes A-elements of B to A-elements of C.

1995, Colin McLarty, Elementary Categories, Elementary Toposes, Oxford University Press, page 17

(category theory) A morphism whose codomain is some specified object.


factor through

en-verb

factor through (third-person singular simple present factors through, present participle factoring through, simple past and past participle factored through)

factors through (present singular third-person)
factoring through (participle present)
factored through (participle past)
factored through (past)

LEMMA 16.3 An arrow f#58;A#92;rightarrowB is epic iff 1#95;B is the smallest sub-object of B that f factors through.

1995, Colin McLarty, Elementary Categories, Elementary Toposes, page 142:

(category theory) Said of a morphism: to be equal to a composition of two morphisms, one of which is the given morphism (that is being said to be "factored through").


generic element

en-noun

generic element (plural generic elements)

(category theory) The identity element of an object when thought of as a generalized element of that object.


split epimorphism

split epimorphism (plural split epimorphisms)

(category theory) A morphism which has a right inverse.


Stone space

Named after Marshall Harvey Stone (1903–1989), an American mathematician.

For every Boolean algebra there is a Boolean ring corresponding to it. The prime spectrum of a Boolean ring is a Stone space.

topological space
topological space#English

(topology, logic) A topological space constructed from a Boolean algebra, whose points are ultrafilters on the algebra.


Hilbert cube

Named after German mathematician David Hilbert (1862–1943)

named-after

(topology) A metrizable topological space which is the product of a countably infinite number of closed intervals.


Cantor set

Named after German mathematician Georg Cantor (1845–1918).

The Lebesgue null sets include not only all countable sets but many sets having the cardinality of the continuum. We now present the standard example, the Cantor set, which is also of interest for other reasons.

1999, Gerald B. Folland, Real Analysis : Modern Techniques and Their Applications, 2nd edition, New York: John Wiley & Sons, Inc., →ISBN, →OCLC, §1.5, page 38:

connected component
connected component#English

(mathematical analysis, topology) A subset of an interval formed by recursively removing an interval in the middle of every connected component of the set.


Parseval's theorem

(mathematics) The result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform.


Peter Pan generation

Coined by American sociologist Kathleen Shaputis, because of the members' perceived tendency for delaying some rites of passage into adulthood.


quadrisecant

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(geometry) A line that passes through four points of the curve.


MMB

(cryptography) Initialism of modular multiplication-based block cipher.


Euclidean norm

(mathematics) A norm of an ordinary Euclidean space, for which the Pythagorean theorem holds, defined by ‖x‖=√


nonsampling

(statistics, of errors or deviations) Not a function of the chosen sample.


pseudolongitudinal

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(statistics, of a study or data) Not actually longitudinal, but treated that way.


mathematical induction

en-noun

mathematical induction (countable and uncountable, plural mathematical inductions)

Mathematical induction is often compared to the behavior of dominos. The dominos are stood up on edge close to each other in a long row. When one is knocked over, it hits the next one (analogous to n in S implies n + 1 in S), which in turn hits the next, etc. If then we hit the first (0 in S), then they will all eventually fall (S is all of ℕ). In Variation 1 above, we start by knocking over the kth domino, so that it and all subsequent ones eventually fall.

2007, Mark Bridger, REAL ANALYSIS: A Constructive Approach, Hoboken, New Jersey: John Wiley & Sons, page 2

(mathematics) A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n>0, P(n) implies P(n+1), then P(n) is true for any natural number n.


homaloid

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Cremona transformation
Cremona transformation

(geometry) An element of a homaloidal system, in particular the image of a hyperplane under a Cremona transformation.


hypercusp

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(geometry) A singularity of a curve of some multiplicity r whose tangent cone is a single line meeting the curve with order r+1.


hyperflex

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(geometry) A point of a curve where the tangent line has contact of order at least 4.


hyperosculate

en-verb

hyperosculate (third-person singular simple present hyperosculates, present participle hyperosculating, simple past and past participle hyperosculated)

hyperosculates (present singular third-person)
hyperosculating (participle present)
hyperosculated (participle past)
hyperosculated (past)

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A hyperosculating point is one where the tangent space meets with order higher than normal.

(geometry) To osculate at multiple points.


flecnode

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(geometry) A double point that is also a point of inflexion of one branch.


fleflecnode

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(geometry) A double point that is also a point of inflexion of both branches.


subset classifier

en-noun

subset classifier (plural subset classifiers)

characteristic function
characteristic function

(mathematics) A set which serves as the codomain of a characteristic function.

subobject classifier
subobject classifier

(category theory, uncountable) The subobject classifier restricted to the category Set.


harmonic series

harmonic series (plural harmonic series)

(mathematics, mathematical analysis) The divergent series whose terms are the reciprocals of the positive integers; the series ∑ₙ₌₁ ᪲1/n.

harmoninen sarja

series of reciprocals of natural numbers


epi

(category theory) Abbreviation of epimorphism.


cointegrate

en-verb

cointegrate (third-person singular simple present cointegrates, present participle cointegrating, simple past and past participle cointegrated)

cointegrates (present singular third-person)
cointegrating (participle present)
cointegrated (participle past)
cointegrated (past)

(statistics, intransitive) To exhibit cointegration.


simultaneous equations

(mathematics) finite set of equations whose common solutions are sought


superincreasing

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(mathematics, of a sequence) Such that every element of the sequence is greater than the sum of all previous elements.


denumerability

(mathematics) The property of being denumerable.


graphlet

(mathematics) A small, connected, non-isomorphic, induced subgraph of a large network


indicator variable

en-noun

indicator variable (plural indicator variables)

(statistics) A binary variable whose value of 0 or 1 indicates which category an individual falls into.


limit ordinal

(set theory) An ordinal number which is neither zero nor a successor of an ordinal.


dogecoin

dogecoin (countable and uncountable, plural dogecoins)

/ˈdəʊd͡ʒkɔɪn/

The success of ransomware could be attributed to wide adoption of digital currencies or crypto currencies, such as bitcoin, litecoin ukash, dogecoin, ripple and monero, among others.

2017 August 19, Roderick Abad, “Slow Internet speed helping PHL fend off cyber felons”, in Business Mirror:

The net worth of Markus and Palmer is unknown due to their tendency to stay off social media and online platforms. However, dogecoin was estimated to be worth almost $17billion as of April 14, 2021.

2021 April 16, Jacob Bentley-York, “Who are Dogecoin founders Billy Markus and Jackson Palmer?”, in The US Sun, retrieved 2021-04-28:

(uncountable, cryptocurrencies) A cryptocurrency featuring the Shiba Inu from the "doge" meme as its logo.


equianharmonic

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(mathematics) equally anharmonic; specifically, whose anharmonic ratio is a cube root of unity


equianharmonic

(geometry) A set of four points whose cross ratio (or anharmonic ratio) is a cube root of 1.


Titchmarsh convolution theorem

Named after Edward Charles Titchmarsh, a British mathematician.

(mathematics) A theorem that describes the properties of the support of the convolution of two functions.


almost surely

(probability theory) With probability equal to one.


mainchain

One user start^([sic]) to withdraw assets from sidechain to mainchain by sending transaction.

2020, Sheng Wen, Albert Zomaya, Laurence T. Yang, Algorithms and Architectures for Parallel Processing, Springer Nature, →ISBN, page 557:

(cryptocurrencies) A blockchain with one or more sidechains attached to it.


compositorial

(mathematics) The product of all composite numbers less than or equal to a particular number.


MoM

(statistics) Initialism of month-over-month/month-on-month; compared to the same time period in the previous month.


YoY

(statistics) Initialism of year-over-year or year-on-year.


skew field

multiplicative inverse
multiplicative inverse

(algebra, dated) A ring in which every nonzero element has a multiplicative inverse; division ring


uncubed

This parameterization also eliminates the apparent algebraic canceling of the two uncubed appearances of the variable C in equation 3.5.

1995, Courtney Brown, Serpents in the Sand, page 42:


neusis

(geometry) A line segment of prescribed length, fitted between two given curves, part of a line that passes through a given point.


integration by parts

integration by parts (countable and uncountable, plural integrations by parts)

(mathematical analysis) A method of integration directly related to the rule for differentiation of products; can be written as ∫udv=uv-∫vdu.

intégration par parties

method of integration related to the product rule of differentiation


anticanonical

en-adj

anticanonical (comparative more anticanonical, superlative most anticanonical)

more anticanonical (comparative)
most anticanonical (superlative)

(mathematics, not comparable) Of or relating to the inverse bundle corresponding to a canonical bundle.


nonresidue

(mathematics) A value that is not a residue.


Pollard's rho algorithm

(mathematics) A general-purpose integer factorization algorithm, particularly effective at splitting composite numbers with small factors.


Kempner series

The series was first studied by Aubrey J. Kempner in 1914.

(mathematics) A modification of the harmonic series, formed by omitting all terms whose denominator expressed in base 10 contains the digit 9.


theta function

(mathematics) Any of a group of special functions of several complex variables, important in many areas, including the theories of abelian varieties and moduli spaces, and of quadratic forms.


vanishing fraction

en-noun

vanishing fraction (plural vanishing fractions)

(mathematics) A fraction which reduces to the form 0/0 for a particular value of the variable which enters it, usually in consequence of the existence of a common factor in both terms of the fraction, which factor becomes 0 for this particular value of the variable.


ferrado

From Galician ferrado, from Medieval Latin modius ferrātus (“reinforced modius”), from Latin ferrātus (“ironed”), from ferrum (“iron”) + -ātus (“-ate”).

(historical) A traditional Galician unit of dry measure, equivalent to about 12–18 L depending on the substance measured.


clothyard

(historical) An old unit of measure for cloth, 36 or 37 inches.


semiconvergent

The semiconvergents to the continued fraction expansion of a real number include all the rational approximations which are better than any approximation with a smaller denominator.

(mathematics) A kind of fraction. If (h_n-1)/(k_n-1), (h_n)/(k_n) are successive convergents, then any fraction of the form (h_n-1+ah_n)/(k_n-1+ak_n), where a is a nonnegative integer and the numerators and denominators are between the n and n+1 terms inclusive, is a semiconvergent.


semiconvergent

(mathematics, of a matrix) For which the limit lim _(k→∞) bold Tᵏ exists.


squeeze theorem

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(calculus) A theorem used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed. Supposing that


almud

From Spanish almud, from Andalusian Arabic المُدّ (al-mudd), from Arabic مُدّ (mudd), probably via Aramaic 𐡬𐡣𐡩𐡠 (mdyʾ) and מוֹדְיָא (moḏyā) or Classical Syriac ܡܘܿܕܝܳܐ (moḏyā) from Akkadian 𒉘𒈨𒌍 (/maddattu, middattu/, “kind of vessel, unit of volume”). Doublet of almude. Cognate with Ancient Greek μόδιος (módios), Latin modius, French muid, and Dutch mud.

der

An almud is a measure of volume rather than weight; an almud of wheat equals about 22 pounds and an almud of potatoes 20 pounds.

1990, Carmen Diana Deere, Household and Class Relations: Peasants and Landlords in Northern Peru, University of California Press, page 79:

Both sexes were equally familiar with and preferred the Spanish almud (equal to four quarts of seed), often rendered almo in Nahuatl, over any indigenous measure.

1997, Stephanie Wood, “Nahuatl Testaments of Rural Women”, in Susan Schroeder, Stephanie Wood, Robert Stephen Haskett, editors, Indian Women of Early Mexico, University of Oklahoma Press, page 174:

(historical) Synonym of celemin, a traditional Spanish unit of dry measure equivalent to about 4.6 liters.

celemin

(historical) A traditional Spanish unit of dry measure, highly variable depending on the location and the substance measured but generally between 3 and 20 liters.

(historical) A traditional Spanish unit of land area (nominally, the area cultivable by an almud of some particular seed), highly variable depending on the location.

(historical) Alternative form of almude, Portuguese forms of the same measure.


hemihelix

en-noun

hemihelix (plural hemihelixes or hemihelices)

hemihelixes (plural)
hemihelices (plural)

a three-dimensional geometric shape similar to a helix, but with one or more perversions causing changes in chirality along its run


tendril perversion

tendril perversion (countable and uncountable, plural tendril perversions)

(geometry) A reversal of handedness in helical curves.


Belphegor's prime

(mathematics) The prime number 1,000,000,000,000,066,600,000,000,000,001, a palindrome which contains 666 (the Number of the Beast) and also two sets of thirteen zeroes.


ball-and-stick model

ball-and-stick model (plural ball-and-stick models)

(physical chemistry) A molecular model of a chemical substance, displaying the three-dimensional position of the atoms (as spheres) and the bonds between them (as connecting rods).


Newton-Raphson method

Named after Isaac Newton and Joseph Raphson.

(mathematics) Synonym of Newton's method


Newton's method

(algebra, calculus) A method for finding successively better approximations to the roots (or zeroes) of a real-valued function.


barrel bulk

A measure equal to five cubic feet, used in estimating capacity, as of a vessel for freight.


hypernode

(graph theory) A kind of graph whose node set can contain other graphs as well as basic nodes.


mixed number

(mathematics) A number consisting of a whole number and a fraction, such as 11½.

sekaluku

a number consisting of a whole number and a fraction


block system

(mathematics) Given a group G that acts on a set X, a partition of X that is G-invariant.


chain rule

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The backward() function uses PyTorch's automatic differentiation package, torch.autograd, to differentiate and compute gradients of tensors based on the chain rule.

2021, Joe Papa, PyTorch Pocket Reference, page 48:

(calculus) A formula for computing the derivative of the functional composition of two or more functions.


Wick rotation

Wick rotation (countable and uncountable, plural Wick rotations)

(mathematics) A method of finding a solution to a mathematical problem in Minkowski space from a solution to a related problem in Euclidean space by means of a transformation that substitutes an imaginary-number variable for a real-number variable.


geometrical pace

geometrical pace (plural geometrical paces)

Calque of Latin passus geometricus or French pas géometrique.

(historical, rare) A unit of measure used in the 16th century, defined as "five feet" or "five geometrical feet".


visual angle

(geometry) The angle formed by two rays of light, or two straight lines drawn from the extreme points of an object to the center of the eye.


winding number

(geometry, topology, mathematical analysis) The total number of times a given curve travels counterclockwise around a specified point.

indeks

the number of times a curve travels counterclockwise around a point


DRL

The primary learning algorithm in AlphaDev is an extension of AlphaZero, a well-known DRL algorithm, in which a neural network is trained to guide a search to solve AssemblyGame.

2023 June, Daniel J. Mankowitz, Andrea Michi, Anton Zhernov, Marco Gelmi, Marco Selvi, “Faster sorting algorithms discovered using deep reinforcement learning”, in Nature, volume 618, number 7964, →DOI, →ISSN, pages 257–263:

reinforcement learning
reinforcement learning#English

(machine learning) Initialism of deep reinforcement learning.


sedenion

Blend of Latin sēdecim (“sixteen”) + quaternion.

blend

According to the logic of doubling the dimensions on which Cayley–Dickson algebra is built, after quaternions the so-called 8D octonions (#92;mathbbO—Octonions) can be obtained, followed by 16D sedenions, 32D pathions, 64D chingons, 128D routons, and 256D voudons.

2022, Zlatka Valkova-Jarvis, Vladimir Poulkov, Viktor Stoynov, Dimitriya Mihaylova, Georgi Iliev, “A Method for the Design of Bicomplex Orthogonal DSP Algorithms for Applications in Intelligent Radio Access Networks”, in Symmetry, volume 14, number 3, MDPI AG, →DOI, →ISSN:

There is no theoretical limit to multispace dimensional numbering as there are definitions for octonion (8D), sedenion (16D), pathion (32D), chingon (64D), routon (128D), and voudon (256D) numbered space.

2023, Melanie Swan, Renato P. dos Santos, “Quantum Intelligence: Responsible Human-AI Entities”, in AAAI 2023 Spring Symposia, Socially Responsible AI for Wellbeing, March 27–29, 2023, USA, CEUR Workshop Proceedings, →DOI:

(mathematics) A 16-dimensional nonalternative extension of an octonion with one real part and 15 imaginary parts, each a real multiple of a distinct, independent square root of −1.

十六元數 /十六元数

nonassociative, nonalternative extension of an octonion


Chen prime

Named after Chinese mathematician Chen Jingrun, who proved in 1966 that there are infinitely many such numbers.

2013, Laura Hemphill, Buying In, Haughton Mifflin Harcourt (New Harvest), page 278,
She tried counting Chen primes. 2, 3, 5... 7, 11... 13... 17... She couldn't concentrate.

There are even magic square of primes, like this one containing Chen primes discovered by Rudolf Ondrejka:[…]

2014, Christian Bessiere et al., “Reasoning about Constraint Methods”, in Duc-Nghia Pham, Seong-Bae Park, editors, PRICAI 2014: Trends in Artificial Intelligence, Springer, page 804:

A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes.[…]There are infinitely [many] Chen primes and the first ten are: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

2014, Rajesh Kumar Thakur, The Power of Mathematical Numbers, Ocean Books, page 155:

(number theory) Any prime number p such that p+2 is either a semiprime or another prime.


cototient

(mathematics) The value of n – φ(n), i.e. the number of positive integers less than or equal to n that are divisible by at least one prime that also divides n.


Cunningham chain

en-noun

Cunningham chain (plural Cunningham chains)

Named after mathematician A. J. C. Cunningham.

(mathematics) A certain kind of sequence of prime numbers, with applications in cryptography.

A Cunningham chain of the first kind of length n is a sequence of prime numbers (p₁, ..., pₙ) such that for all 1 ≤ i < n, pᵢ₊₁ = 2pᵢ + 1.

A Cunningham chain of the second kind of length n is a sequence of prime numbers (p₁,...,pₙ) such that for all 1 ≤ i < n, pᵢ₊₁ = 2pᵢ − 1.


von Mangoldt function

Named after the German mathematician Hans von Mangoldt.

(mathematics) A certain arithmetic function that is neither multiplicative nor additive. It is denoted by Λ(n) and defined as :Λ(n)= log p mbox ifn=pᵏ mbox forsomeprimep mbox andintegerk>1,\0 mbox otherwise.


Merkle tree

Named after American computer scientist Ralph Merkle (1952–), who patented it in 1979.

named-after

2001, Josep Domingo-Ferrer, Mobile Agent Route Protection through Hash-Based Mechanisms, C. Pandu Rangan, Cunsheng Ding (editors), Progress in Cryptology - INDOCRYPT 2001: 2nd International Conference, Proceedings, Volume 2, Springer, LNCS 2247, page 17,
The second solution uses Merkle trees and minimizes the cost of route protection by the agent owner, so that a single digital signature suffices to protect the whole route; for hosts along the route, the verification cost is similar to the cost of previous schemes in the literature, namely one digital signature verification per route step.

2004, Michael Szydlo, Merkle Tree Traversal in Log Space and Time, Christian Cachin, Jan Camenisch (editors), Advances in Cryptology - EUROCRYPT 2004: International Conference, Proceedings, Springer, LNCS 3027, page 541,
Merkle trees have found many uses in theoretical cryptographic constructions, having been specifically designed so that a leaf value can be verified with respect to a publicly known root value and the authentication data of the leaf.

In order to support dynamic data operations, the Merkle Tree is made dynamic by making use of relative index.

2015, Puonam M. Pardeshi, Bharat Tidke, “Improvement of Data Integrity and Data Dynamics for Data Storage Security in Cloud Computing”, in J. K. Mandal, Suresh Chandra Satapathy, Manas Kumar Sanyal, Partha Pratim Sarkar, Anirban Mukhopadhyay, editors, Information Systems Design and Intelligent Applications, Proceedings of 2nd International Conference, Volume 1, Springer, page 279:

(computer science, cryptography) A binary hash tree.


Bézout's identity

greatest common divisor
greatest common divisor

(mathematics) A theorem in the elementary theory of numbers: let a and b be integers, not both zero, and let d be their greatest common divisor. Then there exist integers x and y such that ax + by = d.


pulse wave

A kind of non-sinusoidal waveform that is similar to a square wave but lacks the perfectly symmetrical shape.


Bravais lattice

en-noun

Bravais lattice (plural Bravais lattices)

(geometry, crystallography) An infinite array of discrete points generated by a set of discrete translation operations mathbf R=n_1 mathbf a₁+n_2 mathbf a₂+n_3 mathbf a₃, where nᵢ are any integers and aᵢ are known as the primitive vectors which lie in different directions and span the lattice.


prestack

Grothendieck topology
Grothendieck topology#English

(category theory) The category c is called a prestack over a category C with a Grothendieck topology if it is fibered over C and for any object U of C and objects x, y of c with image U, the functor from objects over U to sets taking F:V→U to Hom(F*x,F*y) is a sheaf.


Grothendieck topology

Grothendieck topology (plural Grothendieck topologies)

Named after the mathematician Alexander Grothendieck.

(category theory) A structure on a category which makes the category's objects act like the open sets of a topological space.

Alexander Grothendieck
Grothendieck topology


geometrography

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(geometry) The study of geometrical constructions.


lensoidal

en-adj

lensoidal (comparative more lensoidal, superlative most lensoidal)

more lensoidal (comparative)
most lensoidal (superlative)

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(geometry) Of a lenticular shaped geometry.


antipodism

(topology) The relation between points on a sphere which are directly opposite each other; or the function which maps a point to its opposite point.


complex-differentiable

This gives the possibility to extend the well-established theory of complex-differentiable operators, a theory with meany^([sic]) deep results.

1993, Victor Khatskevich, David Shoiykhet, Differentiable Operators and Nonlinear Equations, page 75:

Further it can be shown that the holomorphic function also has a convergent Taylor series, that is, a complex differentiable function is also an analytic function (Section 23.7).

2010, Luis Manuel Braga da Costa Campos, Complex Analysis with Applications to Flows and Fields, page 335:

We can of course regard a function f defined on #92;mathbb#123;R#125;#123;2n#125; as a function defined on #92;mathbb#123;C#125;#123;n#125;. If f is differentiable on #92;mathbb#123;R#125;#123;2n#125;, it is said to be real-differentiable, and if f is differentiable on #92;mathbb#123;C#125;#123;n#125;, it is complex-differentiable. A function is complex-differentiable if and only if it is real-differentiable and the Cauchy-Riemann equations hold.

2010, Peter J. Schreier, Louis L. Scharf, Statistical Signal Processing of Complex-Valued Data, Cambridge University Press, page 277:

Cauchy-Riemann equation
Cauchy-Riemann equation

(mathematics, complex analysis, of a function) That is differentiable and satisfies the Cauchy-Riemann equations on a subset of the complex plane.

analytic

differentiable and that satisfies the Cauchy-Riemann Equations on a subset of the complex plane

entire

differentiable and that satisfies the Cauchy-Riemann Equations on the complex plane


polycycle

Recall that the cyclicity of a polycycle in a family of equations is the maximal number of limit cycles that may occur from the polycycle in this family.

2004, Normal Forms, Bifurcations and Finiteness Problems in Differential Equations:

(mathematics) A planar countably locally-finite graph in which all interior vertices have the maximum vertex degree and all interior faces are polygons with the same number of faces.


excenter

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(US, geometry) The center of an excircle.


long line

(mathematics) A topological space, constructed by stringing together an uncountable number of intervals, which is "longer" than the real line.


polynormal

(group theory, of a subgroup) Such that its closure under conjugation by any element of the parent group can also be achieved via closure by conjugation by some element in the subgroup generated.


pronormal

(group theory, of a subgroup) Such that each of its conjugates is conjugate to it already in the subgroup generated by it and its conjugate.


Neyman-Pearson lemma

Named after Jerzy Neyman and Egon Pearson.

(statistics) A lemma stating that when performing a hypothesis test between two point hypotheses H₀: θ = θ₀ and H₁: θ = θ₁, then the likelihood-ratio test which rejects H₀ in favour of H₁ when Λ(x)=(L(θ₀∣x))/(L(θ₁∣x))≤η where P(Λ(X)≤η∣H_0)=α is the most powerful test of size α for a threshold η.


exradius

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maquia

From Portuguese maquia, from Andalusian Arabic مَكِيلَة (makíla), from Arabic مَكِيلَة (makīla, “measured”). Doublet of maquila.

(historical) A traditional Portuguese unit of dry measure, equivalent to 0.8–1.2 liters in different 19th-century contexts.


Riccati equation

en-noun

Riccati equation (plural Riccati equations)

Named after Jacopo Francesco Riccati (1676–1754), Italian mathematician.

ordinary differential equation
ordinary differential equation

(mathematics) Any first-order ordinary differential equation that is quadratic in the unknown function.


pseudomedian

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(statistics) A measure of centrality for data sets and populations, which agrees with the median where the data are symmetric.


Kronecker delta

Kronecker delta (plural Kronecker deltas)

Named after German mathematician Leopold Kronecker (1823–1891)

named-after

The Kronecker delta #92;delta#95;#123;ij#125; is an example of an isotropic tensor. That is, its components remain invariant with rotation of coordinate axes.

1998, Robert G. Deissler, Turbulent Fluid Motion, Taylor & Francis, page 24:

The permutation symbol and the Kronecker delta prove to be very useful in proving vector identities.

2007, J. N. Reddy, An Introduction to Continuum Mechanics, Cambridge University Press, page 20, Further, the Kronecker delta and the permutation symbol are related by the identity, known as the e-δ identity [see Problem 2.5(d)], e_ijke_imn=δⱼₘδₖₙ-δⱼₙδₖₘ. (2.2.43)

The most important property of the Kronecker delta occurs when it shares a common repeated index with another tensor:
Note 10.1.3. When an index of a tensor T is contracted with one of the indices of the Kronecker delta, the result is an expression in which the Kronecker delta is removed and the contracted index of T is replaced by the other index of the Kronecker delta.

2017, Sadri Hassani, Special Relativity: A Heuristic Approach, Elsevier, page 257:

(mathematics) A binary function, written as δ with two subscripts, which evaluates to 1 when its arguments are equal, and 0 otherwise.

(mathematics) A unary function, written as δ with a single index, which evaluates to 1 at zero, and 0 elsewhere.


Dirac delta

Named after English theoretical physicist Paul Dirac (1902–1984); the notation was chosen because the symbol behaves analogously to the Kronecker delta.

(mathematics) A function-like symbol denoted as δ, with the property ∫f(t)δ(x-t)dt=f(x), informally understood as a function with an infinite value at 0 and zero elsewhere, and formally as a distribution or a measure.


subforest

F is a subforest of the tree T.

(mathematics) A subgraph that is a forest.


semipositone

Finally, we mention that several papers studied nonlinear eigenvalue problems of the form

Leszek Gasinski, Nikolaos S. Papageorgiou (2004) Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, CRC Press, page 704

(mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.


bouquet of circles

en-noun

bouquet of circles (plural bouquets of circles)

(mathematics, graph theory) A graph with only one vertex.


wedge of circles

wedge of circles (plural wedges of circles)

(graph theory) A graph with only one vertex.


LERF

(mathematics) Acronym of locally extended, residually finite.


premouse

(set theory) A generalization of a mouse that is not necessarily iterable.


Brunnian link

Named after Hermann Brunn, whose 1892 article Über Verkettung included examples of such links.

(topology) A nontrivial link that becomes a set of trivial unlinked circles if any one component is removed. In other words, cutting any loop frees all the other loops.


Zariski-Riemann space

Zariski-Riemann space (plural Zariski-Riemann spaces)

Named by Nagata (1962) after Oscar Zariski and Bernhard Riemann.

(algebraic geometry) A locally ringed space of a subring k of a field K, whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve.

Bernhard Riemann
Oscar Zariski
Zariski-Riemann space


abelianize

en-verb

abelianize (third-person singular simple present abelianizes, present participle abelianizing, simple past and past participle abelianized)

abelianizes (present singular third-person)
abelianizing (participle present)
abelianized (participle past)
abelianized (past)

(mathematics) to transform into an abelian group


biinfinite

(mathematics) Infinite in both directions, having neither a first nor a last element.


kth

(mathematics) Occurring at position k in a sequence.


lth

(mathematics) Occurring at position l in a sequence.


Dehornoy order

(mathematics, braid theory) A left-invariant total order on the braid group.


uniform distribution

en-noun

uniform distribution (plural uniform distributions)

(mathematics) A symmetric probability distribution wherein every outcome is equally likely to occur at any point in the distribution.

均匀分布

probability distribution where each outcome is equally likely to occur


frameproof

(mathematics) Describing a specific type of code that cannot be exploited by a user claiming to have been framed by others.


epimoric

From the Ancient Greek ἐπιμόρῐος (epimórĭos, “containing a whole + a fraction with 1 for its numerator (1+¹⁄ₓ)”, “superparticular”), from ἐπί (epí, “upon”, “over”, “above”) + μόριον (mórion, “a fraction with 1 for its numerator”) + -ιος (-ios, suffix forming adjectives); for the ending, see the English -ic.


nonrepeating

(mathematics) Describing the representation of a number having the property that no sequence of digits is repeated ad infinitum.

diulitin

describing the representation of a number


biautomatic

(mathematics, of a group) Having two multiplier automata


eigenline

(mathematics) A one-dimensional eigenspace.


selfadjointness

(mathematics) The condition of being selfadjoint


Coxeter-Dynkin diagram

en-noun

Coxeter-Dynkin diagram (plural Coxeter-Dynkin diagrams)

After mathematicians H. S. M. Coxeter and Eugene Dynkin.

A Coxeter-Dynkin diagram encodes the information in a Coxeter matrix, which in turn encodes the presentation of a Coxeter group.

Vertices of a Coxeter-Dynkin diagram represent generators of the corresponding Coxeter group. The generators (algebraic) in turn correspond to the reflecting hyperplanes (geometric). A pair of vertices which are not linked by an edge correspond to a pair of commuting generators. An unnumbered edge between a pair of vertices means that the braid relation between the corresponding generators has length three (e.g., aba = bab if the generators are a and b). An edge numbered ≥4 means that the braid relation between the corresponding generators has a length equal to that number. For example, if the edge is numbered 4 then the braid relation is cdcd = dcdc if the generators are c and d. If a set of edges form a cycle then the Coxeter group can be shown to be infinite. If a tree in a Coxeter-Dynkin diagram has more than one numbered edge then the Coxeter group can be shown to be infinite. There are a few more such rules, which ensure that finite Coxeter groups have Coxeter-Dynkin diagrams with relatively simple shapes.

Let 𝒬 be an indecomposable root lattice and let Γ denote the Coxeter-Dynkin diagram of the underlying root system Δ.

1995 June, R. V. Moody, J. Patera, “Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices”, in Canadian Journal of Mathematics, page 597:

There is a deep and only partially understood connection between the classification and structure of singularities and the Coxeter-Dynkin diagrams introduced by H. S .M. Coxeter for classification of reflection-generated groups and by E. B. Dynkin for classification of semisimple Lie algebras.

2000, Andrei Gabrielov, “Coxeter-Dynkin diagrams and singularities”, in Evgeniĭ Borisovich Dynkin, A. A. Yushkevich, Gary M. Seitz, A. L. Onishchik, editors, Selected Papers of E. B. Dynkin with Commentary, page 367:

For 3 ≤ n ≤ 5, we will use Eₙ to denote the Coxeter-Dynkin diagrams of types A₁ + A₂(N = 3), A₄(N = 4) and D₅(N = 5).

2012, Igor V. Dolgachev, Classical Algebraic Geometry: A Modern View, page 363:

(geometry, algebra) A graph with numerically labelled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

Coxeter-Dynkin diagram
Eugene Dynkin
Harold Scott MacDonald Coxeter


hartley

Named after Ralph Hartley (1888–1970), electronics researcher.

A unit of information (symbol Hart) representing the information content of an event if the probability of that event occurring is 1/10. It is therefore equal to the information contained in one decimal digit


Hartley transform

Hartley transform (plural Hartley transforms)

It was proposed as an alternative to the Fourier transform in 1942 by American engineer Ralph Hartley.

(mathematics) An integral transform closely related to the Fourier transform, but which transforms real-valued functions to real-valued functions.


Riemann-Lebesgue lemma

Named after Bernhard Riemann and Henri Lebesgue.

(mathematics) A lemma, of importance in harmonic analysis and asymptotic analysis, stating that the Fourier transform or Laplace transform of an L1 function vanishes at infinity.


inlier

(statistics) A value that fits a pattern, rather than being an outlier.


girah

A former unit of length in India and Pakistan, approximately 2.25 inches (5.715 cm).


semidecidability

(mathematics) Alternative spelling of semi-decidability (“property of being semi-decidable”)


semi-decidability

(mathematics) The property of being semi-decidable.


Farey sequence

Named after British geologist John Farey Sr., whose letter about the sequences was published in the Philosophical Magazine in 1816.

Students should then see the number of fractions N, in the Farey sequence is equal to #92;phi(2)#43;#92;phi(3)#43;#92;phi(4)#43;#92;dots#43;#92;phi(n), where #92;phi(n) is the number of positive integers less than or equal to n that are relatively prime to n.

2002, Alfred S. Posamentier, Jay Stepelman, Teaching Secondary Mathematics, Merrill, page 403:

2007, Jakub Pawlewicz, Order Statistics in the Farey Sequences in Sublinear Time, Lars Arge, Michael Hoffmann, Emo Welzl (editors), Algorithms - ESA 2007: 15th Annual European Symposium, Proceedings, Springer, LNCS 4698, page 218,
The Farey sequence of order n (denoted ℱₙ) is the increasing sequence of all irreducible fractions from interval [0,1] with denominators less than or equal to n. The Farey sequences have numerous interesting properties and they are well known in the number theory and in the combinatorics.

Riemann sums have also important connections with various problems from number theory, among them the Riemann Hypothesis, through their link with Farey sequences.

2009, Michel Weber, Dynamical Systems and Processes, European Mathematical Society, page 549:

(number theory) For a given positive integer n, the sequence of completely reduced fractions between 0 and 1 which, when in lowest terms, have denominators less than or equal to n, arranged in order of increasing size.

Farey sequence
John Farey Sr.
Philosophical Magazine


Sharkovskii's theorem

Named after Oleksandr Mikolaiovich Sharkovsky.

(mathematics) A theorem about discrete dynamical systems. One of its implications is that if a discrete dynamical system on the real line has a periodic point of period 3, then it must have periodic points of every other period.

Oleksandr Mikolaiovich Sharkovsky
Sharkovskii's theorem


Polybius square

Polybius square (plural Polybius squares)

From Polybius + square (“grid”). It was invented by the Ancient Greek historian and scholar Polybius.

(cryptography) A grid used for fractionating plaintext characters so that they can be represented by a smaller set of symbols.


J-curve

From the shape, which resembles the letter J.

exponential growth, or a graph detailing it.


S-curve

From the shape, which resembles a vertically compressed letter S.

The current S-curve includes much gentler bends starting around Randolph Street and ending just before Monroe Street.

2016 March 15, Justin Breen, “Remember The Old Lake Shore Drive 'S' Curve? It's Been Gone For 30 Years”, in DNAinfo, archived from the original on 2023-07-29:

The so-called “S-curve” on I-25 is a notoriously dangerous stretch of freeway just south of the Big-I.

2024 April 17, Curtis Segarra, “NMDOT hosting public meeting on ‘S-curve’ portion of Albuquerque I-25”, in KRQE:


critical exponent

critical exponent (plural critical exponents)

The critical exponent of "Mississippi" is 7/3, as it contains the string "ississi", which is of length 7 and period 3.

(mathematics, computing theory) The greatest number of times that a contiguous subsequence can be repeated.


demihypercube

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(geometry) Any of a class of n-polytopes constructed from alternation of an n-hypercube.


hosohedron

A tessellation of lunes on a spherical surface, such that each lune shares the same two vertices.


bicylinder

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(geometry) A solid formed by two intersecting cylinders.


tricylinder

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(geometry) A solid formed by three intersecting cylinders.


Steinmetz solid

Steinmetz solid (plural Steinmetz solids)

Named after Charles Proteus Steinmetz, though these solids were known long before Steinmetz studied them.

(geometry) The solid body generated by the intersection of two or three cylinders of equal radius at right angles.


polychoric

2007, Bruno D. Zumbo, 3: Validity: Foundation Issues and Statistical Methodology, C. R. Rao, S. Sinharay (editors), Handbook of Statistics, Volume 26: Psychometrics, page 66,
Because the CES-D items are ordinal in nature (i.e., in our case a four-point response scale, and hence not continuous), a polychoric covariance matrix was used as input for the analyses.

Socioeconomic status (SES) was represented by a factor score derived using the polychoric method, which is a variation on the principle component analysis procedure designed for use with dichotomous and categorical variables (Kolenikov S, 2004).

2008, Emily Anton Bobrow, Factors that influence disclosure and program participation among pregnant HIV-positive women, page 57:

The polychoric correlation coefficient is an estimator of the correlation coefficient in the underlying bivariate normal distribution.

2010, William H. Greene, David A. Hensher, Modeling Ordered Choices: A Primer, page 294:

The authors propose using polychoric correlations in order to estimate the correlation matrix before using PCA.^([Principal Component Analysis]) Polychoric PCA assumes that the observed ordinal variable has an underlying continuous variable and uses maximum likelihood to calculate how that continuous value would have to be split up in order to produce the observed data.

2010, Adriana Rocío Cardozo Silva, Economic Growth and Poverty Reduction in Colombia, page 49:

(statistics) Of or pertaining to the relationship between two latent variables, each assumed to have a normal distribution and associated with an ordinal variable.


Dunning-Kruger effect

Dunning-Kruger effect (plural Dunning-Kruger effects)

Coined on everything2 in 2002 by user uucp, who in 2005 copied the same entry to Wikipedia under the title Dunning-Kruger syndrome, named for David Dunning and Justin Kruger of Cornell University, who studied the phenomenon.

Though it grants them the advantage of higher levels of optimism, the Dunning-Kruger effect also hamstrings low performers with an even greater disadvantage: being less aware of their failings, they remain less likely to see the need, and thus make the effort, to improve themselves.

2012, Alex Lickerman, The Undefeated Mind, Simon and Schuster, →ISBN:

(psychology) A cognitive bias by which an unskilled individual suffers from illusory superiority, mistakenly rating their ability as much higher than it actually is.


latent variable

latent variable (plural latent variables)

The variables are latent (“hidden”) because they are not directly observed, but instead inferred from other variables.

Each of these is a latent variable, which is measured by one or more observable variables.

1995, J. Tague-Sutcliffe, L. Vaughan, C. Sylvain, “Using LISREL to Measure the Impact of Information on Development: London Site Pilot Study”, in Paul McConnell, editor, Making a Difference: Measuring the Impact of Information on Development, Proceedings of a Workshop, page 141:

2002, Cavid J. Bartholomew, 1: Old and New Approaches to Latent Variable Modelling, George A. Marcoulides, Irini Moustaki (editors), Latent Variable and Latent Structure Models, 2012, page 1,
The earliest use of latent variable ideas in time series appears to have been due to Wiggins (1973) but, as so often happens, it was not followed up. […] The basis for this remark can be explained by reference to a simple example which, at first sight, appears to have little to do with latent variables.

As stated earlier, in addition to having df greater than 0, the second condition for model identification is that the latent variables have to be scaled.

2008, Donna Harrington, Confirmatory Factor Analysis, page 26:

(statistics) A variable that is not directly measured but is inferred by means of a mathematical model from one or more directly observed variables.


factor analysis

factor analysis (countable and uncountable, plural factor analyses)

Factor analysis is a generic term that we use to describe a number of methods designed to analyze interrelationships within a set of variables or objects.

1993, Richard A. Reyment, K. G. Jöreskog, Applied Factor Analysis in the Natural Sciences, page 71:

Exploratory factor analysis (EFA) and principal components analysis (PCA) both are methods that are used to help investigators represent a large number of relationships among interval-level variables in a simpler (more parsimonious) way.

2005, Nancy L. Leech, Karen Caplovitz Barrett, George Arthur Morgan, SPSS for Intermediate Statistics: Use and Interpretation, page 88:

Hence, the idea of nonlinear factor analysis should not be treated as an extension of the basic factor analysis concept, but should be considered as an inherent effort to make factor analysis more complete and useful.

2007, Melanie M. Wall, Yasuo Amemiya, “Chapter 16: A Review of Nonlinear Factor Analysis and Nonlinear Structural Equation Modeling”, in Robert Cudeck, Robert C. MacCallum, editors, Factor Analysis at 100: Historical Developments and Future Directions, unnumbered page:

(uncountable, statistics) A statistical method used to describe variability among observed correlated variables in terms of one or more unobserved variables (called factors).

Separate exploratory factor analyses using an oblique rotation were conducted on the item sets measuring task values, task difficulty perceptions, and ability perceptions.

1999, Jacquelynne S. Eccles, Allan Wigfield, “In the Mind of the Actor: The Structure of Adolescents' Achievement Task Values and Expectancy-Related Beliefs”, in Richard M. Lerner, Jasna Jovanovic, editors, Cognitive and Moral Development and Academic Achievement in Adolescence, page 219:

The factor analyses clearly showed significant vectors where variables of campesino identity are related.

2008, Nina K. Müller-Schwarze, When the Rivers Run Backwards, page 368:

Consequently, exploratory factor analyses were utilized to identify a factor structure represented by the survey items.

2010, Nicole Nicotera, Inna Altschul, Andrew Schneider-Munoz, Ben Webman, “Conceptual and Analytic Development of a Civic Engagement Scale for Preadolescents”, in Jeff Keshen, Barbara A. Holland, Barbara E. Moely, editors, Research for What?: Making Engaged Scholarship Matter, page 81:

(countable, statistics) A statistical study performed using the method.


cotype

Coordinate term: type

Rademacher distribution
Rademacher distribution

(functional analysis) A Banach space (X,‖·‖), such that, given a sequence of independent random variables from a Rademacher distribution, (εᵢ), and a rank q in the range from 2 to infinity, there exists a finite constant C≥1 such that for all finite sequences (x_i)∈X, 𝔼_ε[‖∑ limits ᵢ₌₁ⁿεᵢx_i‖^q]≥1/(C^q)(∑ limits ᵢ₌₁ⁿ‖x_i‖^q), if;2≤q<∞ or 𝔼_ε[‖∑ limits ᵢ₌₁ⁿεᵢx_i‖]≥1/C sup ‖x_i‖, if;q=∞ .


stremma

From Byzantine Greek στρέμμα (strémma, “a turning”), referring to the turning of the soil.

A Greek unit of land area, now equal to a decare (1,000 m²) but (historical) previously 10,000 square Greek feet.


micromilligram

Alternative spelling of nanogram. symbol:ŋmg


micromicrogram

From micromicro- + gram, equivalent to micro- + microgram.


rpd

relative pointwise distance
relative pointwise distance#English

(mathematics) Initialism of relative pointwise distance.


Gleason's theorem

A mathematical theorem, important for quantum logic, proving that the Born rule for the probability of obtaining specific results for a given measurement follows naturally from the structure formed by the lattice of events in a real or complex Hilbert space.


quasibarrelled

(mathematics, of a topological vector space) For which every barrelled bornivorous set in the space is a neighbourhood of zero.


partial sum

(mathematics) The sum of the first n terms of an infinite series, where n is a finite number.


Venus zone

Venus (planet) + zone, from being the zone where a Venus-like planet will acquire a Venus-like climate.

A theoretical orbital zone around a star that will result in an Earth-like planet existing in an orbit in the zone having a runaway greenhouse effect, similar to that found on Venus in our Solar System. The inner edge of the zone is where solar radiation is intense enough to strip the atmosphere of a planet away. The outer edge is where solar radiation is insufficient to power a runaway greenhouse.


golygon

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(geometry) A serial isogon of 90 degrees; any polygon with all right angles, whose sides are consecutive integer lengths.


antiflag

(mathematics) A nonincident point-hyperplane pair in a projective space.


block model

(mathematics) A model of a network made by dividing it into blocks


supercompactness

(mathematics) Quality of being supercompact.


GCF

greatest common factor
greatest common factor#English

(arithmetic) Initialism of greatest common factor.


HCF

highest common factor
highest common factor#English

(mathematics) Initialism of highest common factor.


Langton's ant

A simulated ant, part of a cellular automaton with simple rules but complicated emergent behaviour. The ant traverses a square lattice of cells, changing their colours and its direction as it passes over them.


Altuve

After José Altuve, Venezuelan-American baseball player who stands five feet, five inches tall.

So, if you want to know the minimum length of a World Cup Soccer field while watching TV, it's 60.9 Altuves.

2014 June 30, Bob Nightengale, “Diminutive dandy: Jose Altuve keeps reaching new heights”, in USA Today:

In 2012 Houston Astros fan Bryan Trostel was watching a game when he heard the announcers joke about how many “altuves” a home run had traveled.

2015, Uncle John's FACTASTIC Bathroom Reader, →ISBN:

Judge is 1.22 Altuves. Is there a drawback to being a big man in baseball?

2017 October 13, Victor Mather, “David vs. Goliath Gets an Update: It's Now Altuve vs. Judge”, in New York Times:

No matter how you slice it, Altuve is one of the best hitters in baseball despite yielding at least 7 inches (that’s about .108 Altuves) to every other elite hitter.

2018 February 20, Kate Preusser, Isabelle Minasian, Tim Cantu, Connor Donovan, “2018 AL West Preview: The Astros’ Lineup”, in Lookout Landing:

Want to know how many Altuves there are from home plate to first base? That would be 16.61436219309581.

2018 June 1, Melanie Hauser, “Ways to recover from the Rockets' loss”, in Houston Chronicle:

(baseball, slang) A distance of five feet and five inches, used chiefly as a unit to measure distances of home run balls.


acute angle

(geometry) An angle measuring less than 90 degrees.

زَاوِيَة حَادَّة

angle measuring less than ninety degrees


obtuse angle

(mathematics, geometry) An angle that is greater than 90 degrees and less than 180 degrees.


siriometer

From Sirius and meter. It is roughly twice the distance from Earth to the star Sirius.

The siriometer dates its pedigree from the founder of stellar astronomy, William Herschel. As is well known, the distance unit used by Herschel is the mean distance of the first magnitude stars, which distance was called by him the distance of Sirius.

1925, The Observatory, volume 48, page 143:

He had used the star Sirius as his standard, so he decided to call the distance to Sirius, whatever it might turn out to be in miles or kilmetres, one 'siriometer'. Herschel calculated that the grindstone measured 1,000 siriometers across and was 100 siriometers thick.

2013, Kitty Ferguson, Measuring the Universe: The Historical Quest to Quantify Space, Random House, →OCLC:

A unit of distance equal to one million astronomical units or 15.813 light-years.


hoppus

A unit of measure of volume equal to 1.273 cubic feet or 2,200 cubic inches. Used in the British Empire as a measure of lumber.


eggling

"Ode X" in 1834, Charles L. S. Jones, American Lyrics
One Lovling scarcely's fledg'd. One, yet,
An eggling still remains;
A third, from forth the broken shell,
In chirping notes, complains.

But now the little Other eggling was making loud peeping sounds. It was hungry.

A small, miniature, undersized, or underdeveloped egg.


TNT equivalent

The amount of energy released by an explosion expressed in terms of the amount of TNT needed to generate a similar explosion. Used especially to describe nuclear bombs.


reflex angle

(geometry) An angle greater than 180 degrees but less than 360 degrees.


please excuse my dear Aunt Sally

order of operations
order of operations#English

(mathematics) A mnemonic used to help people remember the order of operations, in the PEMDAS order.


Sir Philip Sidney game

Sir Philip Sidney game (plural Sir Philip Sidney games)

Named after a story about Sir Philip Sidney, who allegedly, when fatally wounded, gave his water to another, saying, "Thy necessity is greater than mine."

(biology, game theory) A model for the evolution and maintenance of informative communication between relatives, developed to explain begging behaviour in chicks.

Sir Philip Sidney
Sir Philip Sidney game


carrier set

(algebra) the underlying set of an algebraic structure


essential supremum

essential supremum (plural essential suprema)

essential infimum

antonym(s) of “supremum valid almost everywhere”

mathematical analysis
mathematical analysis

(mathematical analysis) The supremum (least upper bound) of a function which holds almost everywhere. In symbols, ess sup f= inf M:μ(x:f(x)>M)=0

Essential supremum and essential infimum


essential infimum

essential infimum (plural essential infima)

essential supremum

antonym(s) of “infimum valid almost everywhere”

(mathematical analysis) The infimum (greatest lower bound) of a function which holds almost everywhere. In symbols, ess inf f= sup m:μ(x:f(x)<m)=0.


Monster group

We next consider the possible #92;Z#95;n orbifoldings of #92;mathcal#123;V#125;² with respect to elements of the Monster group M [Tul].

1996, Michael P. Tuite, “Monstrous Moonshine and orbifolds”, in K.T. Arasu, J.F. Dillon, K. Harada, S. Sehgal, R. Solomon, editors, Groups, Difference Sets, and the Monster: Proceedings of a Special Research Quarter, Walter de Gruyter, page 443:

We note that c(1)#61;196883; this is not just a numerological coincidence, but follows from a branch of mathematics called moonshine theory which arises from string theory and relates the Monster group and modular functions.

2008, L. J. P. Kilford, Modular Forms: A Classical and Computational Introduction, Imperial College Press, page 106:

They were also crucial in understanding the Monster and Moonshine phenomena, which refers to the fact that the dimensions of the irreducible representations of the largest sporadic finite group, the monster group, show up in the q-expansion coefficients of the elliptic modular function j.

2014, Martin Schlichenmaier, Krichever-Novikov Type Algebras: Theory and Applications, Walter de Gruyter, page 340:

(algebra) The largest sporadic group, of order 2⁴⁶ · 3²⁰ · 5⁹ · 7⁶ · 11² · 13³ · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 (approximately 8 · 10⁵³), denoted M or F₁.


cuban prime

Punningly on cube (mathematical sense) and Cuban, though there is no meaningful connection with the country of Cuba.

(mathematics) A prime number that is a solution to one of two specific equations involving third powers of x and y. The two equations are p=(x³-y³)/(x-y),x=y+1,y>0 and p=(x³-y³)/(x-y),x=y+2,y>0.


idom

(graph theory) Abbreviation of immediate dominator.


eigenhead

(mathematics, computing) One of a set of eigenvectors used in visual recognition systems to represent a person's head.


TFAE

(mathematics) Initialism of the following are equivalent; placed before a sequence of statements to mean that any one of the statements implies and is implied by any of the others.


illumination problem

(mathematics) A mathematical problem, asking whether a room with mirrored walls can always be illuminated by a single-point light source, allowing for repeated reflection of light off the mirrored walls. It was solved in 1958: there are such rooms that cannot be thus illuminated.


tensor product

Linear Transformations on Tensor Products of Vector Spaces
…
Proposition 16. Let V and W be finite dimensional vector spaces over the field F with bases v_1,...,v_n and w_1,...,w_m respectively. Then V⊗_FW is a vector space over F of dimension nm with basis v_i⊗w_j, 1<i<n and 1<j<m.

2004, David S. Dummit with Richard M. Foote, chapter 11, in Abstract Algebra, →OCLC, page 421

[The tensor product] U⊗V is the span of u⊗v:u∈U,v∈V
modulo the relations
·u⊗(v+v')=u⊗v+u⊗v'\·(u+u')⊗v=u⊗v+u'⊗v\·(λu)⊗v=λ(u⊗v)=u⊗(λv)

2012, 27:30 from the start, in Lecture 1 . Hopf Algebras and Combinatorics (Federico Ardila), spoken by Federico Ardila (Federico Ardila), Federico Ardila, via YouTube

(mathematics) The most general bilinear operation in various contexts (as with vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, modules, and so on), denoted by ⊗.

tensor

if the tensor product is between algebraic structures


parallel postulate

parallel postulate (plural parallel postulates)

From the reference to parallel lines in the definition as formulated below, following Scottish mathematician John Playfair; this wording leads to a convenient basic categorization of Euclidean and non-Euclidean geometries. The original formulation in Euclid's Elements makes no mention of parallels.

Before we examine the particulars of the parallel postulates of Hyperbolic and Elliptical geometries, we must see their logic.

1962, Mary Irene Solon, The Parallel Postulates of Non-Euclidean Geometry: The Pentagon: A Mathematics Magazine for Students, Volumes 22-25, page 28:

The earliest known attempt to prove the parallel postulates from the other axioms was by Ptolemy in about 150 A.D.

1969, John B. Fraleigh, Mainstreams of Mathematics, Addison-Wesley, page 95:

Euclid's parallel postulate may not have seemed so important when you studied geometry in high school, since it is used only once in order to derive the basic result 1 on alternate interior angles, which is then constantly used to derive further results.

1989, Walter Prenowitz, Meyer Jordan, Basic Concepts of Geometry, Ardsley House Publishers, published 1965, page 28:

In order to understand this section, it is vital to keep in mind an important fact: The "proof" of the parallel postulate presented here is not correct. In fact, there can be no proof of the parallel postulate that relies only on the other axioms and postulates of Euclid.

1998, David A. Singer, Geometry: Plane and Fancy, Springer, page 16:

After enduring twenty centuries of criticism, Euclid's theory of parallels was fully vindicated in 1868 when Eugenio Beltrami proved the independence of Euclid's parallel postulate by constructing a Euclidean model of the hyperbolic plane.

2006, John Ratcliffe, Foundations of Hyperbolic Manifolds, Springer, page 7:

(geometry) An axiom in Euclidean geometry: given a straight line L and a point p not on L, there exists exactly one straight line parallel to L that passes through p; a variant of this axiom, such that the number of lines parallel to L that pass through p may be zero or more than one.

American Mathematical Society
Euclid's Elements
John M. Lee
John Playfair
parallel postulate


f.g.

finitely generated
finitely generated#English

(mathematics) Abbreviation of finitely generated.