homothety

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From Ancient Greek ὁμο- (homo-, “same”) + θέσις (thésis, “setting, placement, arrangement”).

The product of two homotheties with the same centre is a homothety with that centre.

1927, Henry George Forder, The Foundations of Euclidean Geometry, page 178:

One cannot obtain all similarity mappings from products of homotheties alone, but they are necessary and basic to similarities.

1972, Clayton W. Dodge, Euclidean Geometry and Transformations, published 2004, page 106:

Since homotheties are determined by the fixed point, called the center of the homothety, and by the similitude ratio λ, we shall denote by h_(P,λ) the homothety with center P and similitude ratio λ.

2011, Agustí Reventós Tarrida, Affine Maps, Euclidean Motions and Quadrics, Springer Undergraduate Mathematics Series, page 69:

(mathematics, geometry) An isotropic scaling transformation of an affine space with a single fixed point.

homothecy

isotropic scaling transformation with a fixed point


orthobicupola

(mathematics) A bicupola in which the bases have the same orientation


bicupola

(mathematics) A solid formed from two cupolas joined at the base.


prismatoid

(mathematics) Any polyhedron whose vertices all lie in either of two parallel planes


semispace

(mathematics) Either of two regions making up a space.


stellation

(mathematics) The construction of a stellated polyhedron (or other polytope) by extending edges or planes.


equilaterality

(mathematics) The condition of being equilateral


space-filling curve

en-noun

space-filling curve (plural space-filling curves)

From space-filling curves it can be deduced that ℝ² and ℝ³ have the same cardinality as ℝ.

mathematical analysis
mathematical analysis

(mathematical analysis) a curve whose range contains the entire 2-dimensional unit square (or the 3-dimensional unit cube)


Peano curve

Named after its discoverer, Giuseppe Peano.

(mathematical analysis) A space-filling curve in the 2-dimensional plane.


Hausdorff dimension

Hausdorff dimension (plural Hausdorff dimensions)

Introduced in 1918 by mathematician Felix Hausdorff.

If S is nonempty then if the d-dimensional Hausdorff content of S is zero then d is larger than the Hausdorff dimension of S, and if the d-dimensional Hausdorff content of S is infinite then d is smaller or equal to the Hausdorff dimension of S. If the d-dimensional Hausdorff content of S is finite and positive then d is equal to the Hausdorff dimension of S.

(mathematical analysis) A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero.


apodization

(mathematics) Any of several techniques to modify the form of a mathematical function, or of a spectrum etc. by smoothing or removing irregularities

apodização

technique to modify the a function or spectrum by smoothing or removing irregularities


asymptotics

We shall see in sec. 6.2 that our result for S#95;3(a) can be expressed in terms of special functions, whose asymptotics are well-known. There we show also that the asymptotic form forS#95;3(a) obtained from the asymptotics of the special functions is identical to the asymptotic form obtained via Eq. (3.1).

1995 September 14, Vic Kowalenko, N. E. Frankel, L. Glasser, T. Taucher, Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders (Lecture note series / London mathematical society), Cambridge University Press, →ISBN, →LCCN, page 15:


asymptotic analysis

asymptotic analysis (plural asymptotic analyses)

(mathematics) Any of several methods for describing and analyzing the behaviour of a system at its limits


bimaximal

(mathematics, of a function) Having two maxima


hyperdeterminant

(mathematics) A generalisation of a determinant in a higher dimension.


hyperscalar

(mathematics) A generalisation of a scalar in a higher dimension.


satisfiability

satisfiability (countable and uncountable, plural satisfiabilities)

(mathematics, of a proposition or formula) The property of being able to be satisfied.


superalgebra

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(mathematics) A type of algebra used in supersymmetry.


superconformal

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(mathematics) Describing a conformal algebra related to supersymmetry


triality

triality (countable and uncountable, plural trialities)

(mathematics) A relationship between three vector spaces.


vectorlike

en-adj

vectorlike (comparative more vectorlike, superlative most vectorlike)

more vectorlike (comparative)
most vectorlike (superlative)

(mathematics) Having some characteristics of a vector.


fractal dimension

en-noun

fractal dimension (plural fractal dimensions)

Conventional statistical analyses presuppose that intrinsic variability is white noise. White noise yields a jagged and irregular line with a fractal dimension of 1.5, because successive observations are statistically independent of each other. Its fractal dimension indicates the extent to which white noise occupies 2-D space. White noise is uncorrelated noise. By contrast, the successive observations of pink noise tend to be positively correlated. This results in a less jagged trial series, and lower fractal dimensions that fall in the interval between 1 and 1.5.

2005, John G. Holden, Gauging the Fractal Dimension of Response Times from Cognitive Tasks:

The perimeter of Britain measured in the first dimension yields infinity, and measured in the second dimension yields zero, so it has to be measured in a fractal dimension of approximately 1.25.

(mathematical analysis) A dimension in which it is the most suitable to make measurements on a fractal set.

分形維數 /分形维数

a dimension for making measurements on a fractal set


dromion

From Ancient Greek δρόμος (drómos, “race-track”) + -on (“particle”), confer soliton.

der

partial differential equation
partial differential equation

(mathematics) An exact, nonlinear solution of any of a large class of two-dimensional partial differential equations


linearizable

en-adj

linearizable (comparative more linearizable, superlative most linearizable)

more linearizable (comparative)
most linearizable (superlative)


polylogarithm

(mathematics) A function of complex numbers related to logarithms.

polilogaritmo

a function of complex numbers related to logarithms


F distribution

chi-square distribution
chi-square distribution

analysis of variance
analysis of variance

significance testing
significance testing

correlation coefficient
correlation coefficient

(statistics, probability) A probability distribution of the ratio of two variables, each with a chi-square distribution; used in analysis of variance, especially in the significance testing of a correlation coefficient (R squared).


ANOVA

2015, John Ashton, "ANOVA and the analysis of drug combination experiments", Nature Methods 12 (12): 1108, doi:10.1038/nmeth.3663.
Factorial analysis of variance (ANOVA) can be very misleading in drug combination studies.

analysis of variance
analysis of variance#English

(statistics) Acronym of analysis of variance.


analysis of variance

en-noun

analysis of variance (countable and uncountable, plural analyses of variance)

(statistics) A collection of statistical models, and their associated procedures, in which the observed variance is partitioned into components due to different explanatory variables.

varianssianalyysi

partition of observed variance into components


horosphere

A modern scientific coinage, probably from a Latinized spelling of Ancient Greek ὅρος (hóros, “boundary”) (not to be confused with ὧρος (hôros, “year”), which gave rise to many time-related terms) + sphere

An n-1-dimensional hyperplane in hyperbolic n-dimensional space: it is (in the Poincaré disk) Euclidean-tangent at infinity to the boundary sphere or (in the upper-half-space model) Euclidean-parallel to the boundary hyperplane.


Poincaré disk

The hyperbolic plane, viewed as a disk so that Euclidean circles and lines Euclidean-perpendicular to the disk's surface are hyperbolic lines.


Burali-Forti paradox

Named after Cesare Burali-Forti, who in 1897 published a paper proving a theorem which, unknown to him, contradicted a previously proved result by Georg Cantor.

1984, Michael Hallett, Cantorian Set Theory and Limitation of Size, Oxford University Press (Clarendon Press), 1986, Paperback, page 186,
Like them, Mirimanoff concentrates on the Burali-Forti paradox, and like Russell's analysis before, Mirimanoff shows how. in terms of size, the Burali-Forti paradox is basic and that if we solve this the other paradoxes will be solved too.

1994 [Routledge], Ivor Grattan-Guinness (editor), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, Volume 1, 2003, Johns Hopkins University Press, Paperback, page 632,
In the first place, Berry rejected Russell's solution to the Burali-Forti paradox, claiming that it was easy to prove that the set of all ordinal numbers was a well-ordered set (and that Cantor had actually done it).

The Burali-Forti paradox was discovered by Cantor in 1895 and Burali-Forti in 1897, but was not regarded by them as a paradox.

2002, Marcus Giaquinto, The Search for Certainty: A Philosophical Account of Foundations of Mathematics, Oxford University Press (Clarendon Press), page 37:

(set theory) The paradox that supposing the existence of a set of all ordinal numbers leads to a contradiction; construed as meaning that it is not a properly defined set.

Burali-Forti paradox
Cesare Burali-Forti
Georg Cantor


Mazur game

(topology) A topological game invented by the Polish mathematician Stanisław Mazur in order to illustrate the difference between sets of the first category and second category.


NFU

(set theory) Initialism of New Foundations with urelements.


urelement

1996, Scientific Books staff (translators), Yuri L. Ershov, Definability and Computability, Scientific Books, page viii,
The introduction of urelements would seem to be a technical improvement; however, now we know that just such an extension of the notion of the admissible set led to the universal theory of computability based on the notion of definability by formulas with (in a broad sense) effective semantics.

There may be no urelements; as we shall see, we can still build plenty of sets in this case. At stage 0 we can always build the empty set. If there are no urelements, this is the only set we can build. If there is one urelement, a, we can build the sets #92;empty and #92;#123;a#92;#125;. If there are two urelements, a and b, the possible sets are #92;#123;a#92;#125;, #92;#123;b#92;#125;, and #92;#123;a,b#92;#125;; and so on if there are more urelements.
At stage 1, we can build any set containing urelements or sets built at stage 0; that is, any set whose members are already available at the beginning of stage 1. If there are no urelements, we can build #92;empty and #92;#123;#92;empty#92;#125;.

2012, Nicholas J. J. Smith, Logic: The Laws of Truth, Princeton University Press, page 448:

Let #92;mathcal#123;L#125;#92;alpha#95;#92;in be a version of the language of set-theory with urelements in which each occurrence of a quantifier is restricted by some V#95;#92;beta (#92;betalt;#92;alpha).

2013, Agustín Rayo, The Construction of Logical Space, Oxford University Press, page 95:

(set theory) A mathematical object which is not a set but which can be an element of a set.


Russell's paradox

Named after English mathematician, logician and philosopher Bertrand Russell.

named-after

One concludes that there must be something fishy about the Axiom of Comprehension, and, over time, the replacement of the Axiom of Comprehension by the Schema of Separation was seen to resolve Russell's paradox. Indeed, one cannot apply the Schema of Separation as in Russell's paradox unless one knows in advance that the collection of all sets is itself a set.

1999, R. C. Penner, Discrete Mathematics: Proof Techniques and Mathematical Structures, World Scientific, page 109:

The well-known theorem of Tarski that truth of sentences in any reasonably expressive language L cannot be defined in the language L itself is proved by a diagonalization argument similar to the argument involved in Russell's paradox.[…]It is usual to think that Russell's paradox excludes "large" sets like the universe, but this is actually not the case. An alternate solution to Russell's paradox (and other paradoxes) was proposed by Quine (1937) in his system "New Foundations" (NF): comprehension restricted to stratified formulae.

2001, M. Randall Holmes, “Tarski's Theorem and NFU”, in C. Anthony Anderson, Michael Zelëny, editors, Logic, Meaning and Computation: Essays in Memory of Alonzo Church, Springer (Kluwer Academic), page 469:

2013, Greg Frost-Arnold, Carnap, Tarski, and Quine at Harvard: Conversations on Logic, Mathematics, and Science, Carus Publishing Company (Open Court), page 43,
Roughly, the idea is that Russell's paradox reveals that certain logics suffer serious problems, and therefore these logics should be avoided. […] Here again, Quine asserts that the real lesson of Russell's paradox is that we should give up quantifying over abstracta.

(set theory) The paradox that a set defined to contain all sets which do not contain themselves can neither consistently contain itself nor not contain itself.

Axiom schema of specification
Russell's paradox


hyperreal number

en-noun

hyperreal number (plural hyperreal numbers)

nonstandard analysis
nonstandard analysis

(mathematics) Any of a set of numbers which extends the set of real numbers by including infinitesimals and infinities, and is used in nonstandard analysis.


capacitated

en-adj

capacitated (comparative more capacitated, superlative most capacitated)

more capacitated (comparative)
most capacitated (superlative)

We consider uniqueness and multiplicity of market equilibria in a short-run setup where traded quantities of electricity are transported through a capacitated network in which power flows have to satisfy the classical lossless DC approximation.

2018, Krebs et al, "Uniqueness and multiplicity of market equilibria on DC power flow networks". doi:10.1016/j.ejor.2018.05.016

(transitive, mathematics) Constrained by maximum throughput, often applied to physical networks transporting flows.


mascle

From Middle English mascle, maskel, from Old French mascle, macle, from Medieval Latin mascula, from a Germanic source (compare English mesh). Doublet of mail.

(historical) A lozenge-shaped piece of metal, used in making scale mail.


arithmetic operator

en-noun

arithmetic operator (plural arithmetic operators)

(arithmetic) Any of the four basic operators in arithmetic, namely addition, subtraction, multiplication and division.

թվաբանական օպերատոր

any of the four basic operators in arithmetic


centerless

(group theory, of a group) Whose center is trivial (contains only the identity element).


quartal

(mathematics) Of base four; using only four unique digits.


noncototient

(mathematics) An integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it


bitruncated

(mathematics) Truncated using bitruncation.


bitruncation

(mathematics) An operation on a regular polytope in which every edge is lost and every face is reduced in size.


mastodonic

en-adj

mastodonic (comparative more mastodonic, superlative most mastodonic)

more mastodonic (comparative)
most mastodonic (superlative)


intuitionistic logic

en-noun

intuitionistic logic (plural intuitionistic logics)

law of excluded middle
law of excluded middle

law of double negation
law of double negation

(mathematics, logic) A type of logic which rejects the axiom law of excluded middle or, equivalently, the law of double negation and/or Peirce's law. It is the foundation of intuitionism.

intuïtionistische logica

a type of logic which rejects the axiom "law of excluded middle"


proof by contradiction

proof by contradiction (countable and uncountable, plural proofs by contradiction)

(mathematics, logic) The proof of a statement adduced by deriving a contradiction from the statement's negation.


matric

But throughout this book we look upon the matric algebras as our primary object;

1939, Hermann Weyl, “Chapter 3: Matric algebras and group rings”, in The Classical Groups: Their Invariants and Representations:

[…] the possibility of using matric methods to solve analysis and synthesis problems becomes apparent.

1956, R. J. Kavanagh, “The application of matrix methods to multi-variable control systems”, in Journal of the Franklin Institute, volume 262:

In other words, its controls are homeomorphic to the matric mathematics.

1964 September, The Matrix and Tensor Quarterly, page 110:

(mathematics) Of or pertaining to matrices.


metaregression

(statistics) A form of subgroup analysis that is used to investigate heterogeneity across multiple trials


microdata

In fact, labor groups are more likely to win elections for union representation in small workplaces. In a study released this week by the Century Foundation, we analyzed microdata on every union election in the country from April 2007 to December 2018, more than 22,000 in total.

2019 February 9, Mark Zuckerman, “Unions Need to Think Small to Get Big”, in The Atlantic, retrieved 2022-10-19:

(statistics) Data concerning individuals in a trial, survey etc.


forest plot

(statistics) A graphical display used in meta-analysis designed to illustrate the relative strength of treatment effects in multiple quantitative scientific studies addressing the same question.


type I error

(statistics) Rejecting the null hypothesis when the null hypothesis is true.


type II error

(statistics) Accepting the null hypothesis when the null hypothesis is false.

errors de tipus II

accepting the null hypothesis when false


error of the second kind

error of the second kind (plural errors of the second kind)


error of the first kind

error of the first kind (plural errors of the first kind)


GRU

artificial intelligence
artificial intelligence

gated recurrent unit
gated recurrent unit#English

(artificial intelligence) Initialism of gated recurrent unit.


petajoule

(metrology) An SI unit of energy equal to 10¹⁵ joules. Symbol: PJ


pentachoron

pentachoron (plural pentachorons or pentachora)

pentachorons (plural)
pentachora (plural)

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From penta- (“five”) + -choron (“4-dimensional solid”), from Ancient Greek πέντε (pénte, “five”) and χῶρος (khôros, “room”).

af

A triangle becomes a tetrahedron (a type of pyramid), then a pentachoron (a hyperpyramid).

2008, George Musser, The Complete Idiot's Guide to String Theory, page 174:

Geometrically, K₃ relates to a triangle, K₄ a tetrahedron, K₅ a pentachoron, etc.

2008, Prabhakar Gupta et al., Design and Analysis of Algorithms, page 356:

The tetrahedron is a 3-simplex whose 4-simplex analog is the pentachoron, a four-dimensional body which can be orphographically ^([sic]) projected onto a quincrux (as well as a pentagram and other shapes).

2013, Caspar Henderson, The Book of Barely Imagined Beings, page 7:

(mathematics) A four-dimensional object analogous to a tetrahedron, constructed out of five tetrahedra.


derain

en-verb

derain (third-person singular simple present derains, present participle deraining, simple past and past participle derained)

derains (present singular third-person)
deraining (participle present)
derained (participle past)
derained (past)

From de- + rain. Compare deraining (noun).

Hence, in our proposed pipeline, we derain first, then followed by dehazing and at last finished with deraining.

2017, Yang, Wenhan, Robby T. Tan, Jiashi Feng, Jiaying Liu, Zongming Guo, and Shuicheng Yan, “Deep joint rain detection and removal from a single image.”, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition:

It is demonstrated that the proposed method yields in relatively higher performance in comparison to other state-of-the-art deraining models in terms of derained image quality and computing efficiency.

2018, Chen Li, Yecai Guo, Qi Liu, Xiaodong Liu, “DR-Net: A Novel Generative Adversarial Network for Single Image Deraining”, in Security and Communication Networks, →DOI:

(machine learning) To remove rain from an image.


deraining

In contrast to other common strategies that increase depth or breadth of the network, we use image processing domain knowledge to modify the objective function and improve deraining with a modestly sized CNN.

2017, Xueyang Fu, Jiabin Huang, Xinghao Ding, Yinghao Liao, John Paisley, “Clearing the Skies: A Deep Network Architecture for Single-Image Rain Removal”, in IEEE Transactions on Image Processing, →DOI:

Images captured in rainy days suffer from noticeable degradation of scene visibility. The goal of single image deraining algorithms is to generate sharp images from a rainy image input.

2019, S. Li, I. B. Araujo, W. Ren, Z. Wang, E. K. Tokuda, R. H. Junior, R. Cesar-Junior, J. Zhang, X. Guo, X. Cao, “Single image deraining: A comprehensive benchmark analysis”, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, page 3838:

(machine learning) The removal of rain from an image or video.


micromole

(metrology) An SI unit of amount of substance equal to 10⁻⁶ moles. Symbol: μmol


automorphic

5 is an automorphic number because 5² = 25, which ends in 5; similarly 625² = 390625, ends in 625.

(mathematics) Describing a number whose square ends in the number itself; circular.

automorfinen

describing a number whose square ends in the number itself; circular

(mathematics) Of or pertaining to automorphy or an automorphism.

automorf

of or pertaining to automorphy or an automorphism


bicategorical

(mathematics) Of or pertaining to a bicategory


bicategory

(mathematics) A particular construct in category theory, used to extend the notion of category to handle the cases where the composition of morphisms is not (strictly) associative, but only associative up to an isomorphism.


bivariant

independent variable
independent variable

(mathematics) Having two independent variables.


bivector

(mathematics) An antisymmetric tensor of second rank.


categorification

en-noun

categorification (countable and uncountable, plural categorifications)

2008, E. Krenkel, Ramifications of the Geometric Langlands Program, Michael Cowling, Edward Frenkel, Masaki Kashiwara, Alain Valette, David A. Vogan, Jr., Nolan R. Wallach (editors), Representation Theory and Complex Analysis: Lectures Given at the C.I.M.E. Summer School, Springer, Lecture Notes in Mathematics 1931, page 83,
In Section 3.4 we have already discussed the question of categorification of the algebra of functions on a homogeneous space like G(F)/K.

2009, Volodymyr Mazorchuk, Lectures on sl₂( C )-Modules, Imperial College Press, page 221,
Show that Φ⊕Φ is also a (naïve) homomorphism of naïve categorifications.

Khovanov's categorification of the Jones polynomial by Khovanov homology is the subject of Section 11.6.

2010, Kishore Marathe, Topics in Physical Mathematics, Springer, page 351:

2011, Robert Wisbauer, Categorical aspects of Hopf algebras, Matilde Marcolli, Deepak Parashar (editors), Quantum Groups and Noncommutative Spaces: Perspectives on Quantum Geometry, Springer Science+Business (Vieweg+Teubner), page 146,
Since Lawvere's categorification of general algebra, algebras and coalgebras are used as basic notions in universal algebra, logic, and theoretical computer science, for example (e.g. [AdPo], [Gu], [TuPl]).

(category theory) A procedure that defines theorems in terms of category theory by mapping concepts from set theory to category theory.


categorify

en-verb

categorify (third-person singular simple present categorifies, present participle categorifying, simple past and past participle categorified)

categorifies (present singular third-person)
categorifying (participle present)
categorified (participle past)
categorified (past)

(mathematics, transitive) To define a theorem in terms of category theory


quadric

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(mathematics) A surface or curve whose shape is defined in terms of a quadratic equation

quadrique

surface whose shape is defined in terms of a quadratic equation


quadric

(mathematics) Of or relating to the second degree; quadratic.


estimand

Apparently of mid-20th century coinage from Latin aestimandum, gerundive of aestimo (“I value", "I estimate”).

Statistics needs a term like estimand to replace the lengthy phrase independent variable.

1939, Charles F. Roos with Victor von Szeliski, “The Concept of Demand and Price Elasticity—The Dynamics of Automobile Demand”, in Journal of the American Statistical Association, volume 34, number 208, →DOI, page 656:

We speak of the estimator's target as an estimand (as something to be estimated) rather than just as a parameter.

1968, Frederick Mosteller with John W. Tukey, “Data Analysis--Including Statistics”, in Handbook of Social Psychology, 2nd edition, volume 2: Research Methods, page 106:

When doing causal inference in the competing events setting, it is critical to first ascertain the relevant question and the causal estimand that best answers it, with the choice often being between estimands that do and do not eliminate competing events.

2020 September, Jacqueline E. Rudolph, Catherine R. Lesko, Ashley I. Naimi, “Causal inference in the face of competing events”, in Current Epidemiology Reports, volume 7, number 3:

(statistics) that which is being estimated.


cofibration

(mathematics) A particular form of mapping. A continuous mapping i:A→X, where A and X are topological spaces, is a cofibration if it satisfies the homotopy extension property with respect to all spaces Y.


funnel plot

(statistics) A scatterplot of effect size against a measure of study size or variability, used primarily as a visual aid to detecting and displaying bias or systematic heterogeneity.


standard error

(statistics) A measure of how likely a mean of means is to be wrong. It is the standard deviation of the sample sizes in each to the sample means.


supergraph

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(mathematics) The parent graph that includes a subgraph.


file-drawer problem

en-noun

file-drawer problem (plural file-drawer problems)

From the notion of statistical studies that show no significant effect tending to remain unpublished in file drawers.

The bias to meta-analysis resulting from statistical studies with low statistical power tending to remain unpublished and inaccessible to the analyst.


publication bias

publication bias (plural publication biases)

Studies with negative results tend not to be published in scientific journals, a phenomenon known as "publication bias".

2011, Jacques Pepin, “Out of Africa”, in The Origins of AIDS, 1st edition, →ISBN, page 10:


statistical power

statistical power (usually uncountable, plural statistical powers)

(statistics) The probability that a statistical test will reject a false null hypothesis, that is, that it will not make a type II error, producing a false negative.


effect size

He spent a year breaking down the 45 studies Stapel produced at Tilburg and cataloguing their individual aberrations, noting where the effect size – a standard measure of the difference between the two groups in an experiment – seemed suspiciously large, […]

2017 February 1, Stephen Buranyi, “The high-tech war on science fraud”, in The Guardian:

(statistics) A measure of the strength or magnitude of the effect of an independent variable on a dependent variable in an experiment or a quasi-experiment.

taille d’effet

a measure of the strength or magnitude of the effect


backward induction

backward induction (usually uncountable, plural backward inductions)

Simple game theory tells us that a process of backward induction should, really, at some point, induce the smart money to get out. And were that to happen, investors really should be prepared to lose everything.

2021 December 14, Richard Partington, quoting Thomas Belsham, “Bitcoin could become ‘worthless’, Bank of England warns”, in The Guardian:

(game theory) The process of reasoning backwards in time, from the end of a problem or situation, to determine a sequence of optimal actions.


multiagent

(computing, artificial intelligence) Involving more than one agent (actor that can make decisions).


cross tabulation

cross tabulation (plural cross tabulations)

(statistics) A presentation of data about categorical variable in a tabular form to aid in identifying a relationship between the variables.


determinantal

Our next result […] provides a determinantal test for negative definitess or negative semidefiniteness of a matrix M.

1995, Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green, Microeconomic Theory, Oxford University Press, page 936:

The determinantal equation (9.120) and its expanded form are called the characteristic equation of system (9.116).

2010, Giancarlo Gandolfo, Economic Dynamics, 4th edition, Springer, page 139:

(mathematics) Of or pertaining to a determinant


Diophantine

(mathematics) Of or pertaining to Diophantus, the Greek mathematician.


Diophantus

(mathematics) A Greek mathematician who first developed algebra


fluxions

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The sheltered world of academia suited Clarence, who for the first time was among his intellectual peers. He excelled at geometry, algebra and fluxions.

2022, Hernan Diaz, Trust, Picador (2023), page 141:

differential calculus
differential calculus

(obsolete, mathematics) differential calculus.


fluxion

fluxion (countable and uncountable, plural fluxions)

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From Middle French fluxion, from Late Latin fluxiō, from Latin flūxus + -iō.

(obsolete, mathematics) The derivative of a function.


hyperelliptic

(mathematics) Describing an extension of elliptic functions to complex numbers.

(mathematics) Pertaining to a hyperellipse.


contingency table

contingency table (plural contingency tables)

kontingenciatáblázat

table presenting joint distribution of categorical variables

(statistics) A table presenting the joint distribution of two categorical variables.

(statistics) An arrangement of data containing the joint distribution of two or more categorical variables, usually in a database, a series of tables, or a special visualization.


hyperoctahedral

cocktail party graph
cocktail party graph

(mathematics) Describing a graph more commonly known as the cocktail party graph

(mathematics) Describing a group that can be realized as the group of symmetries of a hypercube or hyperoctahedron.


implicitization

(mathematics) The act of rendering something implicit


injectivity

injectivity (countable and uncountable, plural injectivities)

(mathematics, uncountable) The property of being injective.

(mathematics, countable) An injective function.


intensionality

intensionality (countable and uncountable, plural intensionalities)

(logic, mathematics) The condition of having an intension


finite element

(mathematics) Any of a finite number of discrete elements of a system, interconnected at discrete nodes, used to model a physical system


crosstab

(statistics) Alternative spelling of cross tab; A cross tabulation


cross-tab

(statistics) Alternative spelling of cross tab


factorial table

factorial table (plural factorial tables)

(statistics) A tabular presentation of data used to show the influence of two independent categorical variables on a dependent variable.

(statistics) An arrangement of data showing the effect of more than two categorical variables on a dependent variables.


metabelian

(mathematics) Having an abelian commutator subgroup


monodromy

monodromy (countable and uncountable, plural monodromies)

(mathematics) The globalization of local morphisms in category theory


multivector

(mathematics) A geometric Clifford number (=adding some 0-vector (=scalar) and an oriented rotation (=bivector) or even a volume (=trivector) to a unidirectional 1-vector).


quasigroup

(mathematics) An algebraic structure, resembling a group, whose arithmetic may not be associative


representable functor

representable functor (plural representable functors)

If a representable functor is naturally isomorphic to a hom functor mbox Hom(C,-) or mbox Hom(-,C), then the object C is said to represent that representable functor.

(category theory) A functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor.


contravariant functor

contravariant functor (plural contravariant functors)

A contravariant functor F#58;#92;mathcal#123;C#125;#92;rightarrow#92;mathcal#123;D#125; is the same as a covariant functor F#58;#92;mathcal#123;C#125;#123;op#125;#92;rightarrow#92;mathcal#123;D#125;.

(category theory) A functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if h=g∘f, then F(h)=F(f)∘F(g).


Yoneda lemma

Lemma named after the Japanese mathematician Nobuo Yoneda (1930–1996).

As a corollary of the Yoneda lemma, given a pair of contravariant hom functors #92;mbox#123;Hom#125;(-,A) and #92;mbox#123;Hom#125;(-,B), then any natural transformation #92;alpha from #92;mbox#123;Hom#125;(-,A) to #92;mbox#123;Hom#125;(-,B) is determined by the choice of some function f#58;A#92;rightarrowB to map the identity #92;mbox#123;id#125;#95;A#58;A#92;rightarrowA to, by the component #92;alpha#95;A#58;#92;mbox#123;Hom#125;(A,A)#92;rightarrow#92;mbox#123;Hom#125;(A,B) of #92;alpha. This implies that the Yoneda functor is fully faithful, which in turn implies that Yoneda embeddings are possible.

• Yoneda Lemma: Nat(Hom(A,–), F) ≅ F(A)
∴ Nat(Hom(A,–), Hom(B,–)) ≅ Hom(B,A)
∴ A ≅ B iff Hom(A,–) ≅ Hom(B,–)
i.e. A is isomorphic to B if and only if A's network of relations is isomorphic to B's network of relations.

And then there's the Yoneda Lemma embodied in the classical Gaussian row reduction operation, that a given row reduction operation (on matrices with say k rows) being a "natural" operation (in the sense of natural transformations) is just multiplication (on the appropriate side) by the effect of that operation on the k-by-k identity matrix.
And dually for column-reduction operations :-)

2020, Emily Riehl, quoting Fred E. J. Linton, The Yoneda lemma in the category of Matrices:

natural transformation
natural transformation

(category theory) Given a category 𝒞 with an object A, let H be a hom functor represented by A, and let F be any functor (not necessarily representable) from 𝒞 to Sets, then there is a natural isomorphism between Nat(H,F), the set of natural transformations from H to F, and the set F(A). (Any natural transformation α from H to F is determined by what α_A( mbox id_A) is.)

米田引理

theorem which states that there is a natural isomorphism...


natural transformation

natural transformation (plural natural transformations)

(category theory) A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow).


zonoid

(mathematics) A limit of a vector sum of line segments


vector sum

(mathematics) The vector whose initial and final points are those of a series of other vectors laid end to end.


bigon

(rare) A polygon having two edges and two vertices.


weights and measures

The science and regulation of standards for the quantification of size, weight, temperature, etc.


Hasse diagram

Named after Helmut Hasse (1898–1979), though he was not the first to use them.

(set theory) A diagram which represents a finite poset, in which nodes are elements of the poset and arrows represent the order relation between elements. Transitivity of the order relation is tacit, in other words, if x<y and y<z then no arrow is drawn from x to z, but if there is no distinct z between x and y (such that x<z<y) then an arrow is draw from x to y.


Boolean lattice

Boolean lattice (plural Boolean lattices)

A Boolean lattice always has 2ⁿ elements for some cardinal number 'n', and if two Boolean lattices have the same size, then they are isomorphic. A Boolean lattice can be defined "inductively" as follows: the base case could be the "degenerate" Boolean lattice consisting of just one element. This element is less than or equal to itself, which reflects the first "law of thought". Inductive step: given the structure of a 2ⁿ-element Boolean lattice, make an exact and separate duplicate of it, which preserves the order relation isomorphically. Then connect the two lattices as follows: choose one as the "bottom" and one as the "top", then draw an arrow connecting each element of the "bottom" lattice to its corresponding element of the "top" lattice. The result is the 2ⁿ⁺¹-element Boolean lattice (unique up to order-isomorphism). The 0 of the bottom lattice becomes the new 0, and the 1 of the top lattice becomes the new 1. Note that the 4-element (Boolean) lattice is a square, the 8-element lattice is a cube, the 16-element lattice is a tesseract, and higher-order lattices are higher-dimensional hypercubes in general, with the 0 and 1 always diagonally opposite, i.e., at the highest possible Hamming/taxicab distance from each other (equal to 'n' for an n-dimensional hypercube) and the edges directed so as to connect the vertex closer to 0 to the vertex further away from 0 (in terms of Hamming/taxicab distance).

(algebra) The lattice corresponding to a Boolean algebra.


distributive lattice

distributive lattice (plural distributive lattices)

In a distributive lattice, the set of complemented elements is a sublattice.

(algebra) A lattice in which the "meet" and the "join" operations are distributive with respect to each other.


empty graph

The empty graph with n vertices is denoted as Eₙ.

(graph theory) A graph with vertices but no edges.


meanless

en-adj

meanless (comparative more meanless, superlative most meanless)

more meanless (comparative)
most meanless (superlative)

[…] is stopped (n_k=0) if either the estimation error is within a "dead zone" (|c_k|<|δₖₚ|), or the arrival data are meanless (γₖ=0).

1990, in Experimental Robotics I: The First International Symposium Montreal,, Springer-Verlag, page 208

Another unfailing “mean” to characterize such meanless distributions is the logarithmic mean […]

1994, M.R. Schroeder, “How to generate Thermal Photons - On the Computer”, in Gérard G. Emch et al., editors, On Klauder’s Path: A Field Trip, World Scientific Publishing Co., →ISBN, page 199:

In particular: i) the average is used to get a meanless dataset, as specified in sect. 20; […]

2004, La Rivista del Nuovo cimento, Società italiana di fisica, page 35:

(not comparable, mathematics) Having no (mathematical) mean, or having a mean of zero.


finitism

(mathematics) An extreme form of constructivism, according to which a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps.


ultrafinitism

(mathematics) A form of finitism that is even more extreme in that it denies those constructs whose construction cannot be physically performed (such as a number that no human could have time to calculate).


undirected path

en-noun

undirected path (plural undirected paths)

A path x→y←z is an undirected path.

(graph theory) In a directed graph, a path in which the edges are not all oriented in the same direction.


directed path

A path x→y→z is a directed path.

(graph theory) In a directed graph, a path in which the edges are all oriented in the same direction.


Yoneda embedding

Yoneda embedding (plural Yoneda embeddings)

Named after the Japanese mathematician Nobuo Yoneda (1930–1996).

(category theory) An embedding of a category 𝒞 within the category of functors from 𝒞 to the category of sets. Such an embedding is effected by a Yoneda functor.


adjunction

adjunction (countable and uncountable, plural adjunctions)

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From Latin adjunctio, from adjungere: compare French adjonction, and see adjunct.

The ring obtained after the adjunction of the elements a,b and y to the ring R may be denoted R#91;a,b,y#93;.

The field adjunction #92;mathbb#123;Q#125;(#92;pi) can be obtained from #92;mathbb#123;Q#125; by adjoining #92;pi to #92;mathbb#123;Q#125;.

(mathematics, chiefly algebra and number theory) The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process.

(category theory, loosely) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.

adiunkcja

a form of similarity between a pair of categories mapped to each other by dual morphisms

(category theory, strictly) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.

Meronyms: adjoint, left adjoint, right adjoint

(formally, given two categories 𝒞 and 𝒟 and (covariant) functors F:𝒞→𝒟 and G:𝒟→𝒞) A natural isomorphism Φ: operatorname Hom_( mathcal )C(G·,·)→ operatorname Hom_( mathcal )D(·,F·) (where the hom-functors are understood as bifunctors from 𝒟^( operatorname )op×𝒞 to mathbf Set). See Adjoint functors on Wikipedia.Wikipedia.


measure of location

measure of location (plural measures of location)

(statistics, probability) A single number used to characterize a batch, sample, or distribution or the position of an element of it.


LMS

LMS (countable and uncountable, plural LMSs)

(mathematics) Initialism of least mean squares.


pentakis dodecahedron

pentakis dodecahedron (plural pentakis dodecahedra)

(mathematics) A Catalan solid equivalent to a dodecahedron with a pentagonal pyramid covering each face


Catalan solid

From Catalan (“a surname”) + solid, named for Belgian mathematician Eugène Charles Catalan.

1993, E. Heil, H. Martini, 1.11: Special convex bodies, P. M. Gruber, J. M> Wills (editors), Handbook of Convex Geometry, Volume A, page 352,
These duals are also called Catalan solids, because Catalan was the first mathematician who described all of them, cf. Brückner (1900, p. 160). Some of the Catalan solids are much older, e.g., the rhombic dodecahedron, which plays a role in crystallography (cf. chapter 37), and the rhombic triacontahedron, which is of some importance also in the theory of quasicrystals (cf. chapter 3.5).

The set of thirteen such duals is historically designated the Catalan solids. Perhaps the most striking feature of a Catalan solid is that it is composed of just one kind of face that is not a regular polygon. A face of a Catalan solid can be simply constructed by the Dorman-Luke construction [3, 4, 6, 16], which is based on a dualization process known as polar reciprocation [6], with respect to the midsphere.

2003, Rona Gurkewitz, Bennett Arnstein, Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, page 4:

As the most complex of the Catalan solids, the disdyakis triacontahedron has 1680 geometrical elements surrounding its axis, according to Table 1, whilst 2400 elements surround it when its faces are divided into their sectors, i.e., 720 elements are added by this division. These numbers are ten times the corresponding numbers for the simplest Catalan solid.

2009, Stephen M. Phillips, The Mathematical Connection Between Religion and Science, page 270:

(geometry) The dual polyhedron of any Archimedean solid.


dual polyhedron

(mathematics) Either of a pair of polyhedra in which the faces of one are equivalent to the vertices of the other.


pentacontagon

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From pentaconta- (“50”) + -gon (“-sided”), from Ancient Greek πεντήκοντᾰ (pentḗkontă, “50”) and γωνία (gōnía, “corner”).


winsorization

en-noun

winsorization (usually uncountable, plural winsorizations)

Named for the engineer-turned-biostatistician Charles Winsor (1895–1951), + -ization.

(statistics) A transformation of statistics of a batch or sample by transforming extreme values.


winsorize

en-verb

winsorize (third-person singular simple present winsorizes, present participle winsorizing, simple past and past participle winsorized)

winsorizes (present singular third-person)
winsorizing (participle present)
winsorized (participle past)
winsorized (past)

Named for the engineer-turned-biostatistician Charles P. Winsor (1895–1951), with -ize.

(statistics) To transform statistics of a batch or sample by transforming extreme values.


hypoelliptic

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hypoelliptic operator
hypoelliptic operator

(calculus) Related to or involving hypoelliptic operators.

гипоэллиптический

related to or involving hypoelliptic operators


hypoelliptic operator

en-noun

hypoelliptic operator (plural hypoelliptic operators)

(calculus) A differential operator that preserves mathematical smoothness.


pentakis-

(mathematics) A variant of penta-, used for multiplication with a second numerical prefix.


DAO

DAO (countable and uncountable, plural DAOs)

As the name suggests, DAOs are autonomous entities that subsist independently from any legal or moral entity. After they have been created and deployed onto the internet, they no longer need (nor heed) their creators.

2014 March 8, Primavera De Filippi, “Tomorrow's Apps Will Come From Brilliant (And Risky) Bitcoin Code”, in Wired, →ISSN:

Humans aren't in charge, they are on the edges. AI is what makes the decisions and the DAO maintains itself. DAOs aren't just defined by having AI make all the decisions, they also have their own internal capital.

2016, Siraj Raval, Decentralized Applications, O'Reilly Media, →ISBN:

But with the mayor’s backing, Mr. Nelson is planning to establish a trust fund that would serve as the basis of the DAO. “I’m dreaming,” he said. “Two Harbors could turn into Disneyland.”

2022 January 25, David Yaffe-Bellany, “The Rise of the Crypto Mayors”, in The New York Times, →ISSN:

DAOs, which have been described as “financial flash mobs” or “group chats with bank accounts,” are among the fastest-growing parts of the crypto ecosystem.

2022 March 2, Erin Woo, Kevin Roose, “This Social Club Runs On Crypto Tokens and Vibes”, in The New York Times, →ISSN:

decentralized autonomous organization
w:decentralized autonomous organization

(cryptocurrencies, Web3) Acronym of decentralized autonomous organization, an autonomous entity based on smart contracts on a blockchain.


additive group

additiivinen ryhmä

group or algebraic object regarded as a group with operation called addition

(mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:

(group theory) Any (often, but not necessarily, abelian) group whose binary operation is called addition.

(algebra) Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition.

(category theory) Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition.


pentacube

(mathematics) A polycube composed of five cubes


midhinge

(statistics) A measure of location of a batch or sample equal to the average of the first and third quartiles. Equivalently, it is the 25% trimmed mid-range.


L-estimator

(statistics) Any estimator that is a linear combination of order statistics of the measurements.


breakdown point

breakdown point (plural breakdown points)

(statistics, of an estimator) The number or proportion of arbitrarily large or small extreme values that must be introduced into a batch or sample to cause the estimator to yield an arbitrarily large result.


big O notation

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From the capital letter O (short for order, originally German Ordnung) used in the notation.

(mathematics, computing theory) A particular notation, useful in the analysis of algorithms, which describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions.


hexakis-

From Ancient Greek ἑξάκις (hexákis, “six times”).

uder

a solid figure contained by 48 scalene triangles

a solid figure contained by 24 scalene triangles

(mathematics) A variant of hexa-, used for multiplication with a second numerical prefix.


bis-

Bis (η⁶-arene) metal complexes have been made for many transition metals by the Al/AlCl₃ reduction method.

(mathematics, chemistry) A variant of di-, used for substitutions of two complex rather than simple units.


octakis-

From Ancient Greek ὀκτάκις (oktákis, “eight times”).

bor

(mathematics) A variant of octo-, used for multiplication with a second numerical prefix: octakishexahedron


heptakis-

From Ancient Greek ἑπτάκις (heptákis, “seven times”).

der

(mathematics) A variant of hepta-, used for multiplication with a second numerical prefix.


decakis-

(mathematics) A variant of deca-, used for multiplication with a second numerical prefix


superconnected

en-adj

superconnected (comparative more superconnected, superlative most superconnected)

more superconnected (comparative)
most superconnected (superlative)

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For a superconnected probe interval graph G, a tree 4-spanner can be constructed easily.

2003, H. L. Bodlaender, Graph-theoretic concepts in computer science: 29th International Workshop:

(graph theory, of a graph) Whose every minimum vertex cut leads to isolated vertices.


integrity

en-noun

integrity (countable and uncountable, plural integrities)

/ɪnˈtɛɡɹəti/

/ɪnˈtɛɡɹɪti/

Borrowed from Middle French intégrité, from Latin integritās (“soundness, integrity”), from integer. Doublet of entirety.

der

(cryptography) With regards to data encryption, ensuring that information is not altered by unauthorized persons in a way that is not detectable by authorized users.


penteract

(mathematics) A five-dimensional hypercube.


TSS

en-noun

TSS (countable and uncountable, plural TSSs)

total sum of squares
total sum of squares#English

(statistics) Initialism of total sum of squares.


without loss of generality

We wish to prove two ellipses in the plane intersect in an even number of points or are tangent. Without loss of generality, assume one of them has the equation x²#43;y²#61;1.

(mathematics) With a constraining assumption that, however, makes it clear how to apply the proof performed under this assumption to the general case unconstrained by the assumption.

zonder verlies van algemeenheid (z.v.v.a.)


trustless

A trustless network can run even if none of its nodes trusts another.

In the trustless cryptocurrency world, you can still trust the cryptocurrency community and its mechanisms to ensure that the blockchain contains an accurate and immutable—unchangeable—record of cryptocurrency transactions.

2019, Peter Kent, Tyler Bain, Cryptocurrency Mining For Dummies, John Wiley & Sons, →ISBN, page 30:

This article draws from the extensive academic discussion on the concepts of “trust” and “confidence” to argue that blockchain technology is not a ‘trustless technology’ but rather a ‘confidence machine’.

2020 August, Primavera De Filippi, Morshed Mannan, Wessel Reijers, “Blockchain as a confidence machine: The problem of trust & challenges of governance”, in Technology in Society, volume 62, →DOI:

If it becomes cheaper to use a TTP to verify the transaction than some cryptographic or other automated mechanism, then the benefit of being “trustless” becomes an illusion.

2021, Shin'ichiro Matsuo, Nat Sakimura, editors, Blockchain Gaps: From Myth to Real Life, Springer Nature, →ISBN, page 34:

And the system would be “trustless” — that is, it would not rely on a trusted party, such as a bank or government, to arbitrate transactions.

2022 June 7, Siobhan Roberts, “How ‘Trustless’ Is Bitcoin, Really?”, in The New York Times, →ISSN:

(computing, cryptocurrencies) Which does not need any trust, or a trusted third party.


upper semi-continuous

(of a real-valued function on a topological space) Such that for each fixed point x there is some neighborhood whose image's limit superior is x's image.


lim sup

(mathematics) Clipping of limit superior.


complementary region

complementary region (plural complementary regions)

(topology) A connected component of the complement in a manifold of a lamination of that manifold.


accumulation point

accumulation point (plural accumulation points)

LEMMA 5.2 Let X be a Hausdorff space and A a subset of X. A point a#92;inX is an accumulation point of A if and only if a is a limit point of A.

1975, Bert Mendelson, Introduction to Topology, 3rd edition, New York: Dover Publications, Inc., published 1990, →ISBN, →OCLC, §5.3, page 173:

2008, Brian S. Thomson, Andrew M. Bruckner, Judith B. Bruckner, Elementary Real Analysis, Volume 1, Thomson-Bruckner (ClassicalRealAnalysis.com), 2nd Edition, page 153,
Definition 4.9 (Closed): The set E is said to be closed provided that every accumulation point of E belongs to the set E.
Thus a set E is not closed if there is some accumulation point of E that does not belong to E. In particular, a set with no accumulation points would have to be closed since there is no point that needs to be checked.

(topology, "of" a subset of a topological space) Given a subset S of a topological space X, a point x whose every neighborhood contains at least one point distinct from x that belongs to S.


punctured neighborhood

punctured neighborhood (plural punctured neighborhoods)

(mathematics) A neighborhood of a point, minus the point itself.


nine-point circle

nine-point circle (plural nine-point circles)

So called because the circle passes through nine points of interest: the feet of the three altitudes, the centers of the three sides, and the midpoints of the segments which join the triangle's vertices with its orthocenter.

That circle which passes through the feet of the altitudes of a given triangle.


superadditive

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Knot genus is superadditive under band sum because g(K#95;1#92;sharp#95;bK#95;2)#92;geg(K#95;1)#43;g(K#95;2).

(mathematics, of a function) Such that the image of a sum is at least the sum of the images of the summands.


deformation retract

deformation retract (plural deformation retracts)

(topology) A subspace such that there is a retraction onto it of the ambient space homotopic to the identity function on the ambient space.


totally disconnected

(mathematics) Such that each connected subspace is a singleton.

algjörlega ósamanhangandi

having only singletons as connected components


Riemannian

where R is the Riemannian curvature of the metric g, regarded as an operatorname End(TM)-valued two form, and √ is the Pfaffian, which is an invariant polynomial defined on the Lie algebra of skew symmetric matrices in even dimensions.

2003, Maung Min-Oo, The Dirac Operator in Geometry and Physics, Steen Markvorsen, Maung Min-Oo (editors), Global Riemannian Geometry: Curvature and Topology, Springer, page 62, Similarly, ̂A(M) is represented by the closed differential form ̂A(M)=√((R/2)/(sinh (R/2)))

As the preferred metrics applied to symplectic forms are Kähler metrics one could ask for the Riemannian structure which would make the cone with the metric #92;overlineg#61;dt²#43;t²ᵍ together with the symplectic form #92;omega into a Kähler manifold. Then #92;overlineg and #92;omega define a complex structure #92;overline#92;Phi. Alternatively, one could ask for a Riemannian metric g on M which would define a Kähler metric h on #92;mathcalZ via a Riemannian submersion.

2010, Charles P. Boyer, Krzysztof Galicki, “Chapter 3: Sasakian geometry, holonomy, and supersymmetry”, in Vicente Cortés, editor, Handbook of Pseudo-Riemannian Geometry and Supersymmetry, European Mathematical Society, page 41:

2012, Yves Carriere, Appendix A: Variations on Riemannian Flows, Pierre Molino, Riemannian Foliations, Springer, page 217,
The object of this appendix is to give a summary of known results on 1-dimensional oriented Riemannian Foliations.

(mathematics) Of or relating to the work, or theory developed from the work, of German mathematician Bernhard Riemann, especially to Riemannian manifolds and Riemannian geometry.


Riemannian

(mathematics) One who uses or supports the work of German mathematician Bernhard Riemann.


centner

Probably from Low German, cp. German Zentner, comparable to the hundredweight.

A nonstandard metric unit of weight equal to 100 kilograms, commonly used as an agricultural measure in Eastern Bloc countries (similar to a bushel).

Zentner

Germany: 50 kg, Austria, Switzerland: 100 kg


zeroary

(computing, mathematics, nonstandard) Nullary.


multicollinearity

multicollinearity (countable and uncountable, plural multicollinearities)

(statistics) A phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, so that the coefficient estimates may change erratically in response to small changes in the model or data.


gömböc

From Hungarian gömböc (“short, plump person; gömböc”).

bor

(geometry) A convex shape which, if made of a uniformly dense material, has one stable equilibrium orientation and one unstable equilibrium orientation.


UEA

universal enveloping algebra
universal enveloping algebra#English

(mathematics) Initialism of universal enveloping algebra.


sieve of Eratosthenes

(mathematics) An ancient algorithm for finding prime numbers that works by discarding multiples from a list of potential primes.


half-integer

(mathematics) Any number obtained by dividing an odd integer by two; a number equals to some integer plus one half.


bicorn

Borrowed from Latin bicornis (“two-horned; two-pronged”). Compare French bicorne (“two-cornered hat; two-horned monster”) and Middle English bicorne (“two-horned anvil; two-pronged fork; fabulous (two-horned) beast”). Doublet of bicorne.

cog

(mathematics) A plane curve having two cusps.


saddle point

(geometry) A point in the range of a smooth function, every neighbourhood of which contains points on each side of its tangent plane.

(game theory) Such a point in the graphical representation of the possible outcomes of a game.


koku

A unit of measure in feudal Japan, the amount of rice needed to feed one person for a year.


minorant

Borrowed from French minorant, present participle of minorer (“to diminish”), from Latin minor. By surface analysis, minor + -ant.

Coordinate term: majorant

(mathematics) A function, all of whose values are not greater than the corresponding values of another function.


long division

en-noun

long division (countable and uncountable, plural long divisions)

Lord Harvey is doing his best to find if there be a 'yes' in the world. It would require—what is that rule in arithmetic? ah!—long division, to reckon up the number of refusals he has had this season!

1837, L[etitia] E[lizabeth] L[andon], “Ranelagh”, in Ethel Churchill: Or, The Two Brides. […], volume III, London: Henry Colburn, […], →OCLC, page 8:

(mathematics) A procedure for dividing multidigit numbers, breaking down the division into a series of easier steps.


dunce hat

(topology) The topological space obtained by identifying the sides comprising the boundary of a triangle, two sides with consistent orientation and the third with the reverse orientation.


derived group

(algebra) The subgroup of a specified group generated by the larger group's commutators.


commutator subgroup

commutator subgroup (plural commutator subgroups)

The commutator subgroup is important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian.


maximax

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The first criterion is the Hurwicz criterion, often referred to the maximax criterion. […] the decision-maker is always optimistic and attempts to maximize profits by a go-for-broke strategy.

2009, Harold Kerzner, Project Management: A Systems Approach to Planning, Scheduling, and Controlling, Tenth Edition, John Wiley and Sons, →ISBN, page 749:

(economics, computer science, decision theory) A strategy or algorithm that seeks to maximize the maximum possible result (that is, that prefers the alternative with the chance of the best possible outcome, even if its expected outcome and its worst possible outcome are worse than other alternatives); often used attributively, as "maximax strategy", "maximax approach", and so on.


atomic authorization

atomic authorization (countable and uncountable, plural atomic authorizations)

(cryptography) (A digitally signed document containing) published rights with cryptographically verifiable integrity, secured independently of the applications that utilize them and entities to which they apply.


interpenetrative

en-adj

interpenetrative (comparative more interpenetrative, superlative most interpenetrative)

more interpenetrative (comparative)
most interpenetrative (superlative)

(mathematics, physics) Mutually penetrative (overlapping each other in space)


ultrafilter

A proper filter of a set has these three properties: (1) it does not contain the empty set, (2) if it contains a subset then it contains all supersets of that subset, and (3) if it contains a pair of subsets then it also contains their intersection. To make it into an ultrafilter it must be made as large as possible without including the empty set. That can be prevented by not allowing any pair of disjoint sets to be both included. If, given a pair of complementary subsets, one of them is prevented from being included, then all subsets of it should be prevented from being included as well, by the second rule. That takes care of all subsets disjoint from the other complementary subset, which should then be included, in order to make the filter approach maximality, i.e., turn it into an ultrafilter.

(mathematics, of a set, whose subsets are partially ordered by inclusion) A proper filter which has a law of dichotomy for complements.

An ultrafilter is maximal in the sense that if any other element of the poset not already in it were added to it, one could deduce (from the laws which define the filter, and the given ordering relation, i.e., the structure of the poset) that the resulting filter must be improper; i.e., it must contain all the elements of the poset.

(mathematics, order theory) A filter (subset of a poset) that is maximal as a set with respect to the definition of proper filter.


identification space

en-noun

identification space (plural identification spaces)

equivalence relation
equivalence relation

(topology) A space obtained from another by identification of points that are equivalent to one another in some equivalence relation.


factor space

(topology, idiomatic) A space obtained from another by identification of points that are equivalent to one another in some equivalence relation.

(topology, literally, relatively rare) A space which is a factor (multiplicand) in a product space.


T-shaped

en-adj

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

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

丁字

having a shape similar to a capital letter T

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


lingula

From Latin lingula (“tonguelet, small unit of volume”), from lingua (“tongue”) + -ula (“-ule: forming diminutives”).

bor

(historical) A Roman unit of liquid measure reckoned as the volume of 5/12 Roman ounce of wine, equivalent to about 11 mL.

congius (144 lingulas) urna (1152 lingulas)


data smoothing

(mathematics, statistics) The mathematical process of fitting a smooth curve to dispersed data points.


hyperedge

(graph theory) The equivalent of a graph's edge in a hypergraph.


hypervertex

(graph theory) The equivalent of a graph's vertex in a hypergraph.


mereotopology

/ˌmɛɹɪətəˈpɒləd͡ʒi/

(mathematics) A theory combining mereology and topology, investigating relations between parts and wholes and boundaries between them.


ar-

Shortened from area (because the function describes the area under a hyperbola), by analogy with arc-, the corresponding prefix for the circular trigonometric functions.

inverse hyperbolic function
inverse hyperbolic function#English

(trigonometry) Used to form the names of inverse hyperbolic functions, and the symbols for these functions.


Kaprekar number

en-noun

Kaprekar number (plural Kaprekar numbers)

After the Indian mathematician Dattaraya Ramchandra Kaprekar (1905-1986).

(mathematics) A non-negative integer, the representation of whose square in its base can be split into two parts that add up to itself (such as 297, whose square, 88209, can be split into 88 and 209, totalling 297).


subaverage

(statistics) A subordinate or local average.


subaverage

en-verb

subaverage (third-person singular simple present subaverages, present participle subaveraging, simple past and past participle subaveraged)

subaverages (present singular third-person)
subaveraging (participle present)
subaveraged (participle past)
subaveraged (past)

(statistics) To calculate or otherwise obtain such subordinate averages.


congius

From Latin congius, from Ancient Greek κογχίον (konkhíon), from κόγχη (kónkhē) and κόγχος (kónkhos, “mussel shell”) + -ίον (-íon, “-y: forming diminutives”).

(historical) A Roman unit of mass instituted by Vespasian equivalent to about 3.3 kg, the weight of a congius of water.


Lorentz invariant

en-noun

Lorentz invariant (plural Lorentz invariants)

Lorentz transformation
Lorentz transformation

(mathematics, relativity) A quantity that does not change due to a Lorentz transformation; a quantity that is independent of the inertial frame.


leavable

en-adj

leavable (comparative more leavable, superlative most leavable)

more leavable (comparative)
most leavable (superlative)

(mathematics, theory of gambling) Of or pertaining to a problem where the gambler is free to stop playing at any time.


pseudo-edge

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pseudo-Hamiltonian-connected graph
pseudo-Hamiltonian-connected graph

(mathematics) The connection between vertices in a pseudo-Hamiltonian-connected graph.


hypoellipse

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(geometry) A superellipse with an exponent (shape parameter) smaller than that of the ellipse, i.e. less than two.


to the moon

The marketing of this relatively new money has so far been limited mostly to ads on trade websites and targeted pushes on social media, where aficionados swap meme-fueled in-jokes about coin values rocketing to the moon.

2021 July 7, Tiffany Hsu, Coral Murphy Marcos, “Cryptocurrency Seeks the Spotlight, With Spike Lee’s Help”, in The New York Times:

(cryptocurrencies, slang) Of a cryptocurrency, increasing rapidly and substantially in value.


to the moon

(cryptocurrencies, slang) An aspirational or rallying call for confidence that the value of a cryptocurrency will greatly increase in the future.


petaliter

(US) A unit of volume equivalent to 10¹⁵ liters. Symbol: Pl


yoctoliter

(metrology) An SI unit of volume equal to 10⁻²⁴ liters. Symbol: y


yoctolitre

(metrology) An SI unit of volume equal to 10⁻²⁴ litres. Symbol: y


logit

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Blend of logistic + unit, by analogy with probit, coined by Joseph Berkson in 1944: “I use this term [logit] for ln p/q following Bliss, who called the analogous function which is linear on x for the normal curve ‘probit.’”

operatorname logit(p)= log (p/(1-p))= log (p)- log (1-p).!,

(mathematics) the inverse of the "sigmoid" or "logistic" function used in mathematics, especially in statistics. The logit of a number p between 0 and 1 is given by the formula:


twip

Abbreviation of twentieth of a point (referring to a printer's point).

(computing) A unit of measure equal to one twentieth of a point.


lexicographic order

en-noun

lexicographic order (plural lexicographic orders)

partially ordered set
partially ordered set

(mathematics) Formally, given two partially ordered sets A and B, the order ≤ on the Cartesian product A × B such that (a,b) ≤ (a′,b′) if and only if a < a′ or (a = a′ and b ≤ b′).

(mathematics) Given sets (A₁, A₂, ..., Aₙ) and their total orderings (<₁, <₂, ..., <ₙ), the order <ᵈ of A₁ × A₂ × ... × Aₙ such that (a₁, a₂, ..., aₙ) <ᵈ (b₁,b₂, ..., bₙ) iff (∃m > 0) (∀ i < m) (aᵢ = bᵢ ) and (aₘ <ₘ bₘ )


cofinality

cofinality (countable and uncountable, plural cofinalities)

The cofinality of any set with a greatest element is 1.

(mathematics, countable) The least of the cardinalities of the cofinal subsets of a partially ordered set.

(mathematics, uncountable) The property of being cofinal.


biomathematics

(biology, mathematics) The application of mathematics to the study of biological systems and processes


bisecant

(mathematics) A secant that cuts a curve at exactly two points


dots per inch

My printer prints at 300 dots per inch.

(graphic design, typography) The measure of a number of pixels per inch used in a graphic or supported by a digital display device, used to specify type or image resolution.


circulant

a circulant graph; a circulant matrix


edgepath

(mathematics) A path comprising edges laid end to end.


non-strict

(mathematics) Of an inequality, such that it includes the possibility of equality.


bitransitive

The critical Fatou components are bitransitive

2007, Tokyo Journal of Mathematics, volume 30, numbers 1-2, page 539:

Let f be the semiprojection defined by the bitransitive relation R. Then [f] is a minimal clone. Moreover, distinct bitransitive relations determine distinct minimal clones.

2012, Janos Aczel, Aggregating clones, colors, equations, iterates, numbers, and tiles, page 13:

(mathematics) For a mapping F, given any two sets S₁ and S₂, F²(S₁) has a nonzero intersection with S₂.


banker's dozen

A play on the phrase baker's dozen; it is one less than a dozen as compared to one more. See also bankers' hours.

Not a low baker's dozen, you will perceive, but two high banker's dozen !

There were 11 in number (a reference has been made to them as constituting a banker's dozen), representing the following organizations :

1960, United States. Congress. House. Select Committee on Small Business, Small Business Problems in Food Distribution:

It concludes with a banker's dozen of 11 items labeled "What to Read" — a well chosen list on the urban, technological disruption of man's life and the earth's biosphere.

1968, JOH, Journal of Housing - Volume 25, page 432:

Caroline arranged to have appear at her concert a banker's dozen (eleven) of New York's most admired amateur and professional musicians, including the alluring divorcee Fanny Ronalds, who — it was rumored — was accomplished in arts more erotic than the one she would demonstrate that night.

1981, David Black, The King of Fifth Avenue: the fortunes of August Belmont, page 240:

George counted eleven of them. A banker's dozen, he said to himself.


hyperreal

en-adj

hyperreal (comparative more hyperreal, superlative most hyperreal)

more hyperreal (comparative)
most hyperreal (superlative)

(mathematics, of a number) Belonging to an extension of the real numbers containing those that cannot be produced by repeatedly adding 1; hence infinite.


upper quartile

(mathematics) The median of the upper or highest half of a data set, especially of a sample, population, or probability distribution.


superlinear

superlinear (comparative more superlinear, superlative most superlinear)

more superlinear (comparative)
most superlinear (superlative)

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[…] in their study of Mono (a F/OSS implementation of Microsoft's .NET services, libraries and interfaces), their measurements indicate superlinear growth rate in the code size and the number of code updates that are committed […]

2006, Nazim H. Madhavji, Juan Fernandez-Ramil, Dewayne Perry, Software Evolution and Feedback: Theory and Practice, John Wiley & Sons, →ISBN, page 187:

(especially mathematics) Describing a function (or rate of growth, etc) that eventually grows faster than any linear one.

superlineær

describing a function that eventually grows faster than any linear one


unassociated

(statistics) Having no statistical association.

Not associated, as:
Having no statistical association.


autoregression

en-noun

autoregression (countable and uncountable, plural autoregressions)

(mathematics) An autoregressive process that is used to model many types of natural behaviour


isochrone

semicubical parabola
semicubical parabola


-angle

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(geometry, of a two-dimensional shape) having the specified number of internal angles


arshin

From Russian арши́н (aršín), from Ottoman Turkish آرشون / آرشین (arşın) (Turkish arşın).

bor

آرشون / آرشین

An obsolete Russian length unit, equal to 71.12 centimeters, or 28 inches.


paracompact

(mathematics, of a topological space) In which every open cover admits an open locally finite refinement.


nonconstant

(mathematics) A value that is not constant.


isoperimetric

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(geometry) Having the same perimeter; applied to the problem of finding a plane figure of the largest possible area whose boundary has a specified length


twistor

Holonym: amplituhedron

Meronym: spinor

(mathematics, physics) Any of the complex-valued coordinates in twistor theory, which maps the geometric objects of conventional 3+1 space-time into geometric objects in a four-dimensional space, twistor space, with metric signature (2,2), a proposed path to a theory of quantum gravity.


hyperkähler

(geometry, of a manifold) Being a quaternionic analogue of a Kähler manifold.


tridiagonal

(linear algebra, of a matrix) Having nonzero elements only in the main diagonal and the diagonals directly above and below it


mollifier

I particularly remember how, at that time, I was using his mollifier method to study the zero density of L-functions and was stuck with something.

2009, Notices of the American Mathematical Society, volume 56, number 6:

(mathematics) An "approximation to the identity", a smooth function with special properties, used in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution.


irrep

The interesting aspect here is that U₃ is irreducible, even though all irreps over the complexes are one-dimensional because ℤ₄ is abelian.

1996, Barry Simon, Representations of Finite and Compact Groups, page 50:

(mathematics) Clipping of irreducible representation.


pointclass

(mathematics, set theory) A collection of sets of points (ordinarily understood to be elements of some perfect Polish space), characterized by some sort of definability property.


solvmanifold

(mathematics) A homogeneous space of a connected solvable Lie group.


nonreal

(mathematics) Not real; not of the real numbers.


semifield

(mathematics) An algebraic structure with two binary operations, addition and multiplication, similar to the field but with some axioms relaxed.


subbundle

(mathematics) A collection of linear subspaces of the fibers Vₓ of V at x in X (where V is a vector bundle and X a topological space), that make up a vector bundle in their own right.


subconvexity

(mathematics) The state or condition of being subconvex.


sumset

(mathematics) The set of all sums of an element from A with an element from B, where A and B are subsets of an abelian group.


Zeno

Via Latin Zēnō, from Ancient Greek Ζήνων (Zḗnōn), an ancient derivative of Ζεύς (Zeús), from Proto-Hellenic *dzéus, from Proto-Indo-European *dyḗws. Modern scientific and philosophical use derives from Zeno of Elea, poser of Zeno's paradoxes.

It is therefore important to be able to determine if a model is Zeno and in applicable cases remove Zenoness.

2000, J. Zhang et al., “Dynamical Systems Revisted: Hybrid Systems with Zeno Executions”, in Hybrid Systems: Computation and Control, page 458:

While this system is not Zeno, it can nevertheless not be considered implementable; thus, the boundedness of activity seems to be a more appropriate abstract concept of implementability of a system with respect to the amount of activity in finite intervals of time.

2005, Heinrich Rust, “Chapter 3”, in Operational Semantics for Timed Systems: A Non-standard Approach to Uniform Modeling of Timed and Hybrid Systems, page 17:

That is, it is necessary to check whether a run is Zeno so as to avoid presenting Zeno runs as counterexamples.

2013, Y. Si et al., “Improving Model Checking Stateful Timed CSP with non-Zenoness through Clock-Symmetry Reduction”, in Formal Methods and Software Engineering : 15th International Conference on Formal Engineering Methods, ICFEM 2013, page 183:

(mathematics, philosophy) Requiring or involving an infinite number of intervals within a finite time.


beka

From Hebrew בֶּקַע (beqáʿ, “half-sheqel”, literally “broken”).

an ancient Biblical unit of weight, half a shekel


HMM

hidden Markov model
hidden Markov model#English

(computer science) Initialism of hidden Markov model.


scalogram

(signal processing) A visual representation of a wavelet transform, having axes for time, scale, and coefficient value, analogous to a spectrogram


constructible

destructible

antonym(s) of “capable of being constructed”

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(geometry, of a regular polygon) That can be constructed in a plane using only a pair of compasses and a straightedge.

(mathematics, of a complex number) Such that the line segment joining it to the origin can be constructed using only a pair of compasses and a straightedge.

(algebraic geometry, of a subset of the spectrum of a noetherian ring) Admitting description as a finite union of locally closed (with respect to the Zariski topology) sets.


nonfunction

en-noun

nonfunction (countable and uncountable, plural nonfunctions)

(mathematics, computing) Anything that is not a function.


family size

Near-synonyms: multiserve, multiserving

(marketing, singular only, often attributive) A size for a container of goods, among the largest sizes meant for sale to a householder consumer.


backpropagation

backpropagation (countable and uncountable, plural backpropagations)

In machine learning, backpropagation of error (‘backprop’) is the algorithm most often used to train deep neural networks and is the most successful learning procedure for these networks.

2020, Timothy P. Lillicrap, Adam Santoro, Luke Marris, Colin J. Akerman, Geoffrey Hinton, “Backpropagation and the brain”, in Nature:

(machine learning) An error correction technique used in neural networks.


EGA

Éléments de géométrie algébrique
w:Éléments de géométrie algébrique

(algebraic geometry) Initialism of Éléments de géométrie algébrique.


nonprimitive

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(programming, computer graphics, geometry) An object that is not a primitive.


nondeath

(chiefly statistics) An outcome other than death; a survival.


line plot

(statistics) A plotting of data above an axis to show frequency of data in each category.


overfitting

overfitting (countable and uncountable, plural overfittings)

(statistics, machine learning) The production of a statistical model that, due to an excess of parameters relative to the sample size, fits the sample data extremely well but fails to fit new data.


overparameterize

en-verb

overparameterize (third-person singular simple present overparameterizes, present participle overparameterizing, simple past and past participle overparameterized)

overparameterizes (present singular third-person)
overparameterizing (participle present)
overparameterized (participle past)
overparameterized (past)

(transitive, intransitive, statistics) To use an excessive number of parameters.

(transitive, intransitive, statistics) To increase the degree of the line of best fit to the point that the fit of the line decreases.


bicone

(geometry) The three-dimensional shape swept by revolving an isosceles triangle around its edge of unequal length, or by joining two identical right circular cones, base to base.


scalar curl

Since the curl of the vector field #92;vec#123;F#125;#61;(xy,xy,0) is the vector field #92;vec#123;#92;nabla#125;#92;times#92;vec#123;F#125;#61;(0,0,y-x), the scalar curl of the vector field #92;vec#123;G#125;#61;(xy,xy) is the scalar field y-x#92;#59;.

(mathematics) The coefficient of k in the three-dimensional curl of a two-dimensional vector field.


improper integral

en-noun

improper integral (plural improper integrals)

(calculus) An integral where at least one of the endpoints is taken as a limit, either to a specific number or to infinity.


equipotent

(mathematics) Of two sets, having a bijection with one another.


Jupiter mass

(astronomy) A unit of mass equal to the mass of the planet Jupiter, used to express the mass of other planets. 1 M_J = 2 × 10²⁷ kg.


attojoule

energy, work, and heat
energy, work, and heat#English

(metrology) An SI unit of energy, work, and heat equal to 10⁻¹⁸ joules. Symbol: aJ


pseudoreplicate

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(statistics) Any of a group of interdependent data that are mistakenly treated as independent.


decigrade

/ˈdɛsɪɡɹeɪd/

(mathematics) An angular measure equal to one tenth of a grade


pons asinorum

From New Latin pons asinorum, from Latin pōns (“bridge”) + genitive plural of asinus (“donkey”). Literally, “bridge of donkeys”.

[H]e had scarce advanced beyond the Pons Asinorum, when his ardour abated, the test of truth by demonstration did not elevate him to those transports of joy with which his preceptor had regaled his expectation; and before he arrived at the fortieth and seventh proposition, he began to yawn drearily […].

1751, [Tobias] Smollett, The Adventures of Peregrine Pickle […], volume (please specify |volume=I to IV), London: Harrison and Co., […], →OCLC:

(geometry) A proposition in Euclid stating that the angles at the base of an isoceles triangle are equal.


superlinearity

superlinearity (usually uncountable, plural superlinearities)

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(mathematics) The state or condition of being superlinear.


antitransform

(mathematics) The inverse of a transform


approximable

en-adj

approximable (comparative more approximable, superlative most approximable)

more approximable (comparative)
most approximable (superlative)


cologarithm

(mathematics) The logarithm of the reciprocal of a number (equal to the negative of the original logarithm)


triacontahedron

en-noun

triacontahedron (plural triacontahedra or triacontahedrons)

triacontahedra (plural)
triacontahedrons (plural)

From Ancient Greek τρῐᾱ́κοντᾰ (trĭā́kontă) + -hedron.


-choron

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From Ancient Greek χῶρος (khôros, “room”).

(geometry) Used to form the names of 4-dimensional solids bounded by a certain number of cells/polyhedra (polychora).


zoomer

→ Russian: зу́мер (zúmer)

Portmanteau from Generation Z and boomer (“baby boomer, a person born between 1945 and early 1960s”). Merriam-Webster identified the earliest use in its current sense as being made on 16 March 2016 by an aviation engineer named Jennie Santoro at HNTB Seattle, in a presentation called "Boomers to Zoomers: Passing the Torch to Generation Z!"
However, the word was ultimately popularized through a variant of the Wojak meme which originated on 4chan on July 21st, 2018, and from there spread to other platforms. Accordingly, Urban Dictionary view statistics suggest that it began gaining traction in mid-2018 before peaking in January 2020.

Coordinate term: millennial

Hug a Boomer/Xer/Millennial/Zoomer In case you missed it: Gen Z is mad at boomers for the state of the world; boomers are mad at Gen Z for being so dismissive; Gen X feels forgotten and yet resents even themselves; […]

2019 December 27, Anya Strzemien, “13 Ways to Be a Better Person in 2020”, in New York Times:


ANCOVA

analysis of covariance
analysis of covariance#English

(statistics) Acronym of analysis of covariance.


open book

open book decomposition
open book decomposition

(mathematics, topology) An open book decomposition.


epic

From epi-, from Ancient Greek ἐπί (epí, “on top of”).

(category theory, of a morphism) That is an epimorphism.


open book decomposition

en-noun

open book decomposition (plural open book decompositions)

(mathematics, topology) A decomposition of a 3-manifold into a link and a fibration over the circle by surfaces bounded by that link.


Lucasian

In 1979, Stephen Hawking became the Lucasian professor of mathematics at Cambridge, one of Britain’s most distinguished chairs, and one formerly held by Isaac Newton.

(mathematics) Of or pertaining to Henry Lucas (c. 1610–1663), Member of Parliament for Cambridge University and founder of the Lucasian Chair of Mathematics.


Pauli matrix

Pauli matrix (plural Pauli matrixes or Pauli matrices)

Pauli matrixes (plural)
Pauli matrices (plural)

Named after Wolfgang Ernst Pauli (1900–1958), Austrian theoretical physicist.

The Pauli matrices satisfy the equation σ₁²=σ₂²=σ₃²=-iσ₁σ₂σ₃=I which is reminiscent of Hamilton's fundamental formula for quaternion multiplication.

The first Pauli matrix is like a reflection about the "y=x" line. The third Pauli matrix is like a reflection about the "x axis". The second Pauli matrix is like a 90° counterclockwise rotation and scalar multiplication by the imaginary unit (which rotates the two complex components by 90° counterclockwise in their own "phasor spaces", as it were).

The eigenspinors are eigenvectors of the Pauli matrices in the case of a single spin 1/2 particle. —Wikipedia

(mathematics) Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics.


68-95-99.7 rule

(statistics mnemonic) The rule stating that a normal distribution will have 68% of its observations within one standard deviation of the mean, 95% within two, and 99.7% within three.


dither

en-verb

dither (third-person singular simple present dithers, present participle dithering, simple past and past participle dithered)

dithers (present singular third-person)
dithering (participle present)
dithered (participle past)
dithered (past)

Variant of didder, from Middle English dideren (“to tremble”). Compare Middle English bididren, bididdren (“to seduce, deceive”), from Old English bedidrian, bedyderian (“to deceive, trick”).
Alternatively, perhaps with expressive voicing from *titeren, from Proto-Germanic *titrōną. If so, then a doublet of teeter and cognate with Old High German zittarōn (German zittern) and Old Norse titra (Faroese titra, Icelandic titra). Alternatively an unrelated reduplicative onomatopoeia.

Look at how pixelly this wall texture is. You almost don't even notice the dithering when driving by quick. Up close though, it's real chunky.

2023, Preston "Pretzel", 4:34 from the start, in Familiar and Unfamiliar Areas in Lego Island:

(electronics, technology, signal processing) To apply an algorithm to digital data to minimize the effects of quantization:

(computer graphics) To use dot patterns in an image or graphic to simulate colors or shades not in the system palette.

koostaa

(computing, graphics) to simulate a color digitally

To intentionally add noise to a signal to remove artifacts caused by digitization.


dither

en-noun

dither (countable and uncountable, plural dithers)

(electronics, technology, signal processing) Any algorithm applied to digital data to minimize the effects of quantization:

A form of noise intentionally added to remove artifacts caused by digitization.

(computer graphics) The use of dot patterns in an image or graphic to approximate colors not available in the system palette.

sirottelu

computer graphics: use of dot patterns to approximate colors


minimin

(economics, computer science, decision theory) A strategy or algorithm that seeks to minimize the minimum possible result.


totalistic

BTW: Of course the rules were parametrised, so any totalistic 2-dimensional 9-neighbourhood CA could be run.

1989 March 21, Mark Kramer, “Fast LIFE (was: Re: summing 9-cell neighborhoods)”, in comp.theory.cell-automata (Usenet):

Note that the game of life is not totalistic: the transition function depends on the cell's own state and on the sum of the neighboring states.

1993 January 17, Dan Gordon, “Universal Cellular Automata.”, in comp.theory.cell-automata (Usenet):

The Xor operation drastically cuts down the number of operations when dealing with totalistic CA rules. For example, a function of four variables a, b, c, d, returning 1 iff there are exactly two ones and two zeros among its arguments, is represented by this Karnaugh diagram:

1994 July 3, Serge Winitzki, “Optimizing "bitblt" functions using Xor”, in comp.theory.cell-automata (Usenet):

Having the state of each cell represented by a number, and the value of a cell dependent only on the sum of the values of nearby cells.

Many good applets run Moore binary totalistic rules such as Conway's Life, but WebsideCA also runs von Neumann rules, rules in the "Brian's Brain" family, non-totalistic binary and decay rules, and Cyclic rules.

1999 September 2, J. Elliott, “ANNOUNCE: WebsideCA Java applet update”, in comp.theory.cell-automata (Usenet):

Since Life is totalistic on 8 neighbours, this requires no extra assumptions.

2000 August 20, Gerard Vriens, “Discussion: neighbourhoods”, in comp.theory.cell-automata (Usenet):

... but the B/S notation is _the_ standard for two-state totalistic rules.

2001 October 31, Erik Francis, “Four new rules with replicators”, in comp.theory.cell-automata (Usenet):


loglikelihood

loglikelihood (countable and uncountable, plural loglikelihoods)

(statistics) The likelihood of a model fitting a data set according to a logarithmic formula.


group ring

(algebra) Given ring R with identity not equal to zero, and group G=g_1,g_2,...,g_n, the group ring RG has elements of the form a_1g_1+a_2g_2+...+a_ng_n (where a_i isin R) such that the sum of a_1g_1+a_2g_2+...+a_ng_n and b_1g_1+b_2g_2+...+b_ng_n is (a_1+b_1)g_1+(a_2+b_2)g_2+...+(a_n+b_n)g_n and the product is ∑ₖ₌₁ⁿ(∑_(g_ig_j=g_k)a_ib_j)g_k.


graph-theoretic

(mathematics) Alternative form of graph-theoretical


ganta

From Spanish ganta, from Cebuano gantang, from Malay gantang. Doublet of gantang.

(Philippines, historical) A unit of volume equivalent to eight chupas.


Lindelöf space

Named for the Finnish mathematician Ernst Leonard Lindelöf.

(topology) A topological space such that any open cover of the space has a countable subcover.


integral domain

integral domain (plural integral domains)

A ring R is an integral domain if and only if the polynomial ring R#91;x#93; is an integral domain.

For any integral domain there can be derived an associated field of fractions.

For integral domains, we will use a⁻¹ to designate the multiplicative inverse of a (if it has one; since not all elements need have inverses, this notation can be used only where it can be shown that an inverse exists).

1990, Barbara H. Partee, Alice ter Meulen, Robert E. Wall, Mathematical Methods in Linguistics, Kluwer Academic Publishers, page 266:

An integral domain is said to have strong pseudo-Dedekind factorization if each proper ideal can be factored as the product of an invertible ideal (possibly equal to the ring) and a finite product of pairwise comaximal prime ideals with at least one prime in the product.

2013, Marco Fontana, Evan Houston, Thomas Lucas, Factoring Ideals in Integral Domains, Springer, page 95:

#91;#92;mathbb#123;Z#125;#59;#43;,#92;cdot#93;, #91;#92;mathbb#123;Z#125;#95;p,#43;#95;p,#92;times#95;p#93; with p a prime, #91;#92;mathbb#123;Q#125;#59;#43;,#92;cdot#93;, #91;#92;mathbb#123;R#125;#59;#43;,#92;cdot#93;, and #91;#92;mathbb#123;C#125;#59;#43;,#92;cdot#93; are all integral domains. The key example of an infinite integral domain is #91;#92;mathbb#123;Z#125;#59;#43;,#92;cdot#93;. In fact, it is from #92;mathbb#123;Z#125; that the term integral domain is derived. Our main example of a finite integral domain is #91;#92;mathbb#123;Z#125;#95;p,#43;#95;p,#92;times#95;p#93;, when p is prime.

2017, Ken Levasseur, Al Doerr, Applied Discrete Structures: Part 2 - Applied Algebra, Lulu.com, page 171:

(algebra, ring theory) Any nonzero commutative ring in which the product of nonzero elements is nonzero.


Gaussian integer

Gaussian integer (plural Gaussian integers)

We could say that a Gaussian integer is larger than another if its norm is larger, that is, if its distance from the origin is larger. That's all right, although it has the peculiarity that 5 is larger than -7 as an integer, but smaller than -7 as a Gaussian integer! In a way, this notion of larger makes more sense: shouldn't -7 be considered larger than 5?

1997, Bernard L. Johnston, Fred Richman, Numbers and Symmetry: An Introduction to Algebra, CRC Press, page 44:

2000, André Weilert, Asymptotically fast GCD Computation in ℤ[i], Wieb Bosma (editor), Algorithmic Number Theory: 4th International Symposium, ANTS-IV, Proceedings, Springer, LNCS 1838, page 595,
We present an asymptotically fast algorithm for the computation of the greatest common divisor (GCD) of two Gaussian integers.

2008, Timothy Gowers, June Barrow-Green, Imre Leader (editors), The Princeton Companion to Mathematics, Princeton University Press, page 319,
For example, in the ring of Gaussian integers, R_-1, we have the factorizations
2=(1+i)(1-i),
5=(1+2i)(1-2i),
13=(2+3i)(2-3i),
17=(1+4i)(1-4i),
29=(2+5i)(2-5i),
⋮
where all the Gaussian integer factors in brackets above are irreducible elements of the ring of Gaussian integers.

(algebra) Any complex number of the form a + bi, where a and b are integers.


nonpolynomial

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


nonpolynomial

(algebra) An expression that is not a polynomial.


shaftment

From Middle English schaftmonde, from Old English sċeaftmund (“a palm, a palm's length”), equivalent to shaft + mound (“hand”).

inh

An obsolete unit of length defined as 6 inches, which equals 2 palms or ²⁄₃ span; today 6 inches equals exactly 15.24 cm. (Before the 12th century, a shaftment was defined as 6+¹⁄₂ inches.)


Hawthorne effect

en-noun

Hawthorne effect (plural Hawthorne effects)

Coined by American social psychologist John R. P. French in 1953 after a 1924–1932 study conducted by Elton Mayo at the Hawthorne Works, a large factory complex in Cicero, Illinois (formerly Hawthorne).

coined

In modern organizations, a Hawthorne effect might occur when a relatively trivial change is made in a person's job, and that person initially responds to this change very positively but the effect does not last long.

2002, Steve M. Jex, Organizational Psychology: A Scientist-Practitioner Approach, John Wiley & Sons, →ISBN, page 13:

Even if methodological shortcomings were waived, there is no proof of a Hawthorne effect in the original data.

2006 October, Michiel AJ Kompier, “The “Hawthorne effect” is a myth, but what keeps the story going?”, in Scandinavian Journal of Work, Environment & Health, volume 32, number 5, →DOI, →ISSN, pages 402–412:

A phenomenon whereby a change in the behavior of a subject being studied is an effect of the change itself or the fact of being observed rather than the nature of the change in question.

Elton Mayo
Hawthorne Works
Hawthorne effect


holyhedron

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

John Conway of Princeton University offered a reward in the 1990s to anyone producing a holyhedron, a polyhedron with a finite number of faces and with a hole in every face. […] Conway had predicted that someone will eventually find a holyhedron with fewer than 100 faces.

1969, Charles Miller, Vern Heeren, John Hornsby, Margaret Morrow, Jill Van Newenhizen, Mathematical Ideas, 11th edition:

(geometry) A polyhedron with a finite number of faces and with a polygonal hole in every face, the holes' boundaries sharing no point with each other or the face's boundary.


nowcasting

(statistics) The use of mathematical models of a current situation that include adjustments to imperfect data.


nowcast

en-verb

nowcast (third-person singular simple present nowcasts, present participle nowcasting, simple past and past participle nowcasted)

nowcasts (present singular third-person)
nowcasting (participle present)
nowcasted (participle past)
nowcasted (past)

The indices are nowcasted at a very low level, meaning thousands of nowcasts. Attention has been focuesed on the nowcasts that fail validation checks.

2010, Economic & Labour Market Review - Volume 4, Issues 1-6, page 33:

First, the value-added contribution from each origin country is adjusted according to their (nowcasted) change in GDP.

2019, United Nations Conference on Trade and Development (UNCTAD), Transnational Corporations, page 124:

Our ability to nowcast will depend on the length of the delay and the quality of data available.

2020, Adam Kucharski, The Rules of Contagion, page 147:

(statistics, modelling) To estimate what is currently happening based on knowledge of how data is biased.


nowcast

(statistics, modelling) An estimate made by nowcasting.


normal form

(game theory) A matrix that represents the possible outcomes of a game

normaalimuoto

game theory: matrix of possible outcomes

(mathematics) A standard, canonical way of presenting an object.


banana-shaped

en-adj

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

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


hourglass-shaped

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

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

Having a shape or cross-section like that of an hourglass.


prior probability

en-noun

prior probability (countable and uncountable, plural prior probabilities)

(statistics) The probability of an event obtained without the knowledge of occurrence of other events that bear on it.


posterior probability

posterior probability (countable and uncountable, plural posterior probabilities)

(statistics) The probability of an event given the knowledge of occurrence of other events that bear on it: P( A | B ) as contrasted to P( A ), where A is the sought event and B is the sign or symptom event.


nonnormal

a nonnormal distribution