bearling

From Middle English berling, equivalent to bear + -ling.

While waiting at the inn up drove a Pau acquaintance in the person of the Marquis de Cherizet, out of whose pony-carriage was lifted a square box, which proved to contain a poor little bearling of about a month old, whose mother had been shot, and itself captured, […]

1871, “May-Day among the Mules”, in Charles Dickens, editor, All the Year Round:

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


radius vector

en-noun

radius vector (plural radii vectores or radius vectors)

radii vectores (plural)
radius vectors (plural)

(geometry) Of a point, a vector going from the origin to that point; equivalently, the transpose of the point.


boomeritis

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From boomer + -itis, coined by Ken Wilber in Boomeritis: A Novel That Will Set You Free (2002).

Techies were the most juvenile, but other wealthy men, in the full throes of boomeritis, also acted like kids in a candy store.

2009, Larry Samuel, Rich: the rise and fall of American wealth culture, page 222:

(informal) A narcissistic liberal worldview associated with baby boomers.


tractory

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Latin tractorius (“of drawing”), from trahere, tractum (“to draw”).


one-form

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procerity

[…] when he met with a tall woman he immediately commanded one of his Titanian retinue to marry her that they might propagate procerity.

1756, Samuel Johnson, Memoires of Frederick III, &c.:


bezzle

en-verb

bezzle (third-person singular simple present bezzles, present participle bezzling, simple past and past participle bezzled)

bezzles (present singular third-person)
bezzling (participle present)
bezzled (participle past)
bezzled (past)

From Middle English besilen, from Old French besiler, besillier (“to mistreat, pillage”); or shortened from English embezzle.

(obsolete) To drink to excess; to revel.


Fourier sine series

en-noun

Fourier sine series (plural Fourier sine series)

a Fourier series consisting solely of sine functions


Fourier cosine series

Fourier cosine series (plural Fourier cosine series)

a Fourier series consisting solely of cosine functions


bicircular

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a bicircular curve

(geometry) Having nodes at the two circular points at infinity.


plurigenus

(mathematics) The dimension of a canonical ring.


halfer

Coordinate term: thirder

Sleeping Beauty problem
Sleeping Beauty problem

(decision theory) With regard to the Sleeping Beauty problem: one who argues that the probability of heads is 1/2.


seah

uder

Hebrew סְאִים֙

(historical units of measure) A former Hebrew unit of dry volume, about 7.7 L or 7 quarts.


subduplicate

(mathematics) Expressed by the square root; said of ratios.


Collatz conjecture

Named after Lothar Collatz, who first proposed it in 1937.

(mathematics) The conjecture that the process of taking a number n and, if n is even, dividing it by 2, or if n is odd, multiplying it by 3 and adding 1, then repeating this process, will eventually yield 1.


cactoid

It is well known that a Peano space is a cactoid if and only if each of its true cyclic elements is a 2-sphere.

1951, John William Theodore Youngs, The Representation Problem for Fréchet Surfaces, page 27:

(topology) A locally connected continuum that is the closure of the union of an at most countable number of spheres and simple arcs, of which every simple closed contour is contained in one and only one of the spheres.


error function

normally distributed
normal distribution

(mathematics, statistics, probability theory) A sigmoid function giving the probability that a measurement, under the influence of normally distributed errors with standard deviation, is within a certain distance from the mean value.


tical

viss

a Burmese unit of weight equal to 100 ticals

(Myanmar) A Burmese measurement of weight, the kyattha, of about 16.3293 grams (0.576 ounces).

ကျပ်သား

Burmese measurement of weight, 16.3293 g


Apollonian gasket

en-noun

Apollonian gasket (plural Apollonian gaskets)

(mathematics) A fractal generated from triples of circles, where each circle is tangent to the other two.


anticomplementary

en-adj

anticomplementary (comparative more anticomplementary, superlative most anticomplementary)

more anticomplementary (comparative)
most anticomplementary (superlative)

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radication

en-noun

radication (usually uncountable, plural radications)

From Middle English radicacyon, from Medieval Latin rādīcātio.

(arithmetic, rare) The process of extracting a number's root.


zero-one law

(mathematics) The fact that, in some circumstances, the probability of an event can only be zero or one and not any intermediate value.


semilogarithmic

(mathematics, of graph paper) Having one logarithmic scale and one arithmetic/linear scale.

semilogaritmický

having one scale logarithmic and the other one linear


semiparabola

semiparabola (plural semiparabolas or semiparabolae)

semiparabolas (plural)
semiparabolae (plural)

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(geometry) One branch of a parabola, terminating at the principal vertex of the curve.


trapdoor function

trapdoor function (plural trapdoor functions)

From the idea that it is easy to fall through a trapdoor but difficult to climb back out.

(mathematics, cryptography) A function that is easy to compute in one direction but difficult to compute in the opposite direction (finding its inverse) without special information.


Leonardo number

Leonardo number (plural Leonardo numbers)

(mathematics) Any of a sequence of numbers related to the Fibonacci numbers. L(0) = 1, L(1) = 1, and then, for all n larger than 1, L(n) = L(n-1)+L(n-2)+1.


osculant

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From Latin osculans, osculantis, present participle of osculari (“to kiss”). See osculate.

(geometry) Tangent, touching at a single point.


osculant

(geometry) The point at which two tangent curves touch.

(algebra) The condition that the solution to a set of simultaneous quantics, is also the solution of the corresponding set of tangential quantics.


osculant

(mathematics) a form of tacinvariant of hypersurfaces that have a point in common


raip

Compare Icelandic reip (“rope”), and English rope.


trisoctahedron

trisoctahedron (plural trisoctahedrons or trisoctahedra)

trisoctahedrons (plural)
trisoctahedra (plural)

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isography

transformation networks
transformation networks

(mathematics) An automorphism of transformation networks.


parabolism

(obsolete, mathematics) The division of the terms of an equation by a known quantity that is involved in the first term.


supertwistor

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The superconformal algebra can be realized on supertwistor space.

(mathematics, physics) A supersymmetric extension of twistors, having n degrees of freedom (where n is the number of supersymmetries) in addition to those of a standard twistor.


conchospiral

the constant angle according to which each traces its conchospiral.

A kind of spiral curve found in certain univalve shells.


intermean

intermean distance


subcardioid

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(geometry) Partially or imperfectly cardioid.


logometric

(mathematics) Of or relating to a system of logarithms constructed to suit a system of ratios and measures.


superpartient

Learned borrowing from Latin superpartiens, from super (“over”) + partiens, the past participle of partire (“to divide”).

lbor

[W]e proceed to a Superpartient Reaſon, which is when the Antecedent exceeds the Conſequent by ſome Aliquot Parts more than one, whence the Name: […] Thus 9 is ſaid to be in a Superpartient Reaſon to 7, because 9 exceeds 7 by two 7th Parts.

1734, Isaac Barrow, “Lecture XIX. Of the Species and Differences of Geometrical Reason.”, in John Kirkby, transl., The Usefulness of Mathematical Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Publick Schools at the University of Cambridge. […], London: […] Stephen Austen, […], →OCLC, page 362:

(mathematics, archaic) Being or relating to a ratio where the larger value exceeds the smaller by more than one unit, as in 3 to 5.


balayage

en-noun

balayage (countable and uncountable, plural balayages)

(mathematics) A method for reconstructing a harmonic function.


semiweak

There are 2⁵⁶ (7.21 × 10¹⁶, about 72 quadrillion) possible keys for DES, of which four are weak and twelve are semiweak.

(cryptography, Data Encryption Standard) Producing only two different subkeys.


superring

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(mathematics) A superalgebra over a ring.


tautochronous

tautochronous motion

(mathematics) Relating to, or having the properties of, a tautochrone.


p-adic absolute value

p-adic absolute value (plural p-adic absolute values)

According to Ostrowski's theorem, only three kinds of norms are possible for the set of real numbers: the trivial absolute value, the real absolute value, and the p-adic absolute value.ᵂᴾ

If cgt;1, then x#92;rightarrowc#123;-v#95;p(x)#125; (with the convention c#123;-#92;infty#125;#61;0) is a nonarchimedean absolute value, denoted #92;vert..#92;vert#95;#123;p,c#125; and called the p-adic absolute value to base c. If cgt;1 and dgt;1 and if r#61;#92;log#95;cd, then #92;vertx#92;vert#95;#123;p,d#125;#61;#92;vertx#92;vertʳ#95;#123;p,c#125; for every x#92;inK. The p-adic topology on K is the topology defined by the p'''-adic absolute values.

1993, Seth Warner, Topological Rings, Elsevier (North-Holland), page 8:

They both gave essentially the same proof, based on the Subspace Theorem (more precisely, Schlickewei's generalisation to p'''-adic absolute values and number fields [30] of the Subspace Theorem proved by Schmidt in 1972 [41]).

1999, Jan-Hendrik Evertse, Hans Peter Schlickewei, “The Absolute Subspace Theorem and linear equations with unknowns from a multiplicative group”, in Kálmán Györy, Henryk Iwaniec, Jerzy Urbanowicz, editors, Number Theory in Progress, Walter de Gruyter, page 121:

It ^([#92;Z#95;p]) can also be defined as the subset ^([of #92;Q#95;p]) with #92;vertx#92;vert#95;plt;p because the p'''-adic absolute value takes no values between 1 and p, and therefore #92;Z#95;p is open.

2007, Anthony W. Knapp, Advanced Algebra, Springer (Birkhäuser), page 320:

(number theory, field theory) A norm for the rational numbers, with some prime number p as parameter, such that any rational number of the form pᵏ(a/b) — where a, b and k are integers and a, b and p are coprime — is mapped to the rational number p⁻ᵏ and 0 is mapped to 0. (Note: any nonzero rational number can be reduced to such a form.)


p-adic ordinal

Notice the resemblance between the p-adic ordinal and the base-p logarithm.

(number theory) A function of rational numbers, with prime number p as parameter, which is defined for some non-zero integer x as the largest integer r such that pʳ divides x; is defined for some non-zero rational number a/b as the p-adic ordinal of a minus the p-adic ordinal of b; and is defined for 0 as infinity.


p-adic norm

2002, M. Ram Murty, Introduction to p-adic Analytic Number Theory, American Mathematical Society, page 114,
By the property of the p'''-adic norm, (or by the “isosceles triangle principle”) we deduce that operatorname ordₚa_r=rλ₁.

2006, Matti Pitkanen, Topological Geometrodynamics, Luniver Press, page 531,
The definition of p-adic norm should obey the usual conditions, in particular the requirement that the norm of product is product of norms.

Given a prime p, we may define the p'''-adic norm #92;Vert#92;#92;Vert#95;p over the field of rational numbers #92;Q.

2012, Claire C. Ralph, Santiago R. Simanca, Arithmetic Differential Operators over the p-adic Integers, Cambridge University Press, page 2:

p-adic absolute value
p-adic absolute value

(number theory) A p-adic absolute value, for a given prime number p, the function, denoted |..|ₚ and defined on the rational numbers, such that |0|ₚ = 0 and, for x≠0, |x|ₚ = p^(-ordₚ(x)), where ordₚ(x) is the p-adic ordinal of x; the same function, extended to the p-adic numbers ℚₚ (the completion of the rational numbers with respect to the p-adic ultrametric defined by said absolute value); the same function, further extended to some extension of ℚₚ (for example, its algebraic closure).

Let K be a field with discrete valuation v, and #92;mathcal#123;O#125;#95;K be the valuation ring.
Definition 2.3.1 A p'''-adic norm on vector space V over K is a function #92;alpha#58;V#92;rightarrow#92;R satisfying:
a) #92;alpha(x)#92;ge 0 and #92;alpha(x)#61;0 if and only if x#61;0.
b) #92;alpha(ax)#61;#92;verta#92;vert#92;alpha(x) for a#92;inK and x#92;inV.
c) #92;alpha(x#43;y)#92;le#92;operatorname#123;sup#125;(#92;alpha(x),#92;alpha(y)) for x,y#92;inV.
If #92;alpha is a p'''-adic norm and tgt;0, then the dilation t#92;alpha is a p'''-adic norm, and we denote by N#95;p(V) the set of dilation classes of p'''-adic norms on V.

2006, Kang Zuo, Representations of Fundamental Groups of Algebraic Varieties, Springer, page 20:

(algebra) A norm on a vector space which is defined over a field equipped with a discrete valuation (a generalisation of p-adic absolute value).


septangle

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p-adic ultrametric

p-adic ultrametric (plural p-adic ultrametrics)

On p'''-adic ultrametrics in the genome / In previous section we demonstrated that codons and amino acids are elements of some p'''-adic ultrametric spaces.

2017 September 15, Branko Dragovich, Andrei Yu. Khrennikov, Nataša Ž. Mišić, “Ultrametrics in the genetic code and the genome”, in Applied Mathematics and Computation, volume 309, →DOI, pages 350–358:

(number theory) The ultrametric with prime number p as parameter defined as d_p(x,y)=|x-y|ₚ; i.e., such that the distance between two rational numbers is equal to the p-adic absolute value of the difference between those two numbers.


trivial absolute value

trivial absolute value (plural trivial absolute values)

The trivial absolute value gives rise to the discrete metric.

(number theory) An absolute value (or norm) for a field which is defined to be equal to one for any element of the field other than the field's zero, for which it is defined to be equal to zero.


empty function

(mathematics) A function whose domain is the empty set.


presheaf

presheaf (plural presheaves or presheafs)

Let X be a topological space. (Following tradition, I will switch from my previous convention of using X to denote an object of a topos.) Write Open(X) for its poset of open subsets. A presheaf on X is a functor F#58;#92;mathbf#123;Open#125;(X)#92;mbox#123;op#125;#92;rightarrow#92;mathbf#123;Set#125;. It assigns to each open subset U a set F(U), whose elements are called sections over U (for reasons to be explained). It also assigns to each open V#92;subseteqU a function F(U)#92;rightarrowF(V), called restriction from U to V and denoted by s#92;rightarrows#124;#95;V. I will write Psh(X) for the category of presheaves on X.
Examples 3.1 i. Let F(U) = {continuous functions U#92;rightarrow#92;mathbb#123;R#125;}; restriction is restriction.

2011 June 27, Tom Leinster, “An informal introduction to topos theory”, in arXiv.org, Cornell University Library, retrieved 2018-03-18:

contravariant functor
contravariant functor

(category theory, sheaf theory) An abstract mathematical construct which associates data to the open sets of a topological space, generalizing the situation of functions, fiber bundles, manifold structure, etc. on a topological space (but not necessarily in such a way as to make the local and global data compatible, as in a sheaf). Formally, A contravariant functor ℱ whose domain is a category whose objects are open sets of a topological space (called the base space or underlying space) and whose morphisms are inclusion mappings. The image of each open set under ℱ is an object whose elements are called sections, and are which are said to be over the given open set; the image of each inclusion map A→B under ℱ is a morphism ℱ(B)→ℱ(A), called the restriction from B to A and denoted operatorname res_(B,A) or |_(B,A).


right inverse

(category theory) For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that f∘s= mbox id_Y.


NBG

(set theory) von Neumann-Bernays-Gödel (axiomatic) set theory


slice category

slice category (plural slice categories)

(category theory) A category whose objects are morphisms (of some given category) with a common codomain, and whose morphisms are commuting triangles where two morphisms of each of such triangles share the said common codomain.


subtriplicate

The subtriplicate ratio of a to b is ∛a to ∛b.

(mathematics) Expressed by the cube root; said especially of ratios.


supermeasure

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(mathematics) A kind of measure on a Hilbert space.


crunode

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Probably from Latin crux (“a cross”) + English node.

(geometry, archaic) node (point where one branch of a curve crosses another branch)


anallagmatic

anallagmatic curves

anallagmatic geometry

anallagmatic surfaces

(mathematics) Not changed in form by inversion.


Didonia

In allusion to the classical story of Queen Dido, who was granted the land she could encompass with a piece of bull hide.

And hence, by Meusnier's theorem, the difference of the squares of the curvatures of curve and surface is constant; the curvature of the surface meaning here the reciprocal of the radius of the sphere which osculates in the reduction of the element of the Didonia.

1867, Peter Guthrie Tait, An Elementary Treatise on Quaternions:

(geometry) The curve which on a given surface and with a given perimeter contains the greatest area.


semiangle

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(geometry) an angle of half a given size


grandboomer

This granddaughter was clearly tapping into the energy and fun that many grandboomers bring to their new role.

2005, Peggy Edwards, Mary Jane Sterne, Intentional Grandparenting: A Boomer's Guide, McClelland & Stewart Ltd., →ISBN, page 4:

A member of the baby boom generation who is a grandparent.


stream cipher

(cryptography) a symmetric-key cipher in which plaintext digits are combined with a pseudorandom cipher digit stream


closed ball

In the set of 3-adic numbers, the closed ball of radius 1/3 "centered" at 1 is the set x|∃n∈ℤ.,x=3n+1. This closed ball partitions into exactly three smaller closed balls of radius 1/9, e.g., x|∃n∈ℤ.,x=4+9n. Then each of those balls partitions into exactly 3 smaller closed balls of radius 1/27, and the sub-partitioning can be continued indefinitely, in a fractal manner.

mathematical analysis
mathematical analysis

(mathematical analysis) A ball which contains its boundary, i.e., a ball which is a closed set.


hyperstructure

(mathematics) Any algebraic structure equipped with a hyperoperation.

One has also to remember that within a hyperstructure - which a regime resembles - not every entity and organization has to be in the same area of state space.

2013 -, Holger Berg, Transitions of Energy Regimes: An Evolutionary Economic Interpretation, →ISBN:

(mathematics) A set of sets or a system of systems.


hypergroup

(mathematics) Any algebraic group equipped with a hyperoperation.

hipearghrúpa

any algebraic group equipped with hyperoperation


semihypergroup

(mathematics) Any hypergroup for which the reproduction axiom is valid.


hyperoperation

The first four hyperoperations are successor, addition, multiplication, and exponentiation.

(mathematics) One of a sequence of operations for compounding numbers that increase in growth iteratively.


hyperoperator

(mathematics) A mapping from operators to operators.


pick up the slack

en-verb

pick up the slack (third-person singular simple present picks up the slack, present participle picking up the slack, simple past and past participle picked up the slack)

picks up the slack (present singular third-person)
picking up the slack (participle present)
picked up the slack (participle past)
picked up the slack (past)

We call them slack variables because they pick up the slack, so to speak; that is, they take on whatever values are necessary to create equalities (notice that each slack variable must be nonnegative).

2009, Glenn Hurlbert, Linear Optimization: The Simplex Workbook, page 32:

take up the slack
take up the slack#English

(mathematics) To act as a slack variable, converting an inequality into an equality.


anguineal

en-adj

anguineal (comparative more anguineal, superlative most anguineal)

more anguineal (comparative)
most anguineal (superlative)

(obsolete, mathematics) Describing a certain type of hyperbola that has a snakelike form


calceolate

calceolate (comparative more calceolate, superlative most calceolate)

more calceolate (comparative)
most calceolate (superlative)

From Latin calceolus (“little shoe, slipper”) + -ate (adjective-forming suffix), from calceus (“calceus, footwear”) + -olus (diminutive noun-forming suffix), from calx (“heel”) + -eus (adjective-forming suffix).

af

(chiefly botany) Slipper-shaped, shaped like a slipper.


nodated

en-adj

nodated (comparative more nodated, superlative most nodated)

more nodated (comparative)
most nodated (superlative)

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From Latin nodatus, past participle of nodare (“to make knotty”), from nodus (“knot”). See node.

Form A to b or B to b, along the circular arc (see fig. 4), the paths of a series of points will give a gradation of symmetrical double nodated figures between the arc of a circle and the cuspidated tirangular figure. This is the first or finite series of symmetrical double nodated lines.

1830, The Mechanics' Magazine, Museum, Register, Journal, and Gazette, page 232:


semicubical

A semicubical parabola is a curve in which the ordinates are proportional to the square roots of the cubes of the abscissas.

(mathematics) Of or relating to the square root of the cube of a quantity.


sethood

William Van Ormen Quine (1969) Set Theory and Its Logic, →ISBN, page 302: “In the first edition I relativized the sethood condition insufficiently, failing to restrict the bound variables to sets”

John Bigelow and Robert Pargetter (1990) Science and Necessity, →ISBN, page 368: “In fact, this can be used as a necessary condition for sethood: a universal is a set only if any given thing instantiates it either in all possible worlds or in none.”

Yiannis N. Moschovakis (2006) Notes on Set Theory, →ISBN, page 111: “Each of (II)–(VI) grants sethood to a specific, explicitly defined collection of objects, it legitimizes a special case of the most appealing (if false) General Comprehension Principle 3.3.”


polygonhood

Richard R. Brockhaus (1991) Pulling up the ladder: the metaphysical roots of Wittgenstein's Tractatus, →ISBN, page 195: “However, the circle lacks an essential property of polygonhood, namely having angles, and thus as a convenient fiction we refer to it as a degenerate case of a polygon.”

W.S. Anglin (1997) The Philosophy of Mathematics: the Invisible Art, →ISBN, page 11: “None the less, for any natural number n > 3, there is a form of n-hood, and a form of n-sided polygon-hood. For example, when n = 4, we have the form of fourness and the form of squareness.”

Stephen Yablo (2008) Thoughts: Papers on mind, meaning and modality, →ISBN, page 267: “To the absolutionist, this can only mean that as n decreases, the property of n-sided regular polygonhood puts stronger and stronger demands on those would seek to know it.”

(mathematics, rare) The state of being a polygon.


polygonality

en-noun

polygonality (usually uncountable, plural polygonalities)

As the number of faces increases, the space-fillers contact more distant neighbours, the polygonalities of the faces of contact decreasing as the order of the neighbours increases.

1985, A. C. Ferro und M. A. Fortes, “A new family of trivalent space-filling parallelohedra”, in Zeitschrift für Kristallographie, volume 173:

M. Glouberman (1986) Descartes: The Probable and the Certain, →ISBN, page 213: “Conversely, (b) the condition of polygonality is a part of each of the conditions of triangularity, quadrilaterality, etc., and hence the latter are more than the term which collects them: the collecting term is, in other words, less than the terms it collects.”

The common feature of these and earlier was that the polygonality was regarded as an indication of nonimpact, or even non-explosive origin.

2010, T. Öhman et al., “Polygonal impact craters in the Solar System: Observations and implications”, in Large Meteorite Impacts and Planetary Evolution IV, →ISBN, page 52:

(mathematics) The state of being a polygon, the degree to which an object is polygonal.


polygonness

Imagine that humans have failed to grasp the nature of Polygonness and that without realizing it, our conception of the Form is constantly changing and is always mistaken.

1990, Rudolf Haller, Johannes Brandl, Wittgenstein—eine Neubewertung, →ISBN:

However many times we may add sides to a polygon, it never becomes a circle; to become a circle, the polygon must undergo an absolute negation (of its polygonness).

1992, Christopher Ives, Zen Awakening and Society, →ISBN, page 38:

For example, quadrilateralness can be analyzed into the attributes polygonness (ie, being a polygon) and four-sidedness.

2001, Gregory Browne, Necessary Factual Truth, →ISBN, page 11:


uniform convergence

uniform convergence (plural uniform convergences)

(mathematics) A type of convergence of a sequence of functions { fₙ }, in which the speed of convergence of fₙ(x) to f(x) does not depend on x.


plus-size

(especially attributive) Alternative spelling of plus size


superconvergent

en-adj

superconvergent (comparative more superconvergent, superlative most superconvergent)

more superconvergent (comparative)
most superconvergent (superlative)

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hemina

From Latin hemina (“half-sextarius”), from Ancient Greek, from ἡμι- (hēmi-, “hemi-: half”) + -ίνα (-ína, “-ina: forming nouns”). As a Spanish unit, via Spanish hemina.

...an Æginean Hemina of Hydromel ...

1727, John Arbuthnot, Tables of Ancient Coins, Weights and Measures. Explain'd and exemplify'd in several dissertations:

(historical) A Roman unit of liquid measure reckoned as the volume of ⁵⁄₆ Roman pound of wine and equivalent to about 0.27 L although differing slightly over time, used in English pharmacy into the 17th century.

(historical) A traditional Spanish unit of dry measure equivalent to about 23 L, used particularly in Leon.

(historical) A traditional Spanish unit of land area, varying in size depending on the land's quality and used particularly in Leon.


tractricoid

(geometry) A surface formed by revolving a tractrix about its asymptote.


floor function

(mathematics) A function that maps a real number to the largest integer that is not greater than it.


ceiling function

en-noun

ceiling function (plural ceiling functions)

(mathematics) A function that maps a real number to the smallest integer that is no smaller than it.


residue class

(number theory) A coset of an ideal of the ring of integers.


plenarily

en-adv

plenarily (comparative more plenarily, superlative most plenarily)

more plenarily (comparative)
most plenarily (superlative)

(mathematics) In the most complete limiting case.


sesquialter

From Latin sēsquialter, from sēsqui- (“a half and a”) + alter (“another, a second”).

(mathematics, archaic) Synonym of sesquialterate, 1½ times.


cuspate

en-adj

cuspate (comparative more cuspate, superlative most cuspate)

more cuspate (comparative)
most cuspate (superlative)

From cusp + -ate (adjective-forming suffix).

Shorelines are molded into smooth arcuate bays interrupted by cuspate horns.

1999 April 2, B. T. Werner, “Complexity in Natural Landform Patterns”, in Science, volume 284, number 5411, →DOI, pages 102–104:


cubation

(mathematics) The act of finding the volume or cubic content of a body; the result thus found.


convexified

(mathematics) converted to a convex form


JWST

(NASA, space science, US) Initialism of James Webb Space Telescope.


Smale's paradox

(topology) The non-intuitive fact that it is possible to turn a sphere inside out in a three-dimensional space with possible self-intersections but without creating any crease.


striction

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(geometry) The definition of a geometric shape as all points with some relationship to a central point, curve, etc., for example, a circle is the striction of all points at a distance of the radius from a single point.


line of striction

en-noun

line of striction (plural lines of striction)

(geometry) The line on a skew surface that cuts each generator in that point of it that is nearest to the succeeding generator.


bicriterion

(mathematics) Either of a pair of related criteria


orthotope

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(geometry) The generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.


hyperrectangle

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nomial

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Grothendieck group

Grothendieck group (plural Grothendieck groups)

(mathematics) An abelian group constructed from a commutative monoid in a universal way.

Alexander Grothendieck
Grothendieck group


groupoidal

(mathematics) Of or relating to groupoids.


supersingular

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(mathematics) Describing a certain class of elliptic curves


Siegel zero

(mathematics) A type of potential counterexample to the generalized Riemann hypothesis, on the zeros of Dirichlet L-function.


law of sines

(trigonometry) A statement that relates the lengths of the sides of a triangle to the sines of its angles.


rigol

→ Welsh: rhigol (“groove, furrow”)

From Middle English rigol, from Middle French rigole. Doublet of rail, regal, regula, and rule.

doublet

(nautical) A ridge or channel above a porthole to redirect water flow from dripping inside the vessel.


trinominal

From tri- + Latin nomen, nominis (“name”). Compare Latin trinominis (“three-named”).


idele

Blend of ideal + element; coined by Claude Chevalley.

(mathematics) An invertible element of the adele ring.


adele

Blend of additive + idele; coined by André Weil.

(mathematics) A member of a self-dual topological ring built on the field of rational numbers (or, more generally, any algebraic number field), and involving in a symmetric way all the completions of the field.


LTE

en-noun

LTE (countable and uncountable, plural LTEs)

lifting the exponent
lifting the exponent#English

(number theory) Initialism of lifting the exponent. (a lemma used to calculate p-adic orders)


twistorian

This identification, using this resolution, first appeared in twistor theory in [30], before twistorians were aware of the full BGG resolution.

1989, Robert J. Baston, Michael G. Eastwood, The Penrose Transform: Its Interaction With Representation Theory:

It is noteworthy that the 'electro- weak' theory seems to offer so helpful a line of advance, and I would suggest that as well as taking twistor diagrams more seriously, twistorians might also take the 'standard model' of quantum field theory more seriously.

1981, Haim Brézis, Jacques-Louis Lions, Nonlinear Partial Differential Equations and Their Applications, →ISBN:

Twistorians were astounded that string theorists, of all people, had answers to the googly problem and other issues that had vexed them.

2015, George Musser, Spooky Action at a Distance, →ISBN:

(mathematics) A mathematician who specializes in twistor theory.


PFS

perfect forward secrecy
w:perfect forward secrecy

(cryptography) Initialism of perfect forward secrecy.


Hopf algebra

(mathematics) A structure that is simultaneously a unital associative algebra and a counital coassociative coalgebra, equipped with an antiautomorphism satisfying a certain property.


coaction

coaction (countable and uncountable, plural coactions)

actions and coactions of measured groupoids on von Neumann algebras

(mathematics) The mapped version of an action to a cogroup.


antiautomorphism

(mathematics) A bijective antihomomorphism, i.e., an antiisomorphism, from a magma to itself.


antihomomorphism

(mathematics) A type of function defined on sets with multiplication that reverses the order of multiplication.


coassociativity

(mathematics) A relationship that is the dual of associativity.


coaugmentation

natural transformation
natural transformation

(mathematics) A natural transformation from the identity functor to a certain endofunctor.


presignature

(cryptography) An intermediate value used in forming a signature, unrelated to the contents of the message being signed.


counit

(mathematics) In an adjunction, a natural transformation from the composition of the left adjoint functor with the right adjoint functor to the identity functor of the domain of the right adjoint functor.


localic

(category theory) Relating to the category of locales.


comodule

A coalgebra is a comodule over itself.


coidentity

(category theory) The identity element of a cogroup.


coinversion

(category theory) The inversion operation of a cogroup object. A coinversion must satisfy the dual versions of the axioms for group objects.


semilune

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primitive root

There are #92;phi(p-1) incongruent primitive roots of p. The fact that there are so many primitive roots causes no difficulty in the theory of the binomial congruence but has caused considerable confusion in the tabulation of primitive roots.

1941, Derrick Henry Lehmer, Guide to Tables in the Theory of Numbers, National Research Council, page 13:

The integers 2, 3, 4, and 6 each have exactly one primitive root and therefore, by default, each has a set of primitive roots consisting of "consecutive" integers.
The integer 5, with primitive roots of 2 and 3 is the only positive integer having at least two primitive roots for which the entire set of primitive roots are consecutive integers.

1992, Joe Roberts, Lure of the Integers, Mathematical Association of America, page 55:

For example, the prime 7 has #92;phi(6)#61;2 primitive roots, namely, 3 and 5. Also, the prime 11 has #92;phi(10)#61;4 primitive roots, namely, 2, 6, 7, 8.
Recall from Theorem 6.7 that if m has primitive roots, and if g is one primitive root (#92;operatorname#123;mod#125;m), then we can obtain all primitive roots (#92;operatorname#123;mod#125;m) by raising g to appropriate exponents.

2006, Neville Robbins, Beginning Number Theory, Jones & Bartlett Learning, page 159:

(mathematics, number theory) For a given modulus n, a number g such that for every a coprime to n there exists an integer k such that gᵏ ≡ a (mod n); a generator (or primitive element) of the multiplicative group, modulo n, of integers relatively prime to n.

原根

number such that gk ≡ a (mod n) exists for every a coprime to n — see also generator, primitive element

generator

number that generates other numbers modulo n


line graph

A graph in which a series of connected straight lines connect points, each of which represents the value of a particular variable as a function of another variable.

(graph theory) A graph L(G) which is derived from a given non-oriented graph G such that the vertices of L(G) represent edges of G and so that a clique in L(G) represents a common end-vertex shared by a set of represented edges. (A star subgraph in G transforms into a clique in L(G).)

Suppose that a graph G has vertices A, B, C, and D such that A is adjacent to each of B, C, and D, but {B, C, D} is an independent set. Then G cannot be a line graph.

A graph which is the line graph (in the above sense) of some other graph.


pentacron

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From Ancient Greek πέντε (pénte, “five”) + ἄκρον (ákron, “summit”).

(geometry) A solid with five summits or angular points.


blindable

Finally, we use the term additive joint encryption scheme to denote a secure, blindable, xor-homomorphic, witnessed probabilistic public-key joint encryption scheme.

1994, Douglas R. Stinson, Advances in cryptology: CRYPTO '93, 13th Annual International Cryptology Conference, Santa Barbara, California, USA, August 22-26, 1993: proceedings:

Blindable encryption also provides a useful way to make a given ciphertext unrecognizable.

2004, Ari Juels, Financial Cryptography: 8th International Conference: volume 8, page 188:

(cryptography) Such that, given an encrypted bit (binary digit), anybody can create a random ciphertext decrypting to the same bit.


decuman

From Latin decumānus (“of the tenth, and by metonymy, large”), from decem (“ten”).

der

decuman billows

c. 1870, Frederic Farrar, The witness of history to Christ; 5 sermons, being the Hulsean lects. for 1870:

(obsolete) Large; chief; applied to an extraordinary billow, supposed by some to be every tenth in sequence.


sexangle

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From Latin sexangulus (“sexangular”), from sex (“six”) + angulus (“angle”). Compare French sexangle and English hexangular; sex- + angle.

the super parts being taken from the Quadrangle will form the Sexangle

1828, James Wilson (translator), Claudius Ptolomaeus, The Tetrabiblos:


lcm

least common multiple
least common multiple#English

(mathematics) Initialism of least common multiple.


lowest common multiple

en-noun

lowest common multiple (plural lowest common multiples)

(mathematics) Synonym of least common multiple


smallest common multiple

smallest common multiple (plural smallest common multiples)


harmonical

(mathematics, archaic) Synonym of harmonic mean


Catalan number

Named after the Belgian mathematician Eugène Catalan (1814–1894).

AMBIGUITY LEADS TO AN EXPONENTIAL NUMBER OF TREES
I saw the man with the telescope on the box in the car under the table ...
n prepositional phrases ⇒ (n + 1)’th catalan number

1998 July 29, Michael Collins, “A CONTEXT-FREE GRAMMAR FOR ENGLISH”, in http://old-site.clsp.jhu.edu/ws98/projects/nlp/, retrieved 2013-04-19:

Cₙ — the nᵗʰ Catalan number — could be described as the number of distinct ways in which a sequence of n + 1 numbers could be associated by means of some specified binary operator.

In combinatorial mathematics, any of a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects; the nᵗʰ Catalan number is equal to (2n choose n) over (n+1).


cyclohedron

(geometry) A certain (n−1)-dimensional polytope that is useful in studying knot invariants.


Tamari lattice

partially ordered set
partially ordered set

(mathematics) A partially ordered set in which the elements consist of different ways of grouping a sequence of objects into pairs using parentheses (e.g. for a sequence of four objects abcd, the five possible groupings are ((ab)c)d, (ab)(cd), (a(bc))d, a((bc)d), and a(b(cd))).


hyperarithmetic

computability theory
computability theory

(mathematics) Pertaining to a generalization of computability theory focusing on certain sets of natural numbers.


birationally

Two varieties are said to be birationally equivalent if there exists a birational map between them.


supersmooth

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(mathematics) Of or relating to a distribution that has derivatives of all orders.


Chinese numeral

Chinese numeral (plural Chinese numerals)

From their original development and chief use in China.

A number represented using a Chinese system involving the characters 一, 二, 三, etc.


null object

(category theory) An object that is both an initial and terminal object.

Nullobjekt

category theory: object that is both an initial and terminal object


Iverson bracket

Iverson bracket (plural Iverson brackets)

Named after Kenneth E. Iverson, who introduced this notation in his programming language APL.

(mathematics) A notation that denotes a number that is 1 if the condition in square brackets is satisfied, and 0 otherwise, i.e. (where P is a true or false statement)


homomorphous

en-adj

homomorphous (comparative more homomorphous, superlative most homomorphous)

more homomorphous (comparative)
most homomorphous (superlative)

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From Ancient Greek ὁμός (homós, “same”) + μορφή (morphḗ, “shape”) + -ous.

(algebra, biology) Characterized by homomorphism.


nonmanifold

manifold

antonym(s) of “a topological space that does not locally resemble the Euclidean space”

(mathematics) Not of or relating to manifolds.

(mathematics, of a topological space) Not locally resembling the "ordinary" Euclidean space ℝⁿ.


covertex

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(geometry) A point of intersection between an ellipse and its minor axis.


subreplacement

The other is the fact that the population of Japan has begun to shrink, the result of years of subreplacement birth rates.

2011, James W. White, Mirrors of Memory: Culture, Politics, and Time in Paris and Tokyo, University of Virginia Press, →ISBN, page 219:

(demography, of a birth rate) Below the level needed to maintain the current population.


Heine-Borel theorem

Named after the German mathematician Eduard Heine (1821–1881) and the French mathematician Émile Borel (1871–1956).

(mathematical analysis) A theorem which states that for any subset S of an n-dimensional Euclidean space, S is compact if and only if it is both closed and bounded.

Eduard Heine
Heine-Borel theorem
Émile Borel


subspace topology

en-noun

subspace topology (plural subspace topologies)

(topology) The topology of a subset S of a topological space X which is obtained by considering any subset of S to be an open set if it corresponds to the intersection of S with some open set of X.


relative topology

relative topology (plural relative topologies)

So called because open sets of such a (subspace) topology are defined in terms of open sets in the topology of the enclosing space.


standard topology

(topology) The topology of the real number system generated by a basis which consists of all open balls (in the real number system), which are defined in terms of the one-dimensional Euclidean metric.

(topology) The topology of a Euclidean space ℝⁿ such that any subset of that space is open (i.e. belonging to the topology) if it can be written as a union of open balls from that space.


product topology

product topology (plural product topologies)

(topology) The topology of the Cartesian product of two or more topological spaces which is generated from a basis whose elements are Cartesian products of open subsets of the original spaces, such that for each such Cartesian product only a finite quantity of such subsets are proper.


inverse system

(algebra) A set of algebraic structures (which are part of a concrete category; e.g., groups) and a set of morphisms between them (e.g., group homomorphisms) which all together form a small category which is the image of a contravariant functor whose domain is a directed poset.


inverse limit

An inverse limit has “natural projections” which are restrictions of the projections of the Cartesian product (to a domain which is the inverse limit). The reason why the projections are described as “natural” would be the following: besides the functor from an index poset to the inverse system, there is another functor from the same index poset to the inverse limit of that system, this functor being a constant functor. Then there is a natural transformation from the constant functor to the inverse limit’s functor: the components of such natural transformation are the said “natural projections”.

Inverse limits are concrete-categorical versions of limits.

(algebra) A subset of the Cartesian product of all the members of an inverse system, such that a member M of the subset is a sort of “cross section” of the inverse system (as fiber bundle) induced by the morphisms of it. (If i<j in the indexing poset then f_ij:A_j→A_i in the inverse system and if a_i∈A_i, a_j∈A_j are components of M then f_ij(a_j)=a_i).


absolute constant

absolute constant (plural absolute constants)

Korenblum conjectured that there is an absolute constant c#92;in(0,1), such that whenever #124;f(z)#124;#92;leqslant#124;g(z)#124; (f,g#92;inA²(D)) in the annulus clt;#124;z#124;lt;1, then #124;#124;f#124;#124;#92;leqslant#124;#124;g#124;#124;.

2004, Chunjie Wang, “On Korenblum's constant”, in Journal of Mathematical Analysis and Applications, volume 296, number 1, Elsevier, →DOI, →ISSN, pages 262–264:

(mathematics) A constant that maintains the same value wherever it occurs; such as π.


absolutely convergent

(mathematics) Of an infinite series, convergent even if the absolute value is taken of each term; a stronger condition than ordinary convergence.


absolute term

(mathematics) The constant in a polynomial.


truel

To effect a yet more complex and challenging truel, we can void the simplification that each player knows his order of firing ab initio.

2014, Richard A. Epstein, The Theory of Gambling and Statistical Logic, Gulf Professional Publishing, →ISBN, page 324:

(game theory) A duel fought between three people.


JPBM

Joint Policy Board for Mathematics
w:Joint Policy Board for Mathematics

(mathematics, US) Initialism of Joint Policy Board for Mathematics.


meandric number

meandric number (plural meandric numbers)

(mathematics) The number of distinct meanders of a given order.


bialtitude

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(geometry) A perpendicular to two opposite edges of a tetrahedron.


orthocentric

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(geometry, of a tetrahedron) Having all three pairs of opposite edges perpendicular.

(geometry) Of or relating to a set of four points in the plane, one of which is the orthocenter of the triangle formed by the other three.


Hintikka set

(set theory) A set with certain openness and completeness properties.


Ackermann function

(computing theory) One of the simplest and earliest examples of a total computable function that is not primitive recursive.


The logogram prefix ⠐ and the letter ⠅ k


elliptic curve

So called because it is the locus of an elliptic function.

(algebraic geometry) The algebraic set of an equation which equates the square of one variable to a reduced cubic polynomial in another variable, over some field, and such that the discriminant of the reduced cubic is non-zero.


Dirac delta function

Dirac delta function (plural Dirac delta functions)

Named after English physicist Paul Dirac.

named-after

(mathematics) A function of one real argument, whose value is zero when the argument is nonzero, and whose integral is one over any interval that includes zero.


elephantic

en-adj

elephantic (comparative more elephantic, superlative most elephantic)

more elephantic (comparative)
most elephantic (superlative)


quasireversibility

(mathematics, probability theory) A property of some queues, differing from reversibility in that a stronger condition is imposed on arrival rates and a weaker condition is applied on probability fluxes.


Olympiad

Hadrian
International Mathematical Olympiad
Olympiad
Summer Olympics
Winter Olympics
inclusive counting

From the plural forms Olimpiades, Olympiades, and Olympiadiz of Middle English Olimpias and Olympias (“ancient Olympic Games, 4-year period between these games, intense battle or competition”) from Middle French Olympiade and Old French Olympiade (“ancient Olympic games, 4-year period between these games”), from Latin Olympias (“4-year period between Olympic Games”) whose genitive form was Olympiados or Olympiadis), from Ancient Greek Ὀλυμπῐᾰ́ς (Olumpĭắs, “ancient Olympic Games, 4-year period between these games”) whose plural form was Ὀλυμπῐᾰ́δες (Olumpĭắdes), from Ὀλυμπῐ́ᾱ (Olumpĭ́ā, “Olympia”), the town in ancient Greece where the games were held, + -ᾰ́ς (-ắs, a suffix forming feminine adjectives or nouns), from either Ὀλῠ́μπῐος (Olŭ́mpĭos, “of or related to Mount Olympus, Olympian, the Olympian Zeus”) or Ὄλῠμπος (Ólŭmpos, “Mount Olympus”) + -ῐ́ᾱ (-ĭ́ā, suffix forming feminine abstract nouns).
The use of olympiad for academic competitions aspiring to the level of the Olympic Games was first popularized by the International Mathematical Olympiad, a calque of its Romanian name Olimpiada Internațională de Matematică.

Olimpiade

period between celebrations of the ancient or modern Olympic Games

olympiade

celebration of the ancient or modern Olympic Games

olympiad

alternative case, typically in generic uses

Ancient sources variously dated the founding of Rome to the 38th year before the first Olympiad, the third or fourth year of the sixth Olympiad, the first year of the seventh or eighth Olympiad, or the fourth year of the 12th Olympiad.

Now was bright Hero weary of the day,
Thought an Olympiad in Leanders ſtay.

1598, George Chapman, “Fifth Sestyad”, in Christopher Marlo[w]e, George Chapman, Hero and Leander: […], London: […] A[ugustine] M[atthews] for Richard Hawkins: […], published 1629, →OCLC:

Olympiad. 42. about the yeare of Rome 142. ſhee [the planet Venus] is bigger then all the other ſtarres, and ſo cleare that (ſome-times) her beames make a ſhadowe.

1610, Saint Augustine, “Of Certaine Starres that the Pagans Call Their Gods”, in J[ohn] H[ealey], transl., St. Augustine, of the Citie of God: […], [London]: […] George Eld, →OCLC, book VII, page 274:

Now therefore ſeeing that the firſt yeare of Cyrus his Monarchie (which was the laſt of the ſixtieth Olympiad, and the two hundredth and fortieth yeare from the inſtitution of thoſe games by Iphitus) followed the laſt of the ſeuentie yeares, of the captiuitie of Iuda, and deſolation of the Land of Iſrael; manifeſt it is, that we muſt reckon back thoſe ſeuentie yeares, and one hundred threeſcore and ten yeares more, the laſt which paſſed vnder the Kings of Iuda, to finde the firſt of theſe Olympiads; which by this accompt is the one and fiftieth of Vzzia, as wee haue alreadie noted.

1614, Walter Ralegh [i.e., Walter Raleigh], “Of Vzzia”, in The Historie of the World […], London: […] William Stansby for Walter Burre, […], →OCLC, 1st book, §. V (Of the Olympiads, and the Time when They Beganne), page 576:

The moſt Antient and Renowned Epoch uſed by the Heathens is that of the Olympiads or Olympick Games, which were inſtituted by one Iphitus, in the Fields of Olympia, a City or Town of the Region Elis in the Peloponneſe; and which laſt whereof fell on the Full Moon, which was the next after the Summer Solſtice. Theſe Games were celebrated every four Years, that is, there were three Years between the Years wherein the next preceding and the next following Olympiad was celebrated. Hence by a compleat Olympiad, is denoted the Space of four Years; the Year wherein the Olympiad was celebrated, being ſtiled the firſt Year of the ſaid Olympiad, and ſo on.

1736, Edward Wells, “Of Epoch’s or Æra’s; and Especially of the Æra of Year of Christ, the Æra of the Olympiads, and the Æra of the Building of Rome”, in The Young Gentleman’s Astronomy, Chronology, and Dialling, […], 4th edition, London: […] James, John, and Paul Knapton, […], →OCLC, paragraph 4, pages 64–65:

When he was fourteen, he went to work on the starcher. […] It marked an era. It was a machine Olympiad, a thing to date from.

1911 January, Jack London, “The Apostate”, in When God Laughs and Other Stories, New York, N.Y.: The Macmillan Company, →OCLC, page 55:

The Games of the XXXII Olympiad is going ahead in Tokyo a year late, despite concerns about coronavirus. […] The International Olympic Committee (IOC) and Japanese government are pressing ahead with the XXXII Olympiad after it was delayed last summer – albeit in a very different manner from usual.

2021 July 12, Natalie Merchant, “Explainer: The Tokyo Olympics by Numbers”, in World Economic Forum, archived from the original on 2021-08-02:

Emperor Naruhito was caught in a conundrum when it came to wording in his speech in Japanese to declare the 2020 Tokyo Olympics open during the July 23 Opening Ceremony at the National Stadium. […] The official English version for the Tokyo Olympics was: "I declare open the Games of Tokyo celebrating the 32nd Olympiad of the modern era." […] Following discussions among central government officials and the Tokyo Olympic organizing committee, it was decided to allow Naruhito to use "kinensuru" for celebrating. The term has more of a nuance of marking or commemorating an important occasion.

2021 July 24, Tatsuro Sugiura, “Emperor in bind over use of ‘celebrate’ for Tokyo Olympiad”, in The Asahi Shimbun, Osaka: The Asahi Shimbun Company, →OCLC, archived from the original on 2021-07-30:

A four-year period, particularly (historical) those based on Hippias's computations of the ancient Olympic Games which placed Coroebus's footrace victory in 776 BCE and (sports) those based on the modern Summer Olympic Games first held in 1896.

Victors at the ancient Olympiads only won an olive wreath but were usually freed from paying taxes for the remainder of their life, but modern Olympians have frequently needed to pay taxes on the market value of their gold, silver, or bronze medals.

It was their [the priests of Jupiter Olympius's] Buſineſs, alſo not only to regiſter the Names of the Victors in the ſeveral Games, with other Matters relating to them, but alſo whatever occurr'd remarkable, during the Intervals between the Celebration of every Olympiad.

1707, Thomas Hind, “Book II. The Second Period, from the Taking of Troy, to the Battle of Marathon, Containing the Space of 700 Years.”, in The History of Greece. […], London: […] S. and J. Sprint, A[wnsham] and J[ohn] Churchill, Tim[othy] Childe, and Rob[ert] Knaplock, →OCLC, page 124:

Strabo […] makes Corœbus the firſt Victor at the firſt Olympiad of Iphitus; who, he ſaies, was the Reſtorer of them. This Olympiad was in the Year before Chriſt 776.

1752, John Jackson, “Of the Origin and Æra of Oracles. [Of the Institution of the Olympic Games.]”, in Chronological Antiquities: Or, The Antiquities and Chronology of the Most Ancient Kingdoms, from the Creation of the World, for the Space of Five Thousand Years. […], volume III, London: Printed for the author; and sold by J. Noon, […], →OCLC, page 340:

The noble and free citizens of Epidaphne being, as they declare, well satisfied of the faith, valor, wisdom, and divinity of their king, […] do think it no more than their duty to invest his brows (in addition to the poetic crown) with the wreath of victory in the foot race—a wreath which it is evident he must obtain at the celebration of the next Olympiad, and which, therefore, they now give him in advance.

1840, Edgar A[llan] Poe, “Epimanes”, in Tales of the Grotesque and Arabesque, volume II, Philadelphia, Pa.: Lea and Blanchard, published 1840, →OCLC, pages 16–17:

After the distribution of the prizes, the athletes formed for the traditional procession around the Stadion. Louës [i.e., Spyridon Louis], the victor of Marathon, came first, bearing the Greek flag; then the Americans, the Hungarians, the French, the Germans. […] The king announced that the first Olympiad was at an end, and left the Stadion, the band playing the Greek national hymn, and the crowd cheering.

1896 November, Pierre de Coubertin, “The Olympic Games of 1896. […]”, in The Century Illustrated Monthly Magazine, volume XXXI (New Series; volume LIII overall), number 1, New York, N.Y.: The Century Co.; London: Macmillan & Co. Ltd., →OCLC, page 50:

[I]t is the intention of the management of the exposition to make the Olympiad of 1904 the greatest ever held. The first of these modern Olympiads—which are the reproduction of the famous games of Ancient Greece—was held at Athens in 1896, when an American astonished the world by winning the discus-throwing championship. […] The representatives of athletics in America propose that nothing shall be left undone to make this first American Olympiad a phenomenal success.

1903 November 20, “Olympic Games”, in Message from the President of the United States, Transmitting a Statement Showing the Receipts and Disbursements of the Louisiana Purchase Exposition Company from Date of Incorporation to September 30, 1903, together with a Report Submitted by the Exposition Company Showing Progress Made by the Various Departments of the Exposition (58th Congress, 1st Session, document no. 12), Washington, D.C.: Government Printing Office, →OCLC, page 58:

1950 marks the twilight of one of the greatest eras of California crew history. Many of the graduating crew men were in the jayvee Poughkeepsie winning boat in 1947; the next year these same men rowed to the eight-oared championship in the 14th Olympiad in England.

1950, “[Athletics] 1950 Varsity”, in Blue and Gold 1950, volume 77, Berkeley, Calif.: Associated Students of the University of California, →OCLC, page 234:

(sports, sometimes proscribed) Synonym of Olympic Games: an instance of the ancient or modern Olympic Games.

Olympic Games

the International Mathematical Olympiad... the Science Olympiad... the International Science Olympiads... the Women's Chess Olympiad...

The Junior Olympiad track and field meet was a major special event with 276 entrants.

1943 November, Margaret King, “Southwest District Association News [California]”, in Mary Wibel, editor, The Journal of Health and Physical Education, volume 14, number 9, Washington, D.C.: American Association for Health, Physical Education, and Recreation, →OCLC, page 492, column 1:

Selected competitively from more than 400,000 high school students to represent the United States in the 19th International Mathematical Olympiad in Belgrade, Yugoslavia, July 5–6, an 8-man team emerged victorious over teams from 20 other nations. […] Credited with developing the International Mathematics Olympiad in 1959 is Rumania, the winner that year in competition with Bulgaria, Czechosolvakia, Poland, German Democratic Republic, and Soviet Union. […] The idea of a U.S. Mathematical Olympiad was spawned in 1971 when Prof. Nura D. Turner of SUNY (State University of New York), Albany, authored an article in the American Mathematical Monthly that led in 1972 to the USA Mathematical Olympiad.

1977 May–July, “USA Team Wins over 20 Nations”, in Clarence T. Smith, editor, Army Research and Development, volume 18, number 3, Alexandria, Va.: Development and Engineering Directorate, HQ. U.S. Army Materiel Development and Readiness Command, →ISSN, →OCLC, page 29, column 2:

[…] Kent Howerton led dominance of the initial Motorcycle Olympiad by AMA professional moto-crossers. […] The fans dug it, the bike press agreed, and the Second Annual Motorcycle Olympiad will be held September 16–17 at Saddleback Park in Orange, California. More on the Olympiad in future issues.

1978 June, “Olympiad Set for Second Go”, in Bill Amick, editor, American Motorcyclist, volume 32, number 6, Westerville, Oh.: American Motorcyclist Association, →ISSN, →OCLC, page 34, column 3:

The Prize distribution ceremony of the First National Science Olympiad was held at National Museum Auditorium, New Delhi on October 18. […] The Second National Science Olympiad will be conducted on 28th January 2000.

1999 December, “Miscellaneous”, in Mahendra Jain, editor, Competition Science Vision, volume 2, number 22, Agra, Uttar Pradesh: Mahendra Jain for M/s Pratiyogita Darpan, →OCLC, page 1266, columns 2–3:

The FIDE Online Chess Olympiad 2021 will be held between August 13 to September 15, the International Chess Federation (FIDE) announced. Each national federation intending to take part in the Online Olympiad shall confirm its participation by July 31, it said.

2021 July 14, “Second Online Chess Olympiad from August 13, says FIDE”, in The Times of India, Mumbai, Maharashtra: The Times Group, →OCLC, archived from the original on 2021-08-06:

(by extension, usually preceded by descriptive words) A competition aspiring to the importance of the Olympic Games or considered similar to them, especially one occurring at 4-year intervals, representing a national or international range of amateur student rather than professional adult competition, and/or requiring the highest level of ability in the field for success.

奧林匹克 /奥林匹克

high-level competitions in other fields, especially among students


horseling

Two of these that she was about to chase and fondle, were not aristocratic horselings, they were but the rough and sturdy children of rough and sturdy dams and sires ; born to the plough, and the heavy waggon, [...]

1874, Bertha De Jongh, The sisters Lawless:

Thork astride the pony raced after, the horseling running in sheer panic.


cannonball problem

It can be visualized as the problem of taking a square arrangement of cannonballs on the ground and building a square pyramid out of them.

Diophantine equation
Diophantine equation

(mathematics) The challenge of proving that the only solution of the Diophantine equation :∑ₙ₌₁ᴺn²=M²; with N > 1 is when N = 24 and M = 70.


Silent Generation

Popularized in a Time article in 1951. So called because they were not often politically strident.

The Silent Generation produced such counterculture leaders as John Lennon, Bob Dylan, Huey Newton and Abbie Hoffman.

Reminiscence therapy targets this age range, and for those Silent Generation members now in their 70s and 80s, that means the 1950s.

2018 September 18, Amanda Kolson Hurley, “Fake Public Squares Are Coming to the Suburbs”, in The Atlantic:

Like his character, Stiller was Gen X, but he didn’t have Boomer parents; his mother and father were part of the Silent Generation, and more important, they were in showbiz.

2019 March 6, Soraya Roberts, “Reality Bites Captured Gen X With Perfect Irony”, in The Atlantic:

The generation of people born from the late 1920s to the early 1940s.


dextrorse

en-adj

dextrorse (comparative more dextrorse, superlative most dextrorse)

more dextrorse (comparative)
most dextrorse (superlative)

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From Latin dextrorsum, contracted from dextrovorsum, dextroversum (“toward the right side”), from dexter (“right”) + versus, vorsus, past participle of vertere, vortere (“to turn”).


paracentric

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(geometry) A planar curve having the property that, when its plane is placed vertically, a body descending along it, by the force of gravity, will approach to, or recede from, a fixed point or centre, by equal distances in equal times.


Hermitian matrix

en-noun

Hermitian matrix (plural Hermitian matrixes or Hermitian matrices)

Hermitian matrixes (plural)
Hermitian matrices (plural)

Named after French mathematician Charles Hermite (1822–1901), who demonstrated in 1855 that such matrices always have real eigenvalues.

Hermitian matrices have real diagonal elements as well as real eigenvalues.

If a Hermitian matrix has a simple spectrum (of eigenvalues) then its eigenvectors are orthogonal.

If an observable can be described by a Hermitian matrix H, then for a given state #92;langleA#92;rangle, the expectation value of the observable for that state is #92;langleA#124;H#124;A#92;rangle.

1988, I. M. Gelfand, M. I. Graev, Geometry of homogeneous spaces, representations of groups in homogeneous spaces and related questions of integral geometry, Israel M. Gelfand, Collected Papers, Volume II, Springer-Verlag, page 366,
There are three types of such spaces: the space of positive definite (or negative definite) Hermitian matrices, the space of nondefinite Hermitian matrices, and finally the space of degenerate Hermitian matrices p, satisfying the condition p ≥ 0 (or p ≤ 0).

where H is a hermitian matrix. Now any linear combination of hermitian matrices with real coefficients is again a hermitian matrix.

1997, A. W. Joshi, Elements of Group Theory for Physicists, New Age International, 4th Edition, page 129, For this we note that if H is a hermitian matrix, exp(iH) is a unitary matrix. The converse is also true, i.e., if U is any unitary matrix, then it can be expressed in the form U = exp(iH), (4.94)

Exploiting the properties of hermitian matrixes [2], it is possible to obtain an analytical expression for the characteristic function of a hermitian quadratic form of gaussian variables, which is useful in the evaluation of transmission system performance.

1998, Eugenio Iannone, Francesco Matera, Antonio Mecozzi, Marina Settembre, Nonlinear Optical Communication Networks, page 442:

(linear algebra) A square matrix A with complex entries that is equal to its own conjugate transpose, i.e., such that A=A^†.

hermitovská matice

square matrix equal to its own conjugate transpose


(mathematics) the proportionality sign, ∷


spectral theorem

spectral theorem (plural spectral theorems)

(mathematics) a theorem providing conditions under which an operator or matrix can be diagonalized

spektraaliteoreema

mathematics: theorem providing conditions under which an operator or matrix can be diagonalized


Generation Jones

Coined by author Jonathan Pontell, from jonesing (“intense craving”).

Generation Jones listened to a lot of classic rock when young.

The later cohort of Generation Jones really seems to combine some Baby Boom qualities with those of later generational cohorts.

2011, Tracy D. Connors, The Volunteer Management Handbook, John Wiley & Sons, →ISBN:

The generation of people born in the late 1950s and early 1960s; they are the younger subset of the baby boomers but are sometimes conceptualized as being sandwiched between the older subset of baby boomers and Gen-Xers.


almude

From Portuguese almude, from Andalusian Arabic المُدّ (al-mudd), from Arabic مُدّ (mudd), probably via Aramaic 𐡬𐡣𐡩𐡠 (mdyʾ) and מוֹדְיָא (moḏyā) or Classical Syriac ܡܘܿܕܝܳܐ (moḏyā) from Akkadian 𒉘𒈨𒌍 (/maddattu/middattu/, “kind of vessel, unit of volume”). Doublet of almud. Cognate with Ancient Greek μόδιος (módios) and Latin modius.

der

(historical, measure) A traditional Portuguese unit of liquid volume, equal to 14–26 liters.

(historical, measure) Alternative form of almud, similar units of liquid volume in Spain and Turkey.


roundrect

Blend of rounded + rectangle. In 1981, a function for quickly creating rounded rectangles was added to the Apple program LisaGraf (later renamed QuickDraw) created by Bill Atkinson at the request of Steve Jobs, with the program referring to this shape as the "RoundRect."

The iPhone is, officially, King of Design: when even Intel is mirroring your new roundrect bezels, you have won that particular game.

2007 September 21, Rob Beschizza, “Intel Touts Toys of Future At Conference”, in Wired:

(computer graphics) A rectangle with rounded corners.


atomless

More formally, we assume that the density f(#92;varepsilon) is atomless.

1992, Robert Gibbons, A Primer in Game Theory, Prentice-Hall, page 80:

(statistics, of a probability distribution) Not assigning strictly positive probability to any single outcome.


elt

(mathematics, computing) Abbreviation of element.


MDP

en-noun

MDP (countable and uncountable, plural MDPs)

Markov decision process
w:Markov decision process

(mathematics) Initialism of Markov decision process.


apotome

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Apotome
Euclid's Elements
Pythagoreanism#Music

Borrowing from Ancient Greek ἀποτομή (apotomḗ, “cutting off”). The musical sense originates from the Pythagorean tradition. The mathematical sense is attested in Euclid's Elements (Book X, proposition 73, et seq.).

bor

Yet it is not until Book X that the properties of such a line (with greater length is an apotome and lesser length a first apotome) are explained and not until Book XIII that this type of line is applied, which will be discussed in more detail later.[…]The likewise is true of apotomes (X. 97).

2012, Jade Roskam, “Book X of The Elements: Ordering Irrationals”, in Bharath Sriraman, editor, Crossroads in the History of Mathematics and Mathematics Education, Information Age Publishing, page 210:

2014, Jacques Sesiano (translator), Liber Mahameleth, Part Two: Translation, Glossary, [12th c, Anonymous (possibly John of Seville), Liber Mahameleth], Springer, page 767,
If some number and the root of the root of a number are multiplied by the corresponding apotome, the result will be an apotome.

(mathematics, geometry) The difference between two quantities or lengths commensurable only in power, as between 1 and the square root of 2, or between the diagonal and side of a square.

ἀποτομή

difference between two quantities commensurable only in power


footmeal

From Middle English footmele, fotmelen, from Old English fōtmǣlum (“step by step, by degrees”), dative plural of Old English fōtmǣl (“a foot-measure, one foot”), equivalent to foot + -meal.

der

Grandees must covet condos, since they let bids rip, And "spaces" measured footmeal now reach record tops.

2001, Arnold Klein, Rangefinder & Powderhorn:

(rare) Step by step: incrementally, little by little, by degrees, one foot (measure) at a time.


homaloidal

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Ancient Greek ὁμαλός (homalós, “even, level”) + + -oid.

uder

(geometry) flat; even; applied to surfaces and spaces in which the definitions, axioms, and postulates of Euclid respecting parallel straight lines are assumed to hold true.


treeness

…such a tree can be built up incrementally by adding the shortest edge not yet explored, which also maintains treeness (acyclicity).

1998, Joseph O'Rourke, Computational Geometry in C, 2nd edition, Cambridge University Press, →ISBN, page 174:

…every link that gives rise to a cycle into the graph (viz., that destroys the graph’s “treeness”) is eliminated….

2010, Massimo Buscema, Pier L. Sacco, “Auto-contractive Maps, the H Function, and the Maximally Regular Graph (MRG)”, in Vittorio Capecchi et al., editors, Applications of Mathematics in Models, Artificial Neural Networks and Arts, Springer, →ISBN, page 265:

To save the treeness of discourse structure – and with that the supplied computational advantages – Egg and Redeker (2008) argue that many apparent crossed dependencies reflect anaphoric relations on the level of discourse cohesion…. They opt for a pure tree structure for discourse relations, keeping anaphoric relations apart.

2011, Matthias Irmer, Bridging Inferences, De Gruyter,, →ISBN, page 139:

(graph theory) The condition of being a tree; acyclicity and connectedness.


w.l.o.g.

without loss of generality
without loss of generality#English

Abbreviation of without loss of generality.


thrave

en-verb

thrave (third-person singular simple present thraves, present participle thraving, simple past and past participle thraved)

thraves (present singular third-person)
thraving (participle present)
thraved (participle past)
thraved (past)

From Middle English thraven, from Old English þrafian (“to press; urge; compel; rebuke; argue; contend”), from Proto-West Germanic *þrabōn, from Proto-Germanic *þrabōną (“to press; drive”), from Proto-Indo-European *trep- (“to scamper; trample; quake; tread”). Cognate with Saterland Frisian troawje, droawje (“to trot”), West Frisian drave (“to trot”), Dutch draven (“to lope; trot”), German traben (“to trot”), Swedish trava (“to trot”), Icelandic þrefa (“to wrangle; dispute”).

der

(transitive, UK, dialectal) To urge; compel; importune.


thrave

From Middle English thrave, threve, thrafe, from Old Norse þrefi (“a bunch or handful of sheaves”), related to Old Norse þrifa (“to grasp”). Cognate with Swedish trave, Danish trave.

A daimen icker in a thrave / 'S a sma' request;

(UK, dialect, obsolete) Twenty-four (or in some places, twelve) sheaves of wheat; a shock, or stook.

c. 16th century, Lansdowne MS
The worst of a thrave.

He sends forth thraves of ballads to the sale.

(UK, dialect, obsolete) Two dozen, or similar indefinite number; a bunch; a throng.


hypervolume

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(geometry) A volume in more than three dimensions.


enneahedron

en-noun

enneahedron (plural enneahedrons or enneahedra)

enneahedrons (plural)
enneahedra (plural)

The enneahedron is a simple all-space filler discovered by myself, based on the cubic antiprism, again omitted by Wood.

1968, Design, numbers 229-234, unnumbered page:

1996, Michael O'Keeffe, Bruce G. Hyde, Crystal Structures, Number 1: Patterns & Symmetry, page 350,
This is based on a packing of 36-vertex icosahedra [5¹².6⁸] and enneahedra (4³.5⁶].

In Figure 9.10.3 we see a projection of the skeleton of an enneahedron (a solid with nine faces). All the faces of this enneahedron are quadrilaterals.

2015, Claudi Alsina, Roger B. Nelsen, A Mathematical Space Odyssey: Solid Geometry in the 21st Century, page 191:

(geometry) A polyhedron with nine faces.


x-intercept

(mathematics) A root; a zero; a point at which a line crosses the x-axis of a Cartesian grid, where y is 0.


y-intercept

(mathematics) A point at which a line crosses the y-axis of a Cartesian grid.


z-intercept

(mathematics) A point at which a line crosses the z-axis of a Cartesian grid.


Cartesian grid

(mathematics) a regular grid consisting of squares, cubes, or more generally unit hypercubes


dendroid

smooth dendroids without ordinary points

(mathematics) An arcwise connected, hereditarily unicoherent continuum.


regular grid

(mathematics) a tessellation of Euclidean space into congruent rectangles, parallelograms, cuboids, or more generally, parallelotopes


parallelotope

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Blend of parallelogram + polytope. Popularized by Canadian geometer H.S.M. Coxeter.

1983 [North Holland/Elsevier], Robert S. Borden, A Course in Advanced Calculus, 1998, Dover, page 83,
Suppose now that P is a k-dimensional parallelotope, 1<k<n, in Eⁿ.

1997, Daniel A. Klain, Gian-Carlo Rota, Introduction to Geometric Probability, Cambridge University Press, Accademia Nazionale dei Lincei, page 30,
We develop next a theory of invariant valuations for the lattice of finite unions of orthogonal parallelotopes, having edgers parallel to a fixed frame. […] This follows from the basic fact that the intersection of two parallelotopes is a parallelotope.

It has 2ᵏ gyrovertices, k#43;1 of which are the gyropoints of S, and k 2#123;k-1#125; gyroedges, in full analogy with parallelotopes.

2015, Abraham Albert Ungar, Analytic Hyperbolic Geometry in N Dimensions, Taylor & Francis (CRC Press), page 187:

(geometry) A generalization of parallelogram and parallelepiped into a figure of arbitrary dimensionality.

Harold Scott MacDonald Coxeter
parallelotope


model-based design

model-based design (plural model-based designs)

(electronics, communication, signal processing, mathematics, software testing) A mathematical and visual method of addressing problems associated with designing complex control, signal processing and communication systems.


semiparametric

(mathematics) Having some, but not all, components that are parametric

semiparametrinen

having some, but not all, components that are parametric


Dixonian

From Alfred Dixon, English mathematician.

(mathematics) Of, relating to or formulated by Alfred Dixon.


SOHCAHTOA

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(mnemonic, trigonometry) sine: opposite over hypotenuse, cosine: adjacent over hypotenuse, tangent: opposite over adjacent


field axiom

(mathematics) Any of the several axioms that an object should meet to be considered a mathematical field.


system of equations

system of equations (plural systems of equations)

(mathematics) a set of equations required to be satisfied simultaneously or considered as a whole


field axioms

associativity and commutativity of addition and multiplication

distributivity of addition over multiplication

additive and multiplicative identity elements

additive and multiplicative inverses (except for additive identity)

(definite, mathematics) the requirements for an object to be considered a field:


projective plane

projective plane (plural projective planes)

Generally, a projective plane of "order" N has N²+N+1 points, and the same number of lines.

2004, David S. Dummit with Richard M. Foote, chapter 6, in Abstract Algebra, page 210

(geometry) A plane in which any pair of distinct points determine a line and any pair of distinct lines intersect at a point.


cyclotomic field

cyclotomic field (plural cyclotomic fields)

A cyclotomic field is the splitting field of the cyclotomic polynomial #92;Phi#95;n(x)#61;#92;prod#95;#92;stackrel#123;1#92;lek#92;len#125;#123;#92;gcd(k,n)#61;1#125;#92;left(x-e#123;#92;frac#123;2k#92;pii#125;#123;n) and consequently is a Galois extension of the field of rational numbers.}}

Cyclotomic fields are fields obtained by adjoining to #92;Q roots of unity, i.e. roots of polynomials of the form Xⁿ-1, although the reader is warned that this terminology will be extended in §2.[…]Cyclotomic fields play a fundamental role in a number of arithmetic problems: for instance primes in arithmetic progression (see VIII,§4) and Fermat's Last Theorem (VII,§1).

1991, A. Fröhlich, M. J. Taylor, “Algebraic Number Theory”, in Paperback, Cambridge University Press, published 1993, page 205:

At about the same time Kummer introduced his "ideal numbers," defined an equivalence relation on them, and derived, for cyclotomic fields, certain special properties of the number of equivalence classes, the so-called class number of a cyclotomic field—in our terminology, the order of the ideal class group of the cyclotomic field.

2007, Israel Kleiner, A History of Abstract Algebra, Springer (Birkhäuser), page 26:

As in the case of the Drinfel'd double,¹³¹ it can be shown that these fields are subfields of the cyclotomic field #92;Q#95;N. Since the Galois group of #92;Q#95;N is abelian, every subfield of the cyclotomic field is normal, and consequently preserved by the action of the Galois group of #92;Q#95;N.

2012, Yorck Sommerhäuser, Yongchang Zhu, Hopf Algebras and Congruence Subgroups, American Mathematical Society, page 94:

(number theory, algebraic number theory) A number field obtained by adjoining a primitive root of unity to the field of rational numbers.

Kreisteilungskörper

extension field of the rational numbers formed by adjoining a primitive root of unity


extension field

extension field (plural extension fields)

Suppose F is a subfield of the field K. Then K is called an extension field of F. So, for instance, GF(4) and GF(8) are extension fields of GF(2), although GF(8) is not an extension field of GF(4).

1992, James G. Oxley, “Matroid Theory”, in Paperback, Oxford University Press, published 2006, page 215:

This extension field of F always contains a root of f in the sense that if K#61;F#91;x#93;#47;(f(x)) then x is a root of f(y) in K#91;y#93;. It then follows that any polynomial will have roots, either in the original field of its coefficients or in some extension field.

1995, Terence Jackson, From Polynomials to Sums of Squares, Taylor & Francis, page 56:

An extension field, by which we mean a bigger field containing F, is automatically a vector space over F. We call it a finite extension if it is a finite vector space. By the degree of a finite extension we mean its dimension as a vector space. One common way of obtaining extension fields is to adjoin an element to F: we say that K#61;F(#92;alpha) if K is the field consisting of all rational expressions formed using #92;alpha and elements of F.

1998, Neal Koblitz, Algebraic Aspects of Cryptography, Volume 3, Springer, page 53:

(algebra, field theory) A field L which contains a subfield K, called the base field, from which it is generated by adjoining extra elements.


minimal polynomial

minimal polynomial (plural minimal polynomials)

minimipolynomi

monic polynomial of smallest degree for which a given element is a root

Each root of the minimal polynomial of a matrix M is an eigenvalue of M and a root of its characteristic polynomial. (A root of the minimal polynomial has a multiplicity that is less than or equal to the multiplicity of the same root in the characteristic polynomial. Thus the minimal polynomial divides the characteristic polynomial. Also, any root of the characteristic polynomial is also a root of the minimal polynomial, so the two kinds of polynomial have the same roots, only (possibly) differing in their multiplicities.)

1965 [John Wiley], Robert B. Ash, Information Theory, 1990, Dover, page 161,
A procedure for obtaining the minimal polynomial of the matrix Tⁱ, without actually computing the powers of T is indicated in the solution to Problem 5.9.

In this section we will show that if #92;#123;A,B,C,D#92;#125; is a controllable and observable realization of #92;mathbfG, then #92;lambda is a pole of #92;mathbfG if and only if #92;lambda is an eigenvalue of A. Moreover, the roots (multiplicities included) of the minimal polynomial of A are the poles of #92;mathbfG.

2003, Martin J. Corless, Art Frazho, Linear Systems and Control: An Operator Perspective, Marcel Dekker, page 77:

2007, A. R. Vasishta, Vipin Vasishta, A.K. Vasishta, Abstract and Linear Algebra, Krishna Prakashan Media, 3rd Edition, page CA-439,
Theorem 1. The minimal polynomial of a matrix or of a linear operator is unique.

(linear algebra) For a given square matrix M over some field K, the smallest-degree monic polynomial over K which, when applied to M, yields the zero matrix.


svedberg

From Swedish Svedberg. Named after the Swedish chemist Theodor Svedberg (1884–1971).

A non-SI unit of sedimentation rate (symbol S or Sv), the rate at which particles of a given size and shape travel to the bottom of a tube under centrifugal force.


Noetherian ring

Noetherian ring (plural Noetherian rings)

/nəˈtɛ.ɹi.ən ˈɹɪŋɡ/

Named after German mathematician Emmy Noether (1882–1935).

The central position occupied by Noetherian rings in commutative ring theory became evident from her^([Noether's]) work.

1986, Hideyuki Matsumura, translated by M. Reid, Commutative Ring Theory, Paperback edition, Cambridge University Press, published 1989, page ix:

In this chapter the focus moves from semiprime rings to general Noetherian rings, although it does concentrate on prime and semiprime ideals.

2000, John C. McConnell, James Christopher Robson, Lance W. Small, Noncommutative Noetherian Rings, 2nd edition, American Mathematical Society, page 97:

2004, K. R. Goodearl, Introduction to the Second Edition, K. R. Goodearl, R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, 2nd Edition, page viii,
During this same period, the explosive growth of the area of quantum groups provided a large new crop of noetherian rings to be analyzed, and thus gave major impetus to research in noetherian ring theory.

(algebra, ring theory) A ring which is either: (a) a commutative ring in which every ideal is finitely generated, or (b) a noncommutative ring that is both left-Noetherian (every left ideal is finitely generated) and right-Noetherian (every right ideal is finitely generated).


algebraic closure

algebraic closure (plural algebraic closures)

The calculation of these various Galois groups leads to a determination of the algebraic closures of the ground fields in the splitting fields of the corresponding vectorial polynomials.

1999, Shreeram S. Abhyankar, “Galois Theory of Semilinear Transformations”, in Helmut Voelklein, David Harbater, J. G. Thompson, Peter Müller, editors, Aspects of Galois Theory, Cambridge University Press, page 1:

It turns out that the algebraic closure #92;mathbf#123;Q#125;#92;mathrm#123;a#125;#95;p is not complete, so we shall consider its completion #92;mathbf#123;C#125;#95;p: This field turns out to be algebraically closed and is a natural domain for the study of "analytic functions."

2000, Alain M. Robert, A Course in p-adic Analysis, Springer, page 127:

While #92;Complex contains an algebraic closure of #92;mathbb#123;Q#125;, it is by no means the only algebraically closed field containing an algebraic closure of #92;mathbb#123;Q#125;. We denote by #92;mathbb#123;Q#125;#92;mathrm#123;alg#125; the algebraic closure of #92;mathbb#123;Q#125; in #92;Complex; this field is simply the subfield of #92;Complex consisting of algebraic numbers. The field #92;mathbb#123;Q#125;#92;mathrm#123;alg#125; is isomorphic, then, to any algebraic closure of #92;mathbb#123;Q#125;, but even knowing that it is unique up to isomorphism very likely leaves us no more familiar with #92;mathbb#123;Q#125;#92;mathrm#123;alg#125; than we were.

2004, John Swallow, Exploratory Galois Theory, Cambridge University Press, page 179:

(algebra, field theory, of a field F) A field G such that every polynomial over F splits completely over G (i.e., every element of G is a root of some polynomial over F and every root of every polynomial over F is an element of G).

algebrallinen sulkeuma

field which is algebraically closed over another one


coaxis

Now draw the characteristic triangle mentioned above, […] of which the hypotenuse is a portion of the tangent or the element of the arc, and the sides are parallel to the axis and the coaxis.

2008, Gottfried Wilhelm Leibniz, J. M. Child, The Early Mathematical Manuscripts of Leibniz, page 43:

(mathematics) One of the directional motion vectors perpendicular to a cocone.


cocomplete

(mathematics, of a category) In which all small colimits exist.


bicomplete

(mathematics, of a category) Both complete and cocomplete.


cocategory

Among the new results there is the existence of a closed monoidal structure on the category of cocomplete augmented cocategories over a ground field k.

2007, American Mathematical Society, Mathematical Reviews:


coplane

In Section 4 we show that any PMD in which a coplane is not the intersection of two hyperplanes is an extension of a projective plane.

1980, Jaya Srivastava, Combinatorial Mathematics, Optimal Designs, and Their Applications, page 61:


comorphism

Concepts of comorphism may be defined for arbitrary modules and for arbitrary vector bundles[…]

2005, Kirill MacKenzie, London Mathematical Society, General Theory of Lie Groupoids and Lie Algebroids, page 177:

(mathematics) A mapping associated with a morphism that, when applied to every member of the morphism, results in the same value as the morphism applied to the image of every member.


counion

the left adjoint […] preserves direct factors, their cointersections, their complements and thus their counions

1986, Yves Diers, Categories of Boolean sheaves of simple algebras:

(mathematics) The join or union of all sets that meet a specified condition.


cointersection

(mathematics) A family of behavioural equivalences which factors through all elements of a second specified family of behavioural equivalences and for which any morphism that factors through the second family of behavioural equivalences also factors through its elements.


comatrix

Better yet, we may take the coalgebra of the preceding corollary to be a comatrix coalgebra.

2011, David E. Radford, Hopf Algebras, page 182:

(mathematics) Adjoint; The transposed matrix of the cofactors of the entries of a matrix.


corank

(mathematics) The dimension of the left nullspace of a matrix.

(mathematics) The dimension of the cokernel of a linear transformation of a vector space

First of all, we can see that coranks are the same for the elements of a conjugacy class.

1995, William M. Kantor, Lino Di Martino, Groups of Lie Type and their Geometries, page 117:

(mathematics) The number of elements of a matroid minus its rank.


light day

(astronomy, physics) A unit of length equal to the distance light travels in one day; about 170 astronomical units


sesquialteral

From Latin sesquialter + English -al, from sesqui (“a half and a”) + alter (“another, a second”).

(mathematics, archaic) Synonym of sesquialterate, 1½ times.


leastness

(chiefly mathematics) The quality of being least.


even number

(mathematics) An integer that is divisible by two.


odd number

(mathematics) Any integer that produces a noninteger when divided by two


Bayesian network

Bayesian network (plural Bayesian networks)

Named after Thomas Bayes (1701–1761), English mathematician.

(statistics) A directed acyclic graph whose vertices represent random variables and whose directed edges represent conditional dependencies. Each random variable can fall into any of at least two mutually disjoint states, and has a probability function which takes as inputs the states of its parent nodes and returns as output the probability of being in a certain state for a given combination of the states of its parent nodes. A node without parent nodes just has an unconditioned probability of being in some given state.


conditional probability

conditional probability (plural conditional probabilities)

The probability that an event will take place given the restrictive assumption that another event has taken place, or that a combination of other events has taken place. (Mathematically, the definition would be that the conditional probability of B given A is equal to the joint probability of A and B divided by the probability of A.)


Bayes' theorem

Named after English mathematician Thomas Bayes (1701–1761), who developed an early formulation. The modern expression of the theorem is due to Pierre-Simon Laplace, who extended Bayes's work but was apparently unaware of it.

The starting point for many techniques in probabilistic classification is Bayes' theorem, which provides a way of relating evidence to a hypothesis.

2010, Jonathan Harrington, Phonetic Analysis of Speech Corpora, page 327:

Bayes's theorem is a relationship between the conditional probabilities of two events.

2011, Allen Downey, Think Stats, O'Reilly, page 56:

We have now seen how Bayes' theorem enables us to correctly update a prior probability for some unknown event when we see evidence about the event.

2013, Norman Fenton, Martin Neil, Risk Assessment and Decision Analysis with Bayesian Networks, Taylor & Francis (CRC Press), page 131:

conditional probability
conditional probability

(probability theory) A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event.

Bayes' theorem
Pierre-Simon Laplace
Thomas Bayes

Bayes' law

theorem or equation describing conditional probability


Mersenne prime

Named after French theologian, philosopher, mathematician, and music theorist Marin Mersenne (1588–1648).

named-after

In addition to being the largest known Mersenne prime, this number is also currently the largest known prime number of any type.

2004, Sheldon Axler, “3: Mathematicians Versus the Silicon Age: Who Wins?”, in David F. Hayes, Tatiana Shubin, editors, Mathematical Adventures for Students and Amateurs, American Mathematical Society, page 20:

2005, Jean-Claude Bajard, Laurent Imbert, Thomas Plantard, Modular Number Systems: Beyond the Mersenne Family, Helena Handschuh, M. Anwar Hasan (editors), Selected Areas in Cryptography: 11th International Workshop, SAC 2004, Revised Selected Papers, Springer, LNCS 3357, page 159,
Mersenne numbers of the form 2ᵐ-1 are well known examples, but they are not useful for cryptography because there are only a few primes (the first Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, etc).

Mersenne primes, named after the French priest first describing them in the 17th century, are of the form of 2ᵖ-1, where the exponent p is a prime itself. Obviously 7 is a Mersenne prime, since 2³-1#61;7, and 3 is a prime. The interesting twist comes in the fact that there are certain primes that are double Mersenne primes. These are of the form 2#123;2ᵖ-1#125;-1, meaning that the exponent now is not just a prime, but it is itself a Mersenne prime. Since 2#123;2²-1#125;-1#61;7, 7 is the very first double Mersenne prime.

2013, Louis Komzsik, Magnificent Seven: The Happy Number, Trafford Publishing, page 71:

(number theory) A prime number which is one less than a power of two (i.e., is expressible in the form 2ⁿ-1; for example, 31=2⁵-1).


Fermat prime

Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665).

It is not hard to prove that the only way that the number 1#43;2ᵉ can possibly be prime is when e is a power of 2, and so all Fermat primes must have the form 1#43;2#123;2ᵃ#125; for integers a#92;ge 0. The numbers F#95;a#61;1#43;2#123;2ᵃ#125; are called Fermat numbers, and although it is true that every Fermat prime is a Fermat number, it is certainly not true that every Fermat number is prime.

2001, I. Martin Isaacs, Geometry for College Students, American Mathematical Society, page 201:

Rather surprisingly, it turns out that Fermat primes play an important special role in this context, a phenomenon hitherto unobserved in the arithmetic theory of Hecke groups, and, as a byproduct of our investigation, several new characterizations of Fermat primes are obtained.

2004, T. W. Müller, “12: Parity patterns in Hecke groups and Fermat primes”, in Thomas Wolfgang Müller, editor, Groups: Topological, Combinatorial and Arithmetic Aspects, Cambridge University Press, page 327:

F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537.
The next 28 Fermat numbers, F₅ through F₃₂, are known to be composite.

2013, Dean Hathout, Wearing Gauss’s Jersey, Taylor & Francis (CRC Press), page xi, Believe it or not, so far only five Fermat primes are known

(number theory) A Fermat number that is prime.


pentamery

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(geometry) the condition of being pentameric


trimery

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(geometry) The condition of being trimeric.


supercatenoid

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(algebra, geometry) a geometric surface constituting a transition between a cube (or similar surface) and a catenoid.


superegg

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(geometry) A surface formed by rotating a superellipse about one of its axes.


supershape

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(geometry) Any closed curve that is a generalization of a superellipse; it is defined by a superformula


superquadric

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(geometry) A three-dimensional relative of a superellipse (or similar curve).


subsetting

(mathematics, computing) The production of a subset.


subsetted

(mathematics, computing) Produced or manipulated by subsetting


picul

From Malay pikul, with influence from earlier Dutch, Spanish, and Portuguese pico.

Powder sugar of China, the hundred cattees or peecull worth fortie to fiftie.

c. 1605, John Saris, quoted in Anthony Farrington's The English Factory in Japan (1991), p. 56

The coal is sold for 130 cash... per picul of 133 pounds.

1888, Archibald John Little, Through the Yang-tse Gorges, page 279:

(units of measure) A traditional South and East Asian unit of weight, based upon the load of a shoulder pole and varying by place and over time but usually standardized at about 60 kg.


porism

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From Ancient Greek πόρισμα (pórisma, “a deduction from a previous demonstration”).

der

(geometry, number theory) A proposition affirming the possibility of finding such conditions as will render a certain determinate problem indeterminate or capable of innumerable solutions.


hermitization

(mathematics) The process of hermitizing.


regular open

From regular + open; apparently a backformation from regular open set.

The set (0,1)∪(1,2) is open, but is not regular open, because its closure is [0,2], so the interior of its closure is (0,2).

(rare, mathematics, of a set) Being the interior of its closure.


regular closed

Apparently a backformation from regular closed set.

The set {0,1,2} is closed, but is not regular closed, because its interior is Ø, so the closure of its interior is Ø.

(rare, mathematics, of a set) Being the closure of its interior.


epimorphic

(mathematics) Relating to an epimorphism.


hyperprior

If we have a hyperprior for λ, the extension is quite easy: we can sample from this hyperprior, apply the procedure for each sample based on p(w; λ), and average over samples.

2007, Brian D. Ripley, Pattern Recognition and Neural Networks, Cambridge University Press, →ISBN, page 166:

(mathematics) A prior distribution on a hyperparameter.


semistrict

(mathematics) Having some, but not all, characteristics of a strict system, category etc.


syndetical

From syndetic + -al. Equivalent to syndeton + -ical.

(grammar, mathematics and library science, uncommon) Synonym of syndetic.


syndetically

From syndetic + -ally. Equivalent to syndeton + -ic + -ally.

(grammar, mathematics and library science) In a syndetic way, employing syndeton, using a conjunction or crossreferences.


biexponential

(mathematics) Having two summed exponential terms.


disordinal

(statistics) Describing a situation in which the rank order of two contributory factors changes at some value


simple fraction

en-noun

simple fraction (plural simple fractions)

(mathematics, arithmetic) A fraction in which both the numerator and the denominator consist of whole numbers.


upper set

(mathematics, order theory) A subset of a poset which contains any ascending chain which starts at any element of itself.


lower set

(mathematics, order theory) A subset of a poset which contains any descending chain which starts at any element of itself.


UFD

unique factorization domain
unique factorization domain#English

(algebra) Initialism of unique factorization domain.


unique factorization ring

unique factorization ring (plural unique factorization rings)

(algebra, ring theory) A ring in which every non-zero, non-unit (i.e., proper) element can be factored into a product of prime elements (not necessarily distinct), such that such factorization is unique up to permutation of the factors and the replacing of primes by their associate primes.


unique factorization domain

unique factorization domain (plural unique factorization domains)

unique factorization ring
unique factorization ring

(algebra, ring theory) A unique factorization ring which is also an integral domain.