darwin

Named after Charles Darwin, coined by J.B.S. Haldane in 1949.

One darwin (d) equals the rate of evolution that would produce a change in size by a factor of approximately 2.7 in one million years.

1999, J. William Schopf, Evolution!: Facts and Fallacies, page 50:

The rate of evolutionary change in a species' wing or leg or beak (remember Darwin's finches mentioned in Chapter 1?) is assessed in degree-of-physical-change units called darwins.

2003, Donald Mitchell, The 2,000 Percent Solution, page 243:

For instance, gradual change is relatively common in vertebrates (about .08 darwins), though some rapidly evolving vertebrates lineages show rates as high as 10 darwins, over short periods.

2010, Sahotra Sarkar, Anya Plutynski, A Companion to the Philosophy of Biology, page 177:

evolutionary biology
evolutionary biology

A unit of evolutionary change in evolutionary biology.


millidarwin

Haldane concluded as Darwin had that the rate of evolution by natural selection in the world around us must be infinitesimally slow, far too slow to watch, that it could only be watched in the long, slow additions of the fossil record. Rates in the living world would have to be measured in millidarwins. In artificial selection, he said, you get rates of thousands of darwins, but that is not something you would see in the wild: "Rates of one darwin would be exceptional in nature."

2014, Jonathan Weiner, The Beak of the Finch: A Story of Evolution in Our Time, Knopf Doubleday Publishing Group, →ISBN, page 110:

A unit of evolutionary change equivalent to one thousandth of a darwin.


catalecticant

From catalectic + -ant, coined by James Joseph Sylvester in 1852.

(mathematics) A polynomial in the coefficients of a form of even degree that vanishes when the form is a sum of an unusually small number of powers of linear forms.


Cayleyan

(mathematics) A variety associated to a hypersurface.


quippian

(mathematics) A degree 5 class 3 contravariant of a plane cubic.


coaxal

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cosingular

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(algebra) Having the same singularities.


trans-Mars injection

en-noun

trans-Mars injection (plural trans-Mars injections)

(astrodynamics) an orbital burn (rocket firing) used to change orbit from local orbit, to a Mars transfer orbit (a Solar orbit that will intercept the planet Mars).


fraternal birth order effect

fraternal birth order effect (uncountable)

Thus the fraternal birth order effect is specific to male sexual orientation, and does not affect female sexual orientation.

2008, Glenn Wilson, Qazi Rahman, Born Gay: The Psychobiology of Sex Orientation, Peter Owen, →ISBN, page 98:

The influence of the fraternal birth order effect is not mediated by a male growing up with older stepbrothers but is influenced by them having biological brothers (who share the same mother) regardless of whether they are raised together or apart (Bogaert, 2006).

2010, Mark J. T. Sargeant, “Brain and Behaviour: Sex Differences”, in Philip Banyard, Mark N. O. Davies, Christine Norman, Belinda Winder, editors, Essential Psychology: A Concise Introduction, SAGE Publications, →ISBN, page 183:

The fraternal birth order effect is one of the most replicated and robust findings in sexual orientation research. Each son increases the odds of homosexuality in the next son by 33% relative to the base population rate […]

2014, Tuck C. Ngun, Eric Vilain, “The Biological Basis of Human Sexual Orientation: Is There a Role for Epigenetics?”, in Daisuke Yamamota, editor, Epigenetic Shaping of Sociosexual Interactions: From Plants to Humans, Academic Press, →ISBN, page 172:

The scientific observation that a man's statistical probability of being homosexual increases with the number of older brothers he has.


seat-mile

(transport) A unit of measure of passenger carrying capacity, equal to the number of seats available multiplied by the number of miles flown.


blobular

en-adj

blobular (comparative more blobular, superlative most blobular)

more blobular (comparative)
most blobular (superlative)

The catfish fillet is hot and flaky inside, a hot blobular doughnut.

1998, Frank Chin, Bulletproof Buddhists and Other Essays, University of Hawaii Press, page 21:

However, on the unusual occasions that a sting mark is observed, it is generally blobular rather than linear, leading to a hypothesis that the bell is responsible for the sting.

2013, Lisa-Ann Gershwin et al., Advances in Marine Biology, Volume 66, Academic Press, page 64:


sphenocorona

Blend of sphenoid + corona or from spheno- + corona. Coined by Norman W. Johnson in 1969.

(geometry) A polyhedron, one of the Johnson solids, whose faces are composed of 12 equilateral triangles and 2 squares.


sphenomegacorona

From spheno- + mega- + corona. Coined by Norman W. Johnson in 1969.

(geometry) A polyhedron, one of the Johnson solids, whose faces are composed of 16 triangles and 2 squares.


augmented sphenocorona

(geometry) A polyhedron, one of the Johnson solids, whose faces are composed of 16 equilateral triangles and one square.


triangular hebesphenorotunda

(geometry) A polyhedron, one of the Johnson solids, whose faces are composed of 13 triangles, 3 squares, 3 pentagons, and 1 hexagon.


minimum spanning tree

en-noun

minimum spanning tree (plural minimum spanning trees)

A spanning tree that has minimum possible weight for a given graph


Eckardt point

(geometry) A point of intersection of three lines on a cubic surface.


equiaffine

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(geometry) Being an affine transformation that preserves area.


equiaffinity

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(geometry) An affine transformation that preserves area.


evectant

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(geometry) A contravariant constructed from an invariant by acting on it with a differential operator called an evector.


evector

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(geometry) A differential operator that allows a contravariant to be constructed from an invariant.


Schläfli double six

Schläfli double six (plural Schläfli double sixes)

(geometry) A configuration of 30 points and 12 lines. The lines can be partitioned into two subsets of six: each line is disjoint from (skew with) the lines in its own subset of six lines, and intersects all but one of the lines in the other subset of six lines. Each of the 12 lines of the configuration contains five intersection points, and each of these 30 intersection points belongs to exactly two lines, one from each subset.


clothoid

From Ancient Greek κλώθω (klṓthō, “I spin”) + -oid.

(mathematics) A plane curve whose curvature at any point is proportional to distance along it.


conservative extension

conservative extension (plural conservative extensions)

(mathematics, logic) An extension of a logical theory such that every theorem expressible in the original theory is also derivable within the original theory.


Desargues configuration

Desargues configuration (plural Desargues configurations)

(geometry) A configuration of ten points and ten lines, with three points per line and three lines per point, whose existence is proven by Desargues' theorem.


perspectivity

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(geometry) The formation of an image in a picture plane of a scene viewed from a fixed point.


Desargues graph

Desargues graph (plural Desargues graphs)

(graph theory) A distance-transitive cubic graph with 20 vertices and 30 edges.


desmic

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(geometry, of polyhedra) Related such that each edge of one cuts a pair of opposite edges of the other.


rubber-hose cryptanalysis

Referring to the use of a rubber hose as a weapon to beat somebody with.

We have shown that GNUnet is vulnerable to rubber-hose cryptanalysis, but we additionally have presented an efficient content filter for GNUnet. If content filtering is legally enforced, censoring GNUnet is possible at a very large scale.

2003, Dennis Kügler, “An Analysis of GNUnet”, in Privacy Enhancing Technologies: Third International Workshop, edited by Roger Dingledine, Springer Science & Business Media, →ISBN, page 175:

Catherine scooted out of the way, giving Terry access to the keyboard. With a labored sigh, Terry began searching the encrypted text. “I could try a ciphertext-only attack,” he mumbled to no one in particular. “Then again,” he glared at the attacker and continued, “I could always try rubber-hose cryptanalysis.” He thought for a moment. “I don't need a total break; I'm only interested in information deduction. Let me check the swap file.”

2005, Ryan Russell, Peter A Riley, Jay Beale, Chris Hurley, Tom Parker, Brian Hatch, Stealing the Network: How to Own an Identity: How to Own an Identity, Syngress, →ISBN, page 279:

Other types of cryptanalytic attacks include chosen cipher text, chosen key, rubber hose cryptanalysis, and purchase key. Algorithms differ by degrees of security; this depends on how hard they are to break.

2010, Hazarathaiah Malepati, Digital Media Processing: DSP Algorithms Using C, Newnes, →ISBN, page 18:

(cryptography, euphemistic) The extraction of cryptographic secrets by coercion or torture.


pmf

probability mass function
probability mass function#English

Initialism of probability mass function.


pdf

probability density function
probability density function#English

Initialism of probability density function.


cumulative distribution function

cumulative distribution function (plural cumulative distribution functions)

cumulative distribution functions (plural)

A function which at each point t of the sample space has as its value the probability that a given random variable is less than (or equal) t. In symbols, F_X(t)=Pr(X<t).


Jordan curve

Named after French mathematician Camille Jordan (1838-1922), who first proved the Jordan curve theorem.

When μ is small and positive, the locus (1) consists of a Jordan curve near each of the Jordan curves belonging to B.

1950, Joseph Leonard Walsh, The Location of Critical Points of Analytic and Harmonic Functions, American Mathematical Society, page 242:

If fis a closed curve that is one-one on [0,1] except for f(0) = f(I), then we say that f is a Jordan curve. A Jordan curve can be seen as a homeomorphism from the circle C onto a subset of the given space.

1992, Konrad Jacobs, Invitation to Mathematics, page 164:

The most general Jordan curves, like the triangle, have the property of dividing the plane into two regions.

2001, Constantin Carathéodory, Theory of Functions of a Complex Variable, volume 1, page 100:

(topology) A non-self-intersecting continuous loop in the plane; a simple closed curve.


one-to-many

(mathematics, of a function) Having the property that the same argument may yield multiple values, but different arguments never yield the same value.

"Being a genetic mother of" is a one-to-many relation from the set of cats to the set of cats.

(mathematics, logic, of a relationship between two sets) Having the property that an element of one set may be assigned by the relationship to several elements in the other set, but that a given element in the second set can have only one member of the first set assigned to it.


many-to-one

(mathematics, logic, of a relationship between two sets) Having the property that many elements of one set may be assigned by the relationship to one element in the other set, and that a given element in the first set can be assigned by only one member of the second set.


many-to-many

"Is a fellow citizen with" is a many-to-many relationship on the set of people (from the set of people to the set of people).

(mathematics, logic, of a relationship between two sets) Having the property that many elements of one set may be assigned by the relationship to any element in the other set, and that a given element in the first set can also be assigned more than one member of the second set.


choice function

choice function (plural choice functions)

(set theory) A function whose domain is a family of nonempty sets, and which selects a member from each of those sets as its value.


epsilontic

From the fact that ε is the usual symbol used to denote an error bound.

The question is of a technical, gymnastic kind, and von Neumann's positive answer [4] uses the set-theoretic and epsilontic trickery appropriate to this domain.

1966, J. C. Oxtoby, B. J. Pettis, G. B. Price, John Von Neumann, 1903-1957, American Mathematical Soc., →ISBN, page 88:

If a parameter such as x in (7.71) is continuous, there are other operations of the group 'as close as one likes' to any given operation; in 'epsilontic' language, we must be able to write T(x + ε) → T(x) as ε → 0. (7.76)

1969, J. M. Ziman, Elements of Advanced Quantum Theory, Cambridge University Press, →ISBN, page 238:

Weierstrass precisely defines a function in the modern sense as a correspondence between two variable quantities—a definition he attributes to Fourier, Cauchy, and Dirichlet—and develops the epsilontic method.

1996, Ronald Calinger, Vita Mathematica: Historical Research and Integration with Teaching, Cambridge University Press, →ISBN, page 168:

Riemann definitely accepts the epsilontic justification of limit analysis, as shown by his well-known introduction of the concept of the integral in his habilitation paper of 1853 (W. 239), and, more fully, by this paper as a whole.

2009, Detlef Laugwitz, Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics, Springer Science & Business Media, →ISBN, page 44:

mathematical analysis
mathematical analysis

(mathematics) Pertaining to mathematical analysis using explicit error bound estimation and the epsilon-delta definition of a limit, especially as opposed to using infinitesimals.


epsilontics

Now epsilontics is losing ground, and after one or two decennia we can expect the "great discovery" that, properly understood, the infinitesimal methods of a century ago are completely rigorous. Algorithms with differentials are already modern.

1973, Hans Freudenthal, Mathematics as an Educational Task, Springer Science & Business Media, →ISBN, page 148:

In principle, we should not then have made any approximation at all; it is a rule of pure mathematics, hallowed by centuries of usage, and justified by the mysteries known to undergraduates as 'epsilontics', that a convergent series is as good as a simple finite algebraic expression for a solution — which is just as well, because almost every expression that appears in any formula in physics, such as a cosine, or a logarithm, is itself only definable algebraically as the sum of an infinite series.

1981, John M. Ziman, Puzzles, Problems and Enigmas: Occasional Pieces on the Human Aspects of Science, Cambridge University Press, →ISBN, page 51:

Both Cauchy and Abel must have been aware that epsilontics is a general tool for making rigorous proofs in analysis, but neither of them, to say nothing of their contemporaries, used it consistently.

2009, Detlef Laugwitz, Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics, Springer Science & Business Media, →ISBN, page 59:

(mathematics) An approach to mathematical analysis using the epsilon-delta definition of a limit, i.e. with explicit estimation of error bounds, as opposed to using infinitesimals.

Key abstract theorems are explained largely by physical reasoning, and are presented in the most concrete, intelligible fashion possible. Epsilontics are minimized.

1973, American Mathematical Society, Notices of the American Mathematical Society:

One might be more precise by giving an error for equation (16.2) or by considering the much smaller errors on the exclusion of other classical properties, but these epsilontics will be omitted.

1999, Roland Omnès, Understanding Quantum Mechanics, Princeton University Press, →ISBN, page 185:

Thus, Hadamard avoids Weierstrassian epsilontics in his text for engineering students.

2001, Peter Schuster, Ulrich Berger, Horst Osswald, Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum, Springer Science & Business Media, →ISBN, page 137:

The sequence of Riemann sums is a constant sequence and converges to its constant value s(b) − s(a). No “epsilontics” are needed.

2007, C Haines, P Galbraith, W Blum, S Khan, Mathematical Modelling: Education, Engineering and Economics - ICTMA 12, Elsevier, →ISBN, page 330:

(mathematics) An instance of reasoning performed using this approach.


AI-complete

Problems like solving crosswords from clues are reputed as AI-complete [7]. This enormous complexity is due to its semantics and the large amount of encyclopaedic knowledge required.

2006, M.Gori, M.Ernandes, G.Angelini, “Cracking Crosswords: The Computer Challenge”, in Oliviero Stock, Marco Schaerf, editors, Reasoning, Action and Interaction in AI Theories and Systems: Essays Dedicated to Luigia Carlucci Aiello, Springer Science & Business Media, →ISBN, page 266:

Just as concept kernels are not AI-complete, sequiturs and resonances are not AI-complete. Sequiturs and resonances also may not need to be human- equivalent to minimally support deliberation; it is acceptable for an early AI to miss out on many humanly obvious thoughts, so long as those thoughts which are successfully generated sum to fully general deliberation.

2007, Ben Goertzel, Cassio Pennachin, Artificial General Intelligence, Springer Science & Business Media, →ISBN, page 452:

... Now imagine a remote descendant of such a system that has acquired the ability to read with as much understanding as a human ten-year-old but with a reading speed similar to that of TextRunner. (This is probably an AI-complete problem.)

2014, Nick Bostrom, Superintelligence: Paths, Dangers, Strategies, Oxford University Press, →ISBN, page 71:

artificial intelligence
artificial intelligence

(artificial intelligence, informal) Of a problem: such that a solution presupposes or entails solving the problem of constructing a general artificial intelligence ("strong AI").


dessin d'enfant

dessin d'enfant (plural dessins d'enfant)

Borrowed from French dessin d’enfant (“child's drawing”).

bor

(mathematics) A type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers.


Galois group

Named after Évariste Galois, who first discovered them.

In this section, we show how to determine the Galois group and the roots of an irreducible polynomial of degree 2, 3, or 4.

1996, Patrick Morandi, Field and Galois Theory, Springer, page 123:

Let B be a Galois algebra over R with Galois group G, C the center of B, and K#61;#92;#123;g#92;inG#92;vertg(c)#61;c#92;#92;mathsf#123;for#92;each#125;#92;c#92;inC#92;#125;. A natural question is whether B is a central Galois algebra with Galois group K.

2004, George Szeto, Liangyong Xue, “On Central Galois Algebras of a Galois Algebra”, in Alberto Facchini, Evan Houston, Luigi Salce, editors, Rings, Modules, Algebras, and Abelian Groups, CRC Press, page 493:

Our work actually gives an algorithm for computing Galois groups of polynomials f(X)#92;in#92;Q#91;X#93;:

2009, Steven H. Weintraub, Galois Theory, 2nd edition, Springer, page 128:

(algebra, Galois theory) The automorphism group of a Galois extension.

زمرة غالوا

specific group associated with a field extension


bicorrelation

(statistics) The correlation between two sets of variables


elementwise

While this elementwise approach required more computation time up front (the combined simulation matrices were approximately 4.6 times higher than a single large simulation), it could be performed in parallel on a computing cluster.

2019 December 26, Nathan McDannold, P. Jason White, and Rees Cosgrove, “Elementwise approach for simulating transcranial MRI-guided focused ultrasound thermal ablation”, in Physical Review Research, →DOI:

(mathematics) Obtained by operating on one element (of a matrix etc) at a time.


supercoordinate

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(mathematics) An additional coordinate in a superconformal algebra


Besselian

(mathematics, astronomy) Relating to Friedrich Bessel


zorch

en-verb

zorch (third-person singular simple present zorches, present participle zorching, simple past and past participle zorched)

zorches (present singular third-person)
zorching (participle present)
zorched (participle past)
zorched (past)

I was well on my way to zorching my GPA as a sophomore and becoming quite the computer hacker when Luis my mentor took me aside. He told me that my grades werent up to snuff when I told him I was getting C's in Spanish (that was my best subject that month).

1990 November 30, Jim Burnes, “"ZOG"?”, in alt.conspiracy (Usenet):

Assuming you are willing to live with the consequences, which include obliterating everything within a hundred kilometers of your launch site, dumping a hundred tons of fallout into the stratosphere, and zorching every piece of electronics sight^([sic]).

2002 April 3, John Schilling, “Interstellar Flight Today”, in rec.arts.sf.science (Usenet):

[…] I probably just wasn't inserting the memory DIMM correctly, not that it was intrinsically unseatable; I zorched the motherboard myself when trying to remove disk drives […]

2002 May 20, Timothy A. McDaniel, “ConJose planning”, in rec.arts.sf.fandom (Usenet):

But if you're doing disk-to-disk backup you want at least two backup disks, since it's kind of a nightmare if your good disk zorches right in the middle of the backup, giving you a zorched backup disk as well.

2003 May 7, Alan Winston - SSRL Admin Cmptg Mgr, “AKICIF: Browser bafflement”, in rec.arts.sf.fandom (Usenet):

Zorching the economy so badly we still haven't dug out two years after he's gone ..

2011 July 15, Curt, “First Rule of Liberalism”, in seattle.politics (Usenet):

(intransitive, transitive, slang) To destroy or ruin, especially by electronic means.


zorch

This is done by using a numerical constant, called zorch, to start marker-passing and dividing it by outbranching […]

1987, John McDermott, Artificial Intelligence: 10th International Joint Conference, volume 1, page 152:

[…] it and all its first set of descendants can be marked, but the zorch runs out quickly.

1989, Noel E. Sharkey, Models of Cognition: A Review of Cognitive Science:

In order to quantify network connectivity between one protein and others, we adapted the idea of zorch originally used to describe cognition (Hendler, 1989).

2008, Richard Trent Llewellyn, Annotating the Biological Process of Proteins with Functional Linkages, page 39:

A numerical factor used to limit semantic searches in cognitive modelling.


Frink ideal

(mathematics) A certain kind of subset of a partially ordered set.


Petersen's theorem

(graph theory) The theorem stating that every cubic bridgeless graph contains a perfect matching.


forgetful functor

en-noun

forgetful functor (plural forgetful functors)

(category theory) a functor that forgets or drops some or all of its input's structure or properties before mapping to the output

gleymskuvarpi

category theory: a functor that forgets its inputs's structure


Sobolev space

Named after the Russian mathematician Sergei Sobolev.

(mathematics) A vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself as well as its derivatives up to a given order.


Dodgson condensation

Named after mathematician Charles Dodgson.

(mathematics) A method of computing the determinants of a square matrix by constructing a series of sequentially smaller matrices.


choenix

If the kings do not come to the public supper, each of them must have two choenixes of meal and a cotyle of wine sent home to him at his house; if they come, they are given a double quantity of each, and the same when any private man invites them to his table.

1942, “Erato”, in George Rawlinson, transl., The Persian Wars, translation of original by Herodotus:

(historical) An ancient dry measure of two pints or greater.


orthoplex

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Coined in 1991 by John Horton Conway and Neil Sloane. Blend of orthant + complex, since it has one facet for each orthant.

We made use of another way of considering the 120 cells, starting with the eight at the vertices of an orthoplex, that is, in the cells of a hypercube.

1990, Mathematica Journal, volumes 1-2, page 84:

It is remarkable that the four-dimensional orthoplex is the same polytope as the four-dimensional hemicube.

1991, J. H. Conway, N. J. A. Sloane, “The Cell Structures of Certain Lattices”, in Peter Hilton, Friedrich Hirzebruch, Reinhold Remmert, editors, Miscellanea Mathematica, page 90:

The combinatorics of this case apply to all members of the Gosset series; in every case, their cells are simplexes and orthoplexes, the latter appearing with only half symmetry.

2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 412:

(geometry) A convex polytope analogous to an octahedron (3 dimensions) or 16-cell (4 dimensions).

Cross-polytope
John Horton Conway
Neil Sloane


Chinese mile

By analogy with the similar Roman and English unit, although the li was somewhat shorter.

A li, a traditional Chinese unit of distance equal to 1500 Chinese feet or 150 zhangs, now standardized as a half-kilometer (500 meters).


Chinese foot

From its rough resemblance to the English foot.

A chi, a traditional Chinese unit of distance based on the human forearm, now standardized variously as (Mainland China) ¹/₃ or (Taiwan) ¹⁰/₃₃ of a meter.


chek

From the Yale romanization of the Cantonese 尺 (cek³). Doublet of chi.


Japanese foot

From its rough similarity to the English foot measurement.

A shaku, a traditional Japanese unit of distance based on the human forearm, now standardized as ¹⁰⁄₃₃ of a meter.


CPCTC

(geometry) Initialism of corresponding parts of congruent triangles are congruent, a theorem regarding congruent triangles, stating that if two or more triangles are proven congruent by any method, then all of their corresponding angles and sides are congruent as well.


CPCFC

(geometry) Initialism of corresponding parts of congruent forms are congruent.


HEO

highly elliptical orbit
highly elliptical orbit#English

(space science) Initialism of highly elliptical orbit.

GEO

geostationary orbit / geostationary Earth orbit

GSO

geosynchronous orbit / geosynchronous Earth orbit


DRO

distant retrograde orbit
distant retrograde orbit#English

(space science) Abbreviation of distant retrograde orbit.


Cardan grille

Proposed in 1550 by Girolamo Cardano (1501-1576), known in French as Jérôme Cardan.

(cryptography) A sheet of card or thin metal, etc., used in composing secret messages. The words of the message are written through a number of holes cut arbitrarily in the sheet, and the remaining paper is then filled with irrelevant words to disguise it.


antistable

(mathematics) That becomes increasingly unstable


mgf

moment-generating function
moment-generating function#English

Initialism of moment-generating function.


mean square

The average of the squares of a set of numbers.


paracompactifying

(mathematics) That makes something paracompact.


runcination

runcination (usually uncountable, plural runcinations)

(mathematics) The simultaneous cutting of a regular polytope along its faces, edges, and vertices.


runcinated

(mathematics) Generated or modified by a runcination.


runcic

(mathematics, of a polytope) Having the vertices of a runcinated polytope.


pipsqueakery

The quality of being small and insignificant.


candareen

A traditional unit of weight in East Asia, approximately 378 milligrams and equivalent to ten cash. A troy candareen is approximately 374 milligrams.


Schelling point

Schelling point (plural Schelling points)

The concept was introduced by American economist Thomas Schelling in his book The Strategy of Conflict (1960).


QR decomposition

QR decomposition (plural QR decompositions)

(linear algebra) A decomposition of a matrix into a product of a unitary matrix (orthogonal matrix) and an upper-triangular matrix.


plane-parallel

(mathematics) Describing two planes that do not intersect


Remez algorithm

Published by Evgeny Yakovlevich Remez in 1934.

(mathematics) An iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are the best in the uniform norm L_∞ sense.


Dvoretzky's theorem

Proved by Aryeh Dvoretzky in the early 1960s.

(mathematics) An important structural theorem in the theory of Banach spaces, essentially stating that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean.


semi-complete

(mathematics, graph theory) of or pertaining to a graph in which, for any two verticies u, v in the graph, there is another vertex w which is adjacent to both u and v (i.e. u,w,v is a path in that graph).


tridiminished

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(geometry) Having had three cupolae removed.


bidiminished

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(geometry) Having had two cupolae removed.


triaugmented

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(geometry) Having a square pyramid attached to each of three equatorial faces.


deltahedron

deltahedron (plural deltahedrons or deltahedra)

deltahedrons (plural)
deltahedra (plural)

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

From delta (Greek letter) + -hedron referring to the triangular shape of the letter.

There are infinitely many deltahedra, but only eight that are convex.

equilateral triangle
equilateral triangle

(geometry) A polyhedron whose faces are all equilateral triangles.


Napoleon complex

Napoleon complex (plural Napoleon complexes)

(derogatory, psychology) Aggressive or domineering behaviour, claimed to be a form of psychological compensation for one's short physical stature.


straight angle

(mathematics, geometry) An angle that is equal to 180° (pi radians or two right angles).


Wilks's theorem

(statistics) A theorem relating to the distribution of the likelihood ratio.


MLSE

maximum likelihood sequence estimation#English

(mathematics) Abbreviation of maximum likelihood sequence estimation.


braid statistics

(mathematics, physics) A generalization of the statistics of bosons and fermions based on the concept of braid group.


Toeplitz matrix

Toeplitz matrix (plural Toeplitz matrices)

(linear algebra) A matrix in which each descending diagonal from left to right is constant.


pentation

pentation (usually uncountable, plural pentations)

From penta- + (itera)tion. The word was coined by the English mathematician Reuben Goodstein (1912–1985).

coinage

(mathematics) The arithmetic operation of repeated tetration.


Hankel matrix

en-noun

Hankel matrix (plural Hankel matrices or Hankel matrixes)

Hankel matrices (plural)
Hankel matrixes (plural)

(linear algebra) A square matrix with constant skew-diagonals (positive sloping diagonals).


change sides, change signs

(algebra, mnemonic) An acronym to help remember that when a value is moved to the opposite side of the equals sign, then the operator is changed also.


extrabinomial

(statistics) Relating to unexpected variability arising from overdispersion.


Bernoulli process

Bernoulli process (plural Bernoulli processes)

(statistics) A series of independent trials, analogous to repeatedly flipping a coin to determine whether it is fair.


Knaster-Tarski theorem

Named after Bronisław Knaster and Alfred Tarski.

programming language
programming language

(mathematics) A theorem stating that, if L is a complete lattice and f : L → L is an order-preserving function, then the set of fixed points of f in L is also a complete lattice. It has important applications in formal semantics of programming languages and abstract interpretation.


parity game

(game theory) A type of game played on a directed graph whose nodes are coloured by priority.


Karatsuba multiplication

Karatsuba multiplication (countable and uncountable, plural Karatsuba multiplications)

Eponymous, from Anatolii Alexeevitch Karatsuba + multiplication.

(mathematics) Multiplication by means of the Karatsuba algorithm.


Zenoness

Zenoness, which refers to the situation that the system has infinite many “mode switches” in finite time, is a well-known phenomenon arising in multi-mode ( hybrid) systems. In general, there are a number of smooth dynamics in a hybrid system.

2007, Lanshan Han, Topics in Differential Variational Systems, ProQuest, →ISBN, page 20:

A player is responsible for the Zenoness of an execution if she is "elected" infinitely many times for her choosing the smallest delay. A coalition is responsible for Zenoness if at least one of its member is.

2007, Luís Caires, Vasco T. Vasconcelos, CONCUR 2007 - Concurrency Theory: 18th International Conference, CONCUR 2007, Lisbon, Portugal, September 3-8, 2007, Proceedings, Springer Science & Business Media, →ISBN, page 456:

As it has been previously discussed, this may be complicated by the fact that these solutions may exhibit complex phenomena such as non-continuability of solutions or deadlock, beating or livelock, and Zenoness.

2011, Alfonso Baños, Antonio Barreiro, Reset Control Systems, Springer Science & Business Media, →ISBN, page 63:


dabba

(mathematics) del, the partial difference symbol ∂


aLife

Alternative form of A-life (artificial life)


Ore's theorem

Proved in 1960 by Norwegian mathematician Øystein Ore.

(graph theory) A theorem that considers the sum of the degrees of pairs of non-adjacent vertices: if every such pair has a sum that at least equals the total number of vertices in the graph, then the graph is Hamiltonian.


Veblen's theorem

(graph theory) A theorem stating that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree.


Cayley-Dickson construction

Named after Arthur Cayley and Leonard Eugene Dickson.

Cayley-Dickson algebra
Cayley-Dickson algebra

(mathematics) A construction that produces a sequence of Cayley-Dickson algebras: algebras over the field of real numbers, each with twice the dimension of the previous one.


hyperfactorial

(mathematics) The result of multiplying a given number of consecutive integers from 1 to the given number, each raised to its own power.

The result of multiplying a given number of consecutive integers from 1 to the given number, each raised to its own power.
For example, the hyperfactorial of 3 is 1¹ * 2² * 3³ = 1 * 4 * 27 = 108


K-function

(mathematical analysis) A generalization of the hyperfactorial function in mathematics to real and complex numbers.


AGI

AGI (countable and uncountable, plural AGIs)

Coordinate term: (artificial superintelligence) ASI

AGIs will indeed be capable of self-awareness – but that is because they will be General: they will be capable of awareness of every kind of deep and subtle thing, including their own selves.

2012 October 3, David Deutsch, “Philosophy will be the key that unlocks artificial intelligence”, in The Guardian:

If AI researchers do eventually manage to make the leap to AGI, there is little reason to believe that the result will be a machine that simply matches human-level intelligence.

2015, Martin Ford, The Rise of the Robots, Oneworld:

Some of my friends have recently reported to me that when people outside the AI industry hear about extinction risk from Artificial General Intelligence for the first time, their reaction is “maybe we should not build AGI, then.”

2023 March 29, Eliezer Yudkowsky, “The Open Letter on AI Doesn't Go Far Enough”, in Time:

artificial general intelligence
artificial general intelligence#English

(artificial intelligence) Initialism of artificial general intelligence.


ASI

ASI (countable and uncountable, plural ASIs)

(programming, uncountable) Initialism of automatic semicolon insertion.

Coordinate term: AGI

artificial superintelligence
artificial superintelligence#English

(countable, artificial intelligence) Initialism of artificial superintelligence.

anti-suit injunction
anti-suit injunction#English

(law, countable) Initialism of anti-suit injunction.


beta function

Considering the equation of the binomial coefficient n choose k described in terms of the factorial, replacing n with p + q and k with p, turning the RHS upside-down and replacing factorials with the Gamma function, then replacing (p + q) choose p with Β(p, q) yields Euler's equation for the Beta function.

Euler integral of the first kind
Euler integral of the first kind

(mathematical analysis) A mathematical function that is also called the Euler integral of the first kind; it is a symmetric special function.

Betafunktion

function which generalizes the notion of a factorial


convex function

convex function (plural convex functions)

(computer science) A mathematical function where the line segment between any two points on the graph of the function lies above the graph in a vector space of at least two dimensions.


concave function

concave function (plural concave functions)

(computer science) The negative of the convex function.


set function

(computer science) A mathematical function whose input is a set (usually of real numbers or a set of points in the Euclidean or some measure space), and whose output is usually a number.


density function

density function (plural density functions)

(probability theory) Clipping of probability density function.


transmission function

transmission function (plural transmission functions)

propagation constant
propagation constant

(mathematical analysis) The mathematical function of an electromagnetic wave is a measure of the change undergone by the amplitude of the wave as it propagates in a given direction, which is also called the propagation constant.


Hellinger distance

Hellinger distance (countable and uncountable, plural Hellinger distances)

It is defined in terms of the Hellinger integral, introduced by Ernst Hellinger in 1909.

probability distribution
probability distribution

(probability, statistics) A measure used to quantify the similarity between two probability distributions.


Hellinger integral

Hellinger integral (plural Hellinger integrals)

(mathematics) A special case of the Kolmogorov integral, used to define the Hellinger distance in probability theory.


coefficientwise

(mathematics) For each coefficient; with respect to coefficients.


Pi Day

pi + day, from the date March 14th in the month/day format (that is, 3/14), 3, 1 and 4 being the first three significant digits of the mathematical constant π.

Did you know that March 14 is Pi Day (no, π is not misspelled). Pi Day is celebrated on 3/14 or 3.14! To commemorate this remarkable ratio, we have a few circular activities. The first is the Pizza Survey. What are the students' favorite toppings on pizza? What do you like best?

1997, Louise Bock, Susan Guengerich, Hope Martin, “March Celebrations”, in Multicultural Math Fun: Holidays around the Year, Portland, Me.: J. Weston Walch Publisher, →ISBN, page 83:

As Quakers, we do not as a matter of religion celebrate any holidays (more accurately, all days are to be considered holidays because they have equal potential for revealing the Divine to us), but as a cultural matter we celebrate all kinds: Hindu, Christian, Jewish, ethnic, birthdays of famous composers, artists, writers, and scientists, π Day (March 14th – we bake several pies and divide them into fractions before eating), even some we just make up ourselves.

1999, David H. Albert, “Exits and Entrances”, in And the Skylark Sings with Me: Adventures in Homeschooling and Community-based Education, Gabriola Island, B.C.: New Society Publishers in cooperation with Holt Associates/Growing Without Schooling, →ISBN, page 128:

Of all known mathematical constants, however, pi continues to attract the most attention. […] The Exploratorium in San Francisco continues to celebrate Pi Day on March 14 each year, starting at 1:59 pm.

2002, Ivan Peterson, “A Passion for Pi”, in Mathematical Treks: From Surreal Numbers to Magic Circles (Spectrum Series; a Science News Book), [Washington, D.C.]: Mathematical Association of America, →ISBN, page 17:

Whereas Pi can be approximated as 3.14, and thus March 14, 2009, is an appropriate day for "National Pi Day": Now, therefore, be it / Resolved, That the [United States] House of Representatives— / (1) supports the designation of a "Pi Day" and its celebration around the world; […]

2009 March 12, H. Res. 224 Supporting the Designation of Pi Day, and for Other Purposes, [Washington, D.C.]: United States Government Publishing Office, archived from the original on 2016-12-28, page 2:

Likewise, March 14 in North America has been π Day, since in the USA the month is written before the day ('314'). In schools throughout North America, it has become a reason for mathematical projects, especially focussing on π.

2012 June 19, Jonathan M[ichael] Borwein, “The Life of Pi: From Archimedes to Eniac and Beyond”, in David H[arold] Bailey, Jonathan M. Borwein, Pi: The Next Generation: A Sourcebook on the Recent History of Pi and Its Computation, Switzerland: Springer Nature, published 2016, →DOI, →ISBN, page 446:

March 14, or 3/14, is recognized by math geeks as Pi day. That happens every year. But as UBS’s Art Cashin notes, next year’s Pi day will be a once-in-a-century Pi day. “At 9:26:53 a.m., they can write 3/14/15; 9:26:53, which you should also recall are the first ten digits of Pi in perfect order,” said Cashin.

2015 March 14, Sam Ro, “March 14, 2015 will be a once-in-a-century thrill for math geeks”, in Business Insider, archived from the original on 2016-03-04:

Pi lovers like to celebrate Pi Day every year. In the US, they write the date with the month first, then the day and year. So in 2015, 14th March was 3 14 15, the first five digits of π. So that was a really special Pi Day when, of course, they sang their special song, Pi, Pi, Mathematical Pi, to the tune of that great song everyone danced to in the 1970s, 'Bye-bye, Miss American Pie' by Don McLean.

2016, Liz Strachan, “A Little More Pi”, in Easy as Pi: Maths Made Simple, London: Robinson, →ISBN:

March 14th, an annual celebration of the mathematical constant π (pi).


RBF

RBF (countable and uncountable, plural RBFs)

radial basis function
radial basis function#English

(mathematics, countable) Abbreviation of radial basis function., a type of equation used to approximate a vector field, used in neural networks.


beknottedness

(mathematics) The measure or degree to which a knot is complicated, i.e., a knot's complexity; the number of times that it is necessary to pass one part of the curve of the knot projected upon a plane through another in order to untie the knot.


octadecagon

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A regular octadecagon cannot be constructed using a compass and straightedge.

(geometry, rare) A polygon with 18 sides and 18 vertices.


gonihedric

From gonio- + ἕδρᾱ (hédrā, “seat; face of a regular solid”) + -ic.

(mathematics, quantum mechanics) of or pertaining to the generalization of the Feynman path integral to an integral over random surfaces


omega point

To begin, let AB be a given segment, and l and m be sensed parallel lines with shared omega point Ω.

2018, Maureen T. Carroll, Elyn Rykken, Geometry: The Line and the Circle, page 319:

(geometry) A well-defined point outside the hyperbolic plane.


deciare

A measure of area, equivalent to one tenth of an are, or ten square metres.


caballeria

From Spanish caballería, from caballero (“horseman, gentleman, cowboy”) + -ía (“-y: forming nouns”), from Late Latin caballārius (“horseman, rider”), from Latin caballus (“horse”) + -ārius (“-ary”). Doublet of cavalry and chivalry.

der

(historical, law) A medieval Spanish land tenure equivalent to a knight's fee, held under an obligation for military service.

(historical) A traditional Spanish unit of land area, equivalent to 38.64 ha.


Italian mile

From Calque of Italian miglio (“(Italian) mile”), with a qualifier to distinguish it from other miles.

calque

(units of measure) Various traditional Italian units of length, particularly the Genovese and Roman miles


survey mile

From its continued use until the 1980s in reference to the US Geological Survey's 1927 geodetic datum.

(US) The mile of ⁶³³⁶⁄₃₉₃₇ kilometers employed by the United States prior to its adoption of the international mile by treaty in the 1950s.


land mile

(unit of measurement) Any of the various miles used to measure length on land, as opposed to the nautical mile.


quartilho

From Portuguese quartilho, from quarto (“fourth”) + -ilho (“-elle: forming diminutives”), in reference to its size being one-fourth the canada. Doublet of cuartillo and cuartilla.

(historical, measure) A traditional Portuguese unit of liquid volume, varying in size between 350 and 530 mL.


synthetic division

en-noun

synthetic division (countable and uncountable, plural synthetic divisions)

(algebra) A method of polynomial long division in which one does not write the variables and some of the calculations.

daglating paghahati

a method of polynomial long division in which one does not write the variables and some of the calculations


u-substitution

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(calculus) A method of integration in which a function of a variable is replaced with a new variable, conventionally called u.


stress function

stress function (plural stress functions)

(physics) A function that finds a more tractable method for the elastic equations that describe the deformation of an elastic body subject only to boundary surface forces.


number-theoretic function

number-theoretic function (plural number-theoretic functions)

(mathematics) a real or complex valued function of n defined on the set of natural numbers that expresses some arithmetical property of n.


mass function

(astronomy, mathematics) A relationship that describes the mass distribution.


distribution function

distribution function (plural distribution functions)

(mathematics, physics) A function of seven variables of the form f(x,y,z,t;v_x,v_y,v_z) that gives the number of particles per unit volume in single-particle phase space.


unit function

multiplicative function
multiplicative function

(mathematics) a completely multiplicative function on the positive integers that is defined as equal to one for a special value and zero otherwise:


zeta function

(mathematics) function of the complex variable s that analytically continues the sum of the infinite series ∑ₙ₌₁ ᪲1/(nˢ) that converges when the real part of s is greater than 1.


correlation function

correlation function (plural correlation functions)

(mathematics) function giving the statistical correlation between random variables at two different points in space or time


partition function

partition function (plural partition functions)

(mathematics) generalization of the definition of a partition function in statistical mechanics

(number theory) function that represents the number of possible partitions of a natural number.


generating function

generating function (plural generating functions)

The concept was introduced by French mathematician Abraham de Moivre in 1730.

A generating function is a device somewhat similar to a bag. Instead of carrying many little objects detachedly, which could be embarrassing, we put them all in a bag, and then we have only one object to carry, the bag.

1954, George Pólya, Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics, Princeton University Press, page 101:

Most often generating functions arise from recurrence formulas. Sometimes, however, from a generating function you will find a new recurrence formula, not the one you started with, that gives new insights into the nature of your sequence.

1990, Herbert S. Wilf, generatingfunctionology, Academic Press, page 2:

2003, Sergei K. Lando (author & translator), Lectures on Generating Functions, American Mathematical Society.

(mathematics) A formal power series with one indeterminate, whose coefficients encode a sequence that can be studied by algebraic manipulation of the series; any one of several generalizations, such as to encode more than one sequence or use more than one indeterminate.

generoiva funktio

formal power series whose coefficients encode a sequence


stream function

stream function (plural stream functions)

(mathematics) A function used to plot streamlines that represent the trajectories of particles in a steady flow.


discriminant function

discriminant function (plural discriminant functions)

(mathematics) A function used to predict a categorical dependent variable by one or more continuous or binary independent variables.


distance function

distance function (plural distance functions)

(mathematics) a function used to calculate the distance between two points.


Hankel function

Hankel function (plural Hankel functions)

(mathematics) Either of two functions that are solutions to Bessel's equation.


Banzhaf power index

Banzhaf power index (plural Banzhaf power indexes)

(mathematics, politics) An index defined by the probability of changing an outcome of a vote where voting rights are not necessarily equally divided among the voters or shareholders.


hoppus foot

Named after Edward Hoppus, an 18th-century English surveyor.

A unit of measurement for the volume of timber in the round, with a value equal to 1.27 cubic feet, where the cross-sectional area is taken as the square of one quarter of the circumference of the round.


hoppus ton

A unit of measurement for the volume of timber in the round, with a value equal to 50 hoppus feet or 1.8027 cubic metres.


piphilologist

From piphilology + -ist, after philologist.

For quotations using this term, see Citations:piphilologist.

(mathematics) Someone who creates or uses mnemonics to memorize sections of the number pi (π).


gorge circle

(gearing) The outline of the smallest cross section of a hyperboloid of revolution.


circle of the gorge

surface of revolution
surface of revolution

(mathematics) A minimum circle on a surface of revolution, cut out by a plane perpendicular to the axis.


galactic habitable zone

galactic habitable zone (plural galactic habitable zones)

(astrobiology, astronomy) the zone in a disk galaxy lying within the disk which is neither too far from the core so as to be lacking in heavier elements, nor too close to the core as to experience excessive exposures to supernovae, where intelligent life may develop


pignistic

Coined by Philippe Smets from Latin pignus (“a bet”) + -istic.

(decision theory) Being or relating to a probability that a rational person will assign to an option when required to make a decision.


split key

Moreover, even those systems (such as split key systems) that can decrease these risks, do so with a marked increase in cost.

1997, Cryptography and Privacy Sourcebook, →ISBN, page 15:

A toolkit for split key cryptography in and of itself is (almost) a byproduct of developing ultra-high assurance applications such as root certifying authorities.

2007, Matt Blaze, Financial Cryptography, →ISBN, page 233:

Camenisch et al. [CCGS10] define, among other things, split key exchange and give a construction based on the decisional Diffie-Hellman assumption.

2014, Michel Abdalla, Roberto De Prisco, Security and Cryptography for Networks, →ISBN, page 45:

(cryptography) A cryptographic key that is divided into two or more values that individually cannot be used to deduce the entire key.


Hamming distance

Hamming distance (plural Hamming distances)

Named after American mathematician Richard Hamming (1915–1998).

named-after

(information theory) Given two strings of equal length, the number of positions at which the corresponding symbols differ; it therefore indicates the minimum number of substitutions required to change one string into the other.


head

if you torture the data long enough, it will confess to anything

This phrase was coined by economist Ronald Coase. A closely related sentence had been published in Alfred Sauvy's book L'Opinion publique (The public opinion, éd. Presses universitaires de France, coll. « Que sais-je ? », 1961, p. 100):
The figures are innocent people who, under solicitation, under torture, very quickly confess what is asked of them, even if it means retracting later. (Les chiffres sont des innocents qui, sous la sollicitation, sous la torture, avouent très vite ce qu'on leur demande, quitte à se rétracter plus tard.)

Statistics can be manipulated to support any conclusion.


CNN

convolutional neural network
convolutional neural network#English

(machine learning) Initialism of convolutional neural network.


linear foot

A unit of length equal to one foot long.


linear meter

(American spelling) A standard unit of length, symbol m, equal to one meter in length.


linear metre

(British spelling) A standard unit of length, symbol m, equal to one metre in length.


decic

(mathematics) Of the tenth degree or order; e.g. for a polynomial


quefrency

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From frequency with the consonant sounds of the first and second syllables switched, perhaps modelled after cepstrum which is derived from spectrum.

(signal processing) The inverse of the distance between successive lines in a Fourier transform, measured in seconds.


liftering

From filtering with the first part reversed, like cepstrum from spectrum.

(signal processing) Filtering in the cepstral domain.


Paropamisadae

From Latin Paropamisadae, from Ancient Greek Παροπαμισάδαι (Paropamisádai).

der

Παροπαμισάδαι

(historical demography) The people of Paropamisus in ancient Afghanistan.


octogram

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(geometry) A regular eight-pointed star shape.


nonagram

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(geometry) A regular nine-pointed star shape.


overbound

en-verb

overbound (third-person singular simple present overbounds, present participle overbounding, simple past and past participle overbounded)

overbounds (present singular third-person)
overbounding (participle present)
overbounded (participle past)
overbounded (past)

(mathematics) To provide an upper bound to.


overbound

(mathematics, signal processing) A Gaussian model of the (non-Gaussian) error distribution on a signal, which is conservative enough that the resulting confidence interval is guaranteed to be at least as wide as the actual confidence interval.


Hessian matrix

en-noun

Hessian matrix (plural Hessian matrices or Hessian matrixes)

Hessian matrices (plural)
Hessian matrixes (plural)

Named after German mathematician Ludwig Otto Hesse.

named-after

(mathematics) The square matrix of second-order partial derivatives of a scalar-valued function. It describes the local curvature of a function of many variables.


coinvariant

(mathematics) invariant within a cohomology


coinvariant

(mathematics) An invariant within a cohomology


arura

Borrowed from Ancient Greek ἄρουρα (ároura, “arura”), a semantic loan from Egyptian sṯꜣt (“arura”).

(historical) An ancient measure of arable land, a square of 100 Egyptian cubits (mḥ) on each side.


Floridization

term-label

(American spelling, Oxford British English)

/ˌflɔɹɪdaɪˈzeɪʃən/

/ˌflɔɹədəˈzeɪʃən/

From Florida + -ization (suffix denoting the act, process, or result of doing something). Sense 2 (“phenomenon of the percentage of seniors in a specific region progressively increasing as the population ages”) refers to the sizable number of retirees who settle in the US state.

suffix

The investment banker Pete Peterson calls this "the Floridization of America." The decline in births, right after the peak years, has had an impact on every business that targets young adults.

1998, AFTRA, New York, N.Y.: American Federation of Television and Radio Artists, →ISSN, →OCLC, page 27:

Although the percentage and the sheer volume of elders and people with disabilities living in the United States in the 21st century is increasing, their distribution will vary across the country; the Floridization of the country will happen in pockets.

2000 February 1, Robyn I. Stone, “Toward Person-Centered Care”, in Nursing Homes, Cleveland, Oh.: International Pub. Group, →ISSN, →OCLC, archived from the original on 2016-03-10:

While the United States is not yet severely impacted, many European countries and Japan—much further along the road to Floridization—are already confronted with the need for action. The consequences of aging are even more dire in these countries because their populations "are aging even faster, birthrates are lower, the influx of young immigrants from developing countries is smaller, public pension benefits are more generous, and private pension systems are weaker."

2004, Dennis Clark Pirages, Theresa Manley DeGeest, “Demographic Change and Ecological Insecurity”, in Ecological Security: An Evolutionary Perspective on Globalization, Lanham, Md.: Rowman & Littlefield Publishers, →ISBN, page 48:

The greatest twin victory of humanity over health issues has delivered one of the greatest challenges to man: Population ageing. Often described as ‘Floridisation of the World’, population ageing is the outcome of man’s victory over death and deceases as well as unwanted child bearing [...].

2005, The Asian Economic Review, volume 47, Hyderabad, Andhra Pradesh: Indian Institute of Economics, →OCLC, page 1:

Even if policy shifts resources away from hard investment and back into social spending, the "Floridization" of Chinese demographics will intensify the shortage of healthcare provision over the next decade, worsening the frayed contract between patients, providers, and the government.

2013 September, Damien Ma, William Adams, “Welfare: Socialism with Chinese … Actually No, Not Socialism at All”, in In Line Behind a Billion People: How Scarcity Will Define China’s Ascent in the Next Decade, Upper Saddle River, N.J.: FT Press, →ISBN, part II (Social Scarcity), page 103:

(US, demography) The phenomenon of the percentage of seniors in a specific region progressively increasing as the population ages.


Ramanujan prime

en-noun

Ramanujan prime (plural Ramanujan primes)

(mathematics) A prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function.


Carmichael number

Carmichael number (plural Carmichael numbers)

Named after Robert Daniel Carmichael (1879–1967), American mathematician.

(mathematics) A composite number n that satisfies the modular arithmetic congruence relation bⁿ⁻¹≡1(mod n) for all integers 1<b<n that are relatively prime to n.

Carmichael number
Robert Daniel Carmichael


Heegner number

Named after Kurt Heegner, German mathematician.

(mathematics) A squarefree positive integer d such that the imaginary quadratic field Q(√(−d)) has class number 1; equivalently, such that its ring of integers has unique factorization.


taxicab number

From an anecdote of the mathematician G. H. Hardy, who went to visit Srinivasa Ramanujan in a taxicab number 1729. Hardy suggested that the number seemed unremarkable, whereupon Ramanujan identified it as having this mathematical property.

(mathematics) The nth taxicab number, typically denoted Ta(n) or Taxicab(n), is the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways.


Prouhet-Tarry-Escott problem

Named after Eugène Prouhet, who studied it in the early 1850s, and Gaston Tarry and Escott, who studied it in the early 1910s.

(mathematics) The problem of finding two disjoint sets A and B of n integers each, such that ∑_(a∈A)aⁱ=∑_(b∈B)bⁱ for each integer i from 1 to a given k.


cubefree

(mathematics) Not divisible by a nontrivial cube.


Hardy-Ramanujan number

(mathematics) The number 1729, one of the taxicab numbers.


Dirac comb

Named after English physicist Paul Dirac. The functions, when plotted visually, resemble the teeth of a comb.

named-after

tempered distribution
tempered distribution

Dirac delta function
Dirac delta function

(mathematics) A periodic tempered distribution constructed from Dirac delta functions for some given period. It allows both continuous and discrete phenomena to be represented in a single framework.


antialgebra

(mathematics) The algebra of antisets, antigroups, antirings etc.


biautomaton

(mathematics) A finite automaton which arbitrarily alternates between reading the input from the left and from the right


bilanguage

(mathematics, linguistics) A language that has a regular treelike structure


bornology

topological vector space
topological vector space

(mathematics) The set of all bounded subsets of a topological vector space


chirotope

From chiro- (“handed”) + -tope (“place”).

(mathematics) An oriented matroid that exhibits the concept of chirality.


q-analog

(mathematics) A generalization of a theorem, identity or expression that involves a new parameter q that returns the original theorem, identity or expression in the limit as q → 1. They have applications in the study of fractals and the entropy of chaotic dynamical systems.


coresidual

(mathematics) Any of four points on the common chord of a cubic curve intercepted by a cone


cubulation

A cubulation of a topological space Y is a cubical set C:Cubeᵒᵖ→Set together with a homeomorphism h:R_(cub)C→Y.

(mathematics) A particular cubical set together with an isomorphism


duotensor

(mathematics) A form of tensor in which each position is associated with two possible bases


lemmatically

(mathematics) Proceeding through the use or assumption of a series of mathematical propositions.


hypersequent

(mathematics) A multidimensional generalization of a sequent


microtrajectory

(mathematics, physics) A microscopic trajectory (one of a series used in calculating a real trajectory)


autoequivalence

(mathematics, category theory) An equivalence between an object and itself.


borelian

(mathematics) Of or pertaining to a Borel set.


Gilbreath's conjecture

Named after mathematician Norman L. Gilbreath, who presented it in 1958.

(mathematics) A conjecture in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the results unsigned, and then repeating this process on consecutive terms in the resulting sequence, and so forth. The first term in every such sequence appears to be 1.


adjacency matrix

en-noun

adjacency matrix (plural adjacency matrices or adjacency matrixes)

adjacency matrices (plural)
adjacency matrixes (plural)

(graph theory) A matrix showing which vertices of a graph are adjacent to which other vertices.


algebraicity

(mathematics) The quality of being algebraic


algebraizable

(mathematics) Capable of being made algebraic.


algebraizability

(mathematics) The condition of being algebraizable.


martingality

(mathematics) The condition of being like a martingale.


pseudospherical

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quadrilinear

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(geometry) Having, or bounded by, four lines.


spectrahedral

(mathematics) Of or pertaining to a spectrahedron.


semidefinitely

en-adv

semidefinitely (comparative more semidefinitely, superlative most semidefinitely)

more semidefinitely (comparative)
most semidefinitely (superlative)


analytification

en-noun

analytification (countable and uncountable, plural analytifications)

(mathematics) The process or result of making something analytic.


posynomial

(mathematics) A function of the form f(x_1,x_2,…,x_n)=∑ₖ₌₁ᴷc_kx_1^(a_1k)⋯x_n^(a_nk), where all the coordinates x_i and coefficients c_k are positive real numbers, and the exponents a_ik are real numbers.


graphon

This bound almost matches the known upper bound for graphs and, in a certain sense, is the best possible for graphons.

2015, Jacob W. Cooper, Tomáš Kaiser, Daniel Kráľ, Jonathan A. Noel, “Weak regularity and finitely forcible graph limits”, in (Please provide the book title or journal name):

(mathematics, graph theory) The completion of the metric space of the set of finite graphs endowed with the cut metric.


presemifield

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multiplicative identity
multiplicative identity#English

(mathematics, algebra) A finite algebra satisfying all the axioms for a skew field except multiplicative associativity and the existence of a multiplicative identity.


isotopism

The other class #92;mathcal#123;C#125;#95;2 of loops consists of 3-dimensional connected differentiable left A-loops such that the group G#61;PSL#95;2(#92;mathbbR)#92;ltimes#92;mathbbR³ is the group topologically generated by the left translations The loops in this class can be represented by two real parameters a,b and form precisely two isomorphism classes, which coincide with the isotopism classes.

2015, Ágota Figula, “Geodesic loops with non-solvable left translation groups on 3-dimensional reductive spaces”, in (Please provide the book title or journal name):

(mathematics) An instance of an isotopic state.


noncompactness

Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition.

2015, Vatan Karakaya, Bouzara Nour El Houda, Kadri Dogan, Yunus Atalan, “Existence of fixed points for condensing operators under an integral condition”, in (Please provide the book title or journal name):

(topology) The quality or state of being noncompact.


infimal

More precisely, an infimal convolution model is applied to split the corrupted 3D image into the clean image and two types of corruptions, namely a striped part and a laminar one.

2017 February, Jan Henrik Fitschen, Jianwei Ma, Sebastian Schuff, “Removal of Curtaining Effects by a Variational Model with Directional First and Second Order Differences”, in Computer Vision and Image Understanding, volume 155, →DOI, pages 24–32:

(mathematics) Of or pertaining to an infimum.


polyconvexity

Thus we negatively answer Morrey's conjecture in the subclass of isochoric nonlinear energies, since polyconvexity implies quasiconvexity.

2015, Robert J. Martin, Ionel-Dumitrel Ghiba, Patrizio Neff, “Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case”, in (Please provide the book title or journal name):

(mathematics) A generalization of the notion of convexity for functions defined on spaces of matrices.


polyconvex

We show that in the two-dimensional case, every objective, isotropic and isochoric energy function which is rank-one convex on #92;mathrm#123;GL#125;#43;(2) is already polyconvex on #92;mathrm#123;GL#125;#43;(2).


quasi-derivative

(mathematics) A particular generalization of the derivative of a function between two Banach spaces.


quasi-differentiable

Thus we extend the theory of the directed subdifferential from quasidifferentiable to directed subdifferentiable functions.

2015, Robert Baier, Elza Farkhi, Vera Roshchina, “From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules”, in (Please provide the book title or journal name):

(mathematics) That has a quasi-derivative.


rootfinder

In two dimensions, when significant care is taken, they are competitive practical rootfinders.

2015, Vanni Noferini, Alex Townsend, “Are resultant methods numerically unstable for multidimensional rootfinding?”, in (Please provide the book title or journal name):

(mathematics) An algorithm for finding roots of an equation.


subdifferentiable

Coordinate term: superdifferentiable


semiperfect

Let R be a semiperfect commutative Noetherian ring and C a semidualizing R-module.

2015, Arash Sadeghi, “Linkage of finite G_C-dimension modules”, in (Please provide the book title or journal name):

projective cover
projective cover#English

(mathematics) Of a ring over which every finitely generated left module has a projective cover.

(mathematics) Of an integer equal to the sum of all or some of its proper divisors.


outer product

(mathematics, linear algebra) The tensor product of two vectors.


cuspidalization

Finally, we apply this result to obtain results concerning certain cuspidalization problems for fundamental groups of (not necessarily proper) hyperbolic curves over finite fields..

2015, Yasuhiro Wakabayashi, “On the cuspidalization problem for hyperbolic curves over finite fields”, in (Please provide the book title or journal name):

(mathematics) The process of making an object cuspidal.


modular form

analytic function
analytic function#English

functional equation
functional equation#English

(mathematics) A complex analytic function satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.


eigenform

We establish lower bounds for (i) the numbers of positive and negative terms and (ii) the number of sign changes in the sequence of Fourier coefficients at squarefree integers of a half-integral weight modular Hecke eigenform.

2015, Yuk-Kam Lau, Emmanuel Royer, Jie Wu, “Sign of Fourier coefficients of modular forms of half integral weight”, in (Please provide the book title or journal name):

(mathematics) A modular form which is an eigenvector for all Hecke operators T_m,m=1,2,3,...


ultraspherical

Thus, an estimate for 0 < v < 1, can be derived from theorem 6.6.1, by noting that v is an ultraspherical weight function, whose exponent is negative.

2008, Daniele Funaro, Polynomial Approximation of Differential Equations, →ISBN, page 116:

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems.

2015, Richard Mikael Slevinsky, Sheehan Olver, “A fast and well-conditioned spectral method for singular integral equations”, in (Please provide the book title or journal name):

(mathematics) Related to or involving a Gegenbauer polynomial.


Roko's basilisk

Proposed as a transhumanist thought experiment in 2010 by user Roko on the LessWrong Internet discussion forum.
According to LessWrong, discussion of Roko's basilisk was banned from the forum for several years as part of a general policy against spreading potential information hazards. This in fact drew further attention to the topic, and other websites began sharing information about it.

2020, Griffin Kao, Jessica Hong, Michael Perusse, Weizhen Sheng, Turning Silicon into Gold, Springer (Apress), page 177,
Roko's Basilisk closely resembles traditional religious belief systems, merely replacing the role of God with a super-AI instead.

2021, Richard Heimann, Doing AI, BenBella Books (Matt Holt Books), page 137,
Roko's Basilisk is a thought experiment about the potential risks involved in developing so-called true artificial intelligence. The premise is that an all-powerful artificial super-intelligence could retroactively punish those who did not help bring about its existence. Roko's Basilisk resembles a futurist version of Pascal's Wager in that it suggests people should weigh the possible infinite gain and infinite punishment for accepting or rejecting the creation of artificial super-intelligence.

Roko's Basilisk has been described as the most terrifying thought experiment of all time, or as Slate’s David Auerbach subtitled his 2014 article: "Why Are Techno-futurists So Freaked Out by Roko's Basilisk?"

2023, James B. Miles, AI and the End of Humanity, Troubador Publishing (Matador), page 168:

artificial intelligence
artificial intelligence

A hypothetical, otherwise benevolent artificial intelligence of the future that would have an incentive to torture anyone who, having imagined (or even heard about) said AI, had not helped bring about its existence; the thought experiment which posits its existence.


asymptotia

(mathematics, physics) The condition of being asymptotic


hubness

(mathematics) The tendency of high-dimensional data to contain points (hubs) that frequently occur in k-nearest-neighbor lists of other points.


Hahn series

(mathematics) A type of formal infinite series, a generalization of Puiseux series. They allow for arbitrary exponents of the indeterminate so long as the set supporting them forms a well-ordered subset of the value group.


Grundy number

Named after P. M. Grundy, who studied an analogous concept for directed graphs in 1939.


ultrasparsifier

(graph theory) A form of sparsifier that makes a graph particularly sparse.


fibrational

en-adj

fibrational (comparative more fibrational, superlative most fibrational)

more fibrational (comparative)
most fibrational (superlative)

Applying the fibrational form of the Yoneda lemma, we develop a general calculus of modules, proving that they naturally assemble into a multicategory-like structure called a virtual equipment, which is known to be a robust setting in which to develop formal category theory.

2015, Emily Riehl, Dominic Verity, “Kan extensions and the calculus of modules for ∞-categories”, in arXiv:

(algebraic topology) Of or pertaining to a fibration.


nonmonic

We obtain analogous partial results for the case of nonmonic or reducible polynomials by studying their GL2(K[x])-orbit and by establishing some combinatorial constraints on their Newton polytope.

2015, Denis Simon, Martin Weimann, “Plane Curves With Minimal Discriminant”, in arXiv:


rheonomic

We show how the superspace constraints (a.k.a. rheonomic parametrisation) are translated from the space of superforms […]

2015, Leonardo Castellani, Roberto Catenacci, Pietro Antonio Grassi, “Hodge Dualities on Supermanifolds”, in arXiv:

(mathematics) Of a mechanical system whose constraint equations explicitly contain or are dependent upon time.


scleronomic

(mathematics) Of a mechanical system whose constraint equations do not explicitly contain or are not dependent upon time.


rectagraph

Such graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every 2-path lies in a unique quadrangle.

2015, Joanna B. Fawcett, “Locally triangular graphs and normal quotients of the n-cube”, in arXiv:

(graph theory) A triangle-free connected graph where any two vertices have 0 or 2 common neighbors.


triangle-free

undirected graph
undirected graph#English

(graph theory) Of an undirected graph in which no three vertices form a triangle of edges.


isoradial

The critical surface for random-cluster model with cluster-weight q#92;ge 4 on isoradial graphs is identified using parafermionic observables.

2015, Vincent Beffara, Hugo Duminil-Copin, Stanislav Smirnov, “On the critical parameters of the q>4 random-cluster model on isoradial graphs”, in arXiv:

(graph theory) Of a planar graph: where each face is inscribable in a circle of common radius.


web of trust

(cryptography) A decentralized cryptographic mechanism for establishing the authenticity of the binding between a public key and its owner.


antiprismatic

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Hadwiger's theorem

(geometry) A theorem asserting that every valuation on convex bodies in Rⁿ that is continuous and invariant under rigid motions of Rⁿ is a linear combination of the quermassintegrals (or, equivalently, of the intrinsic volumes).


Moufang loop

(mathematics) A special kind of algebraic structure, similar to a group in many ways but not necessarily associative.


microlocal

Coupled with prior results, this yields a concrete combinatorial model for microlocal sheaves, as well as an elementary method for calculating them..

2015, David Nadler, “Non-characteristic expansions of Legendrian singularities”, in arXiv:

(mathematics) Local with respect to both space and cotangent space.


bigluing

This yields a new explanation of the definition of Reedy categories: they are almost exactly those small categories for which the category of diagrams and its model structure can be constructed by iterated bigluing.

2015, Michael Shulman, “Reedy categories and their generalizations”, in arXiv:

(mathematics) A category of quadruples related to the gluing construction.


cadlag

Initialism, from French "continue à droite, limite à gauche".

In this paper we consider the continuous-time martingale transport on the Skorokhod space of cadlag paths.

2015, Gaoyue Guo, Xiaolu Tan, Nizar Touzi, “Tightness and duality of martingale transport on the Skorokhod space”, in arXiv:

(mathematics) A function that is right continuous and has a left limit.


coeffective

Also, in this case, we prove some Hodge decomposition theorems for coeffective basic de Rham cohomology, relating this cohomology with coeffective basic Dolbeault or Bott-Chern cohomology.

2015, Cristian Ida, Paul Popescu, “Coeffective basic cohomologies of K--contact and Sasakian manifolds”, in arXiv:

(mathematics) effective within a cohomology


diskcyclic

In this paper, we introduce new classes of operators in complex Banach spaces, which we call k-bitransitive operators and compound operators to study the direct sum of diskcyclic operators.

2015, Nareen Bamerni, Adem Kılıçman, “k-bitransitive and compound operators on Banach spaces”, in arXiv:

(mathematics) Describing a form of cyclicity operator having criteria midway between a hypercyclic and a supercyclic operator.


multitype

We last analyse the additional error introduced when replacing the multitype sticky particle dynamics by an iterative scheme based on the typewise sticky particle dynamics, and illustrate the convergence of this scheme by numerical simulations..

2015, Benjamin Jourdain, Julien Reygner, “Optimal convergence rate of the multitype sticky particle approximation of one-dimensional diagonal hyperbolic systems with monotonic initial data”, in arXiv:

(mathematics) Relating to or consisting of multiple types


nilprogression

We give a structural description of the finite subsets A of an arbitrary group G which obey the polynomial growth condition forsomeboundedd and sufficiently large n, showing that such sets are controlled by (a bounded number of translates of) a coset nilprogression in a certain precise sense.

2015, Terence Tao, “Inverse theorems for sets and measures of polynomial growth”, in arXiv:

(mathematics) A function of the products of the elements of a nilpotent group and their inverses


profunctor

From pro- + functor. Pro- is in the sense of projective.

(mathematics) A generalization of a relation in category theory


quasifield

(mathematics) An algebraic structure (Q,+,·) where + and · are binary operations on Q, much like a division ring, but with some weaker conditions.


hypertoric

In this note we prove that the crepant transformation conjecture for a crepant birational transformation of Lawrence toric DM stacks studied in \cite{CIJ} implies the monodromy conjecture for the associated wall crossing of the symplectic resolutions of hypertoric stacks, due to Braverman, Maulik and Okounkov..

2015, Yunfeng Jiang, Hsian-Hua Tseng, “The Crepant Transformation Conjecture implies the Monodromy Conjecture”, in arXiv:

(mathematics) Describing quaternionic analogues of toric structures


hypertorus

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(geometry, topology) An N-dimensional equivalent of a torus, where N is a positive integer greater than 3.


superstability

en-noun

superstability (usually uncountable, plural superstabilities)

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(mathematics) The quality of being superstable.


quasibinomial

Variation in frequencies of the ND4 substitution among rivers was negatively correlated to latitude (parameter estimate = −0.12, SE = 0.05, P = 0.02) and summer temperature (estimate = −0.027, SE = 0.13, P = 0.057), and positively correlated to longitude (estimate = 0.04, SE = 0.01, P = 0.006) using a quasibinomial link to correct for overdispersion (residual deviance = 60.580 on 25 degrees of freedom).

2015 July 3, Sofia Consuegra et al., “Patterns of natural selection acting on the mitochondrial genome of a locally adapted fish species”, in Genetics, Selection, Evolution : GSE, volume 47, →DOI:

(mathematics) Describing a generalisation of binomial distributions


shorth

To estimate the mode of a (distance) distribution, we used the midpoint of the shorth (the shortest interval that covers half the values).

2009 January 25, Wu Wei Zhenyu Xu et al., “Bidirectional promoters generate pervasive transcription in yeast”, in Nature, volume 457, number 7232, →DOI, pages 1033–1037:

(statistics) The shortest interval containing a specified fraction (typically a half) of a distribution


surjunctive group

surjunctive group (plural surjunctive groups)

We prove that pre-injective, post-surjective cellular automata over surjunctive groups are reversible.

2015, Silvio Capobianco, Jarkko Kari, Siamak Taati, “Post-surjectivity and balancedness of cellular automata over groups”, in arXiv:

cellular automaton
cellular automaton#English

(mathematics) A group such that every injective cellular automaton with the group elements as its cells is also surjective.


unconstrainted

From un- + constraint + -ed, equivalent to un- + constrained.

We therefore seek a method for response-function normalization method which involves manipulating empirical curves that result from unconstrainted empirical fits of the corrected survivorship data.

2015 July 10, “Data-Driven Method to Estimate Nonlinear Chemical Equivalence”, in PLOS ONE, →DOI:


infit

The infit of all questions ranged between 0.7 and 1.3.

2015 July 6, “PARADISE 24: A Measure to Assess the Impact of Brain Disorders on People’s Lives”, in PLOS ONE, →DOI:

(statistics) An inlier-sensitive or information-weighted fit


infomax

After filtering, an independent component analysis (ICA) was applied to the epoched data, using the extended infomax ICA algorithm [41 ].

2015 July 6, “Stronger Neural Modulation by Visual Motion Intensity in Autism Spectrum Disorders”, in PLOS ONE, →DOI:

(mathematics) A particular optimization method, prescribing that a function that maps a set of inputs to a set of outputs should maximize the average mutual information between the two sets, subject to constraints.


superrigid

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superrigidity

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(mathematics) In the theory of discrete groups, a concept designed to show how a linear representation ρ of a discrete group Γ inside an algebraic group G can, under some circumstances, be as good as a representation of G itself.


pushforward

(mathematics) The differential of a smooth map between smooth manifolds.


shoe size

What's your shoe size?

The size of shoe that fits a person, often indicated by an alphanumeric code.

talle

see also the verb calzar, meaning "to have as shoe size"


subextremal

(mathematics) numerically less than a maximum or minimum


macrosimulation

The macrosimulation model employed has been used previously to undertake similar analyses for the UK [26 ,37 –39 ], Ireland [40 ], France [41 ] and Canada [42 ], and the relative risks to parameterise changes in nutritional risk factors and mortality as a result of changes in diet were sourced from high quality meta-analyses [29 –36 ].

2015 July 9, “Effects of Health-Related Food Taxes and Subsidies on Mortality from Diet-Related Disease in New Zealand: An Econometric-Epidemiologic Modelling Study”, in PLOS ONE, →DOI:

(mathematics, computing) simulation of a system as a whole, without simulating the behaviour of its individual components


tetrachoric

Each rho (ρ) represents the conditional tetrachoric correlation for each pair of outcomes, measuring the extent to which the two outcomes would covary if unobserved characteristics of an individual were indeed observed.

2015 July 9, “Social Participation and Disaster Risk Reduction Behaviors in Tsunami Prone Areas”, in PLOS ONE, →DOI:

(statistics, of a correlation) Between two dichotomous variables


semisymmetric

A new semisymmetrization functor, which maps the category of quasigroups with homotopies to the category of semisymmetric quasigroups with homomorphisms is given.

2015, Aleksandar Krapez, Zoran Petric, “A note on semisymmetry”, in arXiv:

(mathematics, of a graph) edge-transitive but not vertex-transitive


comonotonic

(probability theory) Of a random vector, having components that can be represented as increasing functions of a single random variable.


diffeological

We apply this notion to make some observation on subspaces which split off as smooth direct summands (providing examples which illustrate that not all subspaces do), and then to show that the diffeological dual of a finite-dimensional diffeological vector space always has the standard diffeology and in particular, any pseudo-metric on the initial space induces, in the obvious way, a smooth scalar product on the dual..

2015, Ekaterina Pervova, “On the notion of scalar product for finite-dimensional diffeological vector spaces”, in arXiv:


diffeology

In this case, A and f(A) are both D-open and f#58;A#92;rightarrowf(A) is a diffeomorphism where A and f(A) are equipped with their subset diffeology.

2007, Jan Kubarski, Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann; on the Occasion of the Hundredth Anniversary of His Birthday, page 358:

And, for #92;mathcal#123;G#125;#42;#47;#92;Gamma and #92;mathcal#123;G#125;'#42;#47;#92;Gamma' equipped with the quotient diffeologies, h#42;#95;#92;Gamma is naturally smooth.

2010, Patrick Iglesias-Zemmour, The Moment Maps in Diffeology, American Mathematical Society, page 32:

differential geometry
differential geometry

(differential geometry) The set of smooth parametrizations of a given set X; the set of smooth maps S→X, where S is any open set ⊆ℝⁿ; the theory of such constructs.


maxent

Study results showed that maxent model can be highly robust (99.8%) in predicting the species relative abundance of macrophytes with observed community-weighted mean (CWM) traits as the constraints, while relative low (about 30%) with CWM traits fitted from water depth gradient as the constraints.

2015 July 14, “Predicting Changes in Macrophyte Community Structure from Functional Traits in a Freshwater Lake: A Test of Maximum Entropy Model”, in PLOS ONE, →DOI:


paraproduct

To do this, we will characterize the boundedness of dyadic paraproducts on Lᵖ(W) via a new matrix weighted Carleson embedding theorem.

2015, Joshua Isralowitz, Hyun-Kyoung Kwon, Sandra Pott, “Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols”, in arXiv:

(mathematics) A non-commutative bilinear operator acting on functions that in some sense is like the product of the two functions it acts on.


quasigeodesic

We prove Calegari's conjecture that every quasigeodesic flow on a closed hyperbolic 3-manifold has closed orbits..

2015, Steven Frankel, “Coarse hyperbolicity and closed orbits for quasigeodesic flows”, in arXiv:

(mathematics) Of a map f: textbf R→Y, having constants K>0 and C>0 such that 1/Kd(x,y)-C<d(f(x),f(y))<Kd(x,y)+C.


subexponentially

In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence.

2015, Albert Clop, Renjin Jiang, Joan Mateu, Joan Orobitg, “Flows for non-smooth vector fields with subexponentially integrable divergence”, in arXiv:


superfunction

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(mathematics) An iterated function for complexified continuous iteration index.


autoduality

autoduality (usually uncountable, plural autodualities)

(mathematics) The property of being self-dual.


Henselian

From Hensel (surname) + -ian; after German mathematician Kurt Hensel (1861–1941).

1989, N. Bourbaki, Commutative Algebra: Chapters 1-7, [1985, N. Bourbaki, Éléments de Mathématique Algébre Commutative 1-4 et 5-7, Masson], Springer, page 256,
A local ring satisfying conditions (H) and (C) is called Henselian. Every complete Hausdorff local ring is Henselian. If A is Henselian and B is a commutative A-algebra which is a local ring and a finitely generated A-module, then B is Henselian.

An analogous result holds for Henselian fields. Recall that a field K is said to be Henselian with respect to a valuation v if v has a unique extension (also denoted v) to every algebraic extension of K.[…]It follows that every algebraic extension of an^([sic]) Henselian field K is Henselian.
[…] Every valued field (K,v) has a minimal separable algebraic extension (K#95;v,v) which is Henselian. The valued field is unique up to a K-isomorphism and is called the Henselian closure of (K,v) [Ribenboim, p. 176].

2008, Michael D. Fried, Moshe Jarden, Field Arithmetic, 3rd edition, Springer, page 203:

Although the study of the definability of henselian valuations has a long history starting with J. Robinson, most of the results in this area were proven during the last few years.

2017, Arno Fehm, Franziska Jahnke, “Recent progress on definability of Henselian valuations”, in Fabrizio Broglia, Françoise Delon, Max Dickman, Danielle Gondard-Cozette, Victoria Ann Powers, editors, Ordered Algebraic Structures and Related Topics: International Conference, American Mathematical Society, page 136:

(algebra, of a ring or field) Which satisfies the criteria for (some formulation of) Hensel's lemma.


Fréchet surface

Fréchet surface (plural Fréchet surfaces)

Named after the French mathematician Maurice Fréchet.

(mathematics) An equivalence class of parametrized surfaces in a metric space.


multitree

Second, we used the recursive multitree approach implemented in the R package bGMYC to incorporate phylogenetic uncertainty.

2015 July 17, “Ecological Specialization of Two Photobiont-Specific Maritime Cyanolichen Species of the Genus Lichina”, in PLOS ONE, →DOI:

(mathematics) An acyclic directed graph in which the set of nodes reachable from any node forms a tree.


megaprime

(mathematics) A prime number with at least one million decimal digits.


directed infinity

directed infinity (plural directed infinities)

(mathematics) A type of infinity in the complex plane that has a defined angle θ but an infinite absolute value r.

awanggang itinungo

a type of infinity in the complex plane that has a defined angle θ but an infinite absolute value r


commutant lifting theorem

(mathematics) A theorem in operator theory, stating that, if T is a contraction on a Hilbert space H, and U is its minimal unitary dilation acting on some Hilbert space K, and R is an operator on H commuting with T, then there is an operator S on K commuting with U such that RTⁿ=P_HSUⁿ|_H;∀n≥0, and ‖S‖=‖R‖. In other words, an operator from the commutant of T can be "lifted" to an operator in the commutant of the unitary dilation of T.


operator theory

(mathematics) A branch of functional analysis, being the study of linear operators on function spaces.


superperfect

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From super- + perfect, coined by Suryanarayana in 1969.

(mathematics) Being or relating to a class of positive integers satisfying σ²(n)=σ(σ(n))=2n,, where σ is the divisor function. They are a generalization of perfect numbers.


bivariable

Odds ratio (OR) and 95%CI were used to explore the association between independent variables and NVP RAM. The bivariable analysis was conducted for all mother and child characteristics potentially associated with NVP RAM. All variables with a p value ≤ 0.20 in the bivariable analysis, as well as child’s gender and age, were included in the multivariable logistic regression analysis.

2015 July 11, “Development of Nevirapine Resistance in Children Exposed to the Prevention of Mother-to-Child HIV-1 Transmission Programme in Maputo, Mozambique”, in PLOS ONE, →DOI:

(mathematics) Having two independent variables


subdifferential

We give a characterization of the associated subdifferential and the proximal operator, and discuss efficient optimization algorithms for some structured regularized loss-minimization problems using VGFs.

2015, Amin Jalali, Lin Xiao, Maryam Fazel, “Variational Gram Functions: Convex Analysis and Optimization”, in arXiv:


multicover

multicover (countable and uncountable, plural multicovers)

We consider the set multicover problem in geometric settings.

2012 December, Chandra Chekuri, Kenneth L. Clarkson, Sariel Har-Peled, “On the set multicover problem in geometric settings”, in ACM Transactions on Algorithms, volume 9, number 1:

(mathematics) A combinatorial problem concerning the covering or inclusion of elements by a collection of shapes or sets.

The polylogarithm in (2.33) indicates that the degree k multicover of a curve of genus g contributes with a factor k2g−3 to Fg.

2004, Tilman Wurzbacher, Infinite Dimensional Groups and Manifolds, →ISBN, page 39:

(mathematics) A solution to a multicover problem.


pancyclic

(graph theory, of a graph) Containing cycless of every possible length (from 3 to the order of the graph).


paratopological

Nickolas's [On the topology of free paratopological groups.]

2015, Fucai Lin, Chuan Liu, “The mapping i_2 on the free paratopological groups”, in arXiv:

(mathematics, of a topological semigroup) That is algebraically a group.


paratopological group

paratopological group (plural paratopological groups)

topological semigroup
topological semigroup#English

(mathematics) A topological semigroup that is algebraically a group.


sheafification

sheafification (countable and uncountable, plural sheafifications)

(mathematics) The conversion of a presheaf into a sheaf.


eigensimplified

Our methods are based on the eigensimplified model of Blangero etal.

2015, Habib Ganjgahi et al., “Fast and powerful heritability inference for family-based neuroimaging studies”, in Neuroimage, volume 115, →DOI:

(mathematics) simplified by transforming with a matrix of eigenvectors


cofreeness

In this article, we explore the coalgebraic character of graphs and transfer coalgebraic concepts like cofreeness, simulations or Co-Birkhoff theorems to F-graphs.

2015, Christian Jäkel, “A unified categorical approach to graphs”, in arXiv:

(mathematics) The property of being cofree.


Gompertz distribution

Gompertz distribution (plural Gompertz distributions)

(probability, statistics) A continuous probability distribution, often used to describe adult lifespans.


precompact

(topology) Forming a relatively compact subspace; Having a closure that is compact.

(topology) Totally bounded; Having a cover that consists of finitely many finite subsets.


subquotient

(mathematics) A quotient object of a subobject.


ultrapower

(mathematics) The special case of an ultraproduct where all factors are equal.


vincentization

From Vincent + -ization, after biologist S. B. Vincent (1912), who used a similar technique to construct learning curves.

(statistics) The technique of averaging three or more subjects' estimated or elicited quantile functions in order to define group quantiles from which F can be constructed.


cotranslation

cotranslation (countable and uncountable, plural cotranslations)

(mathematics) An equivalence map that is the dual of a translation.


strategyproof

(game theory) Of an asymmetric game where players have private information: such that there is no incentive for any of the players to hide or lie about their private information from the other players.


antidomain

It is shown that antidomain semirings are more expressive than test semirings and that Kleene algebras with domain are more expressive than Kleene algebras with tests.

2015, Georg Struth, “On the Expressive Power of Kleene Algebra with Domain”, in arXiv:

(mathematics) The boolean complement of the domain.


multidegree

In this paper, we define multiprojective witness sets which will encode the multidegree information of an irreducible multiprojective variety.

2015, Jonathan D. Hauenstein, Jose Israel Rodriguez, “Numerical irreducible decomposition of multiprojective varieties”, in arXiv:

complete intersection
complete intersection

(mathematics) The tuple (properly though a multiset) of the degrees of defining hypersurfaces for a complete intersection.


Arnold's cat map

Named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat.

(mathematics) A chaotic map from the torus into itself.


plethysm

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

Motivated by questions of Mulmuley and Stanley we investigate quasi-polynomials arising in formulas for plethysm.

2015, Thomas Kahle, Mateusz Michalek, “Obstructions to combinatorial formulas for plethysm”, in arXiv:

(algebra) A particular group-theoretic operation on a set of functions of a given symmetry type.


semisimplicity

(mathematics) Quality of being semisimple.


multipermutation

Based on this algorithm, we develop an encoding algorithm for a code proposed by Shieh and Tsai, a code that falls into our class of LP-decodable multipermutation codes.

2015, Xishuo Liu, Stark C. Draper, “LP-decodable multipermutation codes”, in arXiv:

(mathematics) A generalization of a permutation where every element can appear multiple times.


millibitcoin

The current minimum transaction fee is fixed at 0.0001 bitcoin or a tenth of a millibitcoin per kilobyte, recently decreased from one millibitcoin.

2014, Andreas M. Antonopoulos, Mastering Bitcoin: Unlocking Digital Cryptocurrencies:

A thousandth of a bitcoin or 0.001 BTC, equivalent to 1,000 bits or 100,000 satoshi.


microbitcoin

A millionth of a bitcoin, or 0.000001 BTC, equivalent to 100 satoshi.


predual

(mathematics) An object whose dual space is some other specified object.


quasiuniform

(mathematics) Having some but not all of the characteristics of a uniform structure.


sofic

Coined by mathematician Benjamin Weiss in 1973, based on Hebrew סופי (“finite”).

(mathematics, of a group) Whose Cayley graph is an initially subamenable graph.

a sofic subshift

(mathematics) Whose forbidden words form a regular language.


Markov partition

Markov partition (plural Markov partitions)

(mathematics) A tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic systems. By using a Markov partition, the system can be made to resemble a discrete-time Markov process, with the long-term dynamical characteristics of the system represented as a Markov shift.


hyperfair

Meanwhile, selection strongly favored responders that accepted fair or hyperfair offers.

2015 July 31, “Rational Constraints and the Evolution of Fairness in the Ultimatum Game”, in PLOS ONE, →DOI:

(game theory) Excessively fair, typically describing an offer involving more than fifty percent of the stake.


Tannakian

Named after the Japanese mathematician Tadao Tannaka, + -ian.

(mathematics) Being a particular kind of monoidal category equipped with some extra structure relative to a given field.


Lyapunov exponent

Lyapunov exponent (plural Lyapunov exponents)

(mathematics) In a dynamical system, a quantity that characterizes the rate of separation of infinitesimally close trajectories.