chaotic

en-adj

chaotic (comparative more chaotic, superlative most chaotic)

more chaotic (comparative)
most chaotic (superlative)

From Late Latin chaoticus (“of or pertaining to the primordial state of the universe”), from Latin chaos (“chaos”) + -ticus (suffix forming adjectives from nouns); analysable as chaos + -otic. Doublet of gassy.

der

The manipulation of the environment through design involves many branches of mathematics: the projective geometry of light transmission, the chaotic and probabilistic maths of weather patterns, and the statistical algorithms required to make analysis legible and obtain discrete building components from continuous distributions.

2011 April, Martha Tsigkari, Adam Davis, Francis Aish, “A Sense of Purpose: Mathematics and Performance in Environmental Design”, in George L. Legendre, editor, Mathematics of Space (Architectural Design; volume 81, issue 4), London: John Wiley & Sons, →ISBN, →ISSN, page 56, column 2:

(mathematics) Highly sensitive to starting conditions, so that a small change to them may yield a very different outcome.

混沌

(mathematics) highly sensitive to starting conditions


minimal

en-adj

minimal (comparative more minimal, superlative most minimal)

more minimal (comparative)
most minimal (superlative)

mínimu

the smallest possible amount, quantity, or degree

With respect to the ordering induced by set-theoretic inclusion, the power set of the set of natural numbers has a unique minimal element: the empty set.

The smallest possible amount, quantity, or degree.

(mathematics, technical) Among elements of some collection, such that no other element is greater (with respect to some given partial order).


computable

(mathematics) of a number, able to be approximated to arbitrary precision by a computable function

(mathematics, set theory) Of a countably infinite set, having a computable indicator function.


urna

A wine vessel, probably the Roman urna, which contained half the quantity of the amphora.

1810, A Description of the Collection of Ancient Terracottas of the British Museum, British Museum, No. XXXIX, page 22:

The congius was the 8th part of the amphora, and the 4th of the urna: it contained 6 sextarii.

1847, Francis Adams, The Seven Books of Paulus Ægeineta, volume 3, The Sydenham Society, page 623:

It follows that the seah must equal the urna, and the hin equal 2 Attic choes.

1903, Sir Charles Warren, The Ancient Cubit and Our Weights and Measures, page 89:

(historical) A Roman unit of liquid measure reckoned as the volume of 40 Roman pounds of wine and equivalent to about 13 L although differing slightly over time.


group theory

en-noun

group theory (usually uncountable, plural group theories)

THE feeling seems to be developing among physicists that group theory can be used as and when required, as many other techniques already are, without its being necessary for everyone to study all the whys and wherefores of the mathematical details involved.

1968, Arthur P. Cracknell, editor, Applied Group Theory: Selected Readings in Physics, Pergamon Press, page ix:

1995, Jean Brocas, Chapter 4: The Use of Group Theory in the Study of Non-Rigid Molecules, Danail Bonchev, D. H. Rouvray (editors), Chemical Group Theory: Techniques and Applications, Gordon and Breach, page 133,
Planar cis and/or trans internal rotation tunnelling have been discussed in terms of group theory, leading to theoretical spectra which have been compared to experimental work.

(algebra, uncountable) The mathematical theory of groups.


Möbius group

Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer.

projective general linear group
projective general linear group

Möbius transformations
Möbius transformations

(group theory) The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere.

(group theory) For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant.


hypersphere

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

The timing and location of these battles have not been established. “Sphere” in this context is a hypersphere made up of complexes of two and three-D surfaces, or membranes, shortened in this translation to “branes,” extending into higher dimensions that combine vectors of transit, but also scalar tactical probabilities—a difficult concept to grasp, but essential to understanding Forerunner warfare.

2013 March 19, Greg Bear, String 25, in Halo: Silentium (Forerunner Saga; 3), New York: Tor, →ISBN, page 211:

To prove that the hypersphere is a manifold we wish to divide it into polyhedral solids.

2014, Donald W. Blackett, Elementary Topology: A Combinatorial and Algebraic Approach, Academic Press, →ISBN, page 198:

(geometry) The set of all points in a given hyperspace that are at a given distance from a given point; a generalization of a sphere in four or more dimensions.

гиперсфера

the points of a hyperspace at the same distance from a given point


hyperspace

hyperspace (countable and uncountable, plural hyperspaces)

(mathematics) An n-dimensional Euclidian space with n > 3.

(mathematics) A Euclidian space of unspecified dimension.


umbral

(mathematics) Of or relating to umbral calculus.


myriagram

(obsolete) A unit of mass of ten thousand grams, or ten kilograms. Adopted as an equivalent of the French avoirdupois XX.


chiliahedron

chiliahedron (plural chiliahedra or chiliahedrons)

chiliahedra (plural)
chiliahedrons (plural)

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

(geometry) A polyhedron bounded by one thousand plane surfaces.


bandwidth

bandwidth (countable and uncountable, plural bandwidths)

(graph theory) The minimum, over all orderings of vertices of a given graph, of the length of the longest edge.


cuarto

(unit of measure): From Spanish cuarto (“quarter-sack”), from Latin quartus (“fourth, quarter”). Doublet of quart, quarter, and cuarta, etc.

(historical) A traditional Spanish unit of dry measure, equivalent to about 27.8 L.


magic square

(number theory) An n-by-n arrangement of n² numbers such that the numbers in each row, in each column and along both diagonals all have the same sum.


Latin square

(mathematics) An n-by-n arrangement of n different integers such that each row, each column and each of the two diagonals contains each of the integers once and once only.

latinský čtverec

an n-by-n arrangement of n different integers


PDA

PDA (countable and uncountable, plural PDAs)

(cryptocurrencies, Solana) Initialism of program derived address.


strictly

en-adv

strictly (comparative strictlier or more strictly, superlative strictliest or most strictly)

strictlier (comparative)
more strictly (comparative)
strictliest (superlative)
most strictly (superlative)

(mathematics) In a manner that applies to every member of a set or every interval of a function


strictly proper

(mathematics) of a transfer function, where the degree of the numerator is less than that of the denominator


numerator

/ˈnuː.məɹˌeɪ̯.təɹ/

(arithmetic) The number or expression written above the line in a fraction (such as 1 in ½).


denominator

From Late Latin dēnōminātor (“that which names”).

bor

(arithmetic) The number or expression written below the line in a fraction (such as 2 in ½).


up to

From Middle English up to, from Old English up tō.

There’s only one rooted tree with two leaves, up to ordering.

(mathematics) Considering all members of an equivalence class the same.

op ... na

mathematics: considering all members of an equivalence class the same


meta-analysis

en-noun

meta-analysis (countable and uncountable, plural meta-analyses)

(statistics) Any systematic procedure for statistically combining the results of many different studies.

(statistics) An analysis resulting from combining the results of diverse statistical studies.


side chain

The Blockstream developers, meanwhile, were accused of working for the interests of their company, Blockstream, rather than the good of Bitcoin as a whole. Their company, after all, proposed breaking many smaller transactions off onto so called sidechains that would occasionally link back up with the main Bitcoin blockchain, […]

2015, Nathaniel Popper, “Epilogue”, in Digital Gold, 1st edition, New York: Harper, →ISBN, →OCLC:

A sidechain does not have a native token but rather creates a two-way peg or a 1:1 peg between bitcoin (tokens) and the “pegged bitcoin” on the sidechain.

2021, H. Kent Baker, Ehsan Nikbakht, Sean Stein Smith, The Emerald Handbook of Blockchain for Business, Emerald Group Publishing, →ISBN, page 179:

(cryptocurrencies) A separate blockchain attached to a parent blockchain (mainchain) to extend its functionalities.


integrate

en-verb

integrate (third-person singular simple present integrates, present participle integrating, simple past and past participle integrated)

integrates (present singular third-person)
integrating (participle present)
integrated (participle past)
integrated (past)

/ˈɪn.təˌɡɹeɪt/

/ˈɪn.tɪ.ɡɹæɪt/

Borrowed from Latin integrātus, perfect participle of integrō (“I make whole, I renew, I repair, I begin again”), from integer (“whole, fresh”); see integer, integral.

(mathematics) To subject to the operation of integration; to find the integral of an equation.

интегрирам

to subject to the operation of integration; to find the integral of

President Eisenhower had to call out the National Guard to integrate Little Rock Central High School.

I continued on the bus without him. It worked out fine. I went on to Tampa, Fla. That was the first time we integrated the buses. All the way down, sitting in the front row.

2020 July 18, Bernard Lafayette Jr., “The First Time John Lewis and I Integrated the Buses”, in New York Times:

To desegregate, as a school or neighborhood.

integrarsi

to desegregate, as a school or neighborhood


dominate

dominate (third-person singular simple present dominates, present participle dominating, simple past and past participle dominated)

dominates (present singular third-person)
dominating (participle present)
dominated (participle past)
dominated (past)

From Latin dominātus, perfect active participle of dominor (“rule, have dominion”), from dominus (“lord, master”); see dominus.

(computing, graph theory, linguistics) To precede another node of a directed graph in all paths from the start of the graph to the other node.


gradient

From Latin gradiēns, present participle of gradior (“to step, to walk”).

(calculus, of a function) The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.

(calculus) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ


restrict

restrict (third-person singular simple present restricts, present participle restricting, simple past and past participle restricted)

restricts (present singular third-person)
restricting (participle present)
restricted (participle past)
restricted (past)

Borrowed from Latin restrictus, perfect passive participle of restringō (“draw back tightly; restrain, restrict”), from re- (“back, again”) + stringō (“press, tighten, compress”). Doublet of ristretto as an adjective.

If we restrict sine to #92;left#91;-#92;frac#92;pi2,#92;frac#92;pi2#92;right#93;, we can define its inverse.

(specifically, mathematics) To consider (a function) as defined on a subset of its original domain.


unity

en-noun

unity (countable and uncountable, plural unities)

Etymology tree
Middle English unite
English unity
From Middle English unite, from Anglo-Norman, Old French unité, from Latin ūnitās, from ūnus (“one”) + noun of state suffix -itās, ultimately from Proto-Indo-European *óynos (“one, single”), hence distantly related to one and an. Displaced native Old English ānnes (literally “oneness”).

der

the cube roots of unity

(mathematics) The number 1 or any element of a set or field that behaves under a given operation as the number 1 behaves under multiplication.

едини́ца

mathematics: something that behaves like the number 1 in multiplication


polytropic

From polytrope, equivalent to poly- + -tropic, ultimately from Ancient Greek πολύτροπος (polútropos).


sample

From Middle English saumple, sample, from Old French essample (“example”), from Latin exemplum. Doublet of example and exemplum.

Large samples are generally more reliable than small samples due to having less variability.

It is interesting to find that, with the exception of a few imperfectly-observed South Sea Islanders, and whose actual numbers, if the measurements are correct, are very few, the English professional classes head the long list [in average height], and that the Anglo-Saxon race takes the chief place in it among the civilised communities, although it is possible it might stand second to the Scandinavian countries if a fair sample of their population were obtained.

1883, Sir Francis Galton et al., “Final Report of the Anthropometric Committee”, in Report of the British Association for the Advancement of Science, page 269:

(statistics) A subset of a population selected for measurement, observation or questioning, to provide statistical information about the population.


sample

en-verb

sample (third-person singular simple present samples, present participle sampling, simple past and past participle sampled)

samples (present singular third-person)
sampling (participle present)
sampled (participle past)
sampled (past)

(transitive, signal processing) To reduce a continuous signal (such as a sound wave) to a discrete signal.

дигитализирам

signal processing: to reduce a continuous signal to a discrete signal


sampling

en-noun

sampling (countable and uncountable, plural samplings)

(statistics) The analysis of a group by determining the characteristics of a significant percentage of its members chosen at random.

otanta

(signal processing) The measurement, at regular intervals, of the amplitude of a varying waveform in order to convert it to digital form.


snark

Martin Gardner
Mathematical Games
Scientific American
The Hunting of the Snark

From Snark, coined by Lewis Carroll as a nonce word in The Hunting of the Snark (1874), about the quest for an elusive creature. In sense of “a type of mathematical graph”, named as such in 1976 by Martin Gardner for their elusiveness.

(mathematics) A graph in which every node has three branches, and the edges cannot be coloured in fewer than four colours without two edges of the same colour meeting at a point.


scroll

From Middle English scrowle, scrolle, from earlier scrowe, scrouwe (influenced by Middle English rolle), from Old French escroe, escrowe, escrouwe (“scroll, strip of parchment”), from Frankish *skrōda (“a shred”), from Proto-Germanic *skraudō, from *skrew- (“to cut; cutting tool”), extension of *(s)ker- (“to cut”). Doublet of shred and escrow.


sporadic

en-adj

sporadic (comparative more sporadic, superlative most sporadic)

more sporadic (comparative)
most sporadic (superlative)

From Medieval Latin sporadicus (whence also French sporadique, Italian sporadico, Spanish esporádico), from Ancient Greek σποραδικός (sporadikós), from σποράς (sporás, “scattered, dispersed”), from σπορά (sporá), σπόρος (spóros, “a sowing [of seed]”).

(mathematics) Not belonging to any infinite family; an exception to an otherwise orderly classification.


spherical

spherical (comparative more spherical, superlative most spherical)

more spherical (comparative)
most spherical (superlative)

English spheric [from Latin sphaericus, from Ancient Greek σφαιρικός (sphairikós)] + -al.

The ability of a segment of a glass sphere to magnify whatever is placed before it was known around the year 1000, when the spherical segment was called a reading stone, essentially what today we might term a frameless magnifying glass or plain glass paperweight.

2013 September-October, Henry Petroski, “The Evolution of Eyeglasses”, in American Scientist:

(geometry, not comparable) Of, or pertaining to, spheres.

(mathematics) Of a coordinate system, specifying the location of a point in a plane by using a radius and two angles.

a spherical Gaussian distribution

(statistics, econometrics) Of a multivariate probability distribution, to have a covariance matrix equal to the identity matrix up to a multiplicative factor.


crib

en-noun

crib (countable and uncountable, plural cribs)

From Middle English crib, cribbe, from Old English crib, cryb, cribb, crybb (“couch, bed; manger, stall”), from Proto-West Germanic *kribbjā, from Proto-Germanic *kribjǭ (“crib, wickerwork”), from Proto-Indo-European *grebʰ-, *gerbʰ- (“bunch, bundle, tuft, clump”), from *ger- (“to turn, twist”).
Cognate with Saterland Frisian Kräbbe, Krääb, Krääf (“crib”), West Frisian krêbe (“crib”), Dutch krib (“crib, manger”), German Krippe (“rack, crib”), Danish krybbe (“crib”), Icelandic krubba (“crib”). Doublet of crèche. The sense of ‘stealing, taking notes, plagiarize’ seems to have developed out of the verb.
The criminal sense may derive from the 'basket' sense, circa the mid 18th century, in that a poacher could conceal poachings in such a basket (see the 1772 Samuel Foote quotation). The cheating sense probably derives from the criminal sense.

inh

(cryptography) A known piece of information corresponding to a section of encrypted text, that is then used to work out the remaining sections.


realize

en-verb

realize (third-person singular simple present realizes, present participle realizing, simple past and past participle realized)

realizes (present singular third-person)
realizing (participle present)
realized (participle past)
realized (past)
realize (infinitive)

desc

→ Portuguese: realizar (“to realize, become aware of”) (semantic loan)

PIE word
 *reh₁ís
From real (adjective) + -ize (suffix denoting the making of what is indicated by the word it is attached to), possibly modelled after French réaliser, Middle French réaliser (“to make real; to convert (something) into assets or cash”), from real (“actual, real”) + -iser (suffix denoting the making of what is indicated by the word it is attached to). Real is derived from Old French reel, from Latin reālis (“actual, real”), from rēs (“deed; event; matter; thing”) (ultimately from Proto-Indo-European *reh₁ís (“goods; wealth”)) + -ālis (suffix forming adjectives of relationship).

أَدْرَكَ

(transitive) to become aware of or understand (a fact or situation); (intransitive) to become aware of or understand a fact or situation

apiolarse / caer en la cuenta / darse cuenta / percatarse / coscarse / caer en cuenta [de]

tehdä todeksi

(transitive) to cause (something) to seem real; to present (something) clearly to the mind, a person, etc., so that it seems real; (intransitive) to cause to seem real

بَاعَ

(transitive) to convert (an asset or property) into a more easily usable form such as money, especially by selling the asset or property; (intransitive) to convert an asset or property into a more easily usable form such as money

(mathematics) To obtain an entity from (an abstract group or structure).

realisoida

(mathematics) to obtain an entity from (an abstract group or structure)


data set

(statistics) A set of data to be analyzed.


erosion

en-noun

erosion (countable and uncountable, plural erosions)

Guy de Chauliac
Oliver Goldsmith
Robert Copland
The Questyonary of Cyrurygens
erosion

From Middle French erosion, from Latin ērōsiō (“eating away”), derived from ērōdō.
The first known occurrence in English was in the 1541 translation by Robert Copland of Guy de Chauliac's medical text The Questyonary of Cyrurygens. Copland used erosion to describe how ulcers developed in the mouth. By 1774 erosion was used outside medical subjects. Oliver Goldsmith employed the term in the more contemporary geological context, in his book Natural History, with the quote
: "Bounds are thus put to the erosion of the earth by water."

(mathematics, image processing) One of two fundamental operations in morphological image processing from which all other morphological operations are derived.

(mathematics) In morphology, a basic operation (denoted ⊖); see Erosion (morphology).


cuboctahedron

cuboctahedron (plural cuboctahedrons or cuboctahedra)

cuboctahedrons (plural)
cuboctahedra (plural)

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

Blend of cube + octahedron, reflecting the fact that it can be regarded both as a rectified cube and a rectified octahedron.

There are just two polyhedra that will fulfill these conditions: the cuboctahedron and the icosidodecahedron (Diagram 3.3).

1976, Hugh Kenner, Geodesic Math and how to Use it, page 21:

In the case of perfect, symmetric L1₀ cuboctahedra, two of the (001)-surfaces have to be terminated completely with either iron or platinum.

2008, M. E. Gruner, Georg Rollmann, Alfred Hucht, Peter Entel, “Structural and Magnetic Proprties of Transition Metal Nanoparticles from First Principles”, in Rolf Haug, editor, Advances in Solid State Physics 47, page 124:

Octahedra are also needed to make the packing of square-sharing cuboctahedra space filling (Fig. 2.4(c)).

2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 54:

2015, Ke Jiang, Antoliy O. Pinchuk, Chapter Two: Noble Metal Nanomaterials: Synthetic Routes, Fundamental Properties, and Promising Applications, Robert E. Camley, Robert L. Stamps (editors), Solid State Physics, Volume 66, Elsevier, page 151,
Yang and coworkers have prepared Pt cuboctahedrons and cubes by reducing K₂PtCl₄ with H₂ generated in situ from the hydrolysis of NaBH₄ in the presence of tetradecyltrimethylammonium bromide as a surfactant [157,158].

(geometry) An Archimedean solid that has fourteen faces (eight triangular and six square) and is both isogonal and isotoxal.

kuboktaedri

polyhedron with 8 triangular and 6 square faces


triangular

en-adj

triangular (comparative more triangular, superlative most triangular)

more triangular (comparative)
most triangular (superlative)

/tɹaɪˈæŋ.ɡjə.lə/

/tɹaɪˈæŋ.ɡjʊ.lə/

/tɹaɪˈæŋ.ɡjə.lɚ/

From Middle English triangulare, trianguler, triangulere, from Old French triangulaire, triangulier and Latin triangulāris.

Having a triangle as a base; as, a triangular prism, a triangular pyramid.


isometry

From New Latin isometria, from Ancient Greek ἰσομετρία (isometría), from ἰσο- (iso-) + -μετρία (-metría), from ἴσος (ísos, “equal”) and μέτρον (métron, “measurement”) + -ια (-ia, “-y”). Equivalent to iso- + -metry.

Isometry is to metric spaces what isomorphism is to groups.

(mathematics) A function between metric spaces (or on a single metric space) having the property that the distance between two images is equal to the distance between their preimages.


loop

From Middle English loupe (“noose, loop”), earlier lowp-knot (“loop-knot”), of North Germanic origin, from Old Norse hlaup (“a run”), used in the sense of a "running knot", from hlaupa (“to leap”), ultimately from Proto-Germanic *hlaupaną (“to leap, run”). Compare Swedish löp-knut (“loop-knot”), Danish løb-knude (“a running knot”), Danish løb (“a course”). More at leap. The verb is derived from the noun.

der

(graph theory) An edge that begins and ends on the same vertex.

silmukka

edge that begins and ends on the same vertex of a graph

(topology) A path that starts and ends at the same point.

silmukka

topology: path that starts and ends at the same point

(algebra) A quasigroup with an identity element.


transcendental

en-adj

transcendental (comparative more transcendental, superlative most transcendental)

more transcendental (comparative)
most transcendental (superlative)

algebraic

antonym(s) of “not the root of a polynomial with rational coefficients”

algebraic

antonym(s) of “containing elements that are not the root of a polynomial”

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

The theory of transcendental numbers was originated by Liouville in his famous memoir^† of 1844 in which he obtained, for the first time, a class, très-étendue, as it was described in the title of the paper, of numbers that satisfy no algebraic equation with integer coefficients.

1975, Alan Baker, Transcendental Number Theory, 2nd edition, Cambridge University Press, published 1990, page 1:

If the distribution of decimal digits of #92;pi (or any other transcendental number) is truly random (suspected but not yet mathematically proven!), given any arbitrary finite sequence of whole numbers, that sequence would be included an infinite number of times in the decimal expansion of #92;pi.

2005, Juan G. Roederer, Information and Its Role in Nature, Springer, page 28:

(algebra, number theory, field theory, of a number or an element of an extension field) Not algebraic (i.e., not the root of any polynomial that has positive degree and rational coefficients).

irrational

2006, Steven Roman, Field Theory, Springer, 2nd Edition, Graduate Texts in Mathematics 158, page 108,
Suppose that F<E is purely transcendental. Show that any simple extension of F contained in E (but not equal to F) is transcendental over F.

(algebra, field theory, of an extension field) That contains elements that are not algebraic.

transsendenttinen

not algebraic; containing elements that are not algebraic


transcendental number

en-noun

transcendental number (plural transcendental numbers)

(mathematics) any irrational number that is not an algebraic number


irrational number

irrational number (plural irrational numbers)

The square root of a positive integer is an irrational number unless the positive integer is a perfect square, in which case the square root will also be a positive integer.

(mathematics) Any real number that cannot be expressed as a ratio of two integers.


algebraic number

algebraic number (plural algebraic numbers)

The golden ratio (φ) is an algebraic number since it is a solution of the quadratic equation x²+x-1=0, whose coefficients are integers.

The square root of a rational number, √, is an algebraic number since it is a solution of the quadratic equation nx²-m=0, whose coefficients are integers.

Thus, the equation x-eʸ#61;0 is satisfied for x#61;1,#92;y#61;0 and for no other pair of algebraic numbers.

1918, The American Mathematical Monthly, volume 25, Mathematical Association of America, page 435:

As a matter of fact, it is not true that the algebraic numbers above can be factored uniquely, but the first case of failure occurs when p = 23.

1921, L. J. Mordell, Three Lectures on Fermat's Last Theorem, page 16:

(i) It is easily checked that the set of all algebraic numbers is countable, whereas the set of all complex numbers is uncountable (this non-constructive proof goes back to Cantor).

1991, P. M. Cohn, Algebraic Numbers and Algebraic Functions, Chapman & Hall, page 83, The existence of such 'transcendental' numbers is well known and it can be proved at three levels

(algebra, number theory) A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.

代數數 /代数数

element of a number field that is a root of a polynomial with integer coefficients


approximation

approximation (countable and uncountable, plural approximations)

/əˌpɹɔk.sɪˈmæɪ.ʃən/

[əˌpɹɔk.sɪˈmæɪ.ʃn̩]

(uncountable, countable) The act, process or result of approximating, as:

(mathematics) An imprecise solution or result that is adequate for a defined purpose.

For some loanwords borrowed from French into English, the standard English pronunciation is an approximation of the French, as with denoument.

(linguistics) The act of producing a near-simulation of the pronunciation of a foreign language for a loanword therefrom, or any given pronunciation resulting from that act.


round up

en-verb

round up (third-person singular simple present rounds up, present participle rounding up, simple past and past participle rounded up)

rounds up (present singular third-person)
rounding up (participle present)
rounded up (participle past)
rounded up (past)

koota

to collect or gather (something) together

The total is $24,995 — let's round it up to $25,000.

(transitive, arithmetic) To round (a number) to the smallest integer that is not less than it, or to some other greater value, especially a whole number of hundreds, thousands, etc.


round down

round down (third-person singular simple present rounds down, present participle rounding down, simple past and past participle rounded down)

rounds down (present singular third-person)
rounding down (participle present)
rounded down (participle past)
rounded down (past)

The total is $25,715, but to keep the figures simple, I'll round it down to $25,000.

(transitive, arithmetic) To round (a number) to the greatest integer that is not greater than it, or to some other lower value, especially a whole number of hundreds, thousands, etc.

向下取整

to round downwards to the desired accuracy


decimal number

13+¹⁄₄ is 13.25 as a decimal number.

(mathematics) A number expressed in the decimal system (base ten), (particularly) fractional numbers so represented.


transfinite number

en-noun

transfinite number (plural transfinite numbers)

It will be recalled that Cantor called the first transfinite number ℵ₀. He called the second transfinite number—the one describing the set of all real numbers— C. It has not been proved whether C is the next transfinite number after ℵ₀ or whether another number exists between them.

1961, Jane Muir, Of Men and Numbers: The Story of the Great Mathematicians, Courier Dover Publications, →ISBN, page 228:

Let R be a bicompact of dimensionality #92;operatorname#123;ind#125;(R)#92;le#92;alpha. If #92;alpha is an isolated transfinite number, than ^([sic]) at any point x#92;inR there exist arbitrarily small neighborhoods Vx with boundaries of dimensionality #92;operatorname#123;ind#125;#92;overline#123;Vx#125;#92;le#92;alpha-1.

1968, B. T. Levšenko, “Spaces of transfinite dimensionality”, in Fourteen Papers on Algebra, Topology, Algebraic and Differential Geometry, American Mathematical Soc., →ISBN, page 141:

After all, it was the ordinals that made precise definition of the transfinite cardinals possible. And until Cantor had introduced the order types of transfinite number classes, he could not define precisely any transfinite cardinal beyond the first power.

1990, Joseph Warren Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press, →ISBN, page 180:

For example, does there exist a transfinite number that is strictly bigger than ℵ₀ and strictly smaller than ℵ₁? In this case an instance of this in between number is too big to be put into one-to-one correspondence with the set of natural numbers, and too small to be put into one-to-one correspondence with the set of real numbers.

2009, John Tabak, Numbers: Computers, Philosophers, and the Search for Meaning, Infobase Publishing, →ISBN, page 153:

Having demonstrated the existence of a one-to-one correspondence, we can conclude that the class of the squares of all the natural numbers has the same transfinite number as the class of all the natural numbers! This result is not what might have been anticipated, seeing that the second class is a proper subset of the first.

2012, Benjamin Wardhaugh, A Wealth of Numbers: An Anthology of 500 Years of Popular Mathematics Writing, Princeton University Press, →ISBN, page 136:

(set theory) Any cardinal or ordinal number which is larger than any finite, i.e. natural number; often represented by the Hebrew letter aleph (ℵ) with a subscript 0, 1, etc.


aleph-one

continuum hypothesis
continuum hypothesis

(set theory) The second of the transfinite cardinal numbers; according to the continuum hypothesis, it corresponds to the number of real numbers.


summit

PIE word
 *upó
The noun is derived from Late Middle English somet, somete (“head, top”) [and other forms], from Anglo-Norman sumet and Middle French sommet (masculine), somete, sommette (“top of a thing; highest point of a mountain”) (feminine) (modern French sommet), from Old French somet, sommette, from som, sum (“highest point, summit”) + -et (suffix forming diminutive masculine nouns), -ete, -ette (suffix forming diminutive feminine nouns). Som, sum are derived from Latin summum (“top, summit”), a noun use of the neuter of summus (“greatest, highest; top, uppermost”, adjective) (ultimately from Proto-Indo-European *upó (“below, under”) + *-m̥mós, *-tm̥mós (“suffix forming superlative adjectives”)). The modern English spelling was influenced by summity (“height or top of a thing; utmost degree, perfection”) (obsolete).
The verb is derived from the noun.

der

The topmost point or surface of a thing; the apex, the peak.

(mathematics) A vertex of a polygon or polyhedron.


transcendental function

en-noun

transcendental function (plural transcendental functions)

An analytic function is transcendental (i.e., is a transcendental function) if and only if its Riemann surface is noncompact.

mathematical analysis
mathematical analysis

algebraically independent
algebraically independent

(mathematical analysis) Any function that is algebraically independent of its variable(s); a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials.

(specifically, complex analysis) A meromorphic function on the complex plane that is not a rational function.


lax

en-adj

lax (comparative laxer, superlative laxest)

laxer (comparative)
laxest (superlative)

Borrowed from Latin laxus (“wide, roomy, loose”).

(mathematics) Describing an associative monoidal functor.


claw

From Middle English clawe, from Old English clawu, from Proto-Germanic *klawō. Compare West Frisian klau, Dutch klauw, German Klaue, Danish klo, Norwegian klo, and Swedish klo.

(graph theory) A tree with one internal vertex and three leaves.


transverse

Late Middle English, from Latin trānsversus (“turned across; going or lying across or crosswise”). Doublet of transversal.

der

(geometry) (of an intersection) Not tangent, so that a nondegenerate angle is formed between the two things intersecting. (For the general definition, see Transversality (mathematics).)


transverse

(geometry) The longer, or transverse, axis of an ellipse.


Fourier transform

en-noun

Fourier transform (plural Fourier transforms)

Named after French mathematician and physicist Jean Baptiste Joseph Fourier, who initiated the study of what is now harmonic analysis.

Fourier transforms are not limited to acting on functions of time, but the domain of the original function is commonly called the time domain.

The Fourier transform of a function of time is a complex function of frequency, whose magnitude (absolute value) represents the amount of that frequency present in the original function, and whose argument is the phase offset of the basic sinusoid in that frequency.

Since a separate integration is needed to give each point of the transformed function, the process would become extremely tedious if it were to be attempted manually and many ingenious devices have been invented for preforming Fourier transforms mechanically, electrically, acoustically and optically.

2002, J. F. James, A Student's Guide to Fourier Transforms, 2nd edition, Cambridge University Press, page 116:

2005, Emmanuel Letellier, Fourier Transforms of Invariant Functions on Finite Reductive Lie Algebras, Springer, Lecture Notes in Mathematics 1859, page 1,
The trigonometric sums of 𝒢^F are thus (up to a scalar) the Fourier transforms of the characteristic functions of the G^F!!-orbits of 𝒢^F.

2012, David Brandwood, Fourier Transforms in Radar and Signal Processing, Artech House, 2nd Edition, page 1,
The Fourier transform is a valuable theoretical technique, used widely in fields such as applied mathematics, statistics, physics, and engineering.

electrical engineering
electrical engineering

(mathematical analysis, harmonic analysis, physics, electrical engineering) A particular integral transform that when applied to a function of time (such as a signal), converts the function to one that plots the original function's frequency composition; the resultant function of such a conversion.

Fourier transform
Jean Baptiste Joseph Fourier

Fouriertransformatie

mathematics: a type of integral transform


sinusoidal

en-adj

sinusoidal (comparative more sinusoidal, superlative most sinusoidal)

more sinusoidal (comparative)
most sinusoidal (superlative)

An averager of the sort described earlier would operate such that, as the frequency of sinusoidal variation of ITD was increased, more and more samples of the dynamically varying ITD would fall within the averaging window and the effective ITD would tend toward their mean of zero.

2014, Robert Gilkey, Timothy R. Anderson, Binaural and Spatial Hearing in Real and Virtual Environments:

(mathematics) Having the shape or characteristics of a sine wave.


transformer

/tɹɑːnsˈfɔːmə/

Transformer is a deep machine learning model based on the encoder–decoder network architecture and is used primarily in the field of NLP.

2021, Lei Chen, Deep Learning and Practice with MindSpore, Springer Nature, →ISBN, page 116:

The transformer helped machine-learning systems improve at a much faster pace, leading directly to last year’s release of ChatGPT and the attendant boom in interest around AI. (Transformers are the “T” in ChatGPT.)

2023 January 31, Casey Newton, “Instagram’s co-founders are back with Artifact, a kind of TikTok for text”, in The Verge:

(machine learning) A neural network architecture composed of layers of attention which takes sequences of tokens (representing text, images, audio, or other modalities) as input.


randomness

en-noun

randomness (usually uncountable, plural randomnesses)

probability distribution
probability distribution

(mathematics) A type of circumstance or event that is described by a probability distribution.


biased

en-adj

biased (comparative more biased, superlative most biased)

more biased (comparative)
most biased (superlative)

(statistics) Exhibiting a systematic distortion of results due to a factor not allowed for in its derivation; skewed.

مُتَحَيِّز

of statistics - showing an imbalance of a result


tetration

en-noun

tetration (usually uncountable, plural tetrations)

/tɛˈtɹeɪʃn̩/

/tɛˈtɹeɪʃən/

PIE word
 *kʷetwóres
From tetra- (prefix meaning ‘four’) + (itera)tion, from the fact that tetration is in fourth place after addition, multiplication, and exponentiation. The word was coined by the English mathematician Reuben Goodstein (1912–1985).

coinage

You don't ordinarily hear much about tetration because it is so powerful an operation that tetrating even very small numbers with each other produces inordinately large numbers. A tetration is worked out below.
⁴²#61;2#123;(2#123;(#123;2²#125;)#125;)#125;
 #61;2#123;(#123;2⁴#125;)#125;
 #61;2#123;16#125;
 #61;64,536

1982 May, Rudy Rucker, “All the Numbers”, in Infinity and the Mind: The Science and Philosophy of the Infinite, Boston, Mass.; Stuttgart, Baden-Württemberg: Birkhäuser, →ISBN, page 69:

Repeated exponentiation—called tetration—is so rare that a shorthand for it is hardly worth the trouble, appealing only to research mathematicians. Most professional engineers and scientists never encounter tetration, and the shorthand for it is seldom taught anywhere but in mathematics departments. But it doesn't stop there, and for the almost-unheard-of "multiple tetration" there is yet a stronger cousin operation, waiting in the wings.

1993, Alexander Humez, Nicholas Humez, Joseph Maguire, “One”, in Zero to Lazy Eight: The Romance of Numbers, New York, N.Y.: Touchstone, Simon & Schuster, →ISBN, page 39:

Tetration is usually symbolized with a number drawn to the upper left of another number, as opposed to the upper right used for exponents. Let's look at an example: what is 2 tetrated to the 4th? We would draw this as a 2 with a little 4 to the upper left side: ⁴². This is equivalent to 2#123;2#123;2²

2016, Erik Seligman, “Simple Surprises”, in Math Mutation Classics: Exploring Interesting, Fun and Weird Corners of Mathematics, New York, N.Y.: Apress, Springer Science+Business Media, →DOI, →ISBN, page 11:

(arithmetic) The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times.


trigonometric function

en-noun

trigonometric function (plural trigonometric functions)

(trigonometry) Any function of an angle expressible as the ratio of two of the sides of a right triangle that has that angle (e.g., sine), or that subtracts 1 from such a ratio or subtracts such a ratio from 1 (e.g., coversed sine).


cotangent

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

(trigonometry) In a right triangle, the reciprocal of the tangent of an angle. Symbols: cot, ctg, or ctn


cosecant

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

(trigonometry) In a right triangle, the reciprocal of the sine of an angle. Symbols: cosec, csc


polynomial equation

polynomial equation (plural polynomial equations)

(algebra) Any algebraic equation in which one or both sides are in the form of a polynomial.


algebraic equation

algebraic equation (plural algebraic equations)

(algebra) A mathematical equation in which one or both sides is an algebraic expression, such as 2x + 7y = 3.


algebraic

en-adj

algebraic (comparative more algebraic, superlative most algebraic)

more algebraic (comparative)
most algebraic (superlative)

transcendental

antonym(s) of “that is the root of some polynomial”

transcendental

antonym(s) of “whose every element is the root of some polynomial”

/ˌæl.d͡ʒɪˈbɹeɪ.ɪk/

/ˌæl.d͡ʒɪˈbɹæɪ.ɪk/

Partly from algebra + -ic and partly from French algébraïque.

(mathematics, of an expression, equation, or function) Containing only numbers, letters, and arithmetic operators.

equation; or function; equation; or function

algebraïes

containing numbers, letters, and arithmetic operators

(algebra, number theory, of a number) Which is a root of some polynomial whose coefficients are rational.

(algebra, of a field) Whose every element is a root of some polynomial whose coefficients are rational.


arithmetic function

en-noun

arithmetic function (plural arithmetic functions)

(mathematical analysis) Any function that is defined for all positive integers, and has values that are either real or complex.


carrier wave

From carrier + wave. Sense 2 (“soliton”) was coined by the Scottish civil engineer, naval architect, and shipbuilder John Scott Russell (1808–1882): see the quotations.

The same propagation through the same ether brought the rays of the sun's light from the sun to the earth, and the same carrier wave brought from the other side of the globe, from the oceans there, which were disturbed by the attraction of the sun and moon, those waves all round the coasts which were called tides. All these phenomena, from the tides and the wind to the rays of light and to the sounds of the telephone, were the motion of one simple phenomenon, the carrier wave, the wave of translation.

1877 November 30, J[ohn] Scott Russell, “[The Telephone. By Professor A[lexander] Graham Bell.] Discussion.”, in Journal of the Society of Arts, volume XXVI, number 1,306, London: Published for the Society [Royal Society of Arts] by George Bell and Sons, […], published 1878, →OCLC, page 23, column 2:

Noise is caused by a shock or stroke or beat given to some mass of matter. The shock tells on the mass of air near the struck body. It sends this mass of air into a heap near the struck body. This heap forms an air wave. [...] This wave is the carrier of the shock through great distances in the air, it travels with great speed. This "carrier wave" takes the shock of the stroke from afar, to the ear of the listener.

1878, J[ohn] Scott Russell, “Symmetry, Harmony, and Melody”, in Geometry in Modern Life, Being the Substance of Two Lectures on Useful Geometry, Given before the Literary Society at Eton, Eton, Berkshire: Williams and Son; London: Simpkin, Marshall, and Co., →OCLC, page 137:

Mr. [John Scott] Russell not only observed the shape and characteristics of the wave, which he called the carrier wave, or wave of translation, but he noticed the form which water assumed in filling up a cavity; and one of the means he used for this purpose was to have a boat towed at moderate and also at high velocities, and to observe the waves which followed her. These waves he found to be different from carrier waves, and he calls them following waves, or waves of replacement.

1878 March 23, J. Hyslop, “Yachting. The Wave-line Theory. Its Practical Application.”, in The Country: A Weekly Journal Devoted to the Dog, the Gun, Yachting, Fishing and All Out-door Sports, volume I, number 22, New York, N.Y.: “The Country” Publishing Association, →OCLC, no. II, page 312, column 1:

[M]eans must be taken first to create a series of solitary waves, and then to make these waves act as carrier waves, transporting the sounds from the instrument to the ear at a distance. In other words, the operation carried on in the instrument differs from the operation carried on through the air and from the effect delivered by the carrier wave.

1885, John Scott Russell, “Part II. The Wave of Translation and the Work It Does as the Carrier Wave of Sound.”, in The Wave of Translation in the Oceans of Water, Air, and Ether, new edition, London: Trübner & Co., […], →OCLC, page 62:

soliton

(mathematics, physics, obsolete) Synonym of soliton (“a self-reinforcing pulse or travelling wave caused by any non-linear effect”)


Mach number

(physics) The ratio of the speed of a body to that of sound in the surrounding medium.


Mach

Mach (countable and uncountable, plural Machs)

From Czech Mach, Slovak Mach, Polish Mach and related languages, from pet forms produced by truncation of personal names beginning with Ma- and the addition of the Slavic suffix -ch. Less commonly, a respelling of Hungarian Mács. In some cases, from Vietnamese or Cambodian.

The 1992 review concluded that Machs are generally less satisfied with their jobs.

2013, Mark R. Leary, Rick H. Hoyle, Handbook of Individual Differences in Social Behavior, page 97:

(informal, countable) Short for Machiavellian.


transparency

transparency (countable and uncountable, plural transparencies)

Borrowed from Medieval Latin trānspārentia.

bor+

(signal processing) Sufficient accuracy to make the compressed result perceptually indistinguishable from the uncompressed input.


isotropic

From iso- + -tropic, from Ancient Greek ἴσος (ísos, “equal”) + τροπικός (tropikós, “of or pertaining to a turn or change; or the solstice; or a trope or figure; tropic; tropical; etc.”).

مُتَمَاثِل المَنَاحِي

having properties which are equivalent in all directions

(mathematics) Having the same components in all rotated coordinate systems


infinitesimal

en-adj

infinitesimal (comparative more infinitesimal, superlative most infinitesimal)

more infinitesimal (comparative)
most infinitesimal (superlative)

Learned borrowing from Latin *infinitesimus. Displaced earlier coordinate term fluxion.

lbor

Do you ever get the feeling that you are but an infinitesimal speck, swallowed by the vastness of the universe and beyond?

"You will conceive a bunch of grapes," said he, "which are covered by some infinitesimal but noxious bacillus."

1913, Arthur Conan Doyle, “(please specify the page)”, in The Poison Belt […], London; New York, N.Y.: Hodder and Stoughton, →OCLC:

Then you could say that the doorway exploded. But the particular verb doesn't do the action justice. Rather, it shattered into infinitesimal pieces.

2001, Eoin Colfer, Artemis Fowl, page 221:

Incalculably, exceedingly, or immeasurably minute; vanishingly small.

(mathematics) Of or pertaining to values that approach zero as a limit.

клонящ към нула

mathematics: pertaining to values that approach zero


infinitesimal

(mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).


anisotropic

en-adj

anisotropic (comparative more anisotropic, superlative most anisotropic)

more anisotropic (comparative)
most anisotropic (superlative)

The crystal has an anisotropic structure, as it is stronger along its length than laterally.

The obtained low and anisotropic thermal conductivity, and feasibility of synthesis, in addition to other reports on high electron mobility, make arsenene a promising material for a variety of applications, including thermal management and thermoelectric devices..

2015, M. Zeraati, S. M. Vaez Allaei, I. Abdolhosseini Sarsari, M. Pourfath, D. Donadio, “Highly Anistoropic Thermal Conductivity of Arsenene: An ab initio Study”, in arXiv:

(physics, mathematics) Having properties that differ according to the direction of measurement; exhibiting anisotropy.


isotropy

en-noun

isotropy (countable and uncountable, plural isotropies)

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

down this road, as they watched, came a wagon, then a couple of riders, then a coach and another wagon, in daylight which slowly lost its stark isotropy and was flowed into by clouds and chimney smoke and even episodes of weather

2006, Thomas Pynchon, Against the Day, Vintage, published 2007, page 478:

(geometry, physics) The property of being identical, or having the same physical properties, in all directions.


extrapolation

extrapolation (countable and uncountable, plural extrapolations)

(mathematics) A calculation of an estimate of the value of some function outside the range of known values.


Laplace

en-proper noun

Laplace (countable and uncountable, plural Laplaces)

(countable) A surname from French, famously held by:

(mathematics) Pierre-Simon Laplace, French mathematician 1749-1827, used attributively in the names of various mathematical concepts named after him (see "Derived terms" below)


slop

en-noun

slop (countable and uncountable, plural slops)

Probably from Middle English *sloppe (attested in plural form sloppes), representing Old English *sloppe (attested in cūsloppe), related to slip.

2023 September 21, Kyle Barr, “YouTube Announces New Tools to Flood Its Platform With AI-Generated Slop”, in Gizmodo, retrieved 2024-05-08

His post describes a sense of unease, paranoia and loneliness, expressing deep disappointment at the state of the modern internet. He suggests that AI has successfully drowned out the majority of online human activity, reshaping the internet into a more controlled, algorithmic form that exists only to sell products and ideas.

2024 January 16, Dani Di Placido, “The Dead Internet Theory, Explained”, in Forbes.com, retrieved 2024-05-08:

Almost all of the AI-generated slop online is peddled for clicks on social media, not published by major news outlets. These publications still get tripped up, of course, but it's rare.

2024 April 4, Kim Komando, “Don't be fooled by deepfake videos and photos this election cycle. Here's how to spot AI”, in USA Today, retrieved 2024-05-08:

Watching in real time as "slop" becomes a term of art. the way that "spam" became the term for unwanted emails, "slop" is going in the dictionary as the term for unwanted AI generated content

“Society needs concise ways to talk about modern A.I. — both the positives and the negatives,” he said. “‘Ignore that email, it’s spam,’ and ‘Ignore that article, it’s slop,’ are both useful lessons.”

2024 June 11, Benjamin Hoffman, quoting Simon Willison, “First Came ‘Spam.’ Now, With A.I., We’ve Got ‘Slop’”, in The New York Times, New York, N.Y.: The New York Times Company, →ISSN, →OCLC, archived from the original on 2024-06-11:

In many ways, political slop is a logical end point for these image generators, which seem most useful for people trying to make a quick buck.

2024 August 21, Charlie Warzel, “The MAGA Aesthetic Is AI Slop”, in The Atlantic:

“Coca-Cola just put out an ad and ruined Christmas,” Dylan Pearce, one of the campaign’s many critics, said on TikTok, adding, “To put out slop like this just ruins the Christmas spirit.”

2024 November 20, Alex Vadukul, “Coca-Cola’s Holiday Ads Trade the ‘Real Thing’ for Generative A.I.”, in The New York Times, New York, N.Y.: The New York Times Company, →ISSN, →OCLC:

artificial intelligence
artificial intelligence

generative artificial intelligence
generative artificial intelligence

(artificial intelligence, derogatory) Junk output from generative artificial intelligence published on the Internet in large quantities, posing as human-made content.


Laplace distribution

exponential distribution
exponential distribution

(statistics) A probability distribution consisting of two exponential distributions, one positive and one negative.


probability distribution

probability distribution (plural probability distributions)

(statistics) A distribution of all possible values of a random variable together with an indication of their probabilities.


exponential distribution

exponential distribution (plural exponential distributions)

The exponential distribution is a basic distribution for constructing a number of other distributions. For example, the gamma distribution is obtained from the distribution of the sum of random variables where each variable follows an exponential distribution.

1998, Vijay Singh, Entropy-Based Parameter Estimation in Hydrology, Kluwer Academic, page 49:

In addition, PH distributions provide a simple framework to demonstrate how one can extend many simple results on exponential distributions to more complex models without losing computational tractability.

1999, G. Latouche, V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, Society for Industrial and Applied Mathematics, page 33:

The exponential distribution was introduced briefly in Chapter 3 in connection with the Poisson discrete probability distribution function. There it was shown that if the number of failures in a given time period t was Poisson distributed, then the time to failure is distributed as an exponential distribution.

2012, Kenneth S. Stephens, Reliability Data Analysis with Excel and Minitab, ASQ Quality Press, page 145:

(statistics) Any of a class of continuous probability distributions used to model the time between events that occur independently at a constant average rate.


Laplace plane

(mathematics, astronomy) The mean plane occupied by the orbit of a satellite during a precession cycle; the plane normal to the orbital precession pole of the satellite.


rotation

rotation (countable and uncountable, plural rotations)

/ɹoʊˈteɪʃən/

Borrowed from Latin rotatiō. By surface analysis, rotate + -ion.

The function mapping (x,y) to (−y,x) is a rotation.

(mathematics, geometry) An operation on a metric space that is a continuous isometry and fixes at least one point.


coordinate system

coordinate system (plural coordinate systems)

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

1992, D. H. Maling, Coordinate Systems and Map Projections, 2nd Edition, Pergamon Press, page 27,
In this chapter we review some of the fundamental ideas about the plane coordinate systems which are used in surveying and mapping, both from the viewpoint of studying the mathematics of map projections and the practical tasks which arise in cartography.

Note that the orientation of Squire's coordinate system relative to the physical coordinate system is changing as a function of wavenumbervector.

2003, Vejapong Juttijudata, Proper Orthogonal Decomposition in Squire's Coordinate System and Its Low-dimensional Model of Channel Turbulence, Cornell University, page 22:

In Chapter 1 the choice of the origin and orientation of the analysis Cartesian coordinate system was made arbitrarily.[…]Note that nothing was said about the origins of the above two Cartesian coordinate systems.

2008, Bruce K. Donaldson, Analysis of Aircraft Structures, 2nd edition, Cambridge University Press, page 38:

(geometry, mathematical analysis) A method of representing the position of any individual point in a space of given dimensionality as a tuple of numerical coordinates.

نِظَامُ إِحْدَاثِيَّاتٍ

method of representing points in a space


Laplace transform

Laplace transform (plural Laplace transforms)

Named after French polymath Pierre-Simon Laplace.

named-after

F(s)=∫₀ ᪲f(t)e⁻ˢᵗ,dt.

(mathematics) an integral transform of positive real function f(t) to a complex function F(s); given by:


Laplace operator

en-noun

Laplace operator (plural Laplace operators)

1975, Various translators, V. Ja. Sikjrjavyĭ, A Quasidifferentiation Operator and Boundary Value Problems Connected With It, V. I. Averbvh, M. S. Birman, A. A. Blahin (editors), Transactions of the Moscow Mathematical Society for the Year 1972, Volume 27, [ТРУДЫ МОСКОВКОГО МАТЕМАҬИЧЕСКОГО ОБЩЕСТВА ТОМ 27 (1972)], American Mathematical Society, page 202,
The first notion of a Laplace operator for functionals on a Hilbert space was introduced by Levy in [l], and the idea was developed further in [2]. Levy's results depended on the posthumous work of Gateaux [3] in which the Dirichlet problem in Hilbert space was considered (without any concise definition of the Laplace operator).

Nevertheless, a systematic analysis of heat semigroups for Laplace operators on metric graphs is still missing.[…]Below we will prove an upper bound on the number of negative eigenvalues (Theorem 3.7) and a lower bound on the spectrum of Laplace operators (Theorem 3.10).

2006, Vadim Kostrykin, Robert Schrader, “Laplacians on Metric Graphs: Eigenvalues, Resolvents, and Semigroups”, in Gregory Berkolaiko, Robert Carlson, Stephen A. Fulling, Peter Kuchment, editors, Quantum Graphs and Their Applications: Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference, American Mathematical Society, page 201:

There are lots of approaches to get rational approximation of fractional order Laplace operator.[…]The rational function approximation gives direction to realize this fractional order Laplace operator in circuit impedance and admittance forms. This section gives insight into simple method of approximating the fractional Laplace operator.

2008, Shantanu Das, Functional Fractional Calculus for System Identification and Controls, Springer, page 153:

differential operator
differential operator

(mathematics, physics) A differential operator,denoted ∆ and defined on ℝⁿ as Δ=∑ᵢ₌₁ⁿ(∂²)/(∂x_i²), used in the modeling of wave propagation, heat flow and many other applications.

Laplace'i operaator

mathematics, physics: differential operator used in modeling of wave propagation, heat flow and many other applications


quilate

From Spanish and Portuguese quilate, from Arabic قِيرَاط (qīrāṭ, “carat”), from Ancient Greek κεράτιον (kerátion, “hornlet, carob seed”). Doublet of carat and ceratium.

der

(historical) Synonym of carat in historical Iberian contexts.


uneven

en-adj

uneven (comparative more uneven, superlative most uneven)

more uneven (comparative)
most uneven (superlative)

From Middle English uneven, from Old English unefen (“unequal, unlike, dissimilar, diverse, irregular”), equivalent to un- + even. Cognate with Dutch oneven (“unequal, uneven, odd”), German uneben (“uneven, rough, irregular, bumpy”).


adjoin

en-verb

adjoin (third-person singular simple present adjoins, present participle adjoining, simple past and past participle adjoined)

adjoins (present singular third-person)
adjoining (participle present)
adjoined (participle past)
adjoined (past)

From Anglo-Norman adjoindre, from Latin adiungō.

The ring adjunction #92;mathbb#123;Q#125;#91;#92;sqrt#123;2#125;#93; can be obtained from #92;mathbb#123;Q#125; by adjoining #92;sqrt#123;2#125; to #92;mathbb#123;Q#125;.

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;.

(transitive, mathematics, chiefly algebra and number theory) To extend an algebraic object (e.g. a field, a ring, etc.) by adding to it an element not belonging to it and then ensuring closure, for example by also adding all finite power series of the element.

adjoindre

mathematics: to add (an element) to a structure


quintal

Late Middle English, from Anglo-Norman quintal, from Middle French quintal, from Old French and Medieval Latin quintale and quintallus (“various medieval hundredweights”), from Arabic قِنْطَار (qinṭār, “100 rottols”), from Classical Syriac ܩܰܢܛܺܝܪܳܐ (qanṭīrā) and ܩܰܢܛܺܝܢܳܪܳܐ (qanṭīnārā), from Byzantine Greek κεντηνάριον (kentēnárion), from Latin centēnārium (“100 Roman pounds”), from the neuter of centēnārius (“having 100 things”). Use for various non-English units, borrowed from French quintal, Spanish quintal, Portuguese quintal, etc. The apparent relation to quint- (“five, fivefold”) and -al (forming adjectives) is accidental, although it possibly influenced the eventual spelling of the term. Doublet of centenary and kantar.

der

In one import license alone, the merchant in question was instructed to bring in 13,000 quintals of alum, which, snapped up by industries in England and the Low Countries, would yield the king a cool £8,666 13s 4d.

2011, Thomas Penn, Winter King, Penguin, published 2012, page 204:

(historical) Synonym of hundredweight, 100 or 112 English or American pounds.


forgetful

en-adj

forgetful (comparative more forgetful, superlative most forgetful)

more forgetful (comparative)
most forgetful (superlative)

From Middle English *forgetful, *forȝetful (suggested by derivative forgetfulnesse, forȝetfulnesse (“forgetfulness”)), equivalent to forget + -ful.

a forgetful mapping; a forgetful functor

(mathematics) Dropping some of the input's structure or properties before producing an output.


subtract

en-verb

subtract (third-person singular simple present subtracts, present participle subtracting, simple past and past participle subtracted)

subtracts (present singular third-person)
subtracting (participle present)
subtracted (participle past)
subtracted (past)

Borrowed from Latin subtractus, perfect passive participle of subtrahō (“I draw from beneath; withdraw, remove”); from sub (“under”) + trahō (“I draw, pull, drag”).

If you subtract the $100 for gas from the total cost, it was a fairly inexpensive trip.

(transitive, arithmetic) To remove or reduce; especially to reduce a quantity or number


dihedral

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(mathematics) An angle between two plane surfaces


dihedral

dihedral angle

(mathematics) Consisting of, relating to or contained between two plane surfaces.


astroid

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

From Ancient Greek ἄστρον (ástron, “a star”) + εἶδος (eîdos, “form, likeness”).

(geometry) A hypocycloid with four cusps.


hypocycloid

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

From hypo- (“below or inside”) + cycloid.

(geometry) The locus of a point on the circumference of a circle that rolls without slipping inside the circumference of another circle.


cycloid

In the firſt Courſe there was a Shoulder of Mutton, cut into an Æquilateral Triangle, a Piece of Beef into a Rhomboides, and a Pudding into a Cycloid.

1726 October 28, [Jonathan Swift], “The Humours and Dispositions of the Laputians Described. […]”, in Travels into Several Remote Nations of the World. […] [Gulliver’s Travels], volume II, London: […] Benj[amin] Motte, […], →OCLC, part III (A Voyage to Laputa, Balnibarbi, Glubbdubdribb, Luggnagg, and Japan), page 20:

(geometry) The locus of a point on the circumference of a circle that rolls without slipping on a fixed straight line.

cicloide

geometry: locus of a point on the circumference of a rolling circle


epicycloid

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From epi- (“above or outside”) + cycloid.

(geometry) The locus of a point on the circumference of a circle that rolls without slipping on the circumference of another circle.


abs

(mathematics) Initialism of absolute value function.


partition

en-noun

partition (countable and uncountable, plural partitions)

/pɑɹˈtɪ.ʃən/

/pɑɹˈtɪ.ʃɪn/

Recorded c.1430, "division into shares, distinction," from Middle English particioun, from Old French particion (modern partition), from Latin partitio, partitionem (“division, portion”), from partitus, the past participle of partire (“to split (up), part(ition)”).

der

(mathematics) An approach to division in which one asks what the size of each part is, rather than (as in quotition) how many parts there are.

(set theory) A collection of non-empty, disjoint subsets of a set whose union is the set itself (i.e. all elements of the set are contained in exactly one of the subsets).


deviate

From Late Latin deviatus, past participle of deviare, from the phrase de via.

It will be noted that for a deviate x = 1.5, the ordinate z will have the value .130 […]

1928, Karl J. Holzinger, Statistical Methods for Students in Education:

This difference is called a deviate. When a deviate is divided by its SD a, it is called a relative deviate or a standard deviate.

2001, Sanjeev B. Sarmukaddam, Indrayan Indrayan, Abhaya Indrayan, Medical Biostatistics:

This is a deviate so the appropriate function is qt. We need to supply it with the probability (in this case p = 0.975) and the degrees of freedom...

2005, Michael J. Crawley, Statistics: An Introduction Using R:

(statistics) A value equal to the difference between a measured variable factor and a fixed or algorithmic reference value.


astromathematics

(mathematics) The branches of mathematics used in the study of astronomy, astrophysics and cosmology.


trident

PIE word
 *tréyes
From Latin tridēns, from tri- (“three”) + dēns (“tooth”).

(geometry) A curve of third order of the form:


escape velocity

en-noun

escape velocity (plural escape velocities)

The gravitational force exerted by a planet determines its surface gravity and escape velocity.

1996, Thomas Arny, Explorations: An Introduction to Astronomy, McGraw-Hill Science, page 74:

(astrophysics) The minimum speed needed to escape the gravitational field of a planet or other body.


indirect

en-adj

indirect (comparative more indirect, superlative most indirect)

more indirect (comparative)
most indirect (superlative)

/ˌɪndɪˈɹɛkt/

/ˌɪndəˈɹɛkt/

From Middle French indirect, from Late Latin indirectus.

law of the excluded middle
law of the excluded middle

(mathematics, logic, of a proof) Employing argument by contradiction; making use the law of the excluded middle; arguing via the contrapositive.


residual

/ɹɪˈzɪd͡ʒ.ʊəl/

/ɹɪˈzɪd͡ʒ.əl/

/ɹɪˈzɪd͡ʒ.ə.wəl/

/ɹɪˈzɪd͡ʒ.wəl/

/ɹɪˈzɪd͡ʒ.əl/

Recorded since 1570. From residue, itself borrowed during the Middle English period from Old French residu (Modern French résidu), from Latin residuum (“a remainder”), the neuter inflection of residuus (“remaining, left over”), perfect participle of resideō (“to remain behind”), from re- (“back, again”) + sedeō (“to sit, to reside”).

(statistics) The difference between the observed value and the estimated value of the quantity of interest.


hypersurface

(mathematics) A n-dimensional surface in a space (often a Euclidean space) of dimension n+1


companion

From Middle English companion, from Old French compaignon (“companion”) (modern French compagnon), from Late Latin compāniōn- (nominative singular compāniō, whence French copain), from com- + pānis (literally, with + bread), a word first attested in the Frankish Lex Salica as a calque of a Germanic word, probably Frankish *galaibo, *gahlaibō (“messmate”, literally “with-bread”), from Proto-Germanic *gahlaibô. Compare also Old High German galeipo (“messmate”) and Gothic 𐌲𐌰𐌷𐌻𐌰𐌹𐌱𐌰 (gahlaiba, “messmate”); and, for the semantics, compare Old Armenian ընկեր (ənker, “friend”, literally “messmate”). More at co-, loaf. Displaced native Old English ġefēra (literally “fellow traveler”). Doublet of company. Compare mate.

noncog

(topology) A knot in whose neighborhood another, specified knot meets every meridian disk.


pigpen

[ˈpʰɪɡˌpʰɛn]


rationalization

en-noun

rationalization (countable and uncountable, plural rationalizations)

First attested in 1831. From French rationalisation, equivalent to rational + -ization or rationalize + -ation.

(mathematics) The simplification of an expression without changing its value.

sieventäminen

simplification of a mathematical expression


reverse Polish notation

Back in my day, we had reverse Polish notation calculators: You had to write "2 4 3 * +" instead of "2 + 4 * 3".

(arithmetic) An arithmetic notation in which numbers precede the operators to be applied to them.


codimension

(mathematics) The difference between the dimension of a space and the dimension of a given subspace of the first one.


hallucinate

en-verb

hallucinate (third-person singular simple present hallucinates, present participle hallucinating, simple past and past participle hallucinated)

hallucinates (present singular third-person)
hallucinating (participle present)
hallucinated (participle past)
hallucinated (past)

From Latin hallūcinātus, alternative form of alūcinātus, from alūcināri (to dream).

In case you were wondering, the yahoo url above doesn’t actually exist, the model just hallucinated it.

2015 May 21, Andrej Karpathy, “The Unreasonable Effectiveness of Recurrent Neural Networks”, in Andrej Karpathy blog:

Despite maintaining plausible general linguistic capabilities, dialogue models are still unable to fully discern facts and may instead hallucinate factually invalid information.

2021 September 14, Nouha Dziri, Andrea Madotto, Osmar Zaiane, Avishek Joey Bose, “Neural Path Hunter: Reducing Hallucination in Dialogue Systems via Path Grounding”, in arXiv:2104.08455 [cs], →DOI:

(artificial intelligence, of a model) To produce information that is not supported by the model's training data.


denier

From Old French denier, from Latin dēnārius. Doublet of denar, denarius, dinar, diner, dinero, and dinheiro.

doublet

Upstairs she rummaged through her chest of drawers, finally unearthing an unopened pack of ten denier barely blacks.

A unit of linear density which indicates the fineness of fiber or yarn, equal to one gram per 9000 meters, used especially to measure or indicate the fineness of hosiery. Originally equal to the weight of a denier coin per 9600 aunes.


icosasphere

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(geometry) A geometric figure with twenty or more triangular faces producing a semi-spherical solid.


immersion

en-noun

immersion (countable and uncountable, plural immersions)

From late Middle English, borrowed from Late Latin immersiō, immersiōnem (“dipping”).

потапяне

the act of immersing or the condition of being immersed

Note that every embedding is an immersion, but the converse is not true. For an immersion to be an embedding, it must be one-to-one and the inverse must be continuous.

2006, William F. Basener, Topology and Its Applications, John Wiley & Sons, →ISBN, page 82:

(mathematics) A smooth map whose differential is everywhere injective, related to the mathematical concept of an embedding.


electron volt

electron volts (plural)
eV (abbreviation)

To get a feel for the size, the energy required to completely liberate an electron from the ground state of a hydrogen atom is 13.6 electron volts.

2011, Brian Cox, Jeff Forshaw, The Quantum Universe, Allen Lane, page 158n:

potential difference
potential difference

(physics) A unit for measuring the energy of subatomic particles; the energy equal to that attained by an electron moving through a potential difference of one volt. Equivalent to 1.6022 × 10⁻¹⁹ joules.

elektron volt

a unit for measuring the energy of subatomic particles


twiddle

en-verb

twiddle (third-person singular simple present twiddles, present participle twiddling, simple past and past participle twiddled)

twiddles (present singular third-person)
twiddling (participle present)
twiddled (participle past)
twiddled (past)

Unknown. Perhaps a blend of twirl, twist, or twitch + fiddle.

blend

equivalence relation
equivalence relation

(transitive, mathematics) To be in an equivalence relation with.


Lorentz group

Named after Hendrik Antoon Lorentz (1853–1928), A Dutch physicist.

Lorentz transformation
Lorentz transformation

(physics, mathematics) The group of all Lorentz transformations in spacetime.


Lorentz transformation

en-noun

Lorentz transformation (plural Lorentz transformations)

Named after the Dutch physicist Hendrik Antoon Lorentz (1853–1928).

(mathematics, relativity) A transformation relating the spacetime coordinates of one frame of reference to another in special relativity.

Hendrik Antoon Lorentz
Lorentz transformation


equivalence

equivalence (countable and uncountable, plural equivalences)

From French équivalence, from Medieval Latin aequivalentia.

(countable, mathematics) An equivalence relation; ≡; ~

(mathematics) A Boolean operation that is TRUE when both input variables are TRUE or both input variables are FALSE, but otherwise FALSE; the XNOR function.

(geometry) A number in intersection theory. A positive-dimensional variety sometimes behaves formally as if it were a finite number of points; this number is its equivalence.


lozenge

From Middle English losenge, from Old French losenge (“rhombus”), of uncertain origin. See the Old French for more.

Wherein the decussis is made within a longilaterall square, with opposite angles, acute and obtuse at the intersection; and so upon progression making a Rhombus or Lozenge figuration [...].

1658, Sir Thomas Browne, The Garden of Cyrus, Folio Society, published 2007, page 167:

How the junior partner of Hobbs and Dobbs leads her smiling to the carriage with the lozenge upon it, and the fat wheezy coachman!

1848, William Makepeace Thackeray, chapter 9, in Vani8ty Fair:

The floor is constructed from marble lozenges and triangles of every imaginable hue: yellow and pink and all manner of mottled and blotched shades, framed in white.

2004, Richard Fortey, The Earth, Folio Society, published 2011, page 14:

(shapes, heraldry) A thin rhombus, having two acute and two obtuse angles.


constructivism

constructivism (countable and uncountable, plural constructivisms)

(mathematics) A philosophy that asserts the need to construct a mathematical object to prove it exists.


subcover

The open intervals cover the real numbers; the open intervals of the form (x, x+1) are a subcover.

(topology) A cover which is a subset of another cover.


percentage

percentage (countable and uncountable, plural percentages)

From percent, from Latin per centum (“for every hundred”), + -age (suffix indicating a rate).

She gets a percentage for every vacuum cleaner sold.

A share of the sales, profits, gross margin or similar.


kilocalorie

A non-SI unit of energy equal to 1,000 calories, used (now rare) in chemistry or physics; equal to 1 calorie as used in nutrition. Symbol kcal.


polymorphism

polymorphism (countable and uncountable, plural polymorphisms)

պոլիմորֆիզմ

computer science: feature of object-oriented programming

polimorfisme

crystallography: ability of a material to exist in more than one form

(mathematics, type theory) The property of certain typed formal systems of allowing for the use of type variables and binders/quantifiers over those type variables; likewise, the property of certain expressions (within such typed formal systems) of making use of at least one such typed variable.


serpentine

From Middle English serpentine, from Old French serpentin, from Latin serpentīnus, from serpēns (“serpent”), equivalent to serpent + -ine.

(mathematics) Any of several related cubic curves; anguinea


entrain

en-verb

entrain (third-person singular simple present entrains, present participle entraining, simple past and past participle entrained)

entrains (present singular third-person)
entraining (participle present)
entrained (participle past)
entrained (past)

First attested in c. 1560. From French entraîner.

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

(mathematics) To set up or propagate a signal, such as an oscillation.


planar

en-adj

planar (comparative more planar, superlative most planar)

more planar (comparative)
most planar (superlative)

From Late Latin plānārius (“relating to a plane”), derived from Latin plānus (“flat”, “level”), equivalent to plane + -ar, ultimately from Proto-Indo-European *pleh₂- (“flat”).

bor

A complete graph with more than four nodes is never planar.

(graph theory, of a graph) Able to be embedded in the plane with no edges intersecting.


dimensional

en-adj

dimensional (comparative more dimensional, superlative most dimensional)

more dimensional (comparative)
most dimensional (superlative)

What is the meaning of an n-dimensional space when n is greater than three, and what purposes can it serve?

1996, Richard Courant with Herbert Robbins and Ian Stewart, What is Mathematics?: An Elementary Approach to Ideas and Methods, page 227:

(comparable) Having dimension or dimensions; three-dimensional.

(mathematics) Appended to cardinal numbers or algebraic symbols to form adjectives meaning "having the stated number of dimensions".


pood

From Russian пуд (pud). Doublet of pound.

A Russian unit of mass used for kettlebells, now rounded off to 16 kg (about 35.274 pounds).


completion

en-noun

completion (countable and uncountable, plural completions)

termination

antonym(s) of “making complete, accomplishment”

Borrowed from Latin completio, completionem, from complere (“to fill up, complete”); comparable to English complete + -ion.

(mathematics) The act of making a metric space complete by adding points.

完备化

mathematics: act of making a metric space complete by adding points

(mathematics) The space resulting from such an act.

vervollediging

mathematics: space resulting from such an act


nanometre

A nanometre is one billionth of a metre. A single atom is between a tenth to half a nanometre across; a million or more of them stacked on top of one another would equal the thickness of a piece of paper.

2010 September 2, Thomas Barfield, “Get ready for a world of nanotechnology”, in The Guardian:

The resulting nanopasta is 372 nanometres thick, or about the same size as a measles virus.

2024 November 25, Ellen Phiddian, “There's nanna's pasta, and then there's nanopasta”, in Cosmos, Adelaide, S.A.: CSIRO Publishing, →ISSN, →OCLC, archived from the original on 2024-11-25:

An SI subunit of length equal to 10⁻⁹ metres. Symbol: nm


nanometer

[ˈnænəˌmiɾɚ]

[ˈnɛənəˌmiɾɚ]

We live our lives in three dimensions for our threescore and ten allotted years. Yet every branch of contemporary science, from statistics to cosmology, alludes to processes that operate on scales outside of human experience: the millisecond and the nanometer, the eon and the light-year.

2012 January, Robert L. Dorit, “Rereading Darwin”, in American Scientist, volume 100, number 1, archived from the original on 2012-11-14, page 23:

Images also indicated that gel porosity was in the nanometer range, similar to previously characterized hyperporous beads generated using the same sol-gel methods, which limits mobility of encapsulated cells (Fig 2B ) [23 ].

2016 January 14, “Toward Bioremediation of Methylmercury Using Silica Encapsulated Escherichia coli Harboring the mer Operon”, in PLOS ONE, →DOI:

It is noteworthy that biological phenomena occur at scales ranging from nanometers to megameters, and from nanoseconds to gigaannums.

2017, Ashok K. Goel et al., “Is Biologically Inspired Design Domain Independent?”, in John S. Gero, editor, Design Computing and Cognition ’16, →ISBN, page 157:


ardeb

From Arabic إِرْدَبّ (ʔirdabb), spoken in Egyptian Arabic something like /ar.ˈdæbb/.

1 ardeb of wheat is about 150 kg

1 ardeb of barley is about 120 kg

A Middle Eastern unit of volume used for agricultural crops.

ardeb

a Middle Eastern unit of volume used for agricultural crops


Abelian

Ex. 2. Show by §§ 187, 188 that there can be no transitive Abelian group of prime degree other than the cyclic group, and that there is no irreducible Abelian equation of prime degree other than the cyclic equation.

1904, Florian Cajori, An Introduction to the Modern Theory of Equations, The MacMillan Company, page 214:

All irreducible Abelian equations of the tenth order belong to the cyclical group of order ten,[…].

1914, Charles Gustave Paul Kuschke, The Abelian Equations of the Tenth Degree Irreducible in a Given Domain of Rationality, University of California Press, page 118:

In this chapter "group" means torsion free Abelian group. The "bible" of Abelian group theory is the two volume work of Fuchs [11].

2004, Friedrich Kasch, Adolf Mader, Rings, Modules, and the Total, Springer (Birkhäuser), page 101:

(mathematics, group theory, dated) Alternative letter-case form of abelian


Blowfish

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(computing) A symmetric block cipher encryption algorithm used in modern cryptographic software, designed by Bruce Schneier in 1993.


Bob

Probably from a medieval hypocorism of Rob.

The key that Alice and Bob are to share cannot be transmitted in the clear. Either it must be enciphered when sent, or Alice and Bob must derive it without an exhange of data from which the key can be derived.

2003, Matt Bishop, Computer Security: Art and Science, Addison-Wesley Professional, →ISBN, page 247:

(cryptography, physics) The person or system receiving a message or signal from a source conventionally known as Alice.


Doge

(informal, cryptocurrencies) Clipping of Dogecoin (“a unit of the cyptocurrency”).


Ether

Coordinate term: gas

After more than 30 bids, the auction ended at 12:32 p.m. Eastern time, with a winning bid of 350 Ether, or about $560,000.

2021 March 26, Kevin Roose, “Why Did Someone Pay $560,000 for a Picture of My Column?”, in The New York Times, →ISSN:

(cryptocurrencies) A unit of the Ethereum digital currency, ETH.


Eve

(cryptography) A conventional name for an agent attempting to intercept a message sent by Alice that is intended for Bob.


L

The ordinal number twelfth, derived from this letter of the English alphabet, called el and written in the Latin script.


Life

Basically, I'm looking for a fast (the fastest?) way of updating grids, where each cell has to look at an arbitrary number of its neighbors. I've seen some fast life-programs, but often they took advantage of particular quirks of the rules of Life.

1988 January 26, David Hiebeler, “Fast way to update grids”, in comp.theory.cell-automata (Usenet):

Is there a known 3D totalistic or semi-totalistic automaton (Life is the latter sort - state at time t+1 depends on state at time t and count of neighbours) which exhibits the same sort of behaviour as Life (that is, a reasonable range of naturally-occuring^([sic]) still lives and short-period oscillators)?

1999 May 13, Thomas Womack, “3D automata with Life-style objects”, in comp.theory.cell-automata (Usenet):

Maybe the RolfLife algorithm could be of value to someone implementing life i.e. in the vertex shader of a (DirectX 9) graphics card, where few lines of code and no LUT are favoured.

2003 February 20, Rolf Wilms, “Fast implementation of core algorithm for Conway's Game of Life”, in comp.theory.cell-automata (Usenet):

(cellular automata) Conway's Game of Life.


M

M (countable and uncountable, plural Ms)


Mallet

Cryptographic scenarios use archetypal characters with standard names chosen to remember their role: Mallet was derived from "malicious" and "man-in-the-middle attack", as well as the tool mallet.

Even if Alice and Bob's public keys are stored on a datavase, this attack will work. Mallet can intercept Alice's database inquiry, and substitute his own public key for Alice's. He can do the same to Bob.

1994, Bruce Schneier, Applied Cryptography, →ISBN, page 44:

(cryptography) The malicious party in examples of threat scenarios. See Alice and Bob.


Ob

(category theory) The set of objects of a category.


Poisson

After Siméon Denis Poisson (1781–1840), French mathematician.

Poisson distribution
Poisson distribution

Poisson distribution
Siméon Denis Poisson


S

From the first letter of set and of stage, two fundamental concepts of the theory.

S has no axiom of extensionality and identity is absent from the other S axioms.

(set theory) An axiomatic set theory, developed by logician George Boolos, in which several of the axioms of ZF are derivable as theorems.


Victor

From a Late Latin personal name Victor, borne by several saints, from victor (“conqueror”). Doublet of victor.

Coordinate term: Peggy

(cryptography) Placeholder name for the party that verifies a proof.


Z

Alternative form: Zed

Take that a step further for Millennials and Zs by crafting an e-mail subject header that does the same but with even fewer characters; […]

2017, Martha M. Ellis, Linda Garcia, Generation X Presidents Leading Community Colleges: New Challenges, New Leaders, Rowman & Littlefield, →ISBN, page 10:

The current progressive movement—and certainly the Millennials and Zs—understand that the Hyde Amendment is discriminatory […]

2020, Zerlina Maxwell, The End of White Politics: How to Heal Our Liberal Divide, New York, N.Y.: Hachette Books, →ISBN:

The current global pandemic is almost certainly a formative moment for younger Millennials and Zs as they navigate through similar challenges.

2022, Morgen Witzel, editor, Post-Pandemic Leadership: Exploring Solutions to a Crisis, Routledge, →ISBN:


uncia

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From Latin uncia (“various Roman units”). Doublet of ounce, inch, onça, onza, oka, ouguiya, and awqiyyah.

doublet

(pharmacy) Synonym of ounce, the English and American avoirdupois unit of mass.

ounce

(algebra, obsolete) A numerical coefficient in a binomial.


gd

(mathematics) Abbreviation of Gudermannian.


enclosing

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(geometry) Of a region, containing all points of a given set within its bounds.


einstein

From German ein Stein, "one stone", coined by scientists in recent decades, but with tongue-in-cheek tacit acknowledgment of the homonymy with einstein and Einstein; "a pun playing with the famous scientist's name and the German term "ein Stein" for "one stone".

In less poetic terms, an einstein is an “aperiodic monotile,” a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. (The term “einstein” comes from the German “ein stein,” or “one stone” — more loosely, “one tile” or “one shape.”)

2023 March 28, Siobhan Roberts, “Elusive ‘Einstein’ Solves a Longstanding Math Problem. And it all began with a hobbyist “messing about and experimenting with shapes””, in New York Times, retrieved 2023-03-28:

(mathematics, physics) A shape that can be repeated to cover a plane with a nonrepeating pattern.


MAC

en-noun

MAC (countable and uncountable, plural MACs)

message authentication code
w:message authentication code

(cryptography) Initialism of message authentication code.


hereditary

en-adj

hereditary (comparative more hereditary, superlative most hereditary)

more hereditary (comparative)
most hereditary (superlative)

/həˈɹɛdɪˌtɛɹi/

From Latin hērēditārius, from hērēditās (“inheritance”), from hērēs (“heir”).

(mathematics) Of a ring: such that all submodules of projective modules over the ring are also projective.


descend

en-verb

descend (third-person singular simple present descends, present participle descending, simple past and past participle descended)

descends (present singular third-person)
descending (participle present)
descended (participle past)
descended (past)
descend (infinitive)

PIE word
 *de
The verb is derived from Middle English descenden (“to move downwards, fall, descend; to slope downwards; to go from a better to a worse condition, decline, degenerate; to be a descendant, derive from (a source); etc.”), from Anglo-Norman descendere, descendre, and Old French descendere, descendre (“to move downwards, fall, descend; to slope downwards; to be a descendant, derive from (a source); etc.”) (modern French descendre), and from their etymon Latin dēscendere, the present active infinitive of dēscendō (“to come or go down, fall, descend; to slope downwards; to be a descendant; etc.”), from de- (prefix meaning ‘from; down from’) + scandō (“to ascend, climb; to clamber”) (from Proto-Indo-European *skend- (“to climb, scale; to dart; to jump”)).
The noun is derived from the verb.

laskea

to pass from a higher to a lower part of (something)

afgaan

to physically move or pass from a higher to a lower place or position

Indefinite numbers I ſuppoſe to be intermediate Numbers lying betvveen finite and infinite: For as vve do not deſcend from 1 to 0 at one Step, but muſt paſs through an infinite Series of Fractions, ½, ⅓, ¼, ¹⁄₅, &c.

1715, George Cheyne, “Of the Use of the Arithmetick of Infinites. Corollary I.”, in Philosophical Principles of Religion: Natural and Revealed: […] Philosophical Principles of Religion. Part II. […], London: […] George Strahan […], →OCLC, page 162:

Senses relating to moving from a higher to a lower position.

(mathematics) Of a sequence or series: to proceed from higher to lower values.

laskea

of a sequence or series: to proceed from higher to lower values


muckle

en-verb

muckle (third-person singular simple present muckles, present participle muckling, simple past and past participle muckled)

muckles (present singular third-person)
muckling (participle present)
muckled (participle past)
muckled (past)

From Middle English mukel, muchel, from the same source as (perhaps a variant of) mickle.

I told him all, / Both bad and good; / I bade him call — / He said he would: / I added much — the more I muckled, / The more that chuckling chummy chuckled!

1896, W.S. Gilbert, “The Grand Duke, or the Statutory Duel”, in The Complete Plays of Gilbert and Sullivan, published 1941:


arctangent

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the tangent function. Symbol: arctan, tan⁻¹


single-valued

(mathematics) Of a function, associating a unique value of its range with each value of its domain.


multivalued

The inverse sine function is multivalued unless it is restricted to a suitable range.

(mathematics) Of a function, associating one or more values of its range with each value of its domain.


arbitrate

arbitrate (third-person singular simple present arbitrates, present participle arbitrating, simple past and past participle arbitrated)

arbitrates (present singular third-person)
arbitrating (participle present)
arbitrated (participle past)
arbitrated (past)

/ˈɑːbɪtɹeɪt/

From Latin arbitratus, past participle of arbitrari (“to be a witness, act as umpire”), from arbiter (“umpire”); see arbiter.

We wish to show f is continuous. Arbitrate epsilon greater than zero...

(mathematics, rare) To assign an arbitrary value to, or otherwise determine arbitrarily.


dividend

From Middle French dividende, from Latin dividendum (“thing to be divided”), future passive participle of divido (“to divide”), by surface analysis, divide + -end.

uder

In "42 ÷ 3" the dividend is the 42.

(arithmetic) A number or expression that is to be divided by another.


divisor

divisor

In "42 ÷ 3" the divisor is the 3.

(arithmetic) In an expression involving division, the number by which another number is being divided.

An integer that divides another integer an integral number of times, the former being called a divisor of the latter.

(algebra, more generally) A ring element which can be multiplied (by some other ring element) to yield a third ring element, the first being called a divisor of the third. If the ring is noncommutative, then one specifies whether a divisor is left, right, or two-sided.

(mathematics, algebraic geometry) Any of several kinds of formal object associated to an algebraic variety, scheme, etc., which play a role similar to that of homology or cohomology groups in the study of topological spaces.

(in the study of Riemann surfaces) An element of the free abelian group on the points of the space.

(on a variety (or integral locally Noetherian scheme)) A Weil divisor: an element of the free abelian group on the codimension-1 subvarieties (or subschemes).

(on a variety (or integral Noetherian scheme)) A Cartier divisor; see Cartier divisors on Wikipedia.Wikipedia


quartile

From Middle French quartil, from Medieval Latin quartilus.

(statistics) Any of the three points that divide an ordered distribution into four parts, each containing a quarter of the population.

This school is ranked in the first quartile.

The Department for Transport's National Travel Survey shows that workers in the lowest income quartile are twice as likely to use public transport.

2021 July 28, Paul Clifton, “Network News: Confusion and dissent over face mask requirements: Reaction to the Guidance: British Safety Council”, in RAIL, number 936, page 6:

(statistics) Any one of the four groups so divided.


CSA

en-noun

CSA (countable and uncountable, plural CSAs)

Cartan subalgebra
Cartan subalgebra#English

(algebra, Lie theory) Initialism of Cartan subalgebra.

central simple algebra
central simple algebra#English

(algebra, ring theory) Initialism of central simple algebra.


inhabited

(mathematics, of a set) Containing at least one element.


smoot

(British, dialectal) A small opening built into a dry-stone wall to allow sheep (and hares) to pass through; a thirl.


latus rectum

latus rectum (plural latera recta or latus rectums)

latera recta (plural)
latus rectums (plural)

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

(geometry) The line drawn through a focus of a conic section parallel to the directrix and terminated both ways by the curve. It is the parameter of the principal axis.


life-size

Coordinate term: larger than life

Many consider the life-size painting of King Peter to be one of the artist's best works.

(of any representation, especially pictures, statues) The same size as the real thing.

especially pictures; statues; especially pictures; statues


cubewano

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

From Acronym of QB1. + -o.
Derived from QB1 ("cue bee one"), short for (15760) 1992 QB1, the first such object discovered

(astronomy) Any Kuiper belt object whose orbit is not determined by resonance with Neptune (orbit ~ 40-50 AU).


induction

induction (countable and uncountable, plural inductions)

Inherited from Middle English induction, from Old French induction, from Latin inductiō, from indūcō (“I lead”). By surface analysis, induct + -ion or induce + -tion.

(mathematics) A method of proof of a theorem by first proving it for a specific case (often an integer; usually 0 or 1) and showing that, if it is true for one case then it must be true for the next.


divisibility

divisibility (countable and uncountable, plural divisibilities)

combinability（state capable of being combined）

mergeability（state capable of being merged）

indivisibility（state incapable of being divided）

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

قَابِلِيَّةُ الْقِسْمَةِ

or, equivalently الْقَابِلِيَّةُ لِلْقِسْمَةِ f (al-qābiliyyatu lilqismati)

(arithmetic) The property of being divisible by a particular integer.


divisible

combinable

antonym(s) of “capable of being divided”

[dɪˈvɪzɪbəɫ]

PIE word
 *dwóh₁
From Middle English divisible, from Old French, from Late Latin divisibilis, from the verb Latin divido.

12 is divisible by 3.

(arithmetic) Of an integer, that, when divided by another integer, leaves no remainder.

делим

of an integer, that when divided leaves no remainder


duodecimal

6B4 is the duodecimal notation for the decimal number 1000.

(arithmetic) Of a number, expressed in base twelve.

дванадесетичен

expressed in a base-twelve number system


duodecimal

(arithmetic) A number system that uses twelve as its base.


octal

octal (countable and uncountable, plural octals)

(arithmetic, computing, uncountable) The number system that uses the eight digits 0, 1, 2, 3, 4, 5, 6, 7.

(arithmetic, computing, countable) A digit or value in the octal number system.


octal

(arithmetic, computing) Concerning numbers expressed in octal or mathematical calculations performed using octal.

八進制 /八进制

concerning numbers expressed in octal or mathematics calculations performed using octal


number system

(arithmetic) A set of numerals for representing numbers.


GP

GP (countable and uncountable, plural GPs or GP)

genetic programming
genetic programming#English

(uncountable, software, artificial intelligence) Initialism of genetic programming.


ansatz

In such cases, scientists often make an ansatz, an educated guess if you like, and then proceed to compute the consequences of the guess.

2011, Brian Cox, Jeff Forshaw, The Quantum World, Allen Lane, published 2011, page 12:

(mathematics) A mathematical assumption used to describe a certain phenomenon, posited in order to help provisionally solve an equation or other problem.

ansatz

a provisional mathematical assumption used to describe a certain phenomenon


spanker

beyond the broad white wing of the spanker sail

1839, Charlotte Elizabeth, Glimpses of the Past:

(nautical) A fore-and-aft gaff-rigged sail on the aft-most mast of a square-rigged vessel.

(dated, slang) Something very large, or larger than usual; a whopper.


padding

padding (countable and uncountable, plural paddings)

(military, cryptography) Extraneous text added to a message for the purpose of concealing its beginning, ending, or length.


equality

equality (usually uncountable, plural equalities)

Borrowed from Middle French equalité (modern French égalité), from Latin aequālitās, aequālitātem. Doublet of equity. By surface analysis, equal + -ity

(mathematics) The fact of being equal, of having the same value.

تَسَاوٍ

mathematics: fact of having the same value


tuple

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

From the ending of the words quintuple, sextuple; from Latin -plus.

(set theory) A finite sequence of terms.


quantization

quantization (countable and uncountable, plural quantizations)

(uncountable, signal processing) The process of approximating a continuous signal by a set of discrete symbols or integer values