Zariski topology

Zariski topology (plural Zariski topologies)

After Russian-born American mathematician Oscar Zariski (1899—1986), regarded as one of the most influential algebraic geometers of the 20th century.

The Zariski topology allows tools from topology to be used in the study of algebraic varieties, even when the underlying field is not a topological field.

Thus the Zariski open subsets are 'very big'; in particular, the Zariski topology is highly non-Hausdorff.
A further difference with the classical topology is that the Zariski topology on the product X#92;timesY of two affine varieties is stronger than the product of the Zariski topologies on X and Y.

1994, V. I. Danilov, “II. Algebraic Varieties and Schemes”, in I. R. Shafarevich, editor, Algebraic Geometry I: Algebraic Curves, Algebraic Manifolds and Schemes, Springer, page 184:

In particular, “singular” is a local notion, where “local” so far was mainly considered with respect to the Zariski topology. However, since the Zariski topology is so coarse, small neighbourhoods in the Zariski topology might not be local enough.

2008, Gert-Martin Greuel, Gerhard Pfister, A Singular Introduction to Commutative Algebra, 2nd edition, Springer, page 523:

If Y#92;subseteqKⁿ is an affine variety, then by definition the Zariski topology on Y has the subvarieties of Y as closed sets.

2011, Gregor Kemper, A Course in Commutative Algebra, Springer, page 34:

algebraic subvarieties
algebraic subvariety

(algebraic geometry) Originally, a topology applicable to algebraic varieties, such that the closed sets are the variety's algebraic subvarieties; later, a generalisation in which the topological space is the set of prime ideals of a commutative ring and is called the spectrum of the ring.


maplet

(mathematics) A pair which is a member of a mapping.


maplet

Michael J. Caulfield, Gannon University (1046-O1-346) 10:40AM - (1105) A maplet for encoding, decoding, and correcting errors in Golay codes.

2009 January, Notices of the American Mathematical Society, volume 56, number 1:

(computing, mathematics) An applet written in the computer algebra system Maple.


pseudodifferential operator

en-noun

pseudodifferential operator (plural pseudodifferential operators)

The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory.

partial differential equation
partial differential equation

quantum field theory
quantum field theory

(mathematics) An extension of the differential operator, used in the theory of partial differential equations and quantum field theory.


Fock space

Named after V. A. Fock, who introduced it in his paper Konfigurationsraum und zweite Quantelung (1932).

(mathematics) An algebraic system used in quantum mechanics to describe quantum states with a variable or unknown number of particles.


Macdonald polynomial

Macdonald polynomial (plural Macdonald polynomials)

(mathematics) Any of a two-parameter family of orthogonal polynomials indexed by a positive weight of a root system.


trefoil knot

From trefoil + knot, from being a knot theory knot, where its simplest symmetrical configuration appears like a trefoil.
File:Trefoil-non-3-symm.svg|A trefoil knot lacking three-fold symmetry
File:Tricoloring.png|The trefoil knot with each lobe highlighted
File:Trefoil Knot.gif|Trefoil knot

(topology) A knot formed by joining the two loose ends of a overhand knot to form a knotted loop; the simplest non-trivial knot.


pronic

Apparently from New Latin pronicus, a misspelling of Latin promicus, from Ancient Greek προμήκης (promḗkēs, “elongated, oblong”), but the spelling has been pronic from its earliest known occurrence in English ( Leonhard Euler, Opera Omnia, series 1, volume 15).

der

1478 - Pierpaolo Muscharello, Algorismus p.163.
Pronic root is as if you say, 9 times 9 makes 81. And now take the root of 9, which is 3, and this 3 is added above 81: it makes 84, so that the pronic root of 84 is said to be 3.

1794 - David Wilkie, Theory of interest, p.6, Edinburgh: Peter Hill, 1794.
When a = 2, and d = 2 also, in this case, in equation 1st, s=n² + n = a pronic number, which is produced by the addition of even numbers in an arithmetic progression beginning at 2; and the pronic root scriptstyle n=(√4s+1-1)/2.

1804 - Paul Deighan, "Recommendatory letters", A complete treatise on arithmetic, rational and practical, vol.1, p.viii, Dublin: J. Jones, 1804.
As I admire each proposition fair,
the pronic number and the perfect square,
the puzzling intricate equation solv'd,
as Grecia's chief the Gordian knot dissolv'd;
- John Bartley

A pronic number is that which is equal to the sum of a square number and its root. Thus, 6, 12, 20, 30, &c. are pronic numbers.

1814 - Charles Butler, Easy Introduction to Mathematics, p.96, Barlett & Newman, 1814

It may be noted that if Lₙ is a pronic number, then Lₙ is two times a triangular number.

1998, Wayne L. McDaniel, “Pronic Lucas Numbers”, in The Fibonacci Quarterly, pages 60–62:

2005 - G. K. Panda1 and P. K. Ray, "Cobalancing numbers and cobalancers", International Journal of Mathematics and Mathematical Sciences, vol.2005, iss.8, pp.1189-1200.
Thus, our search for cobalancing number is confined to the pronic triangular numbers, that is, triangular numbers that are also pronic numbers.

(mathematics) Of a number which is the product of two consecutive integers


heteromecic

[1] Again, then, to take a fresh start, a number is called heteromecic if its representation, when graphically described in a plane, is quadrilateral and quadrangular, to be sure, but the sides are not equal to one another, nor is the length equal to the breadth, but they differ by 1. Examples are 2, 6, 12, 20, 30, 42, and so on, for if one represents them graphically he will always construct them thus: 1 times 2 equals 2, 2 times 3 equals 6, 3 times 4 equals 12, and the succeeding ones similarly, 4 times 5, 5 times 6, 6 times 7, 7 times 8, and thus indefinitely, provided only that one side is greater than the other by 1 and by no other number.

1952 [c. 100], Nicomachus of Gerasa, translated by Martin Luther D’Ooge, edited by Robert Maynard Hutchins, Mortimer J. Adler, and Wallace Brockway, Introduction to Arithmetic II (Great Books Of The Western World; 11), William Benton (Encyclopædia Britannica, Inc.), page 838:

Twice a triangular number is a heteromecic number.

(mathematics) Of a number which is the product of two consecutive integers.


rectangular number

en-noun

rectangular number (plural rectangular numbers)

(mathematics) A number which is the product of two consecutive integers.

suorakulmainen luku

(mathematics) A composite number; or a composite number which is not a square; or a composite number which is neither square nor heteromecic.


oblong number

If, however, the sides differ otherwise than by 1, for instance, by 2, 3, 4 or succeeding numbers, as in 2 times 4, 3 times 6, 4 times 8, or however else they may differ, then no longer will such a number be properly called a heteromecic, but an oblong number. For the ancients of the school of Pythagoras and his successors saw “the other”³ and “otherness” primarily in 2, and “the same” and “sameness” in 1, as the two beginnings of all things, and these two are found to differ from each other only by 1. Thus “the other” is fundamentally “other” by 1, and by no other number, and for this reason customarily “other” is used, among those two speak correctly, of two things and not of more than two.


explementary angles

(geometry) A pair of angles that sum to 360 degrees.


conjugate angles

(geometry) A set of angles that sum to 360 degrees.


antidifference

If f(x)=bˣ then F(x)=bˣ/(b-1)+C is the general antidifference since F(x+1)-F(x) = [bˣ⁺¹/(b-1)+C] - [bˣ/(b-1)+C] = (bˣ⁺¹-bˣ)/(b-1) = bˣ = f(x).

A function F(x) is the antidifference of f(x) if F(x+1)-F(x)=f(x).


pseudoradical

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

(mathematics) The intersection of the set of nonzero prime ideals of a ring.


zeroid

If a semigroup S contains a zeroid, then every left zeroid is also a right zeroid, and vice versa, and the set K of all the zeroids of S is the kernel of S.

1961, Alfred Hoblitzelle Clifford, G. B. Preston, The Algebraic Theory of Semigroups, page 70:

Simplex zeroids seem to provide an alternative framework for discussing the themes broached in this paper, and of course Theorems 1—4 can be reexpressed in terms of simplex zeroids.

1993, Keith Walker, Surveys in combinatorics, 1993, page 166:


DWT

mathematical analysis
mathematical analysis

discrete wavelet transform
discrete wavelet transform

(mathematical analysis) discrete wavelet transform


hypograph

(mathematics, of a function) the set of all points lying on or below its graph.


integraph

(mathematics) A device that determines the value of an integral by measuring the area under a curve (and drawing the curve of its integral)


CWT

continuous wavelet transform
continuous wavelet transform#English

(mathematical analysis) Initialism of continuous wavelet transform.


decare

A unit of surface area equal to 10 ares (that is, 1,000 square metres, 0.10 hectares, or approximately 0.25 acres)


Boolean ring

Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.

From the defining idempotency property of a Boolean ring it is possible to prove that such ring has to have the further properties that each element is its own inverse and that such ring must be commutative.

multiplicative operation
multiplicative operation

(algebra) A ring whose multiplicative operation is idempotent.


LPF

(signal processing) Initialism of low-pass filter.


gigaampere

(metrology) An SI unit of current equal to 10⁹ amperes. Symbol: GA


zeptojoule

When a bundle with a drag coefficient of 200 nN · sec · m⁻¹ (Howard and Hudspeth, 1988) produced a 25 nm, triangle-wave twitch 5 msec in total duration (Fig. 12A), the energy dissipated against viscous drag was ~100 zJ (a zeptojoule is 10⁻²¹ J).

1996 September 15, Michael E. Benser, Robert E. Marquis, A. J. Hudspeth, “Rapid, Active Hair Bundle Movements in Hair Cells from the Bullfrog's Sacculus”, in The Journal of Neuroscience, 16(18), p. 5638:

The associated work is
W = 38.5 nm² × (10⁻⁹m/nm)² 35 pN/μm
(10⁻¹² N/pN) (μm/10⁻⁶ m) = 1.35 × 10⁻²¹ J
or about one zeptojoule.

2012, Christopher R. Jacobs, Hayden Huang, Ronald Y. Kwon, Introduction to Cell Mechanics and Mechanobiology, page 327:

However, with zeptojoule scale switching energies and novel functionality, the BiSFET could add a substantial amount of road!

2015, Tsu-Jae King Liu, Kelin Kuhn, CMOS and Beyond, page 204:

(metrology) An SI unit of energy equal to 10⁻²¹ joules. Symbol: zJ


petakelvin

(metrology) An SI unit of temperature equal to 10¹⁵ kelvins. Symbol: PK


giganewton

For example, the as-received 203-micrometer (7.98-mil) fibers had an average tensile strength of 3.59 giganewtons per square meter (521 ksi) with a coefficient of variation of 23.5 percent.

1976, Robert J. Smith, Changes in boron fiber strength due to surface removal by chemical etching, NASA:

The following values have been calculated for femurs, in units of square metres per giganewton, where 1 giganewton = 10⁹ newtons, and with body mass given in tonnes, where 1 tonne = 10³ kilograms.

1997, Michael J. Sewell, Mathematics Masterclasses: Stretching the Imagination, Oxford University Press, →ISBN, page 172:

If the fibres are all aligned in one direction, it is quite easy to achieve a modulus of 50 GN/m² and a tensile strength of 600 MN/m², although the shear modulus is at best only a few giganewtons per square metre.

1998 August 3, P. C. Powell, A. J. Ingen Housz, Engineering with Polymers, 2nd edition, →ISBN, page 9:

what does a giganewton do to an asteroid in the order of magnitude say 1/100 of a planet (otherwise it would have no impact at the planet).

2002 January 21, Walter Meissl, “Re: More Venus Terraforming Ideas”, in sci.space.science (Usenet), message-ID <a2hkig$k0b$1@news.tuwien.ac.at>:

Modulus of elasticity is given in units of force per unit area, typically giganewtons per square meter (GN/m²), or gigapascals (GPa).

2003 June 30, Kenneth J. Anusavice, Phillips' Science of Dental Materials, Elsevier Health Sciences, →ISBN, page 82:

I found "Electrostatic Levitation" <[…]> inspiring. However, under standard sunheat and ionization, the +.1 C/kg (It should be positive, not negative, as of course the sun boils electrons off the ground and air making them positive.) fee would strain a Static Shock-sizely pad with at least a giganewton.

2005 December 31, Autymn D. C., “Scientists and Engineers: Make a beginner's flying saucer, better than the Avrocar or Lifter”, in sci.physics (Usenet), message-ID <1136050698.560388.57590@g14g2000cwa.googlegroups.com>:

(metrology) An SI unit of force equal to 10⁹ newtons. Symbol: GN


kilomole

(metrology) An SI unit of amount of substance equal to 10³ moles. Symbol: kmol


zeptomole

/ˈzɛptəʊˌməʊl/

It has been repeatedly shown that enzyme-derived ODN-based assays can detect as little as 50 zeptomoles of target DNA corresponding to about 25,000 molecules.

2002, Jeffrey Van Ness, “Present and Future of Tags and Labels in High Throughput Genomic Analysis”, in D. J. Galas, S. J. McCormack, editors, Genomic Technologies: Present and Future: Functional Genomics Series, Caister Academic Press, →ISBN, pages 144–145:

The sensitivity of detection is in the range of zeptomoles […]

2005, Beatriz Sanchez-Vega, “Introduction to Capillary Electrophoresis of DNA: Biomedical Applications”, in John M. Walker, Ralph Rapley, editors, Medical Biomethods Handbook, Humana Press, →ISBN, page 109:

This scatter-based method enables detection of zeptomole quantities of nucleic acid targets […]

2008, Kewal K. Jain, The Handbook of Nanomedicine, Humana Press, →ISBN, page 88:

(physical chemistry) 10⁻²¹ mole, or about 600 molecules. SI symbol: zmol.


zettaampere

An SI unit measure of electrical current, equivalent to 10²¹ amperes (a sextillion amperes). 'ZA' is the SI unit symbol for the zettaampere.

zetta-ampère

SI unit of electrical current equal to 1021 amperes


teraampere

(metrology) An SI unit of current equal to 10¹² amperes. Symbol: TA


megacandela

Under clear sky conditions the luminance of the sun itself is around 1650 Mcd/m² (megacandela/m²)[.]

1980, S. V. Szokolay, Environmental science handbook for architects and builders, page 99:

Searchlights utilized in helicopter operations range in size from a 450-watt, 0.4 megacandela unit using a type PAR-46 incandescent lamp (see Fig 20-3) up to a 30-kilowatt, xenon-lamped unit[.]

1987, John E. Kaufman, Jack F. Christensen, IES Lighting Handbook: Application volume, →ISBN:

The light-emitting capacity of an LED is measured in megacandela [recte millicandelas] or mcd. Small commercial LEDs range from 10 to about 5000 mcd.

2012, Julio Sanchez, Maria P. Canton, Embedded Systems Circuits and Programming, →ISBN, page 12:

luminous intensity
luminous intensity#English

(metrology) An SI unit of luminous intensity equal to 10⁶ candelas. Symbol: Mcd


kilocandela

(metrology) An SI unit of luminous intensity equal to 10³ candelas. Symbol: kcd


kilokelvin

(metrology) An SI unit of temperature equal to 10³ kelvins. Symbol: kK


decaampere

(metrology) An SI unit of current equal to 10¹ amperes. Symbol: daA


megabecquerel

A unit of radioactivity equal to one million becquerels.


gigacandela

An SI unit of measurement equivalent to one billion (10⁹) candelas, abbreviated as Gcd.


exajoule

(metrology) An SI unit of energy equal to 10¹⁸ joules. Symbol: EJ


terabecquerel

A unit of radioactivity equal to one trillion becquerels.


gigabecquerel

A unit of radioactivity equal to one billion becquerels.


kilobecquerel

A unit of radioactivity equal to one thousand becquerels


centimole

amount of substance
amount of substance#English

(metrology) An SI unit of amount of substance equal to 10⁻² moles. Symbol: cmol


nanocandela

(physics) A unit of luminous intensity equal to 10⁻⁹ of a candela


nanokelvin

thermodynamic temperature
thermodynamic temperature#English

(metrology) An SI unit of thermodynamic temperature equal to 10⁻⁹ kelvins. Symbol: nK


yoctomole

A low cost, 0.75-mW helium neon laser, operating in the green region at 534.5 nm, is used to excite fluorescence from tetramethylrhodamine isothiocyanate-labelled DNA fragments that have been separated by capillary gel electrophoresis.The detection limit (3σ) for the dye is 500 ymol [1 yoctomole (1 ymol) = 10⁻²⁴ mol] or 300 analyte molecules in capillary zone electrophoresis

1991, Da Yong Chen et al., “Low-cost, high-sensitivity laser-induced fluorescence detection for DNA sequencing by capillary gel electrophoresis”, in Journal of Chromatography, volume 559, →DOI, page 237:

(metrology) An SI unit of amount of substance equal to 10⁻²⁴ moles. Symbol: ymol. The yoctomole is approximately 0.6 of an individual particle.


clique number

(graph theory) The number of vertices in a maximum clique of a given graph.

Clique (graph theory)
Glossary of graph theory


sweep out

en-verb

sweep out (third-person singular simple present sweeps out, present participle sweeping out, simple past and past participle swept out)

sweeps out (present singular third-person)
sweeping out (participle present)
swept out (participle past)
swept out (past)

(mathematics) To construct a three-dimensional shape by rotation of a two-dimensional one about an axis


group action

en-noun

group action (countable and uncountable, plural group actions)

(group theory) A mapping of a mathematical group to the permutations of an object that is compatible with the group operation.


Cassini oval

Named after the astronomer Giovanni Domenico Cassini, who studied them in 1680.

(geometry) A plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant (related to an ellipse, for which the sum of the distances is constant).


psc

(geometry) Abbreviation of parallax second.


potrzebie

From a case form of Polish potrzeba, adopted as a catchphrase by Mad magazine in the 1950s, and applied to a system of measurement by American computer scientist Donald Knuth (then a high-schooler).

(humorous) A fictional unit of length defined as the thickness of issue #26 (November 1955) of Mad Magazine, or approximately 2.26 millimetres.


setlike

en-adj

setlike (comparative more setlike, superlative most setlike)

more setlike (comparative)
most setlike (superlative)

(mathematics) Resembling or characteristic of a mathematical set.


eutactic

(mathematics, chemistry) Perfectly ordered


aleph number

(set theory) Any of a sequence of numbers used to represent the cardinality of infinite sets, denoted by the Hebrew letter aleph.


weird number

(number theory) A natural number that is abundant but not semiperfect; one for which the sum of the proper divisors (including 1 but not itself) is greater than the number, but no subset of those divisors sums to the number itself.


quasitoric

(mathematics) Describing a smooth 2n-dimensional manifold that admits a smooth, locally standard action of an n-dimensional torus, with orbit space an n-dimensional simple convex polytope.


multibracket

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

(algebra) A partition of a set into disjoint subsets such that each subset contains an even number of elements, and that if those elements are ordered, they divide the subset into ranges (1st to 2nd element, 3rd to 4th element, and so on) such that no element from another subset appears in any of the ranges.


Kolmogorov

Named after Russian mathematician Андре́й Никола́евич Колмого́ров (Andréj Nikolájevič Kolmogórov) (1903–1987)

lang

Андре́й Никола́евич Колмого́ров

Андре́й Никола́евич Колмого́ров

xlit

Андре́й Никола́евич Колмого́ров

Андре́й Никола́евич Колмого́ров

named-after

Андре́й Никола́евич Колмого́ров

(of a topological space) Such that any two distinct points are topologically distinguishable, i.e., there is an open set containing one of the points which does not contain the other point.


Kolmogorov space

en-noun

Kolmogorov space (plural Kolmogorov spaces)

Named in honor of Andrey Kolmogorov (1903–1987), a Soviet mathematician.

The Kolmogorov quotient of any topological space is a Kolmogorov space.

(topology) A topological space for which any pair of distinct points are also topologically distinct, i.e., there is an open set which contains one of the points but not the other one.


overprime

Let q be a minimal overprime of S.

(mathematics) A prime number larger than some given natural number.


infinity symbol

infinity symbol (plural infinity symbols)

A lemniscate; the figure ∞ that represents infinity.


null sign

(set theory) The sign ∅, associated with empty sets.


quadrantal

From Latin quadrantālis (“quarter, containing the fourth part of a measure”).

der

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

quadrantal space; quadrantal triangle; quadrantal versor

(geometry) Of or relating to a quadrant, or included in the fourth part of a circle.


squashable

en-adj

squashable (comparative more squashable, superlative most squashable)

more squashable (comparative)
most squashable (superlative)

All other ergodic invariant Radon measures are squashable, and there are infinitely many such measures.

2006, American Institute of Mathematical Sciences, Discrete and continuous dynamical systems: Volume 16:

(mathematics) Permitting a grouping of 2-cells in oppositely oriented identifiable pairs.


Radon measure

(mathematics) A measure on the σ-algebra of Borel sets of a Hausdorff space that is locally finite and inner regular.


dentable

dentable (comparative more dentable, superlative most dentable)

more dentable (comparative)
most dentable (superlative)

It will be useful to observe that a nonempty bounded set C is dentable if its closed convex hull is dentable...

1992, Gerald A. Edgar, Louis Sucheston, Stopping times and directed processes, page 225:

(mathematics, of a closed convex subset C of a Banach space Y) Admitting slices of arbitrarily small diameter, where a slice of C is a subset of the form S(λ,α) = y∈C;|;λ(y)≥||λ||_(∞,C)-α for some λ∈Y^* and some α>0.


Bellman-Ford algorithm

en-noun

Bellman-Ford algorithm (plural Bellman-Ford algorithms)

Named after its developers, Richard Bellman and L. R. Ford, Jr.

Dijkstra's algorithm
Dijkstra's algorithm

(graph theory, computing) An algorithm that computes single-source shortest paths in a weighted digraph, capable (unlike the faster Dijkstra's algorithm) of handling graphs with negative edge weights.

Bellman-Ford algorithm
L. R. Ford, Jr.
Richard Bellman


Dijkstra's algorithm

/ˈdaɪkstɹəz ˈælɡəɹɪðəm/

(graph theory) An algorithm that computes single-source shortest paths in a weighted digraph.


cryptoprocessing

(cryptography) Cryptographic operations carried out by a computer or cryptoprocessor.


Gini coefficient

Gini coefficient (plural Gini coefficients)

/ˈdʒiːni ˌkəʊˈɪ.fɪʃn̩t/

Named after Italian statistician and sociologist Corrado Gini (1884–1965).

named-after

One big problem with the Gini coefficient, however, is getting an intuitive feel for what it actually means. It's easy enough to picture a country with a Gini coefficient of zero—there, everyone gets exactly the same income.

2020, Tim Harford, “Rule four”, in How to Make the World Add Up, Bridge Street Press, →ISBN:

In fact, France’s Gini coefficient, the measure of inequality in a society, is lower today than it was during les trente glorieuses (1945 to 1975), when postwar France regained confidence by helping to pioneer first Concorde, then the TGV, and then in the early 1980s the proto-internet (the Minitel).

2023 May 1, Alexander Hurst, “Has France really gone to hell? Its catastrophist discourse is at odds with the facts”, in The Guardian, →ISSN:

(statistics, economics) A measure of the inequality of a statistical distribution, ranging from 0 (total equality) to 1 (maximal inequality), used in various disciplines but especially in economics to compare incomes or wealth.


grouplike

en-adj

grouplike (comparative more grouplike, superlative most grouplike)

more grouplike (comparative)
most grouplike (superlative)

(mathematics) Resembling or characteristic of a group.


minoration

en-noun

minoration (countable and uncountable, plural minorations)

/mʌɪnəˈɹeɪʃ(ə)n/

From Late Latin minoratio, from the participle stem of Latin minōrāre.


Dormand-Prince method

Described in a 1980 paper by J. R. Dormand and P. J. Prince.

ordinary differential equation
ordinary differential equation

(mathematics, numerical analysis) A method for solving ordinary differential equations, using six function evaluations to calculate fourth- and fifth-order accurate solutions, the difference between which is then taken to be the error of the (fourth-order) solution.


Runge-Kutta method

Runge-Kutta method (plural Runge-Kutta methods)

Developed around 1900 by the German mathematicians C. Runge and M. W. Kutta.

(mathematics, numerical analysis) Any of an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations.


Cash-Karp method

The method was proposed by Professor Jeff R. Cash and Alan H. Karp.

(mathematics, numerical analysis) One of the Runge-Kutta methods for solving ordinary differential equations.


quadragesimal

(mathematics) Of, related to, or based on the number forty.


quadrinodal

quadrinodal curves


simple majority

simple majority (plural simple majorities)

Oregon and Colorado were chosen by anti-gay groups to build momentum for a nationwide attack, beceause thhe two states have lenient election laws that allow for state constitutions to be amended by a simple majority of voters

1991 December 15, Dawn Schmitz, “Putting Gay Rights To A Popular Vote”, in Gay Community News, volume 19, number 22, page 1:

(Canada, US) Synonym of majority: (of a motion) more votes in favor of a proposition than against it.


subproposition

(philosophy, mathematics) A proposition making up part of a greater proposition.


noncuple

First attested in adjectival use in 1557, in nominal use in 1636, and in verbal use in 1674; from the post-Classical Latin noncuplus (“nine times larger than”), from the Classical Latin nōnus (“ninth”) + -cuplus; compare nonuple.

uder

In the following odd multiples above the ſeptuple arc, the mean arc may be greater than three quadrants: Thus, for inſtance, in the caſe of the noncuple arc, in which the three equidifferent arcs are the quintuple, ſeptuple, and noncuple arcs, ‛tis evident the greateſt magnitude of the ſeptuple, or mean, arc, or that which it has when the noncuple arc is equal to a whole circle, is ⁷⁄₉, or ²⁸⁄₃₆, of the whole circumference, which is greater than ²⁷⁄₃₆ or ¾ of the whole circumference, or three quadrants; and ſince this is true in the noncuple arc, it follows a fortiori that it will be true in all higher multiples.

1760, Francis Maſeres, Elements of Plane Trigonometry, page 109:

(mathematics, rare) Divided into nine equal segments.

Ninefold.
Divided into nine equal segments.


counting rod

In recent archaeological excavations a number of ancient counting-rods have been unearthed. More than 30 rods were found in August 1971 in Qianyang County of Shaanxi Province.

[1983, Rongzhao Mei, “The Decimal Place-Value Numeration and the Rod and Bead Arithmetics”, in 中国古代科技成就 [Ancient China's Technology and Science] (China Knowledge Series), Beijing: Foreign Languages Press, →ISBN, →OCLC, pages 58–59:

(mathematics) One of a set of small bars, used by mathematicians in some Asian countries, placed either horizontally or vertically to represent any number and any fraction.


quintate

First attested in verbal use in 1812, in adjectival use in 1851, and in nominal use in 1889; from the Classical Latin quīntus (“fifth”); in the verbal sense after decimate, and in the botanic senses by mistaken analogy with ternate.

We have as variations for the numbers from 6 to 9, 6 = X + 1…, 7 = X + 2, etc.,…the numerals of the second quintate repeating without the use of the expressed base five.

1913, W.C. Eells, “Number Systems of the North American Indians”, in The American Mathematical Monthly, XX, page 294:

(mathematics, rare, of a quinary-decimal number system) The set of the series of integers that occur between a multiple of five and the next (exclusive of those multiples).


commutative algebra

en-noun

commutative algebra (countable and uncountable, plural commutative algebras)

noncommutative algebra

concerned with rings that are not assumed to be commutative

1992, R. Keith Dennis, Claudio Pedrini, Michael R. Stein, editors, Algebraic K-theory, Commutative Algebra, and Algebraic Geometry: Proceedings of the Joint Seminar, American Mathematical Society:

The subject of these notes is a part of commutative algebra, and is also closely related to certain topics in algebraic number theory and algebraic geometry.

1992, Cornelius Greither, Cyclic Galois Extensions of Commutative Rings, Springer, page vii:

2003, Ragnar-Olaf Buchweitz, Morita contexts, idempotents, and Hochschild cohomology — with applications to invariant rings, Luchezar L. Avramov, Marcel Morales, Marc Chardin, Claudia Polini (editors), Commutative Algebra: Interactions with Algebraic Geometry: International Conference, American Mathematical Society, page 27,
It is not until section 7 that we deal with commutative algebra proper, whereas the sections leading up to it should be seen as advocacy that excursions into noncommutative algebra can help to shed light on problems in commutative algebra.

(mathematics) The branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules).

Theorem. If the complex of the linearly independent numbers of the form #92;zetaa-a#92;zeta be deleted from an algebra, the remaining numbers form a commutative algebra.

1907, James Byrnie Shaw, Synopsis of Linear Associative Algebra, Carnegie Institution of Washington, page 46:

The existence of commutative algebras of Toeplitz operators is not usual, for example there are not non trivial commutative algebras of Toeplitz operators acting on the Hardy space.

2010, M. Loaiza, A. Sánchez-Numgaray, “On C*-Algebras of Super Toeplitz Operators with Radial Symbols”, in Roland V. Duduchava, Israel Gohberg, Sergei M. Grudsky, Vladimir Rabinovich, editors, Recent Trends in Toeplitz and Pseudodifferential Operators, Springer, page 175:

We devote this chapter to the study of unitary commutative algebras in dg-modules, in simplicial modules and in cosimplicial modules.

2017, Benoit Fresse, Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2, American Mathematical Society, page 163:

(algebra) Any algebra (mathematical structure) in which the multiplication operation is commutative.

algebra commutativa

algebra in which multiplication is commutative

Abelian algebra

algebra which has a commutative multiplication operation


Abelian algebra

Abelian algebra (plural Abelian algebras)

From Niels Henrik Abel, Norwegian mathematician.

(mathematics) Any algebra in which multiplication (or its equivalent) is commutative.


octavate

en-verb

octavate (third-person singular simple present octavates, present participle octavating, simple past and past participle octavated)

octavates (present singular third-person)
octavating (participle present)
octavated (participle past)
octavated (past)

First attested in 1922; formed as octav(e) + -ate (verb-forming suffix), in the musical sense after the French octavier.

To octavate the number one hundred the reasoning is as follows. The square of eight goes into one hundred once with remainder thirty-six. This remainder contains eight to the first power four times with remainder four. Hence to express one hundred to the base 8 we write the digits 144 which in somewhat longer form may be put as 100 = 1×8² + 4×8 + 4.

1949, The American Mathematical Monthly, LVI, page 463:

(mathematics, rare) To convert (the expression of a number) from denary to octal notation.


octavation

First attested in 1922; probably formed as octav(e) + -ation, but compare octavate.

The inverse operation, which is termed “decimation,” together with an adequate treatment for the octavation of decimal fractions will be mentioned here without consideration of the details.

The author […] supplied elaborate rules for the use of the octave system and for the reducing of numbers from the decade to the octave system, and the reverse — processes which he called octavation and decimation, respectively.

1956, Hugh Jones, edited by Richard Lee Morton, The Present State of Virginia, page 37:

The 18th century American mathematician Hugh Jones used the words “octavation” and “decimation” to describe octal/decimal conversions.

1973, Donald E. Knuth, The Art of Computer Programming (2nd edition) II: “Seminumerical Algorithms”, page 309

(mathematics) Conversion (of the expression of a number) from denary to octal notation.


postboomer

en-adj

postboomer (comparative more postboomer, superlative most postboomer)

more postboomer (comparative)
most postboomer (superlative)

“Boomer” has gotten such a bum rap that even our new president, who is a clear-cut boomer demographically (the boom years ran through 1964), has sought to link himself to a younger generation with a postboomer mentality, one that types with its thumbs to communicate and is not tainted by the cultural wars of the 1960s.

2009 January 25, Michael Winerip, “They Warned You About Us”, in New York Times:


octile

(statistics) Any of the quantiles that divide an ordered sample population into eight equally numerous subsets.

(statistics, by extension) A subset thus obtained.


multioperation

(mathematics) A mapping f:Xⁿ→𝒫(X) for some n∈ℕ₀.


hyperarc

(graph theory) A directed edge in a hypergraph.


achirality

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

(geometry, physical chemistry) The characteristic of being achiral; the absence of chirality.


carryless

a carryless multiplication

(mathematics) In which no figures are carried over.


biclique

(graph theory) A special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set.


one-time pad

One-time pads have been proven to be impossible to crack if used correctly.

(cryptography) A form of encryption where each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key (or pad) of the same length as the plaintext.


least common multiple

en-noun

least common multiple (plural least common multiples)

120 is the least common multiple of 60, 8 and 15.

The LEAST COMMON MULTIPLE is the smallest number, which can be measured by each of two, or more divisors.
[…]
Since 0 is the least multiple of every number, it must be the least common multiple of any, or of all numbers. It is, however, excluded by common consent in finding the least common multiples of numbers, because as such, 0 has no practical value.

1859, David Henry Cruttenden, The Objective Or Synthetic Arithmetic, J. M. Bradstreet & Son, page 261:

The least common multiple (LCM) is the smallest common multiple of two or more factors.[…]The least common multiple is used to determine the appropriate denominator for adding unlike fractions. In adding unlike fractions, it is important to find the lowest common denominator of the fractions. This is exactly the same thing as finding the least common multiple of the denominators.

2000, Robert W. Smith, Math Challenges, Grades 4-6, Teacher Created Resources, page 75:

It is sometimes necessary to determine the smallest common nonzero multiple of two or more whole numbers. We call this nonzero multiple the least common multiple. In our work with fractions, there will be problems where it will be necessary to find the least common multiple of some numbers, usually the denominators of fractions.

2007, Jerome Kaufmann, Karen Schwitters, Algebra for College Students, 8th edition, Thomson Learning, page 820:

(number theory) The smallest positive integer which is divisible by (equivalently, is an integer multiple of) each of a specified finite set of integers.


antilogarithmic

en-adj

antilogarithmic (comparative more antilogarithmic, superlative most antilogarithmic)

more antilogarithmic (comparative)
most antilogarithmic (superlative)

(mathematics) Of or pertaining to an antilogarithm.


depacketize

en-verb

depacketize (third-person singular simple present depacketizes, present participle depacketizing, simple past and past participle depacketized)

depacketizes (present singular third-person)
depacketizing (participle present)
depacketized (participle past)
depacketized (past)

(transitive, signal processing) To reconstruct (data) from the group of packets used in transmission.


repacketize

repacketize (third-person singular simple present repacketizes, present participle repacketizing, simple past and past participle repacketized)

repacketizes (present singular third-person)
repacketizing (participle present)
repacketized (participle past)
repacketized (past)

(transitive, signal processing) To packetize again or anew.


packetizer

(signal processing) A process that packetizes.


spaghetti model

en-noun

spaghetti model (plural spaghetti models)

(statistics) An illustration of different statistical outcomes that may be plotted from the same set of data.


abstract model

(engineering, logic, mathematics) A model that contains an abstraction or abstractions of the reality.


joint entropy

joint entropy (countable and uncountable, plural joint entropies)

If random variables X and Y are mutually independent, then their joint entropy H(X,Y) is just the sum H(X)#43;H(Y) of its component entropies. If they are not mutually independent, then their joint entropy will be H(X)#43;H(Y)-I(X#59;Y) where I(X#59;Y) is the mutual information of X and Y.

(information theory) The Shannon entropy of a "script" whose "characters" are elements of the Cartesian product of the sets of characters of the component scripts.


conditional entropy

conditional entropy (plural conditional entropies)

The conditional entropy of random variable Y given X (i.e., conditioned by X), denoted as H(Y|X), is equal to H(Y)-I(Y;X) where I(Y;X) is the mutual information between Y and X.

(information theory) The portion of a random variable's own Shannon entropy which is independent from another, given, random variable.


joint probability

joint probability (plural joint probabilities)

The probability distribution of a random variable whose sample space is the Cartesian product of the sample spaces of its (at least two) component random variables.


marginal distribution

marginal distribution (plural marginal distributions)

The projection of a joint probability distribution onto one of its component random variables.


mutual information

mutual information (usually uncountable, plural mutual informations)

Mutual information I(X;Y) between two random variables X and Y is what is left over when their mutual conditional entropies H(Y|X) and H(X|Y) are subtracted from their joint entropy H(X,Y). It can be given by the formula I(X;Y)=-∑ₓ∑_yp_X,Y(x,y) log _bp_X,Y(x,y)/p_X|Y(x|y)p_Y|X(y|x).

From these lists, all combinations of the four major parts of speech were extracted and each phrase was checked for the frequency, dispersion and range criteria respectively. Those that passed the criteria thresholds then had their mutual information scores computed using the tool Collocate (Barlow, 2004) and those failing to meet the threshold were removed.

2018, Clarence Green, James Lambert, “Position vectors, homologous chromosomes and gamma rays: Promoting disciplinary literacy through Secondary Phrase Lists”, in English for Specific Purposes, →DOI, page 6:

(information theory) A measure of the entropic (informational) correlation between two random variables.


Wiener filter

(signal processing) A filter that takes a statistical approach to filtering out noise that has corrupted a signal.


depacketizer

(signal processing) A circuit or system that depacketizes.


Hartogs number

After German-Jewish mathematician Friedrich Hartogs (1874–1943).

1973 [North-Holland], Thomas J. Jech, The Axiom of Choice, 2013, Dover, page 160,
Let p be an infinite cardinal, |X|=p and let א=א(p) be the Hartogs number of p.

1995, The Bulletin of Symbolic Logic, Volume 1, Association for Symbolic Logic, page 139,
If the Power Set Axiom is replaced by "א(x) is bound for every x" where
א(x)={a|∃f(f is one-to-one function from a into x)},
then the theory is denoted by ZFH (H stands for Hartogs' Number).

Since the proof of Hartogs' Theorem does not appeal to the Axiom of Choice, the Hartogs number of a set X exists whether or not X has a well-ordering.

2014, Barnaby Sheppard, The Logic of Infinity, Cambridge University Press, page 341:

(set theory) For a given set X, the cardinality of the least ordinal number α such that there is no injection from α into X.


convex combination

convex combination (plural convex combinations)

(linear algebra) A linear combination (of vectors in Euclidean space) in which the coefficients are non-negative and all add up to one.


Describes a 3D film experience that is supplemented with synchronized physical effects.

Denotes imaging modes with 3D capability that can also record over time.


closed form

closed form (countable and uncountable, plural closed forms)

There is no known representation of π in closed form: each expression for it includes an integral, an infinite series, or an infinite continued fraction.

(mathematics) A form (expression) that does not use limits, implicitly or explicitly.

suljettu muoto

(mathematics) expression that does not use limits

(mathematics) A differential form whose exterior derivative is zero.

suljettu muoto

(mathematics) differential form whose exterior derivative is zero


imaginary unit

So named because it takes on the role of unit for the imaginary part of a complex number.

In Section 4.3 we introduced the imaginary unit i with (i)²#61;-1, in the complex space domain. In section 4.4 we introduced the complex unit j with (j)²#61;-1, in connection with the time dependency of the shape (4.4.16) of the swimming profile. These different imaginary units have no interaction, we leave unaltered the product ij.

2013, J. A. Sparenberg, Hydrodynamic Propulsion and Its Optimization, Springer, page 183:

2014, Dennis G. Zill, Warren S. Wright, Advanced Engineering Mathematics, Ascend Learning (Jones & Bartlett Learning), 5th Edition, page 793,
We now simply say that i is the imaginary unit and define it by the property i²=-1. Using the imaginary unit, we build a general complex number out of two real numbers.

Consider now in addition to the given #92;H#92;subset#92;mathbb#123;O#125;, one of the totally imaginary units not contained in #92;H, and note that #123;SU#125;(2) acts transitively on the set of totally imaginary units of a quaternion algebra; as we are assuming #92;alpha#92;notin#92;H, we may in fact assume that #92;mathbb#123;O#125;#61;#92;H#92;oplus#92;H' with #92;alpha#92;in#92;H'.

2021, Bruce Hunt, Locally Mixed Symmetric Spaces, Springer, page 123:

(number theory, complex analysis, quaternion theory) An imaginary number (in the case of complex numbers, usually denoted i) that is defined as a solution to the equation x²=-1.


Heyting algebra

Heyting algebra (plural Heyting algebras)

After Dutch mathematician Arend Heyting, who developed the theory as a way of modelling his intuitionistic logic.

The laws of Heyting algebra embody a rich and profound mathematical structure that is manifest in a variety of contexts. It arises from the epistemological deliberations of Brouwer, the topologisation (localisation) of set-theoretic notions, and the categorial formulation of set theory, all of which, although interrelated, are independently motivated. The ubiquity lends weight, not to the suggestion that the correct logic is in fact intuitionistic instead of classical, but rather to the recognition that thinking in such terms is simply inappropriate — in the same way that it is inappropriate to speak without qualification about the correct geometry.

1984, Robert Goldblatt, Topoi, the categorial analysis of logic, page xii:

which is just obvious.

1994, Francis Borceux, Handbook of Categorical Algebra 3: Categories of Sheaves, Cambridge University Press, page 13, Proposition 1.2.14 should certainly be completed by the observation that the modus ponens holds as well in every Heyting algebra. Since, in the intuitionistic propositional calculus, being a true formula is being a terminal object (see proof of 1.1.3), the modus ponens of a Heyting algebra reduces to a=1 and a<b imply b=1

1997, J. G. Stell, M. W. Worboys, The Algebraic Structure of Sets and Regions, Stephen C. Hirtle, Andrew U. Frank (editors), Spatial Information Theory A Theoretical Basis for GIS: International Conference, Proceedings, Springer, LNCS 1329, page 163,
The main contention of this paper is that Heyting algebras, and related structures, provide elegant and natural theories of parthood and boundary which have close connections to the above three ontologies.

(algebra, order theory) A bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called "implies", denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover, that x = a→b is the greatest element such that x∧a ≤ b (in the sense that if c∧a ≤ b then c ≤ a→b).

Arend Heyting
Heyting algebra
intuitionistic logic

algebra di Heyting

bounded lattice equipped with operation called implies


antiperiodicity

(mathematics) A generalization of periodicity such that f(x + P) = −f(x) for all x in some function f.


gravity assist

/ˈɡɹævɪti əˈsɪst/

After going into orbit around Jupiter with a gravity assist from the volcanic moon Io, Galileo will spend 22 months studying the planet.

1989 October 10, Warren E. Leary, “Galileo's Itinerary”, in New York Times, retrieved 2011-09-04:

Cassini is supposed to swing by Earth in 1999 for a gravity assist that would sling it out toward Saturn.

1997 September 22, Dick Thompson, Michael D. Lemonick, “Nukes in Space”, in Time:

MESSENGER successfully flew by Mercury yesterday, gaining a critical gravity assist that will enable it to enter orbit about Mercury in 2011.

2009 Oct. 2, "MESSENGER Gains Critical Gravity Assist For Mercury Orbital Observations," spacedaily.com (retrieved 4 Sep. 2011)

(astrophysics) The favorable alteration of the speed and trajectory of a spacecraft as a result of its passing near to a celestial body.

painovoimalinko

the favorable alteration of the speed and trajectory of a spacecraft as a result of its passing near to a celestial body


gravitational slingshot

gravitational slingshot (plural gravitational slingshots)


semicreative

a semicreative set

(set theory) A type of set of natural numbers, related to mathematical logic.


hyperinteger

(mathematics, non-standard analysis) A hyperreal number equal to its own integer part.


hypernatural

From hyper- + natural; see natural number.

(mathematics) Being or pertaining to a positive hyperinteger.


positone

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

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

(mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.


guz

guzes (plural)
guz (plural)
guzzes (plural)

From Hindi गज़ (gaz) and Urdu گز (gaz), from Classical Persian گز (gaz). Doublet of gudge.

A unit of length used in parts of Asia, ranging from 24 to 41 inches and historically used for measuring textiles, comparable to the English yard.


Landau-Ramanujan constant

After its two independent discoverers, Edmund Landau and Srinivasa Ramanujan.

(number theory) The constant of proportionality (approximately 0.7642) in the relationship between the number of positive integers less than x that are the sum of two square numbers, for large x, and the expression x/√.


Jacob's ladder

The infinite Loch Ness monster and Jacob's ladder (Figure 12.1.1) are diffeomorphic surfaces.

2000, Alberto Candel, Lawrence Conlon, Foliations (Graduate Studies in Mathematics), volume 23, American Mathematical Society, →ISBN, page 311:

(mathematics) A noncompact surface resembling a ladder made of handlebodies.


avalanche effect

avalanche effect (plural avalanche effects)

(cryptography) A property of some cipher systems in which a small change in the input results in a very large change in the output.


nonplane

a nonplane curve


BLUP

(statistics) Acronym of best linear unbiased prediction.


kayser

A unit of wavenumber in the CGS system of units, equivalent to the number of waves in one centimeter.


langley

Named in 1947 after Samuel Pierpont Langley (1834-1906).

A unit of heat transmission in the CGS system of units. It is equivalent to 41,840 J/m² in SI units. Symbol: Ly.


carry over

en-verb

carry over (third-person singular simple present carries over, present participle carrying over, simple past and past participle carried over)

carries over (present singular third-person)
carrying over (participle present)
carried over (participle past)
carried over (past)

Attested since the 17th century; listed for instance in Elisha Coles' 1676 dictionary as a translation of transfer, thereby possibly a calque of Latin transfero; compare Dutch overdragen, German übertragen.

(transitive, arithmetic) To carry; to transfer an excess quantity to the next column of digits.


cryptographist

Good cryptographists are rare indeed; and thus their services, although seldom required, are necessarily well requited.

1841, Edgar Allan Poe, A Few Words on Secret Writing:


superexpression

en-noun

superexpression (countable and uncountable, plural superexpressions)

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

(countable, mathematics, programming) An expression that contains multiple subexpressions.


predictor variable

predictor variable (plural predictor variables)

independent variable
independent variable

(mathematics) An independent variable that may be used to predict the value of another, especially in statistical regression


outcome variable

outcome variable (plural outcome variables)

(mathematics) A dependent variable thought to change as a function of changes in a predictor variable.


overrelax

en-verb

overrelax (third-person singular simple present overrelaxes, present participle overrelaxing, simple past and past participle overrelaxed)

overrelaxes (present singular third-person)
overrelaxing (participle present)
overrelaxed (participle past)
overrelaxed (past)

(transitive, mathematics) To solve using overrelaxation.


pre-echo

en-noun

pre-echo (countable and uncountable, plural pre-echos or pre-echoes)

(signal processing) A digital audio compression artifact where a (typically percussive) sound is heard before it should occur.


complex fraction

complex fraction (plural complex fractions)

(mathematics, arithmetic) Any fraction in which either or both of the numerator or denominator are themselves fractions.


majoration

majoration (countable and uncountable, plural majorations)

[…] we could in Theorem 5.1.5 (respectively, Theorem 5.1.10) require only the continuity condition if we strengthened the majoration condition (respectively, local majoration condition) to the strict majoration condition (respectively, local strict majoration condition).

2001, Anatolii Puhalskii, Large Deviations and Idempotent Probability, page 359:

First, the majoration conditions X.1.57(c) in [16] and M(c) in [6] are quite restrictive.

2017, Alexander Gushchin, Esko Valkeila, “Quadratic Approcimation for Log-Likelihood Ratio Processes”, in Vladimir Panov, editor, Modern Problems of Stochastic Analysis and Statistics, page 194:

(mathematics) The establishment of conditions for an upper bound of an expression.


Julia set

Devised by the French mathematician Gaston Julia.

(mathematics) In complex dynamics, a set consisting of values generated by a mathematical function such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.


trihexagonal

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

(geometry) Pertaining to a semiregular tiling of the Euclidean plane with two triangles and two hexagons alternating on each vertex.


hexoctahedron

hexoctahedron (plural hexoctahedrons or hexoctahedra)

hexoctahedrons (plural)
hexoctahedra (plural)

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

(geometry) A solid with forty-eight equal triangular faces.


gyrovector

(mathematics) A type of vector for which addition is defined by a formula that satisfies the axioms for a gyrogroup.


gyrogroup

(mathematics) A groupoid whose binary operation satisfies certain axioms, used with gyrovectors.


gyroparallelogram

The 6 faces of a parallelepiped are parallelograms while, in general, the 6 faces of a gyroparallelepiped are not gyroparallelograms.

2005, Ungar Abraham Albert, Analytic Hyperbolic Geometry:

(hyperbolic geometry) A hyperbolic quadrilateral whose two gyrodiagonals intersect at their gyromidpoints, analogous to a parallelogram in Euclidean space.


gyrotrigonometry

(hyperbolic geometry) The use of gyroconcepts to study hyperbolic triangles.


gyromidpoint

(mathematics) A midpoint in gyrovector space.


gyrodiagonal

(hyperbolic geometry) A diagonal in gyrovector space.


gyroquadrilateral

(hyperbolic geometry) A quadrilateral in gyrovector space.


gyrocircle

(hyperbolic geometry) A hyperbolic circle in gyrovector space.


gyrotriangle

(hyperbolic geometry) A triangle in gyrovector space.


gyrorotation

(mathematics) A rotation in gyrovector space.


gyrocenter

(mathematics) The center of an object in gyrovector space.


gyroangle

(mathematics) An angle in gyrovector space.


gyrocentroid

(mathematics) A centroid in gyrovector space.


gyrotranslation

(mathematics) A translation in gyrovector space.


gyrogeodesic

(hyperbolic geometry) A geodesic in gyrovector space.


gyroautomorphism

(mathematics) An automorphism in gyrovector space.


gyrocommutative

(mathematics, of a gyrogroup) Whose binary operation obeys a ⊕ b = gyr[a, b](b ⊕ a).


superdistribution

superdistribution (countable and uncountable, plural superdistributions)

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

(countable, statistics) Any of various generalizations of a distribution, especially a common distribution that results from applying a single mapping to any distribution from a body of source distributions, which forms the basis of encryption used in the superdistribution of digital products.


Knowledge Interchange Format

It is exemplified by the Knowledge Interchange Format (KIF)¹⁵, part of an approach described in the paper by Tenenbaum.

1992, Charles J. Petrie, Enterprise Integration Modeling: Proceedings of the First International Conference, Introduction, page 7:

The Knowledge Interchange Format is a proposed standard for the specification and interchange of ontologies.

2000, William J. Raynor, Jr., The International Dictionary of Artificial Intelligence, page 155:

The Knowledge Interchange Format (KIF) is an example of a convenient formalism to describe these ontologies, and XML can serve as an implementation technology in the way similar to that outlined briefly in this paper.

2000, Petr Kotásek, Jaroslav Zendulka, “An XML Approach to Knowledge Discovery in Databases”, in Tomáš Hruška, Masa-aki Hashimoto, editors, Knowledge-Based Software Engineering: Proceedings of the Fourth Joint Conference, page 148:

Common Logic Common Logic (CL) evolved from two projects to develop parallel ANSI standards for conceptual graphs and the Knowledge Interchange Format [9].

2008, Frank van Harmelen, Vladimir Lifschitz, Bruce Porter, editors, Handbook Of Knowledge Representation, page 217:

artificial intelligence
artificial intelligence

(computing, artificial intelligence) A computer language designed for communicating knowledge between independently running computer programs.


KIF

Knowledge Interchange Format
Knowledge Interchange Format#English

(computing, artificial intelligence) Acronym of Knowledge Interchange Format.


Airy function

(physics) A function, denoted by Ai(x), that is a solution to the Airy equation.


Airy equation

differential equation
differential equation

(mathematics) (d²ʸ)/(dx²)-xy=0,,!, the simplest second-order linear differential equation with a turning point (a point where the character of the solutions changes from oscillatory to exponential).


zeroization

(cryptography) The erasure of sensitive parameters from a cryptographic module to prevent their disclosure if the equipment is captured.


multilobe

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

Coordinate term: unilobe


Poincaré space

Any closed, orientable, connected manifold is a Poincaré space.

(topology) An n-dimensional topological space with a distinguished element µ of its nth homology group such that taking the cap product with an element of the kth cohomology group yields an isomorphism to the (n − k)th cohomology group.


cap product

A reference to the symbol used, ∩, in this context called "cap"; compare cup product.

(topology) A method of adjoining a chain of degree p with a cochain of degree q, such that q ≤ p, to form a composite chain of degree p − q.


subproof

(mathematics) A proof that makes up part of a larger proof.


Tobit

Coined by A. S. Goldberg in 1964 as these type of models were first proposed by James Tobin and are similar to probit models.

(statistics) a model where the dependent variable is censored.


affine combination

affine combination (plural affine combinations)

(linear algebra) A linear combination (of vectors in Euclidean space) in which the coefficients all add up to one.


discrete set

(topology) A set of points of a topological space such that each point in the set is an isolated point, i.e. a point that has a neighborhood that contains no other points of the set.


doubly even

Eight is a doubly even number.

(arithmetic) Leaving no remainder when divided by 4; divisible by 4.


singly even

Six is a singly even number.

(arithmetic) That leaves a remainder of 2 when divided by 4; divisible by 2 but not by 4.


basepoint

(mathematics) A point that marks the beginning and the end of a topological loop


coideal

(mathematics) A particular linear subspace in a coalgebra


metriplectic

(mathematics) Describing a structure, on a smooth manifold, that consists of a pair of tensors: a skew-symmetric Poisson tensor and a symmetric metric tensor.


faciend

From neuter of Latin faciendus, gerundive of facere (“to do”).

The same process may be applied to the faciends with similar conclusions.

1881, American Journal of Mathematics, volume 4, page 113:

In the case of binomial, or multinomial multenions, the facient or the faciend or both being composed, the law of combination of the facter must be definitely assigned also […]

1895, James Byrnie Shaw, Mathematics, the Science of Algorithms, page 10:

(mathematics, obsolete) The multiplicand.


hyperconnected

(mathematics, of a topological space) That is not the union of two proper closed sets; such that every open set is dense.

(mathematics, of a graph) Having an edge set that spans a matroid defined on its edges via exterior algebra.


biangular

a biangular circle

Before proceeding with the Uniform Circle Formation problem, let us consider a less restricted version of that problem, the biangular circle formation: The robots must be placed on the boundary of a circle at intervals forming a biangular configuration (refer to Chapter 3).

2022, Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, Distributed Computing by Oblivious Mobile Robots, page 87:

(mathematics) Having exactly two angular structures, operations, coordinates, or relative positions.


manifoldness

manifoldness (countable and uncountable, plural manifoldnesses)

(mathematics) A generalized concept of magnitude.


subtriple

[…] then the power at A, will be in a subtriple proportion to the weight E, because the heaviness would be then equally divided unto the three points of the lower diameter B, C, D, each of them supporting a like share of the burthen.

1641, John Wilkins, Mercury, or the Secret and Swift Messenger:

(mathematics, obsolete) Containing a third, or one part to three.


oxygon

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mesologarithm

[…] the antilogarithm of the greatest inclination is added to the mesologarithm of the argument, and thus the sum will be the mesologarithm of the argument of the reduction.

1939, Johannes Kepler, translated by Charles Glenn Wallis, Epitome of Copernican Astronomy:

(mathematics, obsolete) A logarithm of the cosine or cotangent.


extraregular

(mathematics) Meeting stricter criteria than those which define a regular (object, function, space, etc)


enneagonal

enneagonal angle

(geometry) In the form of an enneagon; having nine angles.


vexillary

From Latin vexillarius: compare French vexillaire.


glissette

From French glissette, from glisser (“to slip”).

(mathematics) The locus described by any point attached to a curve that moves continuously along another fixed curve, the movable curve having no rotation at any instant.


curvilinead

(geometry, obsolete) An instrument for drawing curved lines.


unconfidence

Obviously If P ( Hᵢ / E ) > P ( Hᵢ) then we can say that by evidence E the confidence of H by the expert is increased and at the same time the unconfidence of Hᵢ is decreased.

1988, International Conference on Computer-Aided Production Engineering, page 556:

(statistics) The complement of confidence; the probability that something is not the case.


orthotomy

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(geometry) The property of cutting at right angles.


breadth-first search

breadth-first search (countable and uncountable, plural breadth-first searches)

Coordinate term: depth-first search

(graph theory) A search algorithm that begins at the root node and explores all the neighboring nodes.


incomposite

From Latin incompositus. By surface analysis, in- + composite.


Playfair

Playfair (countable and uncountable, plural Playfairs)

* (craters): The craters are Named after Scottish mathematician, scientist and C of S minister John Playfair
* (cipher): The cipher is Named after British Lord, baron, politician and scientist Lyon Playfair, who popularized the cipher.

named-after

(cryptography) Ellipsis of Playfair cipher..

Here's a cipher message. Probably Playfair.

(cryptography) an encryption using the Playfair cipher


kathetal

From Ancient Greek κάθετος (káthetos, “perpendicular”) + -al.

der

(mathematics) Making a right angle; perpendicular, as two lines or two sides of a triangle, which include a right angle.


cucumiform

en-adj

cucumiform (comparative more cucumiform, superlative most cucumiform)

more cucumiform (comparative)
most cucumiform (superlative)

First attested in a glossary in 1826, in a fragment in 1838, and in a grammatical sentence in 1892; formed by the suffixation of cucumi-, the short i-stem of the Latin cucumis (“cucumber”), with the English -form; compare the earlier New Latin cucumeriformis (1703), cucumiformis (1791) and French cucumeriforme (1777), cucumiforme (1804).

Cucumiform (Cucumiformis). Cucumber-shaped. Whose longitudinal section is oblong, and transverse circular.

1826, William Kirby, William Spence, An Introduction to Entomology, volume IV, page 265:

She was there, tumbling the marvelous cucumiform weights down upon a chest which looked as though it would cave in under such manna.

1955, William Gaddis, The Recognitions, Harcourt, Brace, page 329:

Uncharacteristically for him, Lord Vetinari laughed out loud. He very nearly gloated at the downfall of his enemy and slammed his copy of the Ankh-Morpork Times, open at the crossword page, on to his desk. ‘Cucumiform, shaped like a cucumber or a variety of squash! l thumb my nose at you, madam!’

2011, Terry Pratchett,, Snuff: Discworld Novel 39, page 17:

Shaped like a cucumber; having the form of a cylinder tapered and rounded at the ends, and possibly curved.


pseudodigraph

(graph theory) A graph that resembles a directed graph but violates one of the normal rules, as for example by including a directed loop.


subbag

(mathematics) A partial bag (collection of objects with possible duplicates).


fractionary

fractionary (comparative more fractionary, superlative most fractionary)

more fractionary (comparative)
most fractionary (superlative)

fractionary ideals

fractionary power series

fractionary decomposition

(mathematics) Having a common denominator.


equimultiple

14 and 28 are equimultiples of 2 and 4.

(mathematics) One of the products arising from the multiplication of two or more values by the same value.


equimultiple

(mathematics) Multiplied by the same number or quantity.


undulary

undulary (comparative more undulary, superlative most undulary)

more undulary (comparative)
most undulary (superlative)

The undulary curve (fig. 2.6c) is formed by the focus of an ellipse rolling on the axis.

2012, Jean Berthier, Kenneth A. Brakke, The Physics of Microdroplets, pages 1-95:

(mathematics) Pertaining to the wave-like curve formed by the size of an ellipse as a function of the position of its focus.


auln

The Measure is here an Auln, by which all Commodities of Woollen and Linnen is measured, and is accounted 1 ¼ yards English, but those that have made tryal thereof find it to be 46 inches;

1677, Roberts Lewe, The Merchants Map of Commerce, page 176:

They shewed us however some cloth, made as they say entirely of Spanish wool, at 3 liv. 10s the lb. which is not so good as their ratteens, made with ⅔ wool of Navarre and Roussillon, and ⅓ Spanish; they make some Navarre, an auln broad, at 11 liv. the auln; ratteens ¼ of an auln broad, at 22 liv. the auln; a second sort of ratteens, mad with French wool, an auln broad, 11 liv. the auln.

1794, Arthur Young, Travels During the Years 1787, 1788 and 1789, page 542:

The Père Simon, cited by Picart, makes mention of a custom prevailing amongst the Jews at the occurrence of a death; the mourners who are in attendance rend their garments, but so as to occasion no material injury to them—making only a small tear, about an eighth of an auln to the left, except when the mourning is for a father, or mother, or a child, when all the robes are torn on the right side.

1851, Richard Robert Madden, The Shrines and Sepulchres of the Old and New World:

It was the additional weight of the four buttons and one-sixteenth of an auln of cloth, which, he said, must help to fatigue the soldier in his marching .

1889, Silas Deane, Charles Isham, The Deane Papers ... 1774-1790 - Volume 21, page 175:


bigha

Colonel Watson had, within a brick wall, at least four hundred begahs of land, which the East India Company had executed a grant of to him to construct docks […] .

1808–10, William Hickey, Memoirs of a Georgian Rake, Folio Society 1995, p. 208

(India, Bangladesh) A measure of land in India, varying from a third of an acre to an acre.


scedastic

Learned borrowing from Ancient Greek σκεδαστικός (skedastikós), from σκεδάννυμι (skedánnumi, “to scatter, disperse”).

lbor

(statistics) related to the variance of (statistical) errors


trirectangular

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retrosnub

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great retrosnub icosidodecahedron

small retrosnub icosicosidodecahedron

(geometry) Derived from a simpler, regular polyhedron by the addition of extra triangular faces in the back.


honeycomb conjecture

(mathematics) The proven conjecture that a regular hexagonal grid, or honeycomb, is the best way to divide a surface into regions of equal area with the smallest total perimeter.


excentral

en-adj

excentral (comparative more excentral, superlative most excentral)

more excentral (comparative)
most excentral (superlative)

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subsignature

To be able to interpret the revealing of a set of symbols of a given signature, we need to be able to construct a subsignature generated by these symbols.

2000, Marsha Freeman, Challenges of Human Space Exploration, →ISBN, page 257:

(mathematics) The domain of a signature morphism (a mapping of a set of symbols of a given signature into another set of symbols) that is an inclusion.


subunitary

(mathematics) Of a magnitude of less than one unit.


retractive

retractive (comparative more retractive, superlative most retractive)

more retractive (comparative)
most retractive (superlative)

(mathematics) Mapping from a space onto a subset of that space.


fiducially

en-adv

fiducially (comparative more fiducially, superlative most fiducially)

more fiducially (comparative)
most fiducially (superlative)

Closely related to the tests that have previously been described is the notion of fiducially related values of σ and s.

1938, On the Statistical Theory of Errors, page 142:

In arguing fiducially about the value of a parameter, a procedure applicable to some of the simple cases begins by the calculation from the sample of an estimate of the parameter in question.

1967, Samuel Stanley Wilks, Collected Papers; Contributions to Mathematical Statistics, page 252:

That is to say, we might consider the exponent (τ₀ - μ)/Θ to be distributed fiducially as a weighted sum of two Chi-squares.

1971, Technometrics - Volume 13, page 874:

(statistics) Pertaining to or based on the correspondence between a parameter in a sample and the same parameter in the population from which the sample was drawn.


scalenohedron

en-noun

scalenohedron (plural scalenohedrons or scalenohedra)

scalenohedrons (plural)
scalenohedra (plural)

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Though the hexagonal scalenohedron is derived from the double twelve-faced pyramid, by the development of half its faces, and might be constructed from that figure, it is more readily obtained from the positive or negative rhomboid which may be supposed to be inscribed in the scalenohedron.

1859, James Tennant, Walter Mitchell, Mineralogy and Crystallography: Being a Classification of Crystals According to Their Form, page 408:

By bringing together the rhombohedron and the scalenohedron, as has been done in Fig. 119, it will be noticed that the lateral edges of the two forms have a similar position towards the axes, so that for every scalenohedron there must be a rhombohedron whose lateral edges coincide with the lateral edges of the other form. This rhombohedron is called the inscribed rhombohedron of the scalenohedron.

1866, Josiah Parsons Cooke, Elements of Chemical Physics, page 154:

1907, Benjamin K. Emerson, Joseph H. Perry, The Green Schists and Associated Granites and Porphyries of Rhode Island, US Geological Survey, Bulletin Number 311, page 24,
Other steep scalenohedrons of the principal zone are also often present, sometimes in addition to y, sometimes taking its place.

Calcite crystals show a great variety of habits — acute and obtuse rhombohedra and scalenohedra, prisms, and thin tabular forms.

1940, John W. Evans, George MacDonald Davies, Elementary Crystallography, page 111:

(geometry, mineralogy, crystallography) A polyhedron having twelve sides, each in the form of a scalene triangle, that is topologically equivalent to a hexagonal bipyramid and whose middle section can be said to inscribe a rhombohedron.


subtangent

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(geometry) The part of the axis contained between the ordinate and tangent drawn to the same point in a curve.


tripartient

(mathematics) Dividing into three parts.


eotvos

Named after the physicist Loránd Eötvös.

A unit of gravitational gradient in the CGS system of units. 1 eotvos = 10⁻⁹ gals per cm.


hypernet

(mathematics) A kind of collection of linked Petri nets.


cissoid

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From Ancient Greek κισσός (kissós, “ivy”) + εἶδος (eîdos, “form, image”).

The cissoid of a circle and a line is a conchoid

(geometry) Any of a family of curves defined as the locus of a point, P, on a line from a given fixed point and intersecting two given curves, C₁ and C₂, where the distance along the line from C₁ to P remains constant and equal to the distance from P to C₂.


equicrescent

It is well to notice that t, time, is an equicrescent variable, i.e., grows in equal steps. Thus, although time continually increases, it does so uniformly, so that the differential increment, dt, is constant, although time, t, is itself variable.

1913, Louis Adolphe Martin, Text-book of Mechanics, Volume 2:

A variable regarded as taking on equal increments is an equicrescent variable.

1916, Mansfield Merriman, American Civil Engineers' Pocket Book:

The scale I2 is equicrescent, i. e., its subdivisions subtend equal angular intervals at the pivot point.

1947, John W Wilson, Radiograph calculator, US Patent 2484366:

(mathematics) Increasing by equal increments.


orthodiagonal

(mathematics, of a quadrilateral) Having diagonals that are perpendicular to each other.


multinumber

(mathematics) A set with repeated elements that are indistinguishable from one another.


subslice

(chiefly signal processing) A slice that makes up part of a larger slice.


EMA

EMA (countable and uncountable, plural EMAs)

exponential moving average
exponential moving average#English

(statistics) Initialism of exponential moving average.


semicyclic

(mathematics) Describing a polygon that is inscribed within a circle and has one of its sides being the diameter


semitangent

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crunodal

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crunodal curve

crunodal cubic

(geometry) Possessing, or characterized by, a crunode.


keyholder

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A key duplicating machine comprising […] a keyholder attached to said shaft, said keyholder providing for holding a key blank and an existing key having notches thereon; […]

1978, Official Gazette of the United States Patent and Trademark Office, page 32:

(cryptography) The individual or organization with access to a cryptographic key.


antispace

antispace (countable and uncountable, plural antispaces)

There exists a natural one to one mapping from the class of antispaces onto itself […]

1968, Evert Wattel, The Compactness Operator in Set Theory and Topology:

(mathematics) A kind of topological space.


unknottedness

From un- + knottedness or from unknotted + -ness.

(mathematics) The condition of being unknotted


knottedness

(mathematics) The condition of being knotted


distantial

en-adj

distantial (comparative more distantial, superlative most distantial)

more distantial (comparative)
most distantial (superlative)

the distantial spread

distantial transformation

Hence, given the referents of a point, referred to a distantial system, and the Cartesian equations of the lines of reference, referred to a Cartesian system:

1860, Charles Lutwidge Dodgson, A Syllabus of Plane Algebraical Geometry:

We defined a distantial description that describes a set of temporal sequences by their maximal common distantial subsequences, with distances between items.

2021, Salah Eddine Boukhetta, Christophe Demko, Karell Bertet, Jérémy Richard, Cécile Cayèré, “Temporal Sequence Mining Using FCA and GALACTIC”, in Tanya Braun, Marcel Gehrke, Tom Hanika, editors, Graph-Based Representation and Reasoning, page 197:

(mathematics) Pertaining to the difference between items.


monogenous

(mathematics) Having a single differential coefficient considered as a rule of generation.


amblygon

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From Ancient Greek ἀμβλύς (amblús) + -gon.

(geometry, obsolete, rare) An obtuse-angled shape, especially an obtuse triangle.


curvative

Examination of waves larger than 60 metres will depend on the accuracy with which the spatial derivatives (tilts, curvatives, etc.) of the surface can be obtained.

1977, IEEE Council on Oceanic Engineering, Oceanic Engineering Society (U.S.), Oceans:

This equation is descriptive of a Cornu spiral, a spiral whose curvative increases linearly with arclength.

1981, 25th IEEE Machine Tools Conference, 1981:

Assume first that this region is exactly linear, with no curvative (i.e., ∂2ρ/∂x2 = 0).

2010, Daniel M. Zuckerman, Statistical Physics of Biomolecules, →ISBN, page 288:

differential geometry
differential geometry

(differential geometry) The first partial derivative of a function that describes a surface.


zenzizenzizenzizenzike

en-noun

zenzizenzizenzizenzike (plural not attested)

An extension of Robert Recorde's naming system for mathematical powers presented in his 1557 mathematics book The Whetstone of Witte, from the root word zenzic.

A Zenzizenzizenzizenzike or Square of Squares Squaredly Squared

1696, Samuel Jeake, chapter 4, in Arithmetic surveyed or reviewed, volume 3, page 272; 'A compleat body of arithmetic, in four books...' 1701:

(mathematics, obsolete) The sixteenth power of a number.


Hann

en-verb

Hann (third-person singular simple present Hanns, present participle Hanning, simple past and past participle Hanned)

Hanns (present singular third-person)
Hanning (participle present)
Hanned (participle past)
Hanned (past)

From a Middle English given name derived from Johan, variant of John, or less often from Henry or Randolph.

(transitive, signal processing) To apply the Hann function to (a signal).


cyclometry

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(archaic, geometry) The measurement of circles, including calculating circumference, arcs, angles etc.


confidence level

en-noun

confidence level (plural confidence levels)

(statistics) The probability that a measured quantity will fall within a given confidence interval.


subduple

3:6 is a subduple ratio, while 6:3 is a duple ratio.

As one of these under pulleys abates half of that heaviness of the weight, and causes the power to be in a subduple proportion; so two of them abate half of that which remains, and cause a subquadruple proportion, three a sextuple, four a suboctuple.

1648, John Wilkins, Mathematical Magick:

(mathematics) Indicating one part of two; in the ratio of one to two.


partial autocorrelation

partial autocorrelation (plural partial autocorrelations)

(statistics) Remaining correlation of two random variables in a stochastic process after intervening random variables have been accounted for.


triquadrantal

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A triquadrantal triangle is one whose three sides are quadrants, and whose three angles are consequently right angles.


isographic

isographic invariance

(mathematics) Of or pertaining to isography.


death rate

The number of deaths per given unit of population over a given period of time.


surfel

(computer graphics) A unit square between voxels.


spheroconic

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(geometry) A non-plane curve formed by the intersection of the surface of an oblique cone with the surface of a sphere centred at the cone's vertex.


Taylor series

Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.

A series solution about an ordinary point of a differential equation is always a Taylor series having a nonvanishing radius of convergence. A series solution about a singular point does not have this form (except in rare cases). Instead, it may be either a convergent series not in Taylor series form (such as a Frobenius series) or it may be a divergent series.

1978, [McGraw-Hill], Carl M. Bender, Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer, published 1999, page 324:

The usual procedure for deriving finite-difference equations consists of approximating the derivatives in the differential equation via a truncated Taylor series.

1980, Suhas Patankar, Numerical Heat Transfer and Fluid Flow, Taylor & Francis (CRC Press), page 28:

This function has its only singularity at x = 0, implying that the radius of convergence for the Taylor series around x = 1 is only unity.

1998, Kenneth L. Judd, Numerical Methods in Economics, The MIT Press, page 197:

(calculus) A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order derivatives at given reference point a; the series f(a)+(f'(a))/(1!)(x-a)+(f(a))/(2!)(x-a)²+(f'(a))/(3!)(x-a)³+⋯=∑ₙ₌₀∞(f⁽ⁿ⁾(a))/(n!)(x-a)ⁿ.

Brook Taylor
James Gregory (mathematician)
Taylor series

泰勒展開式 /泰勒展开式

power series of a function calculated from derivatives at a reference point


superdominant

en-adj

superdominant (comparative more superdominant, superlative most superdominant)

more superdominant (comparative)
most superdominant (superlative)

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In decision-theoretical tenns, therefore, to believe in God is superdominant over disbelieving.

2009, Peter Hedström, Peter Bearman, The Oxford Handbook of Analytical Sociology, →ISBN:

(decision theory) Comprising the winning strategy in all cases.


bipartient

From Latin bis (“twice”) + partiens, present participle of partire (“to divide”).

But this must be specially looked to in the partition of incommensurable quantities that it will go on eternally without end, as will plainly appear in its proper place; thust of the number 10 and its bipartient root, or, as it is called, square root, no common measure will be found in eternity; much less that greatest divisor; as in its proper place.

1834, Mark Napier, Memoirs of John Napier of Merchiston, page 472:

16 = 6 x 2 (double) + 2/3 of 6 (bipartient).

2007, Henry Mayr-Harting, Church and Cosmos in Early Ottonian Germany, page 159:

(mathematics, dated) Involving an operation on two equal values.


cylindroid

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The intrados of a simple vault is generally formed of the portion of the surface of a cylinder, cylindroid, or sphere, never greater than that of half the solid; and the springing lines of the coussinet, which terminate the walls from which the vault rises, are generally straight lines, parallel to the axis of the cylinder or cylindroid.

1830, Sir David Brewster, The Edinburgh Encyclopaedia, page 523:

(geometry) A cylinder with elliptical cross-section.

(geometry) A certain three-dimensional surface described by a moving straight line, used to illustrate the motions of a rigid body and the forces that act upon it.


metaknowledge

en-noun

metaknowledge (usually uncountable, plural metaknowledges)

/ˈmɛtəˌnɒlɪd͡ʒ/

Metaknowledge is knowledge about knowledge […] The hallmark of metaknowledge is its being a matter of knowing propositions in which one K[nowledge]-operator occurs within the scope of another. Knowledge about someone's ignorance thus counts as metaknowledge.

2005, Nicholas Rescher, Epistemic Logic: A Survey of the Logic of Knowledge, →ISBN, page 20 (Google preview):

(philosophy) Knowledge about knowledge itself (for example, epistemologic awareness).

The acts of monitoring, hypothesizing, and verifying are internal work which require a person's metaknowledge or knowledge concerning what kind of knowledge is needed and how that knowledge is appropriately used in the situation.

1996, Reiko Hayashi, “Cognition, Empathy & Interaction”, in Advances in Discourse Processes, volume 54, →ISBN, page 22 (Google preview):

Meta-knowledge is knowledge about how to acquire and exploit information, rather than basic knowledge about the world.

2004, Andy Clark, Natural-Born Cyborgs: Minds, Technologies, and the Future of Human Intelligence, →ISBN, page 67 (Google preview):

(psychology, artificial intelligence) Knowledge about types, domains, functions, or preconditions of knowledge.


barrelage

barrelage (countable and uncountable, plural barrelages)

That is a very large question, and I do not propose to go into it in any detail; but from such figures as I have been able to obtain, I am bound to say that it does appear that there has been not only a diminution, as was pointed out by the Committee, in the barrelage of beer brewed in the United Kingdom, but also in the consumption of spirits.

"We have made real progress since taking over, illustrated by a very healthy increase in barrelage, and the various investments put us in a good position to move forwards," he said.

2011, Andrew Barker, The Publican's Morning Advertiser:

Quantity of beer (or other drink) measured in barrels.


orthotomic

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(algebra) imaginary; involving the square root of a negative number.


orthotomic

(geometry) The line that joins the poles of the common chord on two orthotomic circles.

(geometry) The envelope of the family of circles that have centers on a specified curve and which pass through a specified point.


tautochrone

From Ancient Greek ταὐτός (tautós, “the same”) + χρόνος (khrónos, “time”).

der

An inverted cycloid with its base horizontal is a tautochrone.

(mathematics) A curve, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall.


Steiner point

(graph theory) An extra vertex that is not a member of the input.

(geometry) The point on the circumcircle of a triangle that lies at the intersection of three lines through the vertices of the triangle, where those lines are parallel to the corresponding sides of the first Brocard triangle.

(geometry) The geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex of the system.

(geometry) Any of the 20 points located at the 3 by 3 intersections of the 60 Pascal lines which are produced by extending the triplets on opposite sides of a conic section in Pascal's theorem for all permutations of verices.


bandle

From Irish banlámh (“cubit”), from Middle Irish bannlám, from bann (“a measure”) + lám (“hand, arm”).

(historical) An Irish measure of two feet (61 cm) in length.


coordinatize

en-verb

coordinatize (third-person singular simple present coordinatizes, present participle coordinatizing, simple past and past participle coordinatized)

coordinatizes (present singular third-person)
coordinatizing (participle present)
coordinatized (participle past)
coordinatized (past)

(mathematics) to apply coordinates to a system


bimedial

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(geometry, of a line) Being the sum of two lines commensurable only in power (such as the side and diagonal of a square).


Poissonian

We saw that the observation of Poissonian and super-Poissonian statistics could be explained by classical wave theory, but not sub-Poissonian statistics.

2006, Mark Fox, Quantum Optics: An Introduction, page 105:

Poisson distribution
Poisson distribution

(mathematics) Of or pertaining to the Poisson distribution.


pollum

For this kind of work, and for the quantity of lime above mentioned, about ten pollums (the pollum ten pagodas weight) of sugar is commonly used.

1799 April 1, James Anderson, Recreations in Agriculture, Natural-History, Arts, and Miscellaneous Literature, page 6:

In the District south of Quilon to Tavallay, a Five Pollum weight is used for weighing cotton, thread, tamarinds, jagherry, &c. which weight answers to 5848.3 gr. and is thus divided […]

1831, P. Kelly, The Universal Cambist and Commercial Instructor:

(metrology, obsolete) A historic unit of weight used in India, equal to 1 ounce plus 3.25 drams.


fertility rate

In America the fertility rate of recent immigrants tends to be higher than that of native population.

In most industrialized countries the fertility rate has dropped well below replacement rate.

The average number of children that would be born to a woman over her lifetime if she followed the current average pattern of fertility among a given group of women and survived through her reproductive years; used as an indicator of strength of population growth.


interaxis

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The principles of analytical geometry afford the means of determining how much the interaxes of the regular octahedron must be increased or diminished to equal the interaxes in these different forms.

1854, James Dwight Dana, A System of Mineralogy, Comprising the Most Recent Discoveries, page 106:

Owing to this I was only able, by breaking a number of the quartz pieces, to obtain one small crystal representing a distorted rhombic dodecahedron 8 0(110), i.e, one extended in the line of an octahedral or trigonal interaxis, giving it the appearance of an hexagonal prism terminated by a rhombohedron (see fig. 2) in striking resemblance to dioptase.

1885, George H. F. Ulrich, “Notes on some Mineral Occurrences At Dusky Sound, West coast of Middle Island, New Zealand”, in The New Zealand Journal of Science, volume 1, page 309:

When the position is as given in the stereographic projection in Fig. 265, the angle over the axial-plane polar edges is the more acute, but if the pole were placed nearer to the crystallographic than to the interaxis, as in the case of the dihexagonal pyramid {2131} of beryl shown in Fig . 266, the case would be reversed.

1911, Alfred Edwin Howard Tutton, Crystallography and Practical Crystal Measurement, page 306:

In the traditional valence bond approach above, the decrease of the bron position parameter improves the bond strength of the (sp³)_z hybrid, but it increases the misfit between direction of the boron-metal interaxis and direction (z-axis) of (sp³)_z hybrid.

1968, Forrest L. Carter, “Valence Bonding in Some Refractory Transition Metal Compounds with High Coordination”, in NBS Special Publication, page 548:

(geometry) A line from the center of a regular solid to the center of one of its edges.


amblygonal

en-adj

amblygonal (comparative more amblygonal, superlative most amblygonal)

more amblygonal (comparative)
most amblygonal (superlative)

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semiheap

(mathematics) A variety of heap that is required to satisfy only the para-associative law and need not obey the identity law.


groud

From Russian груда (gruda, “pile, heap”).

(mathematics) A heap, or mathematical generalization of a group, in abstract algebra.


spherics

(mathematics) The geometry and trigonometry of the surface of a sphere.


amphoric

From Latin amphoricus (“of or related to an amphora”), from amphora + -icus (“-ic: forming adj.”). Equivalent to amphora + -ic.

der

amphoric respiration or resonance

(medicine) Produced by or indicating a hollow cavity in the lungs, giving a sound like that produced by blowing into an empty decanter.

amphorique

medicine: produced by or indicating a hollow cavity in the lungs


excentricity

en-noun

excentricity (countable and uncountable, plural excentricities)

(mathematics) Archaic form of eccentricity.


precompose

en-verb

precompose (third-person singular simple present precomposes, present participle precomposing, simple past and past participle precomposed)

precomposes (present singular third-person)
precomposing (participle present)
precomposed (participle past)
precomposed (past)

(transitive, mathematics) To apply (an operation) before another operation occurs.


double factorial

en-noun

double factorial (plural double factorials)

The symbolical representation of the results of this paper is much facilitated by the introduction of a separate symbol for the product of alternate factors, n#92;cdotn-2#92;cdotn-4#92;cdots 1, if n be odd, or n#92;cdotn-2#92;cdots 2 if n be odd^([sic – meaning even]). I propose to write n#33;#33; for such products, and if a name be required for the product to call it the "alternate factorial" or the "double factorial." Full advantage of the new symbol is only gained by extending its meaning to the negative values of n. Its complete definition may then be included in the equationsn#33;#33;#61;n(n-2)#33;#33;,#92;quad 1#33;#33;#61;1,#92;quad 2#33;#33;#61;2.

1902, Arthur Schuster, “On some Definite Integrals and a New Method of reducing a Function of Spherical Co-ordinates to a Series of Spherical Harmonics”, in Proceedings of the Royal Society of London, volume 71, →DOI, →JSTOR, page 99:

The double factorial notation #92;begin#123;align#125;(2n)#33;#33;amp;#61;2#92;cdot 4#92;cdot 6#92;cdots(2n-2)(2n)#61;2#123;n#125;n#33;#92;#92;(2n#43;1)#33;#33;amp;#61;1#92;cdot 3#92;cdot 5#92;cdots(2n-1)(2n#43;1)#61;#92;frac#123;(2n#43;1)#33;#125;#123;2#123;n#125;n#33;#125;#92;end#123;align#125;may be considered as a generalization of n#33;#61;1#92;cdot 2#92;cdot 3#92;cdotsn.

1948 September, B. E. Meserve, “Double Factorials”, in The American Mathematical Monthly, volume 55, number 7, →DOI, →JSTOR, page 425:

We prefer now to write the expansion in a slightly different way in order to exhibit more clearly the symmetry properties of the expansion coefficients:f#95;k(m,m')#61;(#92;tfrac#123;1#125;#123;2#125;#92;pi)#92;tfrac#123;1#125;#123;2#125;2#123;-2#92;bar#123;m#125;-3#125;#92;sum#95;#123;#92;sigma#125;(2#92;bar#123;m#125;-2#92;sigma#43;1)#33;#33;#92;,T#95;k#123;#92;,2#92;sigma#125;(m,m')J#95;#123;2#92;sigma#125;,where, as above, #92;bar#123;m#125; is the average of m and m', #92;bar#123;m#125;#61;#92;tfrac#123;1#125;#123;2#125;(m#43;m'), and the double factorial notation is used, (2n#43;1)#33;#33;#61;1#92;cdot 3#92;cdot 5#92;cdots(2n#43;1).

1958–1959, Kenneth W. Ford, E. J. Konopinski, “Evaluation of Slater integrals with harmonic oscillator wave functions”, in Nuclear Physics, volume 9, number 2, →DOI, page 219:

The symbol #33;#33; in Eq. (9) denotes the double factorial given by n#33;#33;#61;n(n-2)(n-4)#92;dots#92;kappa#95;n, where #92;kappa#95;n is 1 for odd n and 2 for even n.

2008 April, Adriana Pálffy, Jörg Evers, Christoph H. Keitel, “Electric-dipole-forbidden nuclear transitions driven by super-intense laser fields”, in Physical Review C, volume 77, number 4, →DOI, page 044602-3:

Double factorials can also be defined recursively. Just as we can define the ordinary factorial by n#33;#61;n#92;cdot(n-1)#33; for n#92;geq 1 with 0#33;#61;1, we can define the double factorial byn#33;#33;#61;n#92;cdot(n-2)#33;#33;for n#92;geq 2 with initial values 0#33;#33;#61;1#33;#33;#61;1. With our convention that (-1)#33;#33;#61;1, the recursion is valid for all positive integers n.

2012 June, Henry Gould, Jocelyn Quaintance, “Double Fun with Double Factorials”, in Mathematics Magazine, volume 85, number 3, →DOI, pages 177–178:

(mathematics, combinatorics) For an odd integer, the result of multiplying all the odd integers from 1 to the given number; or for an even integer, the result of multiplying all the even integers from 2 to the given number; symbolised by a double exclamation mark (!!). For example, 9!! = 1 × 3 × 5 × 7 × 9 = 945.


Gen-Xer

From Gen X, shortened from Generation X + -er.


dedecoration

Dedecoration did not produce any advantages in observing the size of the displacement of dislocations.

Applying the star-triangle and dedecoration transformations[…]

(graph theory) Decimation (the elimination of points from a lattice); the inverse of decoration.


cental

From Latin centum (“a hundred”) + -al, perhaps modeled after quintal.

Thin native steers, dressing 56 pounds per cwt., $10.50 per cental;

1873 April, Monthly Report of the Department of Agriculture, page 206:

The practice of buying or selling grain by the 100 pounds, or the cental system, is becoming almost universal, and has many advantages over the old practice of selling grain by the bushel.

1888, C. Frusher Howard, Howard's Anglo-American art of reckoning, page 75:

John Hudson & Co. are prepared to undertake the business at a ½d. per cental advance on the price of wheat on 4th July 19000, which is 6s. 5½d. per cental, thus obtaining 6s. 6d. per cental as the contract price.

1901 July 6, Arthur F. Dodd, “Corn Options and Cotton Futures: Their Object and Effect upon Commercial Transactions”, in The Accountant, page 783:

(historical) A weight of one hundred avoirdupois pounds.


osculatrix

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From New Latin osculātrīx (literally “female kisser”), from Latin osculor (“to kiss”) + -trīx.

bor

(geometry) A curve whose contact with a given curve at a given point is of a higher order (or involves the equality of a greater number of successive differential coefficients of the ordinates of the curves taken at that point) than that of any other curve of the same kind.


fotmal

From Middle English fotmal, from Old English fōtmǣl (“step by step”, literally “foot-measure”), equivalent to foot + -meal. Doublet of footmeal.

der

(obsolete, units of measure) An old English unit of weight of 70 pounds, used particularly for lead

1⁄70 fotmal & for smaller subdivisions

Tower pound, troy pound, avoirdupois pound


Green's function

en-noun

Green's function (plural Green's functions)

Named after British mathematician George Green, who first developed the concept in the 1830s.

(calculus) a type of function used in the analysis of inhomogeneous differential equations.

Greense functie

function used to analyse differential equations


trichotomous

From trichotomy + -ous. Modelled on dichotomous.

> is a trichotomous relation, while the relation "divides" over the natural numbers is not.

(set theory) Such that, for all x and y in X, and for a binary relation R, exactly one of xRy, yRx or x=y holds.


conducible

en-adj

conducible (comparative more conducible, superlative most conducible)

more conducible (comparative)
most conducible (superlative)

If G (G) is conducible, then R splits directly into a sum of linear subspaces on which G(G) acts irreducibly.

2011, Hans Freudenthal, H. de Vries, Linear Lie Groups, page 185:

(mathematics) Able to be decomposed into a direct sum of ideals, such that each ideal corresponds to a certain structure or property.


sursolid

From French sursolide, equivalent to sur- + solid.

32 is the sursolid of 2.

(mathematics, obsolete) The fifth power of a number.


graphing calculator

en-noun

graphing calculator (plural graphing calculators)

(mathematics, computing) A hand-held (usually programmable) electronic calculator which is capable of solving equations, plotting graphs and performing other tasks with variables.


trivariate

(mathematics) Having or involving exactly three variables.


beaverling

The wife stumbled into the water, and as soon as her loot was wet, she immediately resumed her old shape as a beaver, her son became a beaverling, and the brooklet, changing to a roaring river, bore them to the lake.

(diminutive) A small, young, or juvenile beaver.