medial

en-adj

medial (comparative more medial, superlative most medial)

more medial (comparative)
most medial (superlative)

LL-Q1860 (eng)-I learned some phrases-medial.wav

Borrowed from Latin mediālis (“middle”), from medius (“that is in the middle or midst”) + -ālis (“-al”, adjectival suffix).

среден

in or near the middle; not at either end

medial allegation

(mathematics) Of or pertaining to a mean or average.


micron

From French micron, from Ancient Greek μικρόν (mikrón), neuter of μικρός (mikrós, “small”).

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

2009, Jonathan Amos, (bbc.co.uk) Satellites weigh California water
As one spacecraft lurches and drags through the Earth's uneven gravity field, the second follows 210 km behind, measuring changes in their separation to the nearest micron (a thousandth of a millimetre).

(physics, metrology) The thousandth part of one millimeter; the millionth part of a meter.


mitre

From Middle English mytre, from Old French mitre, from Ancient Greek μίτρα (mítra, “headband, turban”). Its use in reference to a counterfeit coin derived from the bishop's mitre stamped upon it. Doublet of Mithras, Mithra, Mitra, and Mehr.

doublet

(geometry, rare) A square with one triangular quarter missing from the outside.


mod

en-noun

mod (countable and uncountable, plural mods)

(mathematics, programming) Abbreviation of modulus.


monad

From Latin monas (“unit”) (from Ancient Greek μονάς (monás), from μόνος (mónos), from Proto-Indo-European *men-) + -ad.

Coordinate term: comonad

(category theory) A monoid object in the category of endofunctors of a fixed category.


neuron

From New Latin, from Ancient Greek νεῦρον (neûron, “nerve”), doublet of nerve and sinew. By surface analysis, neuro- + -on.

artificial intelligence
artificial intelligence

(artificial intelligence) an artificial neuron (mathematical function serving as an essential unit of an artificial neural network)


nonce

Inherited from Middle English nonse, nones, a rebracketing of Middle English to þen anes, for þen anes (to/for the once (i.e., the one occasion or instance)), from the dative singular neuter of þe. The cryptography sense is commonly said to be a contraction of number used once, although this is probably incorrect.

gl

The protocol opens with A communicating in clear to AS his own claimed identity and the identity of the desired correspondent, B, together with A's nonce identifier for this transaction, I_(A1). ("Nonce" means "used only once.")

1978 December, Roger M. Needham, “Using Encryption for Authentication in Large Networks of Computers”, in Communications of the ACM, volume 21, number 12:

The information gained by the eavesdropper would permit a replay attack, but only with a request for the same document, and even that may be limited by the server's choice of nonce.

1999, Network Working Group, RFC 2617 – HTTP Authentication: Basic and Digest Access Authentication, The Internet Society, page 22

Both CCM and GCM require a unique nonce (N used once) value to maintain their privacy and authenticity goals.

2006, Tom St Denis, Cryptography for Developers, page 340:

The main idea with the challenge-response type of authentication protocol is that the challenge sent by the server is used only once (referred to as a cryptographic nonce, which means “number used once”).

2012, Steven Anson, Mastering Windows Network Forensics and Investigation:

(cryptography) A value constructed so as to be unique to a particular message in a stream, in order to prevent replay attacks.


octant

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

(geometry) The eighth part of a disc; a sector of 45 degrees; half a quadrant.


pica

en-noun

pica (countable and uncountable, plural picas)

From Medieval Latin pica (“pica: a service book”), possibly from Latin pīca (“magpie”) after the piebald appearance of the typeset page (cf. pie (“disordered type”)). The relation to the printer's measure is unclear, as no edition of the text in pica type is known. The French pica derives from English rather than vice versa.

der

I had been at Baldwin's before dinner in consequence of a letter from him which showed me that, by using a pica instead of an English letter in printing my book, I might comprise it within such a number of sheets as a guinea-volume should contain […].

1790, James Boswell, edited by Danziger & Brady, Boswell: The Great Biographer, Yale, published 1989, page 30:

(typography, printing, uncountable) A size of type between small pica and English, now standardized as 12-point.


pith

From pi (“constant representing the ratio of the circumference of a Euclidean circle to its diameter”) + -th (suffix forming ordinal numerals).

suffix

The pith root of pi is approximately 1.439…

(e^pi*i*i/2), or e^(-pi/2), which is the reciprocal of the square root of e to the pith power.

1998 June 21, Hbr…@my-dejanews.com, “For what x is x^x real?”, in alt.algebra.help (Usenet), message-ID <6mhv6n$13l$1@nnrp1.dejanews.com>:

That's nothing. I have an IMEI changer that will do all of the above and beat you off at the same time, while whistling the adaggio from Spartacus in Armenian and calculating pi to the pith power in swahili.

2000 August 9, alice, “IMEI Changer T-10”, in aus.comms.mobile (Usenet), message-ID <B5B6F806.53B5%alice@alice-didit.com>:

already, we know what is minus one from Euler: it is the I*pith power of e, such that ln(-1) = i*pi

2017 March 5, abu.ku…@gmail.com, “The non existence of p’th root of any prime number, for (p>2) prime”, in sci.math (Usenet), message-ID <cabe6746-8a13-44f0-9e95-30eec727654a@googlegroups.com>:

(mathematics) The ordinal form of the number pi (π; approximately 3.14159…).


pith

not only that, but your "radian" axis can be labelled as *being* in units of pis, as opposed to the redundancy of 0pi, pi/2, pi etc.; conversely, your circumferential measure can be rational (or units) and your radius can be transcendental (or piths .-)

1997 April 26, Brian Hutchings, “Trigonometric Functions”, in sci.math (Usenet), message-ID <1997Apr26.204554.24471@lafn.org>:

thought it was the two-sixths power of pi, and teh^([sic]) secondpower of six piths

2016 April 2, abu.ku…@gmail.com, “pi^2/6 and 6/pi^2”, in sci.math (Usenet), message-ID <d1d13d13-c4c0-43c3-b4cb-7911dcb24cc7@googlegroups.com>:

of course, although a pith is less than a third, hence pi is more than three, say, thirty-one tenths, but 22/7 is still less than pi, and that's a rather small gore

2017 January 13, thugst…@gmail.com, “Electron-positron annihilation”, in sci.physics (Usenet), message-ID <89a35ff8-1df1-4ab5-baf5-fdc605207710@googlegroups.com>:

(mathematics) One divided by pi, that is, 1/π (approximately 0.31831…).


radix

Learned borrowing from Latin rādīx (“a root”). Doublet of radish.

lbor

(mathematics) The number of distinct symbols used to represent numbers in a particular base, as ten for decimal.

ভেঁটি

mathematics: number of distinct symbols used to represent numbers


rotor

From an irregular shortening of rotator. Doublet of rota and ruote.

The following figure shows examples of the most versatile class of these oscillators. The first emulates the p10 shown above; the second has period 62 and a rotor of size 10.

1997 November 30, David Bell, “Day & Night - An Interesting Variant of Life (part 2/5)”, in comp.theory.cell-automata (Usenet):

The problem of determining the asymptotic colouring for a cyclic pattern from a given initial black and white pattern is completely solved. The analysis leads to the proposal of the distinction between primary and secondary rotor cells (i.e. a refinement of the classical stator-rotor distinction).

1998 March 18, Gunnar Johnsson, “Genetic aspects of the Game of Life.”, in comp.theory.cell-automata (Usenet):

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

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

(cellular automata) The set of cells within an oscillator that switch between being alive and dead over the course of the oscillator's period.


rutty

en-adj

rutty (comparative ruttier, superlative ruttiest)

ruttier (comparative)
ruttiest (superlative)

I am lying here stifling in the rutty goat smell

1970, Ramon Guthrie, “Loin de Moi …”, in Maximum Security Ward, New York: Farrar, Straus & Giroux, page 45:

You may even get picked up by a German soldier. They’re a rutty bunch now that they’re away from their fat frauleins and meeting some real French women.

2001, Fred Mustard Stewart, chapter 30, in The Savages in Love and War,, New York: Forge, page 275:

Related to a rut; being in a state of sexual arousal.


rutty

[…] the shoare of siluer streaming Themmes,
Whose rutty Bancke, the which his Riuer hemmes,
Was paynted all with variable flowers,

1596, Edmund Spenser, Prothalamion, London: William Ponsonby:

[…] whistling reeds, that rutty Iordan laues,
And with their verdure his white head embraues,
To chide the windes,

1610, Giles Fletcher, Christs Victorie, and Triumph in Heauen, and Earth, Over, and After Death, Cambridge, page 47:


rutty

en-noun

rutty (plural rutties or ruttys or ruttees)

rutties (plural)
ruttys (plural)
ruttees (plural)

From Hindi रत्ती (rattī), literally “the seed of the plant Abrus precatorius.”

[…] they immediately desired to capitulate, and sent him, by way of ransom, a perfect diamond weighing two hundred and twenty four ruttys […]

1768, Firishta, translated by Alexander Dow, The History of Hindostan, London: T. Becket and P.A. de Hondt, Volume 2, Section 12, p. 112:

1858, Henry Yule, Narrative of the Mission … to the Court of Ava, London: Smith, Elder, Appendix, “Note on Metals, Minerals, &c., of Burma,” p. 348,
[Sapphires] of ten to fifteen rutties without a flaw are common, whereas a perfect ruby of that size is hardly ever seen.

[…] vast numbers of infatuated wretches have accustomed themselves to consume from 6 rutties (9 grains) to a rupee’s weight (180 grains) of nearly pure opium daily […]

1870, Norman Chevers, A Manual of Medical Jurisprudence for India, Calcutta: Thacker, Spink, page 227:

(India, obsolete) A unit of weight used for metals, precious stones and medicines, equivalent to 1+¹⁄₂ grains.


secant

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

From Latin secāns, present participle of secō (“to cut”).

(geometry) A straight line that intersects a curve at two or more points.

(trigonometry) In a right triangle, the reciprocal of the cosine of an angle. Symbol: sec


sen

From a syncopation of Middle English selven, selfen, variants of selfe, self. More at self.

Hear all, see all, say nowt. Eyt all, sup all, pay nowt. An if ivver tha does owt fer nowt, mek sure tha does it fer thi sen.


septic

Enriques states that it is possible to construct a family of septics with a singular curve of degree 7 and genus 4 having a triple point that degenerates to the above configuration[…].

2002, Ingrid C. Bauer, Fabrizio Catanese, Roberto Pignatelli, “Canonical Rings of Surfaces Whose Canonical System has Base Points”, in Ingrid C. Bauer et al., editors, Complex Geometry: Collection of Papers Dedicated to Hans Grauert, page 66:

Now consider the two septics C = U⁷ᵢ₌₁Cᵢ, D = U⁷ᵢ₌₁Dᵢ and note that for i = 1,2,3,4,5,6 the lines Cᵢ and Dᵢ are parallel, so that the intersection of two septics S' consists of 6⁶^([sic]) + 6 + 1 = 43 points and it is the singular set of a foliation of degree 6.

2003, Antonio Campillo, Santiago Encinas, “Two Dimensional Complete Ideals”, in Luchezar L. Avramov et al., editors, Commutative Algebra: Interactions with Algebraic Geometry: International Conference, page 71:

(mathematics) A mathematical object (function, curve, surface, etc.) of degree seven.


septic

(mathematics) Of the seventh degree or order.


spline

Mid-1700s East Anglian dialect. Origin uncertain but perhaps from Old Danish splind or North Frisian splinj and ultimately related to the root of splinter.

However, it should be possible to give more sophisticated spherical spline curves based on the de Castaljau method that are computed using multiple slerps between pairs of points and which work well for arbitrary knot positions (indeed, knot insertion methods for spline curves should suffice for this, cf Farin [1993])

2001 April, Samuel R. Buss, Jay P Fillmore, “Spherical averages and applications to spherical splines and interpolation”, in ACM Transactions on Graphics (TOG), volume 20, number 2:

These conditions provide a framework which encompasses some notable approximation kernels including splines, so-called cardinal functions, and many radial basis functions such as the Gaussians and general multiquadrics.

2016, Keaton Hamm, Jeff Ledford, “Regular Families of Kernels for Nonlinear Approximation”, in arXiv:

(mathematics, computing) Any of a number of smooth curves used to join points.


spline

en-verb

spline (third-person singular simple present splines, present participle splining, simple past and past participle splined)

splines (present singular third-person)
splining (participle present)
splined (participle past)
splined (past)

(mathematics, computing) To smooth (a curve or surface) by means of a spline.


tensor

en-noun

tensor (plural tensors or (muscle) tensores)

Borrowed from New Latin tensor (“that which stretches”), equivalent to tense + -or. Anatomical sense from 1704.
Introduced in the 1840s by William Rowan Hamilton as an algebraic quantity unrelated to the modern notion of tensor.
The contemporary mathematical meaning was introduced (as German Tensor) by Woldemar Voigt (1898) and adopted in English from 1915 (in the context of general relativity), obscuring the earlier Hamiltonian sense. The mathematical object is so named because an early application of tensors was the study of materials stretching under tension. (See, for example, Cauchy stress tensor on Wikipedia.Wikipedia)

pedia

The tensor #92;alpha#95;#123;ij#125; should really be called a “tensor of second rank,” because it has two indexes. A vector—with one index—is a tensor of the first rank, and a scalar—with no index—is a tensor of zero rank.

1963, Richard Feynman, “Chapter 31, Tensors”, in The Feynman Lectures on Physics, volume II:

multidimensional array
multidimensional array

(mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array.

(engineering) A multidimensional array with (at least) two dimensions.

(mathematics, obsolete) A norm operation on the quaternion algebra.

tenzor

image of a tuple under a tensor product map


toroid

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

(mathematics) A surface generated by a closed curve (especially a circle) rotating about, but not intersecting or containing, an axis in its own plane.


torr

Clipping of Torricelli; named after Italian physicist Evangelista Torricelli (1608–1647), who discovered the principle of the barometer.

named-after

millimeter of mercury

not exactly synonyms, but practically equal

(metrology) A unit of pressure that is equal to approximately 0.001316 atmospheres or 133.3 pascals.


umbra

en-noun

umbra (plural umbras or umbrae or (obsolete) umbræ)

umbras (plural)
umbrae (plural)
umbræ (obsolete plural)

Borrowed from Latin umbra (“shadow”). Doublet of umber.

In order to set up such an algorithm, we need the notion of multiplicative inverse of an umbra. Two umbrae are said to be multiplicative inverse to each other when αγ ≡ u.

2009, Ernesto Damiani, Ottavio D'Antona, Vincenzo Marra, From Combinatorics to Philosophy: The Legacy of G.-C. Rota, (page 113)#:

(mathematics) An element of the umbral calculus.


unary

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

From Latin ūnus (“one”) + -ary, on the pattern of binary, ternary, etc.

Negation is a unary operation.

Zadeh’s claim is that if the meaning of an expression (X) can be modeling by a fuzzy membership function variable, then the meaning of an expression such as “very X” is simply a membership function over the same variable determined by applying a unary operator to the membership function for X.

1990, Dominic A. Clark, “Verbal uncertainty expressions: A critical review of two decades of research”, in Current Psychology, volume 9, number 3, →DOI, page 229:

On the other hand, blank spaces should not be used for unary operators such as unary minus (−), address of (&), indirection (*), member access (.), increment (++), and decrement (−−).

2011, Robert Green, Henry Ledgard, “Coding Guidelines: Finding the Art in the Science”, in Communications of the ACM, volume 54, number 12, →DOI:

(mathematics, programming, computer engineering) Of an operation, function, procedure, or logic gate, taking exactly one operand, argument, parameter, or input; having domain of dimension 1.

unární

mathematics, programming: of a function, to take one argument


unary

unary (countable and uncountable, plural unaries)

(mathematics) The unary, or bijective base-1, numeral system.

(information theory) Unary coding, an entropy encoding for natural numbers.


strength

strength (countable and uncountable, plural strengths)

[st̠͡ɹ̠ɛŋkθ]

[st̠͡ɹ̠ɛn̪θ]

[s̠t͡ʃɹ̥ɛn̪θ]

[st̠͡ɹ̠ɪŋkθ]

[st̠͡ɹ̠ɛɪŋkθ]

[st̠͡ɹ̠eɪŋkθ]

From Middle English strengthe, from Old English strengþu (“strength”), from Proto-West Germanic *strangiþu (“strongness; strength”), equivalent to strong + -th. Cognate with Dutch strengte (“strength”), German Low German Strengde, Strengte (“harshness; rigidity; strictness; severity”).

inh

(graph theory) The minimum ratio of the number of edges removed from a given graph to components created, over all possible removals.


oblique circle

(projection) a circle whose plane is oblique to the axis of the primitive plane


oblique line

(geometry) A line that, meeting or tending to meet another, makes oblique angles with it.


oblique system of coordinates

(analytic geometry) A system in which the coordinate axes are oblique to each other.


bifurcation

en-noun

bifurcation (countable and uncountable, plural bifurcations)

(mathematics) The change in the qualitative or topological structure of a given family as described by bifurcation theory.


calculation

calculation (countable and uncountable, plural calculations)

/ˌkælkjəˈlæɪʃən/

From Middle English calculation, borrowed from Latin calculatio, calculationis.
Morphologically calculate + -ion

(mathematics, uncountable) The act or process of calculating.

As a check on these calculations we note that the total probability for 0, 1, 2, or 3 successes must be one since there are no other possibilities.

1962, Hugh D. Young, chapter 3, in Statistical Treatment of Experimental Data, →ISBN, page 53:

Some of the most beautiful and thus appealing physical theories, including quantum electrodynamics and quantum gravity, have been dogged for decades by infinities that erupt when theorists try to prod their calculations into new domains. Getting rid of these nagging infinities has probably occupied far more effort than was spent in originating the theories.

2012 January, Michael Riordan, “Tackling Infinity”, in American Scientist, volume 100, number 1, archived from the original on 2013-04-30, page 86:

(mathematics, countable) The result of calculating.


cancellation

cancellation (countable and uncountable, plural cancellations)

From Latin cancellātiō, from cancellō + -tiō.

(mathematics) The operation of striking out common factors, e.g. in both the dividend and divisor.


condensation

condensation (countable and uncountable, plural condensations)

From condense + -ation, borrowed from Latin condēnsātiō, condēnsātiōnem.

directed acyclic graph
directed acyclic graph

strongly connected component
strongly connected component

(graph theory, countable) For a given directed graph G, a directed acyclic graph with one vertex for each strongly connected component of G, and an edge connecting pairs of components that contain the two endpoints of at least one edge in G.


configuration

configuration (countable and uncountable, plural configurations)

/kənˌfɪɡ.əˈɹeɪ̯.ʃən/

/kənˌfɪɡ.jəˈɹeɪ̯.ʃən/

/kənˌfɪɡ.əˈɹæɪ̯.ʃən/

From Middle French configuration, from Latin cōnfigūrātiō.
Morphologically configure + -ation

määritys

computing: process of customizing a computing environment

(countable, algebra) A finite set of points and lines (and sometimes planes), generally with equal numbers of points per line and equal numbers of lines per point.


decimation

decimation (countable and uncountable, plural decimations)

/ˌdɛsɪˈmeɪʃən/

Borrowed from Latin decimātiō, a punishment where every 10th man in a unit would be stoned to death by the men who were spared. Used by the Romans to keep order in their military. Compare septimation and vicesimation.

desimointi

creation of a new sequence comprising every nth element of the original

(mathematics) The creation of a new sequence comprising only every nth element of a source sequence.

(signal processing) A digital signal-processing technique for reducing the number of samples in a discrete-time signal; downsampling

quintation (1

proportionate reduction, by single aliquot part


deck

From Middle English dekke, borrowed from Middle Dutch dec (“roof, covering”), from Middle Dutch decken, from Old Dutch thecken, from Proto-West Germanic *þakkjan, from Proto-Germanic *þakjaną. Formed the same: German Decke (“covering, blanket”). Doublet of thatch and thack.

rearrange the deck chairs on the Titanic

shuffle the chairs on the deck of the Titanic

Meronym: card

(graph theory) The multiset of graphs formed from a single graph by deleting a single vertex in all possible ways.


demean

en-verb

demean (third-person singular simple present demeans, present participle demeaning, simple past and past participle demeaned)

demeans (present singular third-person)
demeaning (participle present)
demeaned (participle past)
demeaned (past)

LL-Q1860 (eng)-Mélange a trois-demean.wav

Concerning FE estimation, it makes no difference whether you demean the data with unit-specific means computed on (balanced) T observations per unit, or with unit-specific means computed on (unbalanced) Tᵢ observations per unit.

2013, Hans-Jürgen Andreß, Katrin Golsch, Alexander W. Schmidt, Applied Panel Data Analysis for Economic and Social Surveys, page 177:

(statistics, transitive) To subtract the mean from (a value, or every observation in a data set).


derivation

en-noun

derivation (countable and uncountable, plural derivations)

From Middle English derivacioun, borrowed from Middle French dérivation, from Latin dērīvātiō, dērīvātiōnem.
Morphologically derive + -ation

The process of deriving one thing from another, especially in logic; a deduction.

(mathematics) A formal proof: a sequence of statements, each of which is logically entailed by those preceding (with respect to some collection of rules of inference), the initial statements being taken as axioms.

(mathematics, calculus) The process of application of the derivative operator to a function, yielding another function called the derived function of the first.

(mathematics, differential algebra) An algebraic generalization of the derivative operator (from its natural setting in the ring of real-valued functions) to a general associative algebra over a field. Formally, (given an algebra A over a field K) a K-linear endomorphism that satisfies Leibnitz's Law.

Any of several generalizations of this notion: a Hasse–Schmidt derivation, a graded derivation, etc.


deviation

deviation (countable and uncountable, plural deviations)

From Middle French deviation, from Medieval Latin deviatio. Morphologically deviate + -ion.

(statistics) For interval variables and ratio variables, a measure of difference between the observed value and the mean.


differentiation

differentiation (countable and uncountable, plural differentiations)

/ˌdɪf.əˌɹɛn.ʃiˈeɪ.ʃən/

From differentiate + -ion, from different + -iate, from differ + -ent, from Middle English differen, from Old French differer, from Latin differō (“carry apart, put off, defer; differ”), from dis- (“apart”) + ferō (“carry, bear”); cognate with Ancient Greek διαφέρω (diaphérō, “to differ”).

видоизменение

gradual formation or production of organs or parts by a process of evolution or development

The integration and differentiation of vital function on the one hand, and the preparation and composition of food-material on the other hand form — as we will become fully aware further on — the two great divisions in the subject-matter of the science of organization, divisions corresponding to the fundamental biplicity of all advanced organization, its animal and its vegetative life.

1878, Edmund Montgomery, “Monera, and the problem of life”, in The Popular Science Monthly, volume XIII, page 680:

(mathematics, calculus) The process of applying the derivative operator to a function; of calculating a function's derivative.


digest

From Latin dīgesta, neuter plural of dīgestus, past participle of dīgerō (“separate”).

(cryptography) The result of applying a hash function to a message.

resumo

cryptography: the result of applying a hash function to a message


dilation

en-noun

dilation (countable and uncountable, plural dilations)

(mathematics) In morphology, a basic operation (denoted ⊕) that usually uses a structuring element for probing and expanding the shapes contained in the input image.


domination

domination (countable and uncountable, plural dominations)

/ˌdɒməˈneɪʃən/

/ˌdɑːməˈneɪʃən/

From Middle English domynacion, from Old French dominacion, from Latin dominātiō (“rule, dominion”), from dominor (“domineer; rule”); see dominate.

With more than 200 research papers published on the algorithmic complexity of domination and related parameters of graphs, it is difficult to know what to cover in a relatively short chapter on the subject, especially since it could take quite a few pages just to cover the preliminaries of computational complexity and the many algorithm design paradigms that have been applied to domination problems.

1998, Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater, Fundamentals of Domination in Graphs, →ISBN, page 299:


elation

elation (countable and uncountable, plural elations)

From Middle English elacioun, from Old French elacion, from Latin ēlātiōnem, accusative singular of ēlātiō (“exaltation, elevation; pride, elation”), from ēlātus, perfect passive participle of efferō (“bring forth or out; raise; exalt”), from ē (“out of”), short form of ex, + ferō (“carry, bear”).

(geometry) A collineation that fixes all points on a line (called its axis) and all lines though a point on the axis (called its center).


elimination

elimination (countable and uncountable, plural eliminations)

(mathematics) The act of causing a quantity to disappear from an equation; especially, in the operation of deducing from several equations containing several unknown quantities a less number of equations containing a less number of unknown quantities.


embed

en-verb

embed (third-person singular simple present embeds, present participle embedding, simple past and past participle embedded)

embeds (present singular third-person)
embedding (participle present)
embedded (participle past)
embedded (past)

The torus S¹#92;timesS¹ can be embedded in #92;mathbb#123;R#125;³.

(mathematics, transitive) To define a one-to-one function from one set to another so that certain properties of the domain are preserved when considering the image as a subset of the codomain.


equator

From Late Latin (circulus) aequator (diei et noctis).

bor

Baishui is about as close to the equator as Tampa, Florida.

2018, VOA Learning English > China's Melting Glacier Brings Visitors, Adds to Climate Concerns:

(geography, often “the Equator”) An imaginary great circle around Earth, equidistant from the two poles, and dividing earth's surface into the northern and southern hemisphere.

(astronomy) A similar great circle on any sphere, especially on a celestial body, or on other reasonably symmetrical three-dimensional body.

Slice the onion through the equator.

The midline of any generally spherical object, such as a fruit or vegetable, that has identifiable poles.


evaluation

en-noun

evaluation (countable and uncountable, plural evaluations)

From Middle French évaluation.
Morphologically evaluate + -ion

(mathematics) A completion of a mathematical operation; a valuation.


exceptional

en-adj

exceptional (comparative more exceptional, superlative most exceptional)

more exceptional (comparative)
most exceptional (superlative)

ordinary

antonym(s) of “superior due to exception or rarity”

an exceptional curve; an exceptional divisor

(geometry) Corresponding to something of lower dimension under a birational correspondence.


expectation

en-noun

expectation (countable and uncountable, plural expectations)

From Middle French expectation, from Latin exspectātiō, from exspectō (“expect”). By surface analysis, expect + -ation. Displaced native Old English wēn.

(statistics) The first moment; the expected value; the long-run average value of a variable over many independent repetitions of an experiment.

(statistics, colloquial) The arithmetic mean.


extension

extension (countable and uncountable, plural extensions)

From Middle English extensioun, from Old French estension, from Latin extensiō, extensiōnem.

(ring theory, of an ideal in the domain of a ring homomorphism) The ideal in the codomain generated by the image of the given ideal under the given homomorphism.


extract

en-verb

extract (third-person singular simple present extracts, present participle extracting, simple past extracted, past participle extracted or (archaic) extraught)

extracts (present singular third-person)
extracting (participle present)
extracted (past)
extracted (participle past)
extraught (archaic participle past)

Borrowed from Latin extractum, neuter perfect passive participle of extrahō, from ex- (“out of”) + trahō (“I drag”).

Please extract the cube root of 27.

[…] Mr. Nackybal was thoroughly examined, both in cubing and extracting, from the table that Louit had provided.

1953, Samuel Beckett, Watt, 1st American edition, New York, N.Y.: Grove Press, published 1959, →OCLC:

(transitive, arithmetic) To determine (a root of a number).


filtration

en-noun

filtration (countable and uncountable, plural filtrations)

(mathematics, set theory, probability theory) A totally ordered collection of subsets.


flabby

en-adj

flabby (comparative flabbier, superlative flabbiest)

flabbier (comparative)
flabbiest (superlative)

From a variant of flappy, from flap (“to hang loose”). Compare English dialectal flapsy (“flabby”), Middle Dutch flabbe (“a slap in the face; a fan-blade; a hair ribbon; a wagging tongue”), Middle Low German flabbe (“a gaping mouth; a chatterbox”), Danish flab (“the jaw; cheeks; a malapert”), Swedish flabb, fläff (“the hanging underlip of an animal; guffaw; driveller”), German Flabbe (“a gob; muzzle”).

a flabby sheaf on a paracompact space

(mathematics) Which forms a surjection from the domain to every open subset of the codomain.


flap

From Middle English flap, flappe (“a slap; blow; buffet; fly-flap; something flexible or loose; flap”), related to Saterland Frisian Flappert (“wing, flipper”), Middle Dutch flabbe (“a blow; slap on the face; fly-flap; flap”) (modern Dutch flap (“flap”)), Middle Low German flabbe, vlabbe, flebbe, from the verb (see below). Related also to English flab and flabby.

cog

(graph theory) A connected component of the induced subgraph formed by deleting a set of vertices.


foliation

en-noun

foliation (countable and uncountable, plural foliations)

/fəʊlɪˈeɪʃn/

From French foliation, from Latin folium (“leaf”).

Historically, the formalism which first arose for the material we discuss is that of measured foliations in surfaces.

1992, R. C. Penner, Combinatorics of Train Tracks, page 204:

We will show that every closed 3-manifold has a foliation of codimension one. In 1952, G. Reeb published his construction of a foliation of the 3-sphere. About twelve years later, W. Lickorish [123] exhibited foliations of codimension one on every closed, orientable 3-manifold.

2003, Alberto Candel, Lawrence Conlon, Foliations, Vol.2, p.253

The simplest example of a foliation is provided by a single submersion F : M → N, M and N being manifolds.

2004, Paweł Grzegorz Walczak, Dynamics Of Foliations, Groups And Pseudogroups, Monografie Matematyczne: Vol.64, New Series, p.6

(topology) A set of submanifolds of a given manifold, each of which is of lower dimension than it, but which, taken together, are coextensive with it.

叶层结构

topology: a set of subspaces coextensive with a manifold


gauge

gauge (countable and uncountable, plural gauges)

From Middle English gauge, gaugen, from Anglo-Norman, Old Northern French gauger (compare Modern French jauger from Old French jaugier), from gauge (“gauging rod”), from Frankish *galga (“measuring rod, pole”), from Proto-Germanic *galgô (“pole, stake, cross”), from Proto-Indo-European *ǵʰalgʰ-, *ǵʰalg- (“perch, long switch”). Cognate with Old High German galgo, Old Frisian galga, Old English ġealga (“cross-beam, gallows”), Old Norse galgi (“cross-beam, gallows”), Old Norse gelgja (“pole, perch”). Doublet of gallows.

cog

mathematical analysis
mathematical analysis

(mathematics, mathematical analysis) A semi-norm; a function that assigns a non-negative size to all vectors in a vector space.

ijk

a semi-norm; a function that assigns a non-negative size to all vectors in a vector space


core

en-noun

core (countable and uncountable, plural cores)

desc

Translingual: core eudicots, core Malvales

From Middle English core, kore, coor (“apple-core, pith”), of obscure and uncertain origin. Possibly of native English origin, from Old English *cor, related to Old English *coruc, *corc (diminutive) (> Middle English cork, crok (“core of an apple or other fruit, heart of an onion”)) and Old English corn (“seed", also "grain”); or alternatively perhaps from Old French cuer (“heart”), from Latin cor (“heart”); or from Old French cors (“body”), from Latin corpus (“body”). Compare also Middle English colk, coke, coll (“the heart or centre of an apple or onion, core”), Dutch kern (“core”), German Kern (“core”). See also heart, corpse.

unc

obscure and uncertain

non-rhotic, without the horse–hoarse merger

сърцеви́на

something that produces a hollow space in a casting

The most important part of a thing or aggregate of things wherever located and whether of any determinate location at all; the essence.

A technical term for classification of things denoting those parts of a category that are most easily or most likely understood as within it.

(game theory) The set of feasible allocations that cannot be improved upon by a subset (a coalition) of the economy's agents.


corollary

/ˈkɔɹəˌlɛɹi/

/kɔˈɹoʊˌlɛɹi/

From Middle English, from Late Latin corōllārium (“money paid for a garland; gift, gratuity, corollary; consequence, deduction”), from corōlla (“small garland”), diminutive of corōna (“crown”).

der

We have proven that this set is finite and well ordered; as a corollary, we now know that there is an order-preserving map from it to the natural numbers.

(mathematics, logic) A proposition which follows easily from the statement or proof of another proposition.


gyration

en-noun

gyration (countable and uncountable, plural gyrations)

/ˌd͡ʒaɪˈɹeɪʃ(ə)n/

From gyre (“to spin around; to gyrate, to whirl; (rare) to make (something) spin or whirl around; to spin, to whirl”) + -ation (suffix indicating actions or processes). Gyre is from Late Middle English giren (“to turn (something) away; to cause (something) to revolve or rotate; to travel in a circle”), from Old French girer (“to turn”), and directly from its etymon Latin gȳrāre, the present active infinitive of gȳrō (“to turn in a circle, rotate; to circle or revolve around”) (from gȳrus (“circle; circular motion; circuit, course”), from Ancient Greek γῦρος (gûros, “a circle, a ring”), from Proto-Indo-European *gew- (“to bend; to curve”)) + -ō (suffix forming regular first-conjugation verbs).

ĝirado

act of turning or whirling, especially around a fixed axis or centre — see also rotation

(also figuratively) The act of turning or whirling, especially around a fixed axis or centre; a circular or spiral motion; rotation.

(specifically, Euclidean geometry) A rotation around an axis which is not the centre of rotational symmetry; an eccentric or off-centre rotation.


immerse

en-verb

immerse (third-person singular simple present immerses, present participle immersing, simple past and past participle immersed)

immerses (present singular third-person)
immersing (participle present)
immersed (participle past)
immersed (past)

Borrowed from Latin immersus, from immergō, from in + mergō.

Thus, in mathematical terms a Klein bottle cannot be "embedded" but only "immersed" in three dimensions as an embedding has no self-intersections but an immersion may have them.

2002, Kari Jormakka, Flying Dutchmen: Motion in Architecture, page 40:

(transitive, mathematics) To map into an immersion.


improper

en-adj

improper (comparative more improper, superlative most improper)

more improper (comparative)
most improper (superlative)

From Middle French impropre, from Latin improprius (“not proper”), from in- + proprius (“proper”). By surface analysis, im- + proper.

(mathematics) Of a complex random variable, correlated with its conjugate.


insight

en-noun

insight (countable and uncountable, plural insights)

From Middle English insight, insiht (“insight, mental vision, intelligence, understanding”), equivalent to in- + sight. Perhaps continuing Old English insiht (“narrative, argument, account”), from Proto-Germanic *insahtiz (“account, narrative, argument”). Compare West Frisian ynsjoch (“insight”), Dutch inzicht (“insight, awareness, view, opinion”), German Low German Insicht (“insight”), German Einsicht (“insight, knowledge, perception, understanding”), Danish indsigt (“insight”), Swedish insikt (“insight”), Icelandic innsýn (“insight”).

cog

(artificial intelligence) An extended understanding of a subject resulting from identification of relationships and behaviors within a model, context, or scenario.

Verstehen

extended understanding of a subject in artificial intelligence


integration

en-noun

integration (countable and uncountable, plural integrations)

/ˌɪn.tɪˈɡɹeɪ.ʃən/

/ˌɪn.təˈɡɹeɪ.ʃən/

/ˌɪn.təˈɡɹæɪ.ʃən/

From French intégration, from Latin integratio.
Morphologically integrate + -ion

(calculus) The operation of finding the integral of a function.


knapsack

From Low German knapzak or Dutch knapzak (older form cnapsack), from Middle Dutch cnappen (“to bite with teeth”), ultimately from knappen (“to eat, crack”), of imitative origin, + sack. German Knappsack is from Dutch.

onomatopoeic

imitative

(cryptography) A set of values from which a subset is chosen.


meander

From Latin Maeander, from Ancient Greek Μαίανδρος (Maíandros) – a river in Asia Minor (present day Turkey) known for its winding course (modern Turkish Menderes).

(mathematics) A self-avoiding closed curve which intersects a line a number of times.


node

→ Irish: nód

From Middle English node, borrowed from Latin nōdus. Doublet of knot, knout, and nodus.

(geometry) The point at which a curve crosses itself, being a double point of the curve. See crunode and acnode.

duaalipiste

geometry: point at which a curve crosses itself

(geometry) A similar point on a surface, where there is more than one tangent-plane.

(graph theory) A vertex or a leaf in a graph of a network, or other element in a data structure.


peak

→ Russian: пик (pik) (in час пик (čas pik))

From earlier peake, peek, peke, from Middle English pek (in place names), itself an alteration of pike, pyke, pyk (“a sharp point, pike”), from Old English pīc, piic (“a pike, needle, pin, peak, pinnacle”), from Proto-Germanic *pīkaz (“peak”). Cognate with Dutch piek (“pike, point, summit, peak”), Danish pik (“pike, peak”), Swedish pik (“pike, lance, point, peak”), Norwegian pik (“peak, summit”). More at pike.

cog

(mathematics) A local maximum of a function, e.g. for sine waves, each point at which the value of y is at its maximum.

pic

point where a function attains a maximum


peak

en-verb

peak (third-person singular simple present peaks, present participle peaking, simple past and past participle peaked)

peaks (present singular third-person)
peaking (participle present)
peaked (participle past)
peaked (past)

"Dr. Reynders?" Udo prodded.

2023 September 22, HarryBlank, “Off Track”, in SCP Foundation, archived from the original on 2024-05-25:

(transitive, signal processing) To exceed the maximum signal amplitude of (a piece of equipment), resulting in clipping of the signal.


peck

Probably from Anglo-Norman pek, pekke, of uncertain origin.

She figured most children probably ate a peck of dirt before they turned ten.

a peck of uncertainties and doubts

1644, J[ohn] M[ilton], The Doctrine or Discipline of Divorce: […], 2nd edition, London: [s.n.], →OCLC, book:

A great deal; a large or excessive quantity.


predecessor

From Middle English predecessour, from Old French predecesseor (“forebear”), from Late Latin praedēcessor, from Latin prae- (“pre-”) + Latin dēcessor (“retiring officer”), from Latin dēcēdō (“I retire, I die”) (English decease).

(mathematics) A vertex having a directed path to another vertex


primitive

From Middle English primitif, from Old French primitif, from Latin prīmitīvus (“first or earliest of its kind”), from prīmus (“first”); see prime. Doublet of primitivo.

der

(mathematics) A function whose derivative is a given function; an antiderivative.


primitive

en-adj

primitive (comparative more primitive, superlative most primitive)

more primitive (comparative)
most primitive (superlative)

prymitywny

old-fashioned; characterized by simplicity

(mathematics) Not derived from another of the same type


regress

en-verb

regress (third-person singular simple present regresses, present participle regressing, simple past and past participle regressed)

regresses (present singular third-person)
regressing (participle present)
regressed (participle past)
regressed (past)

(verb) From Latin regressus, past participle of regredior (“to go back”), from re- (“back”) + gradior (“to go”).

When we regress Y on X, we use the values of variable X to predict those of Y.

(transitive, statistics) To perform a regression on an explanatory variable.


remain

remain (third-person singular simple present remains, present participle remaining, simple past and past participle remained)

remains (present singular third-person)
remaining (participle present)
remained (participle past)
remained (past)

From Middle English remainen, from Old French remain-, stressed stem of remanoir, from Latin remaneō, maneō, from Proto-Indo-European *men- (“to stay”).
Displaced native Middle English beliven, bliven (“to remain”) (from Old English belīfan (“to remain, stay”)) due to confluence with related Middle English beleven (“to leave behind”), with which it merged. More at beleave and belive.

cog

If you divide 20 apples between three people, each gets six and two remain.

(mathematics) To be left after a number or quantity has been subtracted or cut off; to be left as not included or comprised.

ҡалыу

to be left over after a portion is removed


revert

en-verb

revert (third-person singular simple present reverts, present participle reverting, simple past and past participle reverted)

reverts (present singular third-person)
reverting (participle present)
reverted (participle past)
reverted (past)

From Old French revertir, from Vulgar Latin *revertiō, variant of Latin revertō.

връщам

to cause to return to the previous owner

First we revert the series expansion (3.6) to give z(#92;zeta) as a series in z.

1990, George A. Baker, Jr., J. D. Johnson, “Thomas-Fermi Equation of State - The Hot Curve”, in Valdir C. Aguilera-Navarro, editor, Condensed Matter Theories, volume 5, →ISBN, page 5:

To express z as a power series of n#92;lambda³, we first expand g#95;#123;3#47;2#125;(z) in z […] We then revert the power series to express z in terms of n#92;lambda³.

2005, Frank Y. Wang, Physics with MAPLE: The Computer Algebra Resource for Mathematical Methods in Physics, →ISBN, pages 518–9:

We can revert the series expansion of #92;langlen#92;rangle#92;lambda³#95;T#47;g […] and obtain a series expansion for the fugacity z in terms of #92;langlen#92;rangle#92;lambda³#95;T#47;g, […]

2016, Linda E. Reichl, A Modern Course in Statistical Physics, 4th edition, →ISBN, page 218:

(transitive, mathematics) To treat (a series, such as y=a+bx+cx²+⋯, where one variable y is expressed in powers of a second variable x), so as to find the second variable x expressed in a series arranged in powers of y.


robust

en-adj

robust (comparative more robust or (uncommon) robuster, superlative most robust or (uncommon) robustest)

more robust (comparative)
robuster (comparative uncommon)
most robust (superlative)
robustest (superlative uncommon)

LL-Q1860 (eng)-I learned some phrases-robust.wav

robust association of massive baryonic objects

(statistics) Not greatly influenced by errors in assumptions about the distribution of sample errors.


roulette

en-noun

roulette (countable and uncountable, plural roulettes)

Borrowed from French roulette (“roulette, little wheel”). The sense "situation with a random chance of incurring serious harm" may be abstracted from Russian roulette.

bor

(countable, geometry) The locus of a point on a plane curve that rolls without slipping along another fixed plane curve.


shell

en-verb

shell (third-person singular simple present shells, present participle shelling, simple past and past participle shelled)

shells (present singular third-person)
shelling (participle present)
shelled (participle past)
shelled (past)

From Middle English schelle, from Old English sċiell, from Proto-West Germanic *skallju, from Proto-Germanic *skaljō, from Proto-Indo-European *(s)kelH- (“to split, cleave”).
Compare West Frisian skyl (“peel, rind”), Dutch schil (“peel, skin, rink”), Low German Schell (“shell, scale”), Irish scelec (“pebble”), Latin silex (“pebble, flint”), siliqua (“pod”), Old Church Slavonic сколика (skolika, “shell”). More at shale.
Doublet of sheal.
* (computing): From being viewed as an outer layer of interface between the user and the operating-system internals.


site

From Middle English site, from Anglo-Norman site, from Latin situs (“position, place, site”), from sinere (“to put, lay, set down, usually let, suffer, permit”). Doublet of sitio and situs.

Grothendieck topology
Grothendieck topology

(category theory) A category together with a choice of Grothendieck topology.


slice

From Middle English sclise, sklise, from Old French esclice, esclis (“a piece split off”), deverbal of esclicer, esclicier (“to splinter, split up”), from Frankish *slitjan (“to split up”), from Proto-Germanic *slitjaną, from Proto-Germanic *slītaną (“to split, tear apart”), from Proto-Indo-European *sleyd- (“to rend, injure, crumble”). Akin to Old High German sliz, gisliz (“a tear, rip”), Old High German slīzan (“to tear”), Old English slītan (“to split up”), modern French éclisse. More at slite, slit.

der

(mathematics) Having the properties of a slice knot.


slight

en-adj

slight (comparative slighter, superlative slightest)

slighter (comparative)
slightest (superlative)

From Middle English slight (“bad, of poor quality, unimportant, trivial, slender, slim, smooth, level”), from Old English sliht (“smooth, level”), from Proto-Germanic *slihtaz (“slippery, flat, level, plain”), related to English slick. Cognate with Scots slicht (“bad, of poor quality”), West Frisian sljocht (“smooth, level, plain, simple”), Dutch slecht (“bad”), Low German slecht (“bad”), German schlecht (“bad”) and schlicht (“plain, artless, natural”), Danish slet (“bad, evil, poor, nasty, wrong”), Swedish slät (“smooth”), Norwegian slett (“even”), Icelandic sléttur (“even, smooth, level”).

cog

give it a slight kick

a slight hint of cinnamon

a slight effort

a slight (i.e. not convincing) argument

Mother very rightly resented the slightest hint of condescension. She considered that the exclusiveness of Peter's circle was due not to its distinction, but to the fact that it was an inner Babylon of prodigality and whoredom,[…].

1921, Ben Travers, chapter 2, in A Cuckoo in the Nest, Garden City, N.Y.: Doubleday, Page & Company, published 1925, →OCLC:

Even though there is slight quality variation between the long and short versions of Arabic vowels, the variation is rarely noticeable even by some phoneticians; hence, it does not amount to a source of even phonetic accent except for those learners of Arabic whose language has a strictly centrifugal vowel system such as Spanish, Italian, Tagalog, among others.

2014, Edward Y. Odisho, “Some Primary Sources of Accent Generation in the Pronunciation of Arabic by Native Speakers of English”, in Mediterranean Language Review, volume 21, →DOI, page 100 of 91–104:

Gentle or weak, not aggressive or powerful.

make a slight examination

we made a slight mistake

a slight pain

Some firmly embrace doctrines upon slight grounds.

1741, John Locke, Some Thoughts Concerning Education & of the Conduct of the Understanding:

Slight is the subject, but not so the praise.

1714, Alexander Pope, “The Rape of the Lock”, in The Works of Mr. Alexander Pope, volume I, London: […] W[illiam] Bowyer, for Bernard Lintot, […], published 1717, →OCLC, canto I:

Small.
Trifling; unimportant; insignificant.

in the slight future

(archaic or rare) Not far away in space or time.


span

From Middle English spanne, from Old English spann, from Proto-Germanic *spannō (“span, handbreadth”), from Proto-Indo-European *(s)pend- (“to stretch”).
Cognate with Dutch span, spanne, German Spanne. The sense “pair of horses” is probably from Old English ġespan, ġespann (“a joining; a fastening together; clasp; yoke”), from Proto-West Germanic [Term?]. Cognate with Dutch gespan, German Gespann.

der

(mathematics) The space of all linear combinations of vectors within a set.

viritelmä

mathematics: the space of all linear combinations of something

We use the term span (also called depth, or dependence depth) to refer to the number of parallel steps assuming an unbounded number of processors.

2017, Ananya Kumar, Guy E. Blelloch, Robert Harper, “Parallel Functional Arrays”, in ACM SIGPLAN Notices, →DOI:

(computing) The time required to execute a parallel algorithm on an infinite number of processors, i.e. the shortest distance across a directed acyclic graph representing the computation steps.


span

en-verb

span (third-person singular simple present spans, present participle spanning, simple past and past participle spanned)

spans (present singular third-person)
spanning (participle present)
spanned (participle past)
spanned (past)

From Middle English spannen, from Old English spannan, from Proto-Germanic *spannaną (“to stretch, span”). Cognate with German spannen, Dutch spannen.

inh

(mathematics) To generate an entire space by means of linear combinations.

aufspannen

mathematics: to generate an entire space by means of linear combinations


spire

(geometry) The part of a spiral generated in one revolution of the straight line about the pole.


splitter

lumper

antonym(s) of “one who prefers to split categories”

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

Coordinate term: cleaver

(geometry) A line segment through one of the vertices of a triangle that bisects the perimeter of the triangle.


stack

LL-Q1860 (eng)-I learned some phrases-stack.wav

From Middle English stack, stacke, stakke, stak, from Old Norse stakkr (“a barn; haystack; heap; pile”), from Proto-Germanic *stakkaz (“a barn; rick; haystack”).
The data structure sense is a calque of Dutch stapel, introduced by Edsger W. Dijkstra. Cognate with Icelandic stakkur (“stack”), Swedish stack (“stack”), Danish stak (“stack”), Norwegian stakk (“stack”). Related to stake and sauna.

der

(mathematics) A generalization of schemes in algebraic geometry and of sheaves.


stadium

From Latin stadium (“a measure of length, a race course”) (commonly one-eighth of a Roman mile; translated in early English Bibles by furlong), from Ancient Greek στάδιον (stádion, “a measure of length, a running track”), especially the track at Olympia, which was one stadium in length. The Greek word may literally mean "fixed standard of length" (from στάδιος (stádios, “firm, fixed”), from Proto-Indo-European *steh₂-, whence also stand and Latin stare). Doublet of stade, stadion, and estadio.

der

An Ancient Greek racecourse, especially, the Olympic course for foot races.

stadion

race course, especially, the Olympic course for foot races


strict

en-adj

strict (comparative stricter or more strict, superlative strictest or most strict)

stricter (comparative)
more strict (comparative)
strictest (superlative)
most strict (superlative)

Borrowed from Latin strictus, past participle of stringere (“to draw tight, bind, contract”). Doublet of strait and stretto. See stringent, strain.

(set theory, order theory) Irreflexive; if the described object is defined to be reflexive, that condition is overridden and replaced with irreflexive.


tractable

tractable (comparative more tractable, superlative most tractable)

more tractable (comparative)
most tractable (superlative)

From Middle English tractable, tractabel, from Latin tractābilis (“that may be touched, handled, or managed”), from tractō (“take in hand, handle, manage”), frequentative of trahō (“draw”).

der

This assumption is in the Raiffa and Schlaifer (1961, p. 72) spirit of using ‘a little ingenuity. . . to find a tractable function’ to quantify risk-preferences and probability judgments so as to make the analysis feasible.

1987, Ira Horowitz, “Market Structure Implications of Export-Price Uncertainty”, in Managerial and Decision Economics, volume 8, number 2, page 134:

(mathematics) Sufficiently operationalizable or useful to allow a mathematical calculation to proceed toward a solution.


trapeze

From French trapèze, from Latin trapezium. Doublet of trapezium.


trend

From Middle English trenden (“to roll about, turn, revolve”), from Old English trendan (“to roll about, turn, revolve”), from Proto-West Germanic *trandijan (“to turn, roll, revolve”), apparently derived from a strong verb Proto-West Germanic *trindan. Cognate with Dutch trent (“circumference”). Akin to Old English trinde (“ball”), Old English tryndel (“circle, ring”). More at trindle, trundle.

inh

LL-Q1860 (eng)-I learned some phrases-trend.wav

(mathematics) A line drawn on a graph that approximates the trend of a number of disparate points.


trope

Japanese: トロープ (torōpu)

Korean: 트로프 (teuropeu)

From Latin tropus, from Ancient Greek τρόπος (trópos, “a manner, style, turn, way; a trope or figure of speech; a mode in music; a mode or mood in logic”), related to τροπή (tropḗ, “solstice; trope; turn”) and τρέπειν (trépein, “to turn”); compare turn of phrase. The verb is derived from the noun.

der

Hence the section must be a conic passing through six nodes, that is, the plane touches the surface all along a conic, and is therefore a trope. The complete section of the surface by a trope is a conic counted twice; since this passes through six nodes, the trope must touch the six quadric tangent cones along generators which are tangents to the singular conic.

1905, R[onald] W[illiam] H[enry] T[urnbull] Hudson, “The Quartic Surface”, in Kummer’s Quartic Surface, Cambridge: At the University Press, →OCLC; republished Cambridge: Cambridge University Press, 2001, →ISBN, page 15:

A tangent space meeting a quartic surface in a conic.

troop

music, Roman Catholicism: phrase or verse added to the Mass

I take account of conical and biplanar nodes, or, as I call them, cnicnodes, and binodes; of pinch-points on the nodal curve; and of close-points and off-points on the cuspidal curve: viz. I assume that there are / C, cnicnodes, / B, binodes, / j, pinch-points, / #92;chi, close points, / #92;theta, off-points, / deferring for the present the explanation of these singularities. The same letters, accented, refer to the reciprocal singularities. Or using "trope" as the reciprocal term to node, these will be / C', cnictropes, / B', bitropes, / j', pinch-planes, / #92;chi', close-planes, / #92;theta', off-planes; / but these present themselves, not in the equations above referred to, but in the reciprocal equations.

1868 November 12, [Arthur] Cayley, “VI. A Memoir on the Theory of Reciprocal Surfaces”, in Philosophical Transactions of the Royal Society of London, volume 159, part I, London: Printed by Taylor and Francis, Red Lion Court, Fleet Street, published 1869, →OCLC, page 202:

(archaic) The reciprocal of a node on a surface.

Mathematical senses.
The reciprocal of a node on a surface.


tweak

From Middle English twikken, from Old English twiccian (“to pluck”), from Proto-West Germanic *twekkōn (“to fasten; clamp; pinch”). Related to twitch. The drug-related sense may be a blend of twitch and freak.

inh

(cryptography) An additional input to a block cipher, used in conjunction with the key to select the permutation computed by the cipher.


formal

en-adj

formal (comparative more formal, superlative most formal)

more formal (comparative)
most formal (superlative)

From Middle English formel, borrowed from Old French formel, from Latin fōrmālis, from fōrma (“form”); equivalent to form + -al.

A set of words can be formal cognates only if they can be derived from a common ancestor by regular sound laws.

Only formal proofs, which derive theorems logically from their given axioms, are considered satisfactory in modern mathematics.

(especially sciences, mathematics, linguistics) In accordance with a methodological framework with well-defined rules or laws; rigorous.

Formal series are defined without any reference to convergence.

(mathematics, philosophy) Relating to mere manipulation and construction of strings of symbols, without regard to their meaning.

формален

mathematics, logic: relating to mere manipulations of symbols


commute

en-verb

commute (third-person singular simple present commutes, present participle commuting, simple past and past participle commuted)

commutes (present singular third-person)
commuting (participle present)
commuted (participle past)
commuted (past)

заменям

to put or substitute something else in place of

A pair of matrices share the same set of eigenvectors if and only if they commute.

(intransitive, mathematics) Of an operation, to be commutative, i.e. to have the property that changing the order of the operands does not change the result.


candy

From Marathi खंडी (khaṇḍī), from Sanskrit खण्डन (khaṇḍana), from root खण्ड् (khaṇḍ, “to divide, break into pieces”).

(obsolete) A unit of weight used in southern India, equal to twenty maunds, roughly equal to 500 pounds avoirdupois but varying locally.


probability

en-noun

probability (countable and uncountable, plural probabilities)

[ˌpɹɑbəˈbɪləɾi]

[ˌpɹɑbəˈbɪlɪɾi]

From Middle French probabilité, from Latin probābilitās (“probability, credibility”), from probābilis (“probable, credible”).

der

For, a man may with as great probability derive the Scots pedigree from the Gods, as from Scota that ſuppoſed and counterfeit daughter of the Ægyptian King Pharao, wedded (forſooth) unto Gaithelus, the ſonne of Cecrops founder of Athens. But, as this conceit ariſing from the unskilfulneſſe of Antiquitie, is of the better ſort of ingenuous Scots rejected: […]

1610, William Camden, “Scoti”, in Philémon Holland, transl., Britain, or A Chorographicall Description of the Most Flourishing Kingdomes, England, Scotland, and Ireland, […], London: […] [Eliot’s Court Press for] Georgii Bishop & Ioannis Norton, →OCLC, page 119:

Thus, firſt Traditions were a proof alone; / Cou’d we be certain ſuch they were ſo known: / But ſince ſome Flaws in long deſcent may be, / They make not Truth but Probability.

1682, John Dryden, Religio Laici: Or, A Layman’s Faith, London: H. Hills, published 1710, page 21:

As Demonſtration is the ſhewing the agreement, or diſagreement of two Ideas, by the intervention of one or more Proofs, which have a conſtant, immutable, and viſible connexion one with another : ſo Probability is nothing but the appearance of ſuch an agreement, or diſagreement, by the intervention of Proofs, whoſe connexion is not conſtant and immutable, or at leaſt is not perceived to be ſo, but is, or appears for the moſt part to be ſo, and is enough to induce the Mind to judge the Propoſition to be true, or falſe, rather than the contrary.

1690, John Locke, “Of Probability”, in An Essay Concerning Humane Understanding, 3rd edition, London: Awnsham and John Churchil, published 1695, book IV, page 376:

Thus though this degree of faith is but one remove from disbelief, (denial) nevertheless as much probability is given to one side of the question as the other, and we stand, as it were, on an average between two.

1822, Paul Brown, “Of the Degrees of Faith, according to probability, and force of impression”, in A Disquisition on Faith, Washington, D.C.: […] [F]or the Author[, b]y Andrew Way, page 24:

The probability of an event A occurring is denoted P(A).

(mathematics) A number, between 0 and 1, expressing the precise likelihood of an event happening.


caustic

From the Latin causticus (“burning”), from Ancient Greek καυστικός (kaustikós, “burning”), from καυστός (kaustós, “burnt”) + -ικός (-ikós).

suffix

(mathematics) The envelope of reflected or refracted rays for a given curve.


strict-sense stationary

en-adj

strict-sense stationary (not comparable)

(statistics) Of a random process X(t), having characteristics that do not change as t varies.


nonic

(mathematics) Describing a polynomial that has 9 as the highest exponent of its terms.

(algebraic geometry) Describing a curve the equation of which is nonic.


key exchange

en-noun

key exchange (countable and uncountable, plural key exchanges)

(cryptography) An exchange of peers' keys at the initialization phase of connection.


reciprocal

From Latin reciprocus, possibly from a phrase such as reque proque (“back and forth, to and fro”), from re- (“back”), prō (“forwards”) and -que (“and”).

مُتَبَادَل

done by each of two people towards the other

(mathematics) Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities.


reciprocal

0.5 is the reciprocal of 2.

(arithmetic) The number obtained by dividing 1 by another given number; the result of exchanging the numerator and the denominator of a fraction.


pointless

en-adj

pointless (comparative more pointless, superlative most pointless)

more pointless (comparative)
most pointless (superlative)

From Middle English pointles, poynteles, poyntlees; equivalent to point + -less.

a pointless topology


origin

/ˈɒɹ.ɪ.d͡ʒɪn/

/ˈɒɹ.ə.d͡ʒən/

/ˈɔɹ.ɪ.d͡ʒɪn/

/ˈɑɹ.ɪ.d͡ʒɪn/

From Middle English origine, origyne, from Old French origine, orine, ourine, from Latin origo (“beginning, source, birth, origin”), from orior (“to rise”); see orient. Doublet of origo.

der

language analysis for the determination of origin

(mathematics) The point at which the axes of a coordinate system intersect.


clip

en-verb

clip (third-person singular simple present clips, present participle clipping, simple past and past participle clipt or clipped)

clips (present singular third-person)
clipping (participle present)
clipt (participle past)
clipt (past)
clipped (participle past)
clipped (past)

From Middle English clippen, from Old Norse klippa (“to clip, cut the hair, shear sheep”). Cognate with Icelandic klippa (“to clip”), Swedish klippa (“to clip”), Danish klippe (“to clip”), Norwegian Bokmål klippe (“to clip”).

der

The WFM display above shows a very contrasty picture with clipped whites and blacks.

2004, John Jackman, Lighting for Digital Video and Television, page 25:

(signal processing) To cut off a signal level at a certain maximum value.


decimal point

(arithmetic, proscribed) A decimal place.


eon

From Latin aeon, from Ancient Greek αἰών (aiṓn, “age, era”).

It’s been eons since we last saw each other.

(US, informal, hyperbolic) A long period of time.

вечност

informal, hyperbolic: a long period of time


GOP

Acronym of group of pictures, a collection of successive pictures within a coded video stream.

group of pictures
group of pictures#English

(signal processing, video compression) Acronym of group of pictures.


HMS

36.24° = 36° 14' 24"

(mathematics) Initialism of hour-minute-second.:

Initialism of hour-minute-second.:
A format for writing decimal angles.

14:37:12 = 14:37 (2:37 pm) and 12 seconds

A 24 or 12-hour time format that includes seconds, in addition to hours and minutes.

7.4138 base-10 decimal hours = 7ʰ 41ᵐ 38ˢ

A format for writing decimal time, usually associated with base-10 time such as during the French Revolution.


algorithm

en-noun

algorithm (countable and uncountable, plural algorithms)

→ Japanese: アルゴリズム (arugorizumu)

→ Korean: 알고리즘 (algorijeum)

/ˈælɡəɹɪðəm/

[ˈæɫɡəɹɪðm̩]

/ˈælɡəˌɹɪðəm/

[ˈæɫɡəˌɹɪðm̩]

Muḥammad ibn Mūsā al-Khwārizmī
algorithm

From Middle English algorisme, augrym, from Anglo-Norman algorisme, augrim, from Medieval Latin algorismus, from Arabic الخَوَارِزْمِيّ (al-ḵawārizmiyy), the nisba of Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī and a toponymic name meaning "person from Chorasmia". The spelling change (-s- > -th-) was influenced by unrelated Ancient Greek ἀριθμός (arithmós) (whence English arithmo-).

der

الخَوَارِزْمِيّ

(uncountable, obsolete) Calculation with Arabic numerals; algorism.


International System of Units

(metrology) A standard set of units of measurement for use in scientific literature worldwide. The newest and most widespread version of the metric system.

Beynəlxalq vahidlər sistemi

standard set of basic units of measurement

Sistema internazionale di unità di misura

Sistemul Internațional de Unități (de măsură)


differential calculus

(calculus) The calculus that deals with instantaneous rates of change.


arccosine

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the cosine function.


arcsine

/ˈɑːɹkˌsaɪn/

(trigonometry) Any of several single-valued or multivalued functions that are inverses of the sine function. Symbol: arcsin, sin⁻¹


sine wave

(trigonometry, signal processing) A periodically oscillating waveform as described by the sine function, possibly multiplied by some amplitude, shifted by some phase, and translated by an additive constant.


hypotenuse

From Latin hypotenusa, from Ancient Greek ὑποτείνουσα πλευρά (hupoteínousa pleurá, “side subtending [the right angle]”), from ὑποτείνουσα (hupoteínousa, “stretching, extending, subtending”), active participle of ὑποτείνω (hupoteínō, “subtend, stretch under”).

uder

ὑποτείνουσα πλευρά

Coordinate term: cathetus

(geometry) The side of a right triangle opposite the right angle.

وَتَر

the side of a right triangle opposite the right angle


equilateral triangle

en-noun

equilateral triangle (plural equilateral triangles)

(geometry) A triangle having all three sides equal.


isosceles triangle

isosceles triangle (plural isosceles triangles)

(geometry) A triangle having at least two sides equal.


evanescent

en-adj

evanescent (comparative more evanescent, superlative most evanescent)

more evanescent (comparative)
most evanescent (superlative)

Borrowed from French évanescent (“evanescent”), from Latin ēvānēscēns (“disappearing, vanishing”), present participle of ēvānēscō (“to disappear, vanish; to die out, fade away; to lapse”), from ē- (variant of ex- (prefix meaning ‘away, out’)) + vānēscō (“to vanish”) (from vānus (“empty, vacant, void”), from Proto-Indo-European *h₁weh₂- (“to abandon, leave”)) + -ēscō (suffix forming verbs with the sense ‘to become’)).

намаляващ

disappearing, vanishing — see also disappearing, vanishing

[…] I choſe rather to reduce the demonſtrations of the following propoſitions to the firſt and laſt ſums and ratio's of naſcent and evaneſcent quantities, that is, to the limits of thoſe ſums and ratio's; […] Perhaps it may be objected, that there is no ultimate proportion of evaneſcent quantities; becauſe the proportion, before the quantities have vaniſhed, is not the ultimate, and when they are vaniſhed, is none. […] [B]y the ultimate ratio of evaneſcent quantities is to be underſtood the ratio of the quantities, not before they vaniſh, nor afterwards, but with which they vaniſh.

1729, Isaac Newton, “Section I. Of the Method of First and Last Ratio’s of Quantities, by the Help whereof We Demonstrate the Propositions that Follow.”, in Andrew Motte, transl., The Mathematical Principles of Natural Philosophy. […] , volume I, London: […] Benjamin Motte, […], →OCLC, book I (Of the Motion of Bodies), pages 54–55:

And what are theſe Fluxions? The Velocities of evaneſcent Increments? And what are theſe ſame evaneſcent Increments? They are neither finite Quantities, nor Quantities infinitely ſmall, nor yet nothing. May we not call them the Ghoſts of departed Quantities?

1734, [George Berkeley], The Analyst; or, A Discourse Addressed to an Infidel Mathematician. […], London: Printed for J[acob] Tonson […], →OCLC, section XXXV, page 59:

Some hold the evaneſcent increments to be real quantities, ſome to be nothings, ſome to be limits. As many Men, ſo many minds: Each differing one from another, and all from Sir Iſaac Newton.

1735, [George Berkeley], A Defence of Free-thinking in Mathematics. […], London: Printed for J[acob] Tonson, →OCLC, paragraph XLIV, page 55:

[Leonhard] Euler emphasized that the derivative is the ratio of the evanescent differentials and said that the integral calculus was concerned with finding the function itself.

1972, Morris Kline, “Calculus in the Eighteenth Century”, in Mathematical Thought from Ancient to Modern Times, New York, N.Y.: Oxford University Press, →ISBN; paperback edition, volume 2, New York, N.Y., Oxford, Oxfordshire: Oxford University Press, 1990, →ISBN, section 3 (The Technique of Integration and Complex Quantities), page 406:

(mathematics) Of a number or value: diminishing to the point of reaching zero as a limit; infinitesimal.


quantum

en-noun

quantum (countable and uncountable, plural quantums or quanta)

[ˈkʰwɑ̃ntʰə̃m]

[ˈkʰwɑ̃ɾ̃ə̃m]

From Late Latin quantum, noun use of neuter form of Latin quantus (“how much”).

Defined parts of a manifoldness are called Quanta

1882, William Kingdon Clifford, Mathematical Papers:

(mathematics) A definite portion of a manifoldness, limited by a mark or by a boundary.


explode

en-verb

explode (third-person singular simple present explodes, present participle exploding, simple past and past participle exploded)

explodes (present singular third-person)
exploding (participle present)
exploded (participle past)
exploded (past)
explode (infinitive)

First recorded around 1538, from the Latin verb explōdere (“drive out or off by clapping”). The meaning was originally theatrical, "to drive an actor off the stage by making noise," hence meaning to "to drive out" or "to reject". From ex- (“out”) + plaudere (“to clap; to applaud”). In English it used to mean to "drive out with violence and sudden noise" (from around 1660), and later meaning to "go off with a loud noise" (from around 1790). The sense of "bursting with destructive force" is first recorded around 1882.

The function f(x) = 1/x explodes around x = 0.

(mathematics) To increase arbitrarily or boundlessly.


explosive

en-adj

explosive (comparative more explosive, superlative most explosive)

more explosive (comparative)
most explosive (superlative)

From Latin explōs-, stem of the perfect passive participle of explōdō + the suffix -ive.

Notes: A rule set that (very probably) results in explosive growth; certainly in area if not population.

1992 June 2, Dave Boll, “Variations on Conway's LIFE”, in comp.theory.cell-automata (Usenet):

For example, putting a 1 at (0: 1,1) will cause explosive growth in all directions, putting a 1 at (0: 0,2A) will cause pairs of diagonal cells in a 2x2 square to alternate on and off, putting a 1 at (1: 4,4) will cause all solid 1 areas to stay 1 for another cycle, etc.

1994 April 4, Robert Andreen, “CA rules”, in comp.theory.cell-automata (Usenet):

If the rule is further chosen so that active cells can (and must) expand on an inactive background but inactive cells can't do so on an active background (or vice versa), then non-explosive growth becomes possible.

2003 May 12, Ilmari Karonen, “Gliders in 4-neighbor semitotalistic 2D cellular automata”, in comp.theory.cell-automata (Usenet):

en:like an explosion, e.g., of a fast fire

(cellular automata) Of a specific cellular automaton rule, tending to exhibit infinite and unpredictable growth when starting from finite random patterns.


equipartition

en-noun

equipartition (countable and uncountable, plural equipartitions)

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

(mathematics, of a graph) The partition of its vertex set into sets whose sizes differ from each other by no more than 1.


integral calculus

(calculus) The calculus that generalizes summation to find areas, masses, volumes, sums, and totals of quantities described by continuously varying functions.


amalgamate

en-verb

amalgamate (third-person singular simple present amalgamates, present participle amalgamating, simple past and past participle amalgamated)

amalgamates (present singular third-person)
amalgamating (participle present)
amalgamated (participle past)
amalgamated (past)

/əˈmælɡəˌmeɪt/

From Medieval Latin amalgamātus, past participle of amalgamāre, amalgama.

(transitive, mathematics) To combine (free groups) by identifying respective isomorphic subgroups.


FT

en-noun

FT (countable and uncountable, plural FTs)

Fourier transform
Fourier transform#English

(mathematics) Initialism of Fourier transform.


lambda expression

lambda expression (plural lambda expressions)

An algebraic expression representing a function by binding one or more parameters to an expression which may contain those parameters.


transition function

transition function (plural transition functions)

If (U#95;1,#92;psi#95;1) and (U#95;2,#92;psi#95;2) are two complex charts, then the transition function is #92;psi#95;#123;12#125;#58;#92;psi#95;1(U#95;1#92;capU#95;2)#92;rightarrow#92;psi#95;2(U#95;1#92;capU#95;2), given by #92;psi#95;#123;12#125;#61;#92;psi#95;2#92;circ#92;psi#95;1#123;-1#125;. We say M is a complex manifold if it has an atlas of complex charts (U,#92;psi), such that all the transition functions are holomorphic, as maps from #92;mathbb#123;C#125;ᵐ to itself.

2007, Dominic D. Joyce, Riemannian Holonomy Groups and Calibrated Geometry (Oxford graduate texts in mathematics), Oxford University Press, →ISBN, →LCCN, page 76:

differential geometry
differential geometry

(differential geometry) A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed.

transitiokuvaus

homeomorphism between subsets of images of overlapping coordinate charts


DFA

(machine learning) Initialism of direct feedback alignment.


mammoth

desc

→ Arabic: مَامُوث (māmūṯ)

→ Arabic: مَامُوث (māmūṯ)

→ Hebrew: מָמוּתָה (mamúta)

→ Hindi: मैमथ (maimath)

→ Japanese: マンモス (manmosu)

→ Khmer: ម៉ាមម៉ូត (maammout)

→ Korean: 매머드 (maemeodeu)

→ Thai: แมมมอธ (mɛm-mɔ́ɔt)

Cheshire Mammoth Cheese
Thomas Jefferson

From obsolete Russian ма́мант (mámant), modern ма́монт (mámont), probably from a Uralic language, such as Proto-Mansi *mē̮ŋ-ońt (“earth-horn”). Possibly influenced by behemoth.
The current Mansi word could mean "earth stag" ма̄хар (māhar), from Northern Mansi ма̄ (mā, “earth”) and ха̄р (hār, “stag”). Adjectival use was popularized in the early 1800s by references to the Cheshire Mammoth Cheese presented to American paleontologist and president Thomas Jefferson.

Maimanto, as they say a sea elephant which is never seene, but accordinge to the Samuites he workes himselfe under grownde and so they finde his teeth or homes or bones in Pechore and Nova Zemla of which they […]

1618, Richard James, “The Implications of James's Maimanto”, in Robert Auty, I. P. Foote, editors, Oxford Slavonic Papers. New Series., volume 9, Clarendon Press, published 1976, Dictionariolum Russico-Anglicum, page 103:

The Mammotovoy, which is dug out of the Earth in Siberia.

1698, Heinrich Wilhelm Ludolf, edited by Sir James Augustus Henry Murray, Sir William Alexander Craigie, and Charles Talbut Onions, A New English dictionary on historical principles: founded mainly on the materials collected by the Philological Society., volume 6, Oxford: Clarendon Press, published 1908, A. Brand's Emb. Muscovy into China, page 98:

The old Siberian Russians affirm that the Mammuth is very like the Elephant.

1706, Evert Ysbrants Ides, “An Account of Elephants Teeth and Bones, found under Ground”, in The Philosophical Transactions of the Royal Society of London, from Their Commencement in 1665 to the Year 1800., volume 7, London: C. and R. Baldwin, published 1809, Three Years Travels from Moscow Over-land to China: Thro' Great Ustiga, Siriania, Permia, Sibiria, Daour, Great Tartary, Etc. to Peking ; Containing an Exact and Particular Description of the Extent and Limits of Those Countries, and the Customs of the Barbarous Inhabitants; with Reference to Their Religion, Government, Marriages, Daily Imployments, Habits, Habitations, Diet Death, Funerals etc. to which is Annex'd an Accurat Description of China, Done Originally by a Chinese Author., page 243:

Any species of the extinct genus Mammuthus, of large, usually hairy, elephant-like mammals with long curved tusks and an inclined back, which became extinct with the last retreat of ice age glaciers during the late Pleistocene period, and are known from fossils, frozen carcasses, and Paleolithic cave paintings found in North America and Eurasia.


diagram

From French diagramme, from Italian diagramma, from Ancient Greek διάγραμμα (diágramma).

(category theory) A functor from an index category to another category. The objects and morphisms of the index category need not have any internal substance, but rather merely outline the connective structure of at least some part of the diagram's codomain. If the index category is J and the codomain is C, then the diagram is said to be "of type J in C".


representation

en-noun

representation (countable and uncountable, plural representations)

From Late Middle English representacioun, from Old French representacion, from Latin repraesentātiō. By surface analysis, represent + -ation.

(mathematics) An action of some algebraic structure (typically a group or algebra, particularly a Lie algebra) on a vector space, such that each element acts by a linear endomorphism.

kuvaus

mathematics: object that describes an abstract group in terms of linear transformations of vector spaces


imaginary

en-adj

imaginary (comparative more imaginary, superlative most imaginary)

more imaginary (comparative)
most imaginary (superlative)

/ɪˈmæd͡ʒɪnəɹi/

/ɪˈmæd͡ʒɪnɹi/

/ɪˈmæd͡ʒɪˌnɛɹi/

From Middle English ymaginarie, ymagynary, from Latin imāginārius (“relating to images, fancied”), from imāgō, equivalent to imagine + -ary.
The mathematical sense derives from René Descartes's use (of the French imaginaire) in 1637, La Geometrie, to ridicule the notion of regarding non-real roots of polynomials as numbers. Although Descartes' usage was derogatory, the designation stuck even after the concept gained acceptance in the 18th century.

der

purely imaginary → purely imaginary number

(mathematics, of a number) Having no real part; that part of a complex number which is a multiple of √ (called imaginary unit).


imaginary

/ɪˈmæd͡ʒɪnəɹi/

/ɪˈmæd͡ʒɪnɹi/

/ɪˈmæd͡ʒɪˌnɛɹi/

(mathematics, countable) An imaginary number.


concordant

en-adj

concordant (comparative more concordant, superlative most concordant)

more concordant (comparative)
most concordant (superlative)

French concordant, from Latin concordans, present participle of concordare. See concord.


undefined

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

The result of division by zero is undefined.

(mathematics, computing) That does not have a meaning and is thus not assigned an interpretation.


pivot

From Middle English pevet, *pivot, from Old French pivot (“hinge pin, pivot”) (12th c.), possibly from Latin pūgiō.

(mathematics) An element of a matrix that is used as a focus for row operations, such as dividing the row by the pivot, or adding multiples of the row to other rows making all other values in the pivot column 0.


redex

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

(mathematics) Something to be reduced according to the rules of a formal system.


TMI

en-noun

TMI (countable and uncountable, plural TMIs)

(organic chemistry) Initialism of trimethylindium.

transmarginal inhibition
transmarginal inhibition#English

(psychology) Initialism of transmarginal inhibition.

trans-Mars injection
trans-Mars injection#English

(astrodynamics) Initialism of trans-Mars injection.


heteroscedasticity

heteroscedasticity (countable and uncountable, plural heteroscedasticities)

(statistics) The property of a series of random variables in having differing variances of residuals, instead of a uniform variance.


moonshine

moonshine (countable and uncountable, plural moonshines)

From Middle English mone schyne, mone-schyne, moone shone; equivalent to moon + shine. Illegally distilled liquor is so named because its manufacture may be conducted without artificial light at night. The verb sense is a back-formation from moonshiner.

(mathematics, uncountable) A branch of pure mathematics relating the Monster group to an invariant of elliptic functions.


heptagonal

Since 16th century, from heptagon + -al.

(mathematics, of a number) Belonging to the sequence generated by the formula (5n²-3n)/2.


diminish

en-verb

diminish (third-person singular simple present diminishes, present participle diminishing, simple past and past participle diminished)

diminishes (present singular third-person)
diminishing (participle present)
diminished (participle past)
diminished (past)

Formed under the influence of both diminue (from Old French diminuer, from Latin dīminuo) and minish.

verlagen

To reduce a perfect or minor interval by a semitone

Although British involvement in the slave trade prior to 1807 cannot be denied, or its effects diminished, it is also a fact that the Royal Navy was pretty much the only force in the world in the 19th century with the numbers, drive, willingness, firepower, and capability to curtail the global slave trade, and that, without these efforts, many more would no doubt have been taken to slave plantations and other such destinations during the 19th, and possibly even into the 20th, centuries, as it must be remembered that a great many European powers would only begrudgingly commit to ending the slave trade when the other option was continuous war with the British Empire.

2018 December 1, Drachinifel, 11:37 from the start, in Anti-Slavery Patrols - The West Africa Squadron, archived from the original on 2024-11-29:

(transitive) To make appear smaller than in reality; to dismiss as unimportant.


megahertz

en-noun

megahertz (plural megahertz or megahertzes)

A unit equal to one million cycles per second.


inclusion

inclusion (countable and uncountable, plural inclusions)

Borrowed from Latin inclusio, inclusionis, from the verb Latin inclūdō (“to shut in, enclose, insert”), from in- (“in”) + claudō (“to shut”), ultimately from Proto-Indo-European *kleh₂u- (“key, hook, nail”). By surface analysis, include + -sion. Doublet of enclosure.

der

(mathematics) A mapping where the domain is a subset of the image.


collection

en-noun

collection (countable and uncountable, plural collections)

From Middle English colleccioun, collection, from Old French collection, from Latin collēctiō, collēctiōnem, from collēctus, from colligō (“collect together”), composed of con- + legō (“bring together, gather, collect”), ultimately from Proto-Indo-European *leǵ- (“to gather, collect”).

der

(set theory, topology, mathematical analysis) A set of sets; used because such a thing is in general too large to comply with the formal definition of a set.


indivisible

divisible

antonym(s) of “incapable of being divided, arithmetic”

incombinable

antonym(s) of “incapable of being combined”

PIE word
 *dwóh₁
From Middle French indivisible, from Late Latin indivisibilis.

(arithmetic) Incapable of being divided by a specific integer without leaving a remainder.

jaoton

incapable of being divided by a specific integer


indivisible

(geometry) An infinitely small quantity which is assumed to admit of no further division.


permanent

From Middle English permanent, permanente, from Middle French permanent, from Latin permanēns, from permaneō (“I stay through”). First attested in the 15th century.

(linear algebra, combinatorics) Given an n×n matrix a_ij,, the sum over all permutations π, of ∏ᵢ₌₁ⁿa_iπ(i).


negative

en-adj

negative (comparative more negative, superlative most negative)

more negative (comparative)
most negative (superlative)

From Middle English negative, negatif, from Old French negatif, from Latin negātīvus (“that denies, negative”), from negāre (“to deny”); see negate.

der

(mathematics) Of a number: less than zero.

I was out in negative weather today.

(weather) Less than zero degrees Celsius or Fahrenheit.


invariant

en-adj

invariant (comparative more invariant, superlative most invariant)

more invariant (comparative)
most invariant (superlative)

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

The fundamental 2-tensor also leads to a new class of invariant linear differential operators that are canonically associated to these geometries; included is a third equation studied by Gallot et al. We apply the results to study the metrisability equation, in the nullity setting described.

2015, A. Rod Gover, Vladimir S. Matveev, “Projectively related metrics, Weyl nullity, and metric projectively invariant equations”, in arXiv:

(mathematics) Unaffected by a specified operation, especially by a transformation.

invariantní

that is not affected by a specified operation


prodigious

prodigious (comparative more prodigious, superlative most prodigious)

more prodigious (comparative)
most prodigious (superlative)

/pɹəˈdɪd͡ʒəs/

/pɹəˈdɪd͡ʒəs/

Etymology tree
Proto-Indo-European *per-
Proto-Indo-European *pró
Proto-Indo-European *pro-
Proto-Italic *pro-
Latin prō-
Latin aiō
Latin -ium
Latin prōdigium
Latin -ōsus
Latin prōdigiōsusbor.
Middle English prodigious
English prodigious
The adjective is derived from Late Middle English prodigious (“warning of disaster, portentous”), from Latin prōdigiōsus (“strange, unnatural; marvellous, wonderful, prodigious”), from prōdigium (“prophetic sign, omen, portent; prodigy, wonder”) + -ōsus (suffix meaning ‘full of’ forming adjectives from nouns). Prōdigium is derived from prō- (prefix denoting a forward direction, something before or prior, or prominence) + aiō (“to say, speak”) (ultimately from Proto-Indo-European *h₁eǵ- (“to say”)) + -ium (suffix forming abstract nouns). The English word is analysable as prodigy + -ous.
The adverb is derived from the adjective.
Cognates
* Catalan prodigiós
* Middle French prodigieux (“portentous”) (modern French prodigieux)
* Italian prodigioso
* Portuguese prodigioso
* Spanish prodigioso

der

(extent, quantity):

(size):

(size):

[T]he figges […] are a fruit for a king, anſvverable to the mightie, huge, and prodigious tree that beareth it.

1601, C[aius] Plinius Secundus [i.e., Pliny the Elder], “[Book XII.] Of Certain Thornes and Fig-trees of India.”, in Philemon Holland, transl., The Historie of the World. Commonly Called, The Naturall Historie of C. Plinius Secundus. […], 1st tome, London: […] Adam Islip, →OCLC, page 360:

This Urſula is ſaid to have carried over out of Britain, eleven thouſand Maids of prime quality, beſides threeſcore thouſand of meaner rank, (ſeventy one thouſand in all, a prodigious number,) to be married to ſo many in little Britain in France. Prepoſterous in my mind, to proffer themſelves, and it had argued more modeſty if their Husbands had fetcht them hence.

a. 1662 (date written), Thomas Fuller, “Cornwall”, in The History of the Worthies of England, London: […] J[ohn] G[rismond,] W[illiam] L[eybourne] and W[illiam] G[odbid], published 1662, →OCLC, page 199:

VVHEN John firſt brought out the Bills, the Surprize of all the Family vvas unexpreſſible, at the prodigious Dimenſions of them; […]

1712, Humphry Polesworth [pseudonym; John Arbuthnot], “How John Look’d Over His Attorney’s Bill”, in Law is a Bottomless-Pit. […], London: […] John Morphew, […], →OCLC, page 20:

[I]t [a penis] vvas poſitively of ſo tremendous a ſize, […] you might have troll'd dice ſecurely along the broad back of the body of it: the length of it too vvas prodigious; […]

1749, [John Cleland], “[Letter the Second]”, in Memoirs of a Woman of Pleasure [Fanny Hill], volume II, London: […] [Thomas Parker] for G. Fenton [i.e., Fenton and Ralph Griffiths] […], →OCLC, page 188:

[T]hey were not the spoiled children of affectation and refinement, but a bold, vigorous, independent race of thinkers, with prodigious strength and energy, with none but natural grace, and heartfelt unobtrusive delicacy.

1820, William Hazlitt, “Lecture I. Introductory.”, in Lectures Chiefly on the Dramatic Literature of the Age of Elizabeth. […], London: Stodart and Steuart, […]; Edinburgh: Bell and Bradfute, →OCLC, page 2:

Very big in extent, quantity, or size; abundant; intense; colossal, huge.

огромен

very big in extent, quantity, or size — see also abundant, intense, huge


identical

en-adj

identical (comparative more identical, superlative most identical)

more identical (comparative)
most identical (superlative)

(not comparable, mathematics) Exactly equivalent.


equivalent

equivalent (comparative more equivalent, superlative most equivalent)

more equivalent (comparative)
most equivalent (superlative)

From equi- + -valent.
From Latin aequivalentem, accusative singular of aequivalēns, present active participle of aequivaleō (“I am equivalent, have equal power”).

Finite sets A and B are equivalent sets only when n(A) = n(B) i.e., the number of elements in A and B are equal.

c. 2005, P N Gupta Kulbhushan, Comprehensive MCQ's in Mathematics, page 3:

All enumerable sets are equivalent to each other, but not to any finite set.

1950, E. Kamke, Theory of Sets, page 16:

Equivalent sets should, by rights, have the same "number" of elements. For this reason we sometimes say that equivalent sets have the same cardinality.

2000, N. L. Carothers, Real Analysis, page 18:

The equivalence theorem: If both M is equivalent to a subset N₁ of N and N is equivalent to a subset M₁ of M, then the sets M and N are equivalent to each other.

2006, Joseph Breuer, Introduction to the Theory of Sets, page 41:

(mathematics) Of two sets, having a one-to-one correspondence.

等价的

of two sets, having a one-to-one relationship

equivalence relation
equivalence relation

(mathematics) Relating to the corresponding elements of an equivalence relation.

еквивале́нтен

relating to the corresponding elements of an equivalence relation

naturally isomorphic
natural isomorphism

(mathematics, category theory) Of two categories, (informally) such that one is essentially a relabeling of the other; (formally) related by a pair of functors such the composition of the one with the other is naturally isomorphic to the identity functor.

A square may be equivalent to a triangle.

(geometry) Equal in measure but not admitting of superposition; applied to magnitudes.


variety

en-noun

variety (countable and uncountable, plural varieties)

From Middle French varieté (“variety”) (modern French variété (“variety; genre, type”)) or directly from its etymon Latin varietās (“difference; diversity, variety”) + English -ty (suffix forming abstract nouns from adjectives). Varietās is derived from varius (“different, diverse, various; variegated”) (possibly ultimately from Proto-Indo-European *h₁weh₂- (“to abandon; to give out; to leave”)) + -tās (suffix forming feminine abstract nouns indicating a state of being). The English word displaced the native Old English mislīcnes.
Sense 1.3.2 (“total number of distinct states of a system; logarithm to the base 2 of the total number of distinct states of a system”) was coined by the English psychiatrist William Ross Ashby (1903–1972) in his work An Introduction to Cybernetics (1956).
Cognates
* Galician variedade (“variety”)
* Italian varietà (“difference; variety”)
* Portuguese variedade (“variety”)
* Spanish variedad (“breed; variety”)

der

A collection or number of different things.

In universal algebra: an equational class; the class of all algebraic structures of a given signature, satisfying a given set of identities.

varisto

in universal algebra: the class of all algebraic structures of a given signature, satisfying a given set of identities

(algebraic geometry) Ellipsis of algebraic variety (“the set of solutions of a given system of polynomial equations over the real or complex numbers; any of certain generalisations of such a set that preserves the geometric intuition implicit in the original definition”).

algebraic variety
algebraic variety#English

algebraic variety

(cybernetics) The total number of distinct states of a system; also, the logarithm to the base 2 of the total number of distinct states of a system.


hypercomplex number

en-noun

hypercomplex number (plural hypercomplex numbers)

(mathematics) Any of several types of extended complex number, consisting of a real part and two or more imaginary parts (each a real multiple of a distinct square root of −1), which may be imagined as a point in a multi-dimensional space.


mud

mud (countable and uncountable, plural muds)

From Middle English mud, mudde, mode, probably a borrowing from Middle Dutch mod, modde or Middle Low German mudde, ultimately from Proto-Germanic *mud-, *mudra- (“mud”), perhaps from Proto-Indo-European *mū-, *mew- (“moist”). Cognate with Saterland Frisian Mudde (“mud”), Middle High German mot (“mud”), Swedish modd (“slush”). Compare also suffixed variants West Frisian modder (“mud”), Dutch modder (“mud”), German Low German Mudder (“mud”), German Moder (“moldiness, mildew, decay”), English mother (“vinegar-forming sediment in alcohol”), Danish mudder (“mud”). Alternative etymology suggests the Proto-Germanic word is possibly borrowed from a Uralic language (compare e.g. Finnish muta (“mud”), Northern Sami mođđi (“mud”), from Proto-Uralic *muďa).

cog

throw enough mud at the wall and some of it will stick


morbidity

en-noun

morbidity (countable and uncountable, plural morbidities)

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

Recorded since 1656; from morbid, from Latin morbidus (“diseased”), from morbus (“disease”), from the root of morī (“to die”) or from Proto-Indo-European *mer- (“to rub, pound, wear away”).

der

(medicine, countable) Adverse effects caused by a medical treatment such as surgery.

(demography, insurance) The sickness rate of a population.


prompt

From French prompt, from Latin prōmptus (“visible, apparent, evident”), past participle of prōmō (“to take or bring out or forth, produce, bring to light”), from prō (“forth, forward”) + emō (“to take, acquire, buy”).

For instance, using the “instruct” mode, I once gave GPT-3 the prompt: “Write an essay discussing the role of metafiction in the work of Italo Calvino.”

2022 April 15, Steven Johnson, Nikita Iziev, “A.I. Is Mastering Language. Should We Trust What It Says?”, in The New York Times, →ISSN:

(machine learning) Textual input given to a large language model or image model in order to have it generate a desired output.


prompt

en-verb

prompt (third-person singular simple present prompts, present participle prompting, simple past and past participle prompted)

prompts (present singular third-person)
prompting (participle present)
prompted (participle past)
prompted (past)

I want to prompt this new AI art generator to create an image of a panda riding a bike.

ordinary language
ordinary language#English

artificial intelligence
artificial intelligence#English

(transitive, machine learning) To provide textual input in the form of ordinary language to (an artificial intelligence or language model) to have it generate a desired output.

prompter

to give instructions to an artificial intelligence system


stationary point

en-noun

stationary point (plural stationary points)

(mathematics) A point on a curve where the gradient is zero. This point can be a maximum, a minimum, or a point of inflection.


US survey acre

Unit of measure for areas, defined as 43,560 square feet,https://web.archive.org/web/20041204052555/http://ts.nist.gov/ts/htdocs/230/235/appxc/appxc.htm or 4,046.8564224 square meters. A square mile has 640 acres.


derivable

[dɪˈɹaɪvəbəɫ]

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


module

Borrowed from French module, from Latin modulus (“a small measure, a measure, mode, meter”), diminutive of modus (“measure”) (whence mode). Doublet of modulus and mold.

der

Meronym: element

Modules over a ring are a generalization of abelian groups (which are modules over #92;textstyle#92;mathbb#123;Z#125;).

1974, Thomas W. Hungerford, Algebra, Springer, page 168:

Approximately forty-five years ago K. Morita presented the first major results on equivalences and dualities between categories of modules over a pair of rings.

2004, Robert R. Colby, Kent R. Fuller, Equivalence and Duality for Module Categories (with Tilting and Cotilting for Rings), Cambridge University Press, page vii:

One defines in like manner right K-modules and two-sided K-modules. If K is commutative, then every left K-module is automatically equipped with the structure of right and a two-sided K-module.

2012, A. A. Kirillov, Elements of the Theory of Representations, Springer, page 29:

scalar multiplication
scalar multiplication

(algebra, ring theory) An abelian group equipped with the operation of multiplication by an element of a ring (or another of certain algebraic objects), representing a generalisation of the concept of vector space with scalar multiplication.

模

type of algebraic structure, generalization of vector spaces over non-field rings

(fractal geometry, mathematics) A fractal element.