Riemannian geometry

Riemannian geometry (usually uncountable, plural Riemannian geometries)

From Riemannian + geometry, after German mathematician Bernhard Riemann.

Riemannian geometry was introduced by Riemann in 1854 as the n-dimensional generalization of the theory of curved surfaces of the 3D Euclidean space.

2001, Miklós Farkas, Dynamical Models in Biology, page 171:

Such geometries are called Riemannian geometries; they are characterized by invariant distances (for example, the space-time interval) that depend at most on the squares of the coordinate distances (∆x or ∆t).

2005, John F. Hawley, Katherine A. Holcomb, Foundations of Modern Cosmology, 2nd edition, page 235:

Riemannian geometry has found many applications in science, the most spectacular of these being the theory of relativity.[…]Every Riemannian geometry has geodesics, which are defined as the shortest curves joining two points.

2010, Saul Stahl, Geometry from Euclid to Knots, page 22:

At the beginning of the seventies, A. Gray generalized the classical holonomy concept by introducing a classification principle for non-integrable special Riemannian geometries [and] discovered in this context nearly Kähler manifolds in dimension six and nearly parallel G₂-manifolds in dimension seven.

2010, Ilka Agricola, “Chapter 9: Non-integrable geometries, torsion, and holonomy”, in Vicente Cortés, editor, Handbook of Pseudo-Riemannian Geometry and Supersymmetry, page 278:

The concepts of Riemannian geometry are familiar: length, angle, distance, and curvature, among others. Historically tied to the origins of differential geometry, and with such familiar concepts, Riemannian geometry is often presented in textbooks as being synonymous with differential geometry itself, instead of as one differential-geometric structure among many.

2013, Andrew McInerney, First Steps in Differential Geometry: Riemannian, Contact, Symplectic, page 195:

(mathematics, geometry) The branch of differential geometry that concerns Riemannian manifolds; an example of a geometry that involves Riemannian manifolds.


enumerably

(mathematics) In a manner that permits enumeration.


duotensorial

(mathematics) Of or pertaining to a duotensor


supercommutative

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

(mathematics) Describing the algebra of supercommutators


fourgon

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

(geometry) A polygon with four sides; a quadrilateral.


nonrenormalizability

(mathematics) the condition of being nonrenormalizable


bidirected

(mathematics) Describing a graph, each of whose edge has an independent orientation at each end


semiprimitive

(mathematics, ring theory, of a ring) In a technical sense, described by its simple modules. Formally: Having trivial Jacobson radical.


square the circle

en-verb

square the circle (third-person singular simple present squares the circle, present participle squaring the circle, simple past and past participle squared the circle)

squares the circle (present singular third-person)
squaring the circle (participle present)
squared the circle (participle past)
squared the circle (past)

The problem of squaring the circle is the problem of determining the ratio of the circumference of a circle to the diameter, which is called π.

1946, Bertrand Russell, History of Western Philosophy, I.24:

(geometry) To construct a square with the same area as a given circle by using only a finite number of steps with compass and straightedge, a task which is mathematically impossible.

رَبَّعَ الدائِرة

to construct a square with the same area as a circle

square peg in a round hole

semantic overlap regarding a difficult problem


bidiagonalization

(mathematics) A particular form of matrix decomposition


bidiagonal

(mathematics) Describing a matrix that has non-zero entries along the main diagonal and either the diagonal above or the diagonal below.


coframe

(mathematics) A particular system of covectors.


polyharmonic

(mathematics) Consisting of multiple harmonics


treespace

(mathematics) A space whose components are trees.


intersphere

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

(geometry) A sphere that is tangent to every edge of a given polyhedron.


nonmonotonously

en-adv

nonmonotonously (comparative more nonmonotonously, superlative most nonmonotonously)

more nonmonotonously (comparative)
most nonmonotonously (superlative)

From nonmonotonous + -ly or non- + monotonously.


a.e.

almost everywhere
almost everywhere#English

(mathematics) Initialism of almost everywhere.


multidigraph

(graph theory) A directed graph that is permitted to have multiple arcs connecting the same source and target nodes.


subquiver

(mathematics) A quiver that forms part of a larger quiver.


quasivariety

(mathematics) Any of a class of algebraic structures generalizing the notion of variety by allowing equational conditions on the axioms defining the class.


quasihomogeneous

(mathematics, physics) Having some homogeneous characteristics.


kayles

From Middle English keyles, plural of Middle English keyle (see Dutch kegel, German Kegel, Danish kegle, and Swedish kegla).

(uncountable, game theory) A simple impartial game in combinatorial game theory, in which players take turns to knock out one pin or two adjacent pins from a line of imagined bowling pins.


coadjoint

/ˈkoʊˌæd͡ʒ.ɔɪnt/

(mathematics) Describing the dual of an adjoint representation


cograph

(mathematics) A graph formed from another by complementation and disjoin union.

Given a function whose graph is #92;#123;(1,7),(2,5),(3,3),(4,3),(5,2),(6,4),(7,6),(8,5),(9,7),(10,6),(11,6)#92;#125;, append an apostrophe to the abscissas so that they will not be confused with ordinates when obtaining their disjoint union, which is: #92;#123;2,3,4,5,6,7,1',2',3',4',5',6',7',8',9',10',11'#92;#125;. The cograph then is #92;#123;#92;#123;7,1',9'#92;#125;,#92;#123;6,7',10',11'#92;#125;,#92;#123;5,2',8'#92;#125;,#92;#123;4,6'#92;#125;,#92;#123;3,3',4'#92;#125;,#92;#123;2,5'#92;#125;#92;#125;.

(mathematics) The dual of the graph of a function. It is an ordinate-indexed partition of the disjoint union of the set of abscissas and ordinates of the function.


bornological

(mathematics) Describing a form of locally convex space which, in some sense, possesses the minimum amount of structure needed to address questions of boundedness of sets and functions.


credal

It is important to note that there are credal sets that cannot be represented by a credal network of the above form.

2010, Rolf Haenni, Probabilistic Logics and Probabilistic Networks, page 90:

(mathematics) Describes a probability based on belief.


indicatrix

Borrowed from Latin indicatrix; equivalent to indicate + -trix.

(mathematics, crystallography) An ellipsoid whose three axes represent the refractive indices of an anisotropic crystal for light following different directions with respect to the crystal axes


granocentric

(physics, mathematics) Describing the formulation of a packing problem based on the free space around a grain (individual particle)


subcontrary

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

Two planes drawn through the vertex of the cone parallel to the plane of the circular base , and that of a subcontrary section, are called by Chasles the cyclic planes of the cone

1852, John Mulcahy, Principles of Modern Geometry:

(geometry) Having, or being in, a contrary order; said of a section of an oblique cone having a circular base made by a plane not parallel to the base, but so inclined to the axis that the section is a circle; applied also to two similar triangles when so placed as to have a common angle at the vertex, the opposite sides not being parallel.


antiparallelly

From anti- + parallelly or antiparallel + -ly.

(mathematics) In an antiparallel manner.


subtense

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

(geometry) A line which subtends, especially the chord of an arc.

(geometry) The angle subtended by a line at a point.


MVT

mean value theorem
mean value theorem#English

(mathematics) Initialism of mean value theorem.


mean value theorem

en-noun

mean value theorem (plural mean value theorems)

Several mean value theorems in the theory of elasticity have appeared in the recent literature[…].

1964, J. H. Bramble, L. E. Payne, Some Mean Value Theorems in Electrostatics: Journal of the Society for Industrial and Applied Mathematics, volume 12, page 105:

1984 [Nauka, Moscow], Sergey Ermakov, V. V. Nekrutkin (authors and translators), A. S. Sipin (author), Random Processes for Classical Equations of Mathematical Physics, [1984, С. М. Ермаков, В. В. Некруткин, А. С. Сипин, Случайные процессы для решения классических уравнений математической физики], 1989, Kluwer, Softcover Reprint, page xiii,
For parabolic equations (Section 5.1) and for the exterior Dirichlet problem (Section 5.2), it is possible to apply the well known mean value theorems.

However, Anton switches, unannounced, to another conceptualization in justifying the Fundamental Theorem - he bases it on the mean value theorem for integrals.

1994, Patrick W. Thompson, “Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus”, in Paul Cobb, editor, Learning Mathematics, Kluwer, page 167:

We prove mean value theorems in the context of integrals which are analogous to the ones studied in Chapter 5.

2013, Elimhan Mahmudov, Single Variable Differential and Integral Calculus: Mathematical Analysis, Springer, page 259:

The mean value theorem for derivatives provides an important link between the derivative of f on an interval and the behavior of f over the interval.

2013, Peter D. Lax, Maria Shea Terrell, Calculus With Applications, Springer, page 171:

(mathematics) Any of various theorems that saliently concern mean values.

for some ζ on the line segment between ̃x and ̌x.

1990, A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, page 51, In order to get a true bound for the range we may replace the Taylor series in (2) by the mean value theorem, which tells us that f(̃x)=f(̌x)+f'(ζ)(̃x-̌x)

In what follows, we will use the mean value theorem, another one of Lagrange's many contributions to numerical analysis.

2003, Sylvain Raynes, Ann Rutledge, The Analysis of Structured Securities, Oxford University Press, page 397:

The main existence theorems in calculus are the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem.

2007, Denise Szecsei, Calculus, The Career Press, page 10:

(calculus, uncountable) The theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the interval's end points.

differentiaalilaskennan väliarvolause

theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope

Lagrange mean value theorem

theorem that a point exists where the derivative equals the overall slope


intermediate value theorem

greatest lower bound
greatest lower bound

(calculus) A theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.


semicritical

differential equation
differential equation

(mathematics) Related to a differential equation and its criticoids.


yrneh

electrical inductance
electrical inductance

(rare) A reciprocal unit of measurement for electrical inductance.


eventology

(statistics) The branch of statistics that deals with random, vague events


femtomolar

(chemistry, of a solution) Having a concentration of 10⁻¹⁵ moles per litre


trihedral

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

(geometry) Having three plane faces that meet at a common point


noninterview

12 per cent of noninterviews were people who said they were too busy for the survey.

(statistics) A person who is not interviewed.


zenzizenzizenzic

Coined by Robert Recorde (as zenzizenzizenzike) in his 1557 mathematics book The Whetstone of Witte, from the root word zenzic.

From this and the word cube, various denominations of powers were formed, as zenzi-cubic for sixth, zenzizenzizenzic for eighth, &c., from which we are now happily delivered.

1866, Charles Knight, The English Cyclopaedia: a new dictionary of Universal Knowledge, page 1045:

For quotations using this term, see Citations:zenzizenzizenzic.

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


conformality

(mathematics) The condition (of a map) of being conformal.


picokelvin

(physics) A unit of temperature equal to 10⁻¹² of a kelvin


zenzizenzic

Coined by Robert Recorde (as zenzizenzike) in his 1557 mathematics book The Whetstone of Witte, from the root word zenzic.

Take the Zenzizenzike Number of the last Quotient Figure, and with the 3 numbers last above-mentioned, add them (duely placed one nearer than another to the Right Hand) into one total Gnonom, and subtract the same from the given Number : And if the number have more Pricks than 2, the work in the second, third, fourth and fifth Directions is to be repeated.

1701, Samuel Jeake, A compleat body of arithmetic, in four books, T. Newborough, page 200:

While this is the least accurate of the four approximations discussed here, it has the charm that the numerator is the zenzizenzic of 4 […]

1965, Dmitri A. Borgmann, Language on Vacation: An Olio of Orthographical Oddities, page 253:

For quotations using this term, see Citations:zenzizenzic.

(mathematics, obsolete) The fourth power of a number; the biquadrate.


bisymmetric

(mathematics, of a square matrix) Symmetric about both of its main diagonals.


persymmetric

(mathematics, of a square matrix) Such that the values on each line perpendicular to the main diagonal are the same for a given line.

(mathematics, of a square matrix, now more commonly) Symmetrical about the anti-diagonal.


bisymmetry

bisymmetry (usually uncountable, plural bisymmetries)

(mathematics) The property of being bisymmetric.


persymmetry

(mathematics) The property of being persymmetric.


Pfaffian

From Pfaff + -ian, after Johann Friedrich Pfaff.

If A is a skew symmetric matrix then det A is the square of a polynomial in the entries of A. This polynomial is known as the Pfaffian of A, and we denote it by Sym(pf A).

1993, Chris Godsil, “Pfaffians”, in Algebraic Combinatorics, page 113:

(mathematics) The determinant of a skew-symmetric matrix, capable of being written as the square of a polynomial in the matrix entries.


contingence

contingence (countable and uncountable, plural contingences)

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

Borrowed from Latin contingentia, from contingēns, present passive participle of contingō (“I make contact with, I am touching”).


chaology

chaology (usually uncountable, plural chaologies)

(physics, mathematics) The study of chaos and chaotic systems


crosslinear

(mathematics) Describing a linear function formed from two others


histogramming

(mathematics) The construction of histograms.


rediagonalize

en-verb

rediagonalize (third-person singular simple present rediagonalizes, present participle rediagonalizing, simple past and past participle rediagonalized)

rediagonalizes (present singular third-person)
rediagonalizing (participle present)
rediagonalized (participle past)
rediagonalized (past)


supergauge

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

(mathematics, physics) Describing any gauge theory aspect of supersymmetry


beamspace

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

(mathematics, physics) A beam of particles treated as a mathematical space.


antiregular

(graph theory) Of a graph: having either zero or two vertices of the same degree.


squircle

At the NCI, the applicator shapes most often used are circular or "squircular." The squircle applicator has one square and one round end, and it is beveled so that the circular end is longer.

1985, Hospital Practice, volume 20, page 131:

(algebraic geometry) A closed quartic curve having properties intermediate between those of a square and a circle.

kwadratokrąg

shape intermediate between a square and a circle


subcube

A similar idea as above is applied to the volume meshing – the initial cube is split and independent instances of the volume meshing algorithm are run on the subcubes.

2012, Miloslav Feistauer, Vit Dolejší, Peter Knobloch, Numerical Mathematics and Advanced Applications: Proceedings, page 429:


supermodule

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

(mathematics) A particular module over a superring or superalgebra


varimax

(statistics) Describing a rotation that maximizes the sum of the variances of the squared loadings, often used in surveys to see how groupings of questions measure the same concept.


pathwidth

(graph theory) A measure of a path decomposition of a graph.


subresultant

(mathematics) A generalization of a resultant that is the product of the pairwise differences of the roots of polynomials


wavefield

(mathematics) A mathematical description of the amplitude of a wave throughout such an area or space.


positive recurrent

(mathematics, stochastic processes, of a state) recurrent with finite expected return time.


null recurrent

(mathematics, stochastic processes, of a state) Recurrent with infinite expected return time.


null persistent

(mathematics, stochastic processes, of a state) persistent with infinite expected return time.


non-null persistent

(mathematics, stochastic processes, of a state) persistent with finite expected return time.


sesquialtera

en-noun

sesquialtera (countable and uncountable, plural sesquialteras)

From Latin sesquialtera, form of sesquialtera, from sesqui- (“a half and a”) + alter (“another, a second”).

(mathematics) A ratio of 3 to 2 or 1½ to 1.


stationary distribution

stationary distribution (plural stationary distributions)

(mathematics, stochastic processes, of a Markov chain) a row vector π whose entries sum to 1 that satisfies the equation πP=π, where P is the transition matrix of the Markov chain.


transition matrix

transition matrix (plural transition matrices or transition matrixes)

transition matrices (plural)
transition matrixes (plural)

(mathematics, stochastic processes) A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the ith row and jth column describes the probability of moving from state i to state j in one time step.


right stochastic matrix

right stochastic matrix (plural right stochastic matrices)

(mathematics, stochastic processes) A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the i'th row and j'th column describes the probability of moving from state i to state j in one time step.


null recurrence

(mathematics, stochastic processes) The quality of being null recurrent.


positive recurrence

(mathematics, stochastic processes) the quality of being positive recurrent.


Poisson process

Poisson process (plural Poisson processes)

From the related concept of Poisson distribution (specifying a bounded subset of the domain of a Poisson process defines a random variable that has a Poisson distribution). See also stochastic process.

These properties are readily apparent when one considers that the Poisson process is derived from the binomial processes, which, as seen in Section 6.1, can be viewed in terms of coin tosses.

1995, Randolph Nelson, Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling, Springer, page 252:

2012, Peter Guttorp, Thordis L. Thorarinsdottir, Chapter 4: Bayesian Inference for Non-Markovian Point Processes, Emilio Porcu, José–María Montero, Martin Schlather (editors), Advances and Challenges in Space-time Modelling of Natural Events, Springer, Lecture Notes in Statistics 207, page 88,
The doubly stochastic Poisson process, introduced by Cox in [9] and so named by Bartlett in [6] is obtained by letting the rate λ(t) of the Poisson process vary according to a stochastic process, say Λ(t). […] There are instances of doubly stochastic Poisson processes that are identical to cluster processes (for example, the shot noise process driven by a stationary Poisson process is identical to a Neyman-Scott Poisson cluster process, see p.171-172 in [12]).

University buses arrive at the Students Center to take students to their classes according to a Poisson process with an average rate of 5 buses per hour.

2014, Oliver Ibe, Fundamentals of Applied Probability and Random Processes, Elsevier (Academic Press), page 415:

(mathematics, statistics, probability theory) A stochastic process in which events occur continually and independently of one another.

Poisson point field

stochastic process of continuous, independent events


detailed balance

detailed balance (plural detailed balances)

where P is the Markov transition matrix and πᵢ and πⱼ are the equilibrium probabilities of being in states i and j, respectively.

(mathematics, probability theory) a Markov process is said to show detailed balance if the transition rates between each pair of states i and j in the state space obey


heapable

(mathematics) That can be sequentially inserted to form a binary tree with the heap property.


sparsing

(mathematics) The reduction to zero of elements of a matrix


equivariance

equivariance (countable and uncountable, plural equivariances)

(mathematics) The condition of being equivariant


isohedral

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

(geometry) Describing a polyhedron or a tiling all of whose faces are the same.


quadrangulation

quadrangulation (countable and uncountable, plural quadrangulations)

(mathematics) A graph embedded in a surface such that every face is a quadrangle.


supremal

en-adj

supremal (comparative more supremal, superlative most supremal)

more supremal (comparative)
most supremal (superlative)

(mathematics) Of or pertaining to a supremum


semiminor

(mathematics) Describing each of the two segments of the minor axis of a conic section at both sides of the center of the conic section.


filter bank

(signal processing) An array of band-pass filters that separates the input signal into multiple components, each one carrying a single frequency subband of the original signal.


eigenanalysis

(mathematics) analysis using eigenvectors


biorthogonal

(mathematics) Describing a pair of topological vector spaces that are in duality with a pair of indexed subsets in a specific manner


facient

From Latin faciens, facientis, present participle of facere (“do, make”).

(mathematics) One of the variables of a quantic as distinguished from a coefficient.


eigenequation

(mathematics) Any equation containing an eigenfunction


stochastics

(mathematics) The branch of statistics that deals with stochastic systems


subsolution

(mathematics) A subset of solutions in game theory


isodynamic

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

From Ancient Greek ἰσοδῠ́νᾰμος (isodŭ́nămos, “equal in power”) + -ic, after dynamic. By surface analysis, iso- + dynamic.

affix

grc:ἰσοδῠ́νᾰμος

equilateral triangle
equilateral triangle

inversely proportional
inversely proportional

(geometry) In Euclidean geometry, being or relating to certain points associated with a triangle, with the properties that an inversion centered at one of these points transforms the given triangle into an equilateral triangle, and that the distances from the isodynamic point to the triangle vertices are inversely proportional to the opposite side lengths of the triangle.


polytomous

(mathematics) Describing a variable that has multiple (more than two) categories


properness

en-noun

properness (usually uncountable, plural propernesses)

(mathematics) The state or condition of being proper (of a proper fraction, proper subset, etc.).


precongruence

(mathematics) A congruence of a preorder


conchoid

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

From Latin concha (“mussel”) (from Ancient Greek κόγχη (kónkhē)) + -oid or directly from Ancient Greek κογχοειδής (konkhoeidḗs), referring to the curved outline of a mussel shell or anything in this form.

The conchoid of a circle with respect to a point on the circle is a cardioid if the fixed distance is equal to the diameter of the circle.

The Conchoid of Nicomedes is the conchoid of a straight line with respect to a point not on the line.

1815, Charles Hutton, Pappus, entry in A Philosophical and Mathematical Dictionary, Volume 2, page 147,
He next treats of the properties of the Conchoid, which Nicomedes invented for doubling the cube; applying it to the solution of certain problems concerning Inclinations, with the finding of two mean proportionals, and cubes in any proportion whatever.

The classical conchoid construction is a non-orthogonal polar-curvilinear construction in which equal distances along a line are marked off from its point of intersection with a curve for various positions of the line as it rotates about a point.

1982, J. Lee Kavanau, Curves and Symmetry, volume 1, page 3:

These curves are called conchoids of Nicomedes after the ancient Greek scholar Nicomedes. He called them conchoids because the shape of their outer branches resembles that of a conch shell or mussel shell.

2007, James Stewart, Single Variable Calculus, volume 2, page 662:

One of the best choices is the conchoid, according to Newton the simplest curve after the circle.

2009, Niccolò Guicciardini, Isaac Newton on Mathematical Certainty and Method, page 68:

(mathematics, geometry) Any of a family of curves defined as the locus of points p, such that each p is on a line that passes through a given fixed point P and intersects a given curve, C, and the distance from p to the point of intersection with C is a specified constant (note that for nontrivial cases two such points p satisfy the criteria, and the resultant curve has two parts).


deviatoric

(mathematics) Of or pertaining to a deviator


hypercone

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

(geometry) A four-dimensional surface related to the three-dimensional cone


matchgate

(mathematics) A weighted planar graph having some external nodes


antidivision

antidivision (usually uncountable, plural antidivisions)

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

2008, Patrick Bosc, Olivier Pivert, A Family of Tolerant Antidivision Operators for Database Fuzzy Querying Book Series:

It can be noticed that an antidivision is nothing but an antijoin followed by a projection over X […]

2008, Sergio Greco, Thomas Lukasiewicz, Scalable uncertainty management:

(algebra) A particular extension of the antijoin operator.


antijoin

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

(algebra, databases) A type of join, denoted by ▷, such that R▷S yields only those tuples in R for which S has no corresponding tuple of the same value.


prismoid

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

(geometry) A prismatoid that has planar sides, and the same number of vertices in both of its parallel planes.


hyperdiffusion

hyperdiffusion (countable and uncountable, plural hyperdiffusions)

(mathematics, physics) Any form of diffusion whose mathematical representation contains orders greater than cubic.


hyperdiffusive

en-adj

hyperdiffusive (comparative more hyperdiffusive, superlative most hyperdiffusive)

more hyperdiffusive (comparative)
most hyperdiffusive (superlative)

(mathematics, physics) Of, pertaining to, or giving rise to hyperdiffusion


superconvergence

en-noun

superconvergence (usually uncountable, plural superconvergences)

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


difference equation

difference equation (plural difference equations)

(mathematics) An equation involving an ordered sequence of real numbers (a_nₙ₌₁ ᪲) and some of its differences, where the first difference is defined as Δ(a_n)=a_n+1-a_n, and the kᵗʰ difference is defined recursively as Δᵏ(a_n)=Δᵏ⁻¹(a_n+1)-Δᵏ⁻¹(a_n),.

(mathematics) more broadly, any recurrence relation


recurrence relation

recurrence relation (plural recurrence relations)

(mathematics) an equation that recursively defines a sequence; each term of the sequence is defined as a function of the preceding terms.


dozenal

(arithmetic, rare) Of a number, expressed in base 12.


dozenal

(arithmetic, rare) A value in a number system that uses 12 as its base.


mahoosive

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

Probably a blend of massive and a respelling of the letters hu in huge infixed in the former.

Well, I haven't had any real problems with it, it's not the most reliable ISP I've ever used (mahoosive understatement), but considering it's free it's not too bad.

2000 March 27, Laurence Bogle, “Re: DF”, in alt.fab.robert-jordan (Usenet):

I even said to someone look at them mahoosive mosquitoes!! […] I tell ya, between the mahoosive mosquitoes, bees & wasps and caterpillars, I was VERY happy to get back to the city & it's pollution.

2002 September 24, “Frothie” [pseudonym], “Re: More Mahoosive Spiders :S”, in alt.babylon5.uk (Usenet):

We do have a rather mahoosive store locally.

2003 October 10, “Catkins” [pseudonym], “Re: Just ‘done’ Tescos”, in freeserve.chat (Usenet):

Picture this: we had a fat tourist: wandering along in a mahusive pair of budgie smugglers (Speedo's), and wearing this ridiculous flower hat; pawing over a local girl.

2007 February 26, John P. Wood, Woody’s World Turns Left … into South East Asia, Bloomington, Ind., Milton Keynes, Buckinghamshire: AuthorHouse, →ISBN, page 247:

And on that note, I shall bid you all a fond au revoir. This scene-setting commentary will now end, and Phil Harlow will bring you all the action from the Stade de France before, during and after tonight's mahoosive match.

2007 October 20, Sam Lyon, “England v South Africa countdown”, in BBC Sport, archived from the original on 2021-06-08:

Those destinations are the span of England. And it's not exactly a mahoosive country …

2010 January 23, “humble.life” [pseudonym], “Re: get this …”, in alt.support.depression (Usenet):

Rachel McAdams showed off a mahusive baby bump while out and about in Notting Hill, London late yesterday afternoon. Which could just about be the most exciting thing to ever happen, today.

2012 July 6 (updated 2012 September 25), Gilly Ferguson, “Is Rachel McAdams pregnant!? Let’s examine the evidence (the bump)”, in Daily Mirror, London: Reach plc, →ISSN, →OCLC, archived from the original on 2020-12-02:

Bass-thrum and glass-shard music swelled slowly in volume. Despite the sound's sweetness, its painful clarity, something in Ecko shivered – it jagged at his nerves like the old fingernails-down-a-blackboard trick. It was pure power, some ma-hu-sive engine that was just turning over, warming the fuck up.

2015 November, Danie Ware, “Muster”, in Ecko Endgame, London: Titan Books, Titan Publishing Group, →ISBN:

So if you're shy about going to the gym because there is always someone next to you using mahoosive weights, don't be. You do your weights, just make every workout count.

2019 June 17, Matt Goulet, quoting Henry Cavill, “Henry Cavill Reveals His Secret to Getting Big Arms”, in Richard Dorment, editor, Men’s Health, New York, N.Y.: Hearst Magazine Media, →ISSN, →OCLC, archived from the original on 2020-10-03:

(chiefly British, humorous, slang) Massive; huge; very large.


premultiply

en-verb

premultiply (third-person singular simple present premultiplies, present participle premultiplying, simple past and past participle premultiplied)

premultiplies (present singular third-person)
premultiplying (participle present)
premultiplied (participle past)
premultiplied (past)

(mathematics) To multiply a matrix or quaternion by a preceding factor noncommutatively


informetrics

(mathematics, computing) The study of quantitative aspects of information


premetric

(mathematics) Any of several specific generalizations of a metric.


hyperbolism

en-noun

hyperbolism (countable and uncountable, plural hyperbolisms)

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

(countable, geometry) A blow-up of a curve at a point.


biunique

(mathematics, of two sets) that have a one-to-one correspondence in each direction


sparsify

en-verb

sparsify (third-person singular simple present sparsifies, present participle sparsifying, simple past and past participle sparsified)

sparsifies (present singular third-person)
sparsifying (participle present)
sparsified (participle past)
sparsified (past)

(mathematics, transitive) To make (a graph or a matrix) sparse.


Durand-Kerner method

After Emile Durand, a French mathematician, and Immo Kerner, a German mathematician.

The improved Durand-Kerner Method […] Referring to the improved Durand-Kerner and the improved Ehrlich we find that the approximations converging towards the origin will move directly towards this zero on each iteration cycle always reducing their distance away by the fraction 2/(m+1) in the first method and 3/(m+2) in the second […]

1975, International journal of computer mathematics, volumes 5-6:

(mathematics) An algorithm for finding the roots of polynomial equations.


method of Weierstrass

After Karl Weierstrass, a German mathematician.

Durand-Kerner method
Durand-Kerner method


factorability

(mathematics) The condition of being factorable.


semisquare

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

(geometry) A right isocoles triangle, or such figure of which two form a square.


newform

(mathematics, number theory) A cusp form that is "new" at a given level N, where the levels are the nested subgroups Γ₀(N) of the modular group, with N ordered by divisibility.


repetend

From Latin repetendum (something to be repeated).

(mathematics) A repeated part in repeating decimals.


repeating decimal

en-noun

repeating decimal (plural repeating decimals)

(mathematics) A decimal representation of a real number that, at some point, becomes periodic (and repeats some sequence of digits infinitely)


vergée

From Norman vergée, from Anglo-Norman vergé, vergee, originally terre vergee (“measured land”). Doublet of virgate.

Her father had given her a cottage in the Robergerie with a vergée of land and a greenhouse.

1974, GB Edwards, The Book of Ebenezer Le Page, New York, published 2007, page 34:

(Channel Islands) A measure of land, having varying values in Guernsey and Jersey, but approximately 18,000 square feet.


arbelos

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

From Ancient Greek ἄρβηλος (árbēlos) or ἄρβυλος (árbulos), literally "shoemaker's knife".

(geometry) A plane region bounded by a semicircle of diameter 1, connected to semicircles of diameters r and (1 − r), all oriented the same way and sharing a common baseline.


excircle

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

Also since the circle of inversion cuts both excircles orthogonally, each excircle inverts into itself.

1979, Dan Pedoe, Circles: A Mathematical View, published 1995, page 10:

Extend the sides of triangle QRS and construct the three excircles: One excircle is tangent to side QR and rays SQ and SR; one excircle is tangent to side SR and rays QS and QR; and one excircle is tangent to side SQ and rays RS and RQ.

1999, Art Johnson, Famous Problems and Their Mathematicians, Teacher Ideas Press, page 174:

Lemma 4.9 (The Diameter of the Incircle). Let ABC be a triangle whose incircle is tangent to #92;overline#123;BC#125; at D. If #92;overline#123;DE#125; is a diameter of the incircle and ray AE meets #92;overline#123;BC#125; at X, then BD#61;CX and X is the tangency point of the A-excircle to #92;overline#123;BC#125;.
Incircles and excircles often have dual properties.

2016, Evan Chen, Euclidean Geometry in Mathematical Olympiads, page 61:

(geometry) An escribed circle; a circle outside a polygon (especially a triangle, but also sometimes a quadrilateral) that is tangent to each of the lines on which the sides of the polygon lie.


salinon

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

From Ancient Greek *σάλινον (*sálinon, unattested), presumably from and meaning the same as Latin salīnum (“salt-cellar”), derived from sal (“salt”) (compare salillum).

bor

(geometry) A particular figure bounded by four semicircles.


stego

Clipping of various terms relating to steganography.

A stego text might become meaningless if words of the cover text are freely replaced to synonyms without considering the context.

2013, Kazuhiro Kondo, Multimedia Information Hiding Technologies and Methodologies for Controlling Data, Hershey, P.A.: Information Science Reference, →ISBN, page 357, column 1:

(cryptography) Steganographic; relating to or hidden using steganography.


stego

en-noun

stego (countable and uncountable, plural stegos)

One might use traditional steganalysis to find stegos and then identify the guilty actors.

2020, Hanzhou Wu, “Unsupervised steganographer identification via clustering and outlier detection”, in Mahmoud Hassaballah, editor, Digital Media Steganography, London: Academic Press, →ISBN, page 296:

(countable, cryptography) A secret message hidden using steganography.


algebrization

(mathematics) Alternative form of algebraization


quasicontinuum

(mathematics) A system that behaves as a continuum in most but not all respects.


quasidisorder

(mathematics) The condition of an apparently disordered system that has an underlying order.


supercompact

en-adj

supercompact (comparative more supercompact, superlative most supercompact)

more supercompact (comparative)
most supercompact (superlative)

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

(mathematics, topology, of a topological space) Having a subbasis such that every open cover of the topological space from elements of the subbasis has a subcover with at most two subbasis elements.

(mathematics, set theory) Being a type of large cardinal with a variety of reflection properties.


subbasis

(mathematics) A subbase (subcollection of a topological space).


Zorn's lemma

After Max August Zorn 1906-1993, German-born American mathematician. See German Zorn.

(set theory) A proposition of set theory stating that every partially ordered set, in which every chain (i.e. totally ordered subset) has an upper bound, contains at least one maximal element.


vinculate

en-verb

vinculate (third-person singular simple present vinculates, present participle vinculating, simple past and past participle vinculated)

vinculates (present singular third-person)
vinculating (participle present)
vinculated (participle past)
vinculated (past)

The reason why we typically want to vinculate is we want to deal with small single digit numbers. This means we typically want to vinculate numbers that are larger than 5. When we vinculate numbers like 6, 7, 8, 9 we get 4, 3, 2 and […]

2010, Chandramouli Mahadevan, Basics of Speed Mathematics, Lulu.com, →ISBN, page 24:


spectrahedron

(mathematics) The intersection of the cone of positive semidefinite matrices with an affine-linear space


diagram chase

To prove the five lemma, just use a diagram chase.

(mathematics, somewhat informal) A proof in stages, each of which, in general, depends on the previous stages and can be visualized by means of a diagram of morphisms.


diagram chasing

Category theory also contributes new proof techniques, such as diagram chasing or arguments by duality; Steenrod called these methods “abstract nonsense.”³ The aim of this text is to introduce the language, philosophy, and basic theorems of category theory. A complementary objective is to put this theory into practice: studying functoriality in algebraic topology, naturality in group theory, and universal properties in algebra.

2016, Emily Riehl, Category Theory in Context (Aurora: Dover modern math originals), New York: Dover, →ISBN, →OCLC, page x:

To prove the five lemma, just use diagram chasing.

(mathematics, somewhat informal) Proof in stages, each of which, in general, depends on the previous stages and can be visualized by means of a diagram of morphisms.


fractile

The q-quantile is the same as the (1/q)-fractile.

The median is the .5-fractile.

(statistics) The value of a distribution for which some fraction of the sample lies below.


unitate

(mathematics, archaic) The remainder after dividing a number by any digit.


unitate

unitate (third-person singular simple present unitates, present participle unitating, simple past and past participle unitated)

unitates (present singular third-person)
unitating (participle present)
unitated (participle past)
unitated (past)

(mathematics, archaic, transitive) To obtain the unitate of.


primeness

(mathematics) The quality of being prime, or a prime number.


countable additivity

mathematical analysis
mathematical analysis

(mathematical analysis) The following property of a measure: that the measure of a countable union of disjoint sets is equal to the sum of their measures.


extended real number system

en-noun

extended real number system (plural real number systems)

(mathematics) The real number system adjoined with two extra symbols: ∞ and −∞, inheriting the ordering of the real number system, and defining −∞ to be less than any real number, and ∞ to be larger than any real number.


real number system

real number system (plural real number systems)

As we have mentioned before, the structure of Euclidean geometry, as formalized through the axioms of Hilbert, produces an archimedean ordered field. To com- plete the story, one can add to these axioms the further requirement that this field is maximal in the sense that it cannot be embedded inside any larger archimedean ordered field. It turns out then that any such ordered field is isomorphic to any other, and thus there is essentially one such ordered field. This ordered field is the real number system R.

2008 November, Ambar N. Sengupta, “Notes in Introductory Real Analysis”, in www.math.lsu.edu, retrieved 2012-07-13:

The real number system is a complete, linearly ordered field ℛ=(ℝ,+,·,<).

2010 April 16, Lindsay Keegan, “The Ghosts of Departed Quantities”, in www.math.ufl.edu, archived from the original on 2011-09-30

Archimedean ordered field
Archimedean ordered field

(mathematics) The complete Archimedean ordered field (of real numbers).


real number line

real number line (plural real number lines)

(mathematics) A geometric representation of the real number system.


real function

(mathematics) A function whose range is a subset of the set of real numbers.


complex function

complex function (plural complex functions)

(mathematics) A function whose range is a subset of the set of complex numbers.

kompleksifunktio

a function whose range is a subset of the set of complex numbers

komplexe Funktion

with the additional constraint of the domain being a subset of the complex numbers


σ-algebra

/ˈsɪɡ.mə ˈæl.dʒɪ.bɹə/

Consider all the sigma-algebras that contain #92;mathcal#123;F#125; and take their intersection, which we call #92;Sigma, i.e., a subset A#92;subset#92;Omega is in #92;Sigma if and only if A is in every sigma-algebra containing #92;mathcal#123;F#125;. It is easy to check that #92;Sigma is indeed a sigma-algebra.

2001, Elliott H. Lieb, Michael Loss, Analysis, American Mathematical Society, page 4:

Consider all the σ'''-algebras on [0,1] containing all intervals from that segment (there is at least one such σ'''-algebra, for the collection of all the subsets of a given set clearly forms a σ'''-algebra).

2013, Alexandr A. Borovkov, Probability Theory, Springer, page 15:

Denote by #92;mathcal#123;F#125; the set of subsets of [the sample space] Ω which are considered events. #92;mathcal#123;F#125; is called the space of events. In rigorous probability theory, #92;mathcal#123;F#125; is required to be a sigma-algebra on Ω.

2017 February 4, Marco Taboga, Lectures on Probability Theory and Mathematical Statistics, 2nd edition, San Bernardino, CA, USA, →ISBN, §10.5.1, page 75:

(mathematical analysis) A collection of subsets of a given set, such that the empty set is part of this collection, the collection is closed under complements (with respect to the given set) and the collection is closed under countable unions.

σ-field

collection of subsets that obeys certain conditions


measurable set

(mathematical analysis) A subset of a given measurable space which is a member of the σ-algebra of that space.


open ball

(topology, mathematical analysis, restricted to metric spaces) The set of all points in a metric space whose distance from a given point ("the open ball's center") is less than a given length ("the open ball's radius").


open interval

(mathematics) An interval in the real number line which does not contain its supremum and infimum. If specified by a pair of real numbers, then it consists of all the points on the real line whose values lie strictly between those two real numbers.


open rectangle

(mathematics) A rectangle in the real plane which is an open set: i.e., which does not contain its edges. If the sides of the open rectangle are parallel to the plane's axes, then the open rectangle can be described as the Cartesian product of two open intervals.


real plane

(set theory) The Cartesian product of two real lines.


characteristic function

characteristic function (plural characteristic functions)

(mathematical analysis) A function which is equal to 1 for all points in its domain which belong to a given set, and is equal to 0 for all points in the domain which do not belong to that given set.

indicator function

function equal to 1 on elements of a given set

(mathematics, probability theory) A complex function completely defining the probability distribution of a real-valued random variable

karakteristinen funktio

a complex function completely defining a probability distribution


Borel σ-algebra

Borel σ-algebra (plural Borel σ-algebras)

Named after French mathematician Émile Borel (1871–1956), who pioneered measure theory.

named-after

(mathematical analysis) The smallest σ-algebra which contains the topology of a given topological space.


Borel set

A Lebesgue measurable set is expressible as a union of a Borel set and a Lebesgue null set.

(mathematical analysis) Any of the members of a Borel σ-algebra.


half-open interval

en-noun

half-open interval (plural half-open intervals)

(mathematics) An interval in the real line which contains one of its endpoints but not the other one: i.e., it either contains its supremum or its infimum but not both.


Borel measurable

Continuous functions are Borel measurable.

(mathematical analysis, of a function) Such that the inverse image of any open set in its codomain is a Borel set of its domain.


Borel function

(mathematical analysis) A function which is Borel measurable.


Archimedean property

Archimedean property (plural Archimedean properties)

(mathematical analysis) A property of the set of real numbers, that for any real number there is always a natural number greater than that real number.

propriedade arquimediana

the property that there is always a natural number greater than any real number


countably additive

countable additivity
countable additivity

(mathematical analysis) Of a measure: that satisfies countable additivity.


positive measure

positive measure (plural positive measures)

(mathematical analysis) A function whose domain is a σ-algebra, whose codomain is [0,∞], and which is countably additive.

complete measure > Lebesgue–Stieltjes measure > Lebesgue measure


complex measure

complex measure (plural complex measures)

(mathematical analysis) A function whose domain is a σ-algebra, whose codomain is the set of complex numbers, and which is countably additive.


counting measure

counting measure (plural counting measures)

(mathematical analysis) A positive measure which, for each subset of a given measure space, assigns a value equal to the number of points in that subset.


ordered field

(algebra) A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides.

corpo ordenado

field satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides


completeness axiom

completeness axiom (plural completeness axioms)

(mathematics) The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).


upper limit

(mathematical analysis) The upper limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the "first subsequence." Then remove the first term of the first subsequence in order to obtain the "second subsequence." Repeat the removal of first terms in order to obtain a "third subsequence," "fourth subsequence," etc. Find the supremum of each of these subsequences, then find the infimum of all of these supremums. This infimum is the upper limit.

yläraja-arvo

the upper limit of a sequence of real numbers


lower limit

(mathematical analysis) The lower limit of a sequence of real numbers is the real number which can be found as follows: remove the first term of the sequence in order to obtain the "first subsequence." Then remove the first term of the first subsequence in order to obtain the "second subsequence." Repeat the removal of first terms in order to obtain a "third subsequence," "fourth subsequence," etc. Find the infimum of each of these subsequences, then find the supremum of all of these infimums. This supremum is the lower limit.

alaraja-arvo

the lower limit of a sequence of real numbers


hemiequilateral

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

(geometry) Describing the shape of a triangle formed by cutting an equilateral triangle in half through one of the apices


Lebesgue integral

Lebesgue integral (plural Lebesgue integrals)

/ləˈbɛːɡ ˈɪntəɡɹəl/

/ləˈbɛːɡ ˈɪntəɡɹl̩/

Named after Henri Lebesgue, a French mathematician.

The Lebesgue integral is learned in a first-year real-analysis course.

Compute the Lebesgue integral of f over E.

(mathematical analysis, singular only, definite and countable) An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath).


μ-completion

Every σ-algebra has a μ-completion: if a σ-algebra is complete, then it is equal to its μ-completion, otherwise it is contained by its μ-completion.

(mathematical analysis) A σ-algebra which is obtained as a "completion" of a given σ-algebra, which includes all subsets of the given measure space which simultaneously contain a member of the given σ-algebra and are contained by a member of the given σ-algebra, as long as the contained and containing measurable sets have the same measure, in which case the subset in question is assigned a measure equal to the common measure of its contained and containing measurable sets (so the measure is also being completed, in parallel with the σ-algebra).


echo boomer

By 2010, there will be 70 million potential drivers among the echo boomers born from 1977 to 1994.

2002 March 31, Michelle Krebs, “Youth Will Be Served at This Year's New York Auto Show”, in New York Times, retrieved 2010-08-30:

(demographics) A child of a member of the post-World War II baby boom generation, born in the period extending approximately from the late 1970s or early 1980s to the mid-1990s.


describent

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

Latin dēscrībēns, present participle of dēscrībō (“I describe”).


centroidal

(graph theory, of a tree) Having a single centroid.


evolvent

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

Latin ēvolvēns, ēvolventis (“unrolling”), present participle of ēvolvō (“I unroll”).


idealizer

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

(algebra) For a ring R and an ideal m of R, the set of all u ∈ Frac(R) such that um ⊂ m, where Frac(R) is the fraction field of R.


shellable

(topology) For which a shelling is possible.


spherocylinder

(mathematics) A solid, made up of two hemispheres connected by a cylinder.


regressand

(statistics) The dependent variable in a regression.


Goodstein's theorem

Named after Reuben Goodstein (1912-1985), English mathematician.

(mathematics) A theorem stating that every Goodstein sequence eventually terminates at zero.


nonstiff

(mathematics, of an equation) Not stiff.


hyperjump

(mathematics, logic) A form of Turing jump in hyperarithmetic.


ploughland

ploughland (countable and uncountable, plural ploughlands)

From Middle English plowelond, plouȝ-lond, plow-land, equivalent to plough + land. Compare German Pflugland, Old Norse plógsland (“ploughland”).

Land that has been or is meant to be ploughed.


deseasonalize

en-verb

deseasonalize (third-person singular simple present deseasonalizes, present participle deseasonalizing, simple past and past participle deseasonalized)

deseasonalizes (present singular third-person)
deseasonalizing (participle present)
deseasonalized (participle past)
deseasonalized (past)

(transitive, statistics) To offset (data) to reverse the process of seasonalization.


antighost

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

There are as many components in the topological ghosts as in the gauge fields, and to gauge fix the topological freedom, one must also introduce as many antighosts as topological ghosts.

2006, Laurent Baulieu, String theory: from Gauge interactions to cosmology, page 20:

(mathematics, physics) A field with a negative ghost number.


skewsymmetric

(mathematics) Alternative form of skew-symmetric


bialgebraic

(mathematics) Of or pertaining to bialgebra.


JSR

(mathematics) Initialism of Joint Spectral Radius.


endofunctor

(category theory) A functor that maps a category to itself.


light second

(astronomy, physics) A unit of length equal to the distance light travels in one second: about 300 megameters


left inverse

In order for a function to have a left inverse it must be injective.

(mathematics) A related function that, given the output of the original function, returns the input that produced that output.

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


cyclometric

(mathematics) Of or pertaining to the inverse trigonometric functions: arcsine, arccosine, arctangent, arccotangent, arcsecant, and arccosecant.


Voronoi diagram

en-noun

Voronoi diagram (plural Voronoi diagrams)

(mathematics) A diagram that assigns a set of points in a plane to an equal number of cells, such that each point p is inside a cell consisting of all regions closer to p than to any other point.


scalar multiplication

scalar multiplication (countable and uncountable, plural scalar multiplications)

(linear algebra) Multiplication of a vector by a scalar (which belongs to the vector space's field of scalars).


linear functional

linear functional (plural linear functionals)

(mathematics) A linear mapping from a vector space to its field of scalars.


open cover

(topology) A cover whose members are all open sets.


lower semi-continuous

(of a real-valued function on a topological space) Such that, for each fixed number, the subspace of points whose images are at most that number is closed.


locally compact

(topology) Of a topological space: such that, for every point of the space, there is a neighborhood of that point whose closure is compact.


positive linear functional

positive linear functional (plural positive linear functionals)

(mathematical analysis) A kind of linear functional which yields a non-negative scalar when given a non-negative function as parameter.


regular space

(topology) A Hausdorff space with the additional property that for every closed set of that space and every point disjoint from that set, there are a disjoint pair of open sets which contain the closed set and the point, respectively.


normal space

(topology) A regular space with the additional property that for every disjoint pair of closed sets in that space, there is a disjoint pair of open sets which contain the closed sets, respectively.


teenth

(slang, used in measuring drugs) A dram, a sixteenth of an ounce.


sextarius

sextarius (plural sextariuses or sextarii)

From Latin sextārius (“one-sixth”), from sextus (“sixth”) + -ārius (“-ary: forming adj.”). Doublet of sextary.

(historical) A Roman unit of liquid measure reckoned as the volume of 1⅔ Roman pound of wine and equivalent to about 0.54 L although varying slightly over time.

(historical) A Roman unit of dry measure.


Borel measure

We are now in a position to construct a definitive theory for measuring subsets of #92;mathbb#123;R#125; based on the idea that the measure of an interval is its length. We begin with a more general (but only slightly more complicated) construction that yields a large family of measures on #92;mathbb#123;R#125; whose domain is the Borel σ-algebra #92;mathcal#123;B#125;#95;#123;#92;mathbb#123;R

1999, Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edition, New York: John Wiley & Sons, Inc., →ISBN, →OCLC, §1.5, page 33:

(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space.


outer regular

(mathematical analysis) (of a Borel set) That its measure is equal to the infimum of the measures of all open sets which contain it.


inner regular

(mathematical analysis, of a Borel set) Whose measure is equal to the supremum of the measures of all compact sets which are contained by it.


σ-compact

(mathematical analysis, of a set in a topological space) That is expressible as a countable union of compact sets.


σ-finite measure

σ-finite measure (plural σ-finite measures)

(mathematical analysis) A set, in a measurable space, that is expressible as a countable union of sets of finite measure.


Cauchy-Schwarz inequality

Named after Augustin-Louis Cauchy and Hermann Amandus Schwarz.

(linear algebra, mathematical analysis) A theorem which states that the absolute value of the dot product between two vectors is less than or equal to the product of the magnitudes of the two vectors.

Augustin-Louis Cauchy
Cauchy-Schwarz inequality
Hermann Amandus Schwarz


Schwarz inequality

Schwarz inequality (plural Schwarz inequalities)

Cauchy-Schwarz inequality
Cauchy-Schwarz inequality

(linear algebra) Cauchy-Schwarz inequality


real vector space

real vector space (plural real vector spaces)

(linear algebra, mathematical analysis) A vector space over the field of real numbers.


k-cell

(mathematical analysis) A subset of k-dimensional Euclidean space which is obtained by taking the Cartesian product of k intervals (closed, open, or half-closed) which are subsets of the coordinate axes of the ambient Euclidean space.


δ-box

(mathematical analysis) A k-cell which is a Cartesian product of half-closed intervals which are closed at their infima and open at their suprema, and such that the infimum of each interval is the coordinate of a given point (called "the corner" of the δ-box), and the length (i.e., measure) of each interval is equal to (the given value) δ.


obvious by inspection

It is obvious by inspection that the set #92;#123;#91;0,1),#91;1,2),#91;2,3),...#92;#125; is a partition of #91;0,#92;infty).

(mathematics, of a claim) evident in the mind's eye, without formal proof being necessary.


complete measure

complete measure (plural complete measures)

(mathematical analysis) A measure such that, for every set of measure zero belonging to its domain, all subsets of that set are also assigned measure zero by the given measure.

Lebesgue–Stieltjes measure > Lebesgue measure


xylon

The xylon, in which naubia are measured. The royal (xylon) 9 comprises 3 cubits, 18 palms, 72 fingers; 10 the private (xylon) comprises 2⅔ cubits, 16 palms, 64 fingers, so that the surveyor's schoinion comprises 32 royal xyla, and 36 private (xyla).

2020, Roger S. Bagnall, Alexander Jones, Mathematics, Metrology, and Model Contracts, page 81:

(historical) A unit of length in Ancient Greece.


Lebesgue measure

Lebesgue measure (plural Lebesgue measures)

/ləˈbɛːɡ ˈmɛ.ʒɚ/

Named after French mathematician Henri Lebesgue.

(mathematical analysis) A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides).

Lebesgue–Stieltjes measure < complete measure < positive measure < measure


Lebesgue measurable

(mathematical analysis) (of a set in some k-dimensional Euclidean space) That it is an element of the domain of the Lebesgue measure of the ambient Euclidean space.


uniform continuity

uniformly continuous
uniformly continuous

(mathematical analysis, of a function) The property of being uniformly continuous.


uniformly continuous

A uniformly continuous function is a function whose derivative is bounded.

(mathematical analysis, of a function from a metric space X to a metric space Y) That for every real ε > 0 there exists a real δ > 0 such that for all pairs of points x and y in X for which D_X(x,y)<δ, it must be the case that D_Y(f(x),f(y))<ϵ (where D_X and D_Y are the metrics of X and Y, respectively).


graphoid

(combinatorics) A matroid that has two collections of nonempty subsets called circuits and cocircuits such that the intersection of any circuit and cocircuit is not only the identity matroid, no circuit properly contains another circuit, no cocircuit properly contains another cocircuit, and for any painting of M that colors exactly one element green and the rest either red or blue there exists either a circuit containing the green element and no red elements or a cocircuit containing the green element and no blue elements.


Vitali-Carathéodory theorem

Named after Giuseppe Vitali and Constantin Carathéodory.

upper semicontinuous
upper semicontinuous

lower semicontinuous
lower semicontinuous

(mathematical analysis) A theorem which states that any real-valued Lebesgue integrable function can be approached arbitrarily closely from below by an upper semicontinuous function and also from above by a lower semicontinuous function.


σ-additivity

(mathematical analysis) countable additivity


sigma additivity

(mathematical analysis) Alternative form of σ-additivity


flasque

a flasque sheaf


equidecomposable

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

(geometry, of two forms) Capable of being decomposed into a number of pieces that can be reassembled into either of the two.


equidecomposability

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

(geometry) The quality of being equidecomposable.


subcubic

(mathematics) Having an order less than cubic


probability measure

probability measure (plural probability measures)

(mathematics) A mathematical measure on a probability space that can take on values between 0 and 1, with 0 corresponding to the empty set and 1 to the entire space.


horseshoe map

(mathematics) Any of a class of chaotic maps of the square into itself, used in the study of dynamical systems.


abelianized

(mathematics) transformed into an abelian group


effectivization

(chiefly mathematics) The process of making effective.


lumpability

lumpability (countable and uncountable, plural lumpabilities)

(mathematics) The extent to which a matrix is lumpable.


eigengap

(mathematics) The difference between successive eigenvalues.


tridiagonalization

(mathematics) The formation of a tridiagonal matrix


isocontour

(mathematics) level set; an isoline (2D) or isosurface (3D)


hypercylinder

(mathematics) A four-dimensional analog of a cylinder


orbifolding

(mathematics) The generation of an orbifold


rebin

en-verb

rebin (third-person singular simple present rebins, present participle rebinning, simple past and past participle rebinned)

rebins (present singular third-person)
rebinning (participle present)
rebinned (participle past)
rebinned (past)

(statistics, transitive) To divide (data) into a different set of bins, or interval groupings.


attowatt

(metrology) An SI unit of power equal to 10⁻¹⁸ watts. Symbol: aW


unicyclic

(graph theory, of a graph) Having a single cycle.


oblivious transfer

en-noun

oblivious transfer (plural oblivious transfers)

(cryptography) A transfer in which a sender sends some information to a receiver but does not know what is received.


polylinear

(mathematics) Involving many linear functions


sublogic

(mathematics) A subset of a system of logic


arithmetic spiral

arithmetic spiral (plural arithmetic spirals)

It is a spiral whose equation in polar coordinates is linear, which would thus, when quantized, yield an arithmetic progression.

The Parker spiral is the shape of the Sun's magnetic field as it extends through the solar system. Unlike the familiar shape of the field from a bar magnet, the Sun's extended field is twisted into an arithmetic spiral by the magnetohydrodynamic influence of the solar wind.

(mathematics) A spiral that increases in distance from the point of origin at a constant rate.


bicrossproduct

(mathematics) A group constructed from two subgroups by generalization of the direct and semidirect products.


linear operator

linear operator (plural linear operators)

(mathematics, functional analysis) An operator L such that for functions f and g and scalar λ, L (f + g) = L f + L g and L λf = λ L f.


subsum

(mathematics) The sum of a subset of values.


hypersymmetry

(mathematics) symmetry in more than two dimensions


half-plane

(mathematics) Either half of an infinite plane (divided by a straight line)


TLI

trans-lunar injection
trans-lunar injection#English

(space science) Initialism of trans-lunar injection.


GTO

geostationary transfer orbit
geostationary transfer orbit#English

(space science) Abbreviation of geostationary transfer orbit.


(astrophysics) Abbreviation of Lagrange point 3, located 180 degrees away from the smaller object and slightly outside the smaller object's orbit around the larger object.


(astrophysics) Abbreviation of Lagrange point 4, located 60 degrees ahead of the smaller object along its orbit around the larger object.


Lagrange point

Named after Joseph Louis Lagrange, who discovered the points L₄ and L₅, building on earlier work by Leonhard Euler, and in 1772 published an essay on the three-body problem.

Mathematically, the Lagrange points represent solutions to a restricted form of the three body problem in which the mass of one object is assumed negligible compared to that of the two principal bodies—as, for example, an artificial satellite and the Earth–Moon system.

Lagrange points are significant for lunar development in that raw materials, such as near-Earth objects (NEOs) can be safely stored at L-4 and L-5 prior to mining and processing.

2008, David Schrunk, Burton Sharpe, Bonnie L. Cooper, Madhu Thangavelu, The Moon: Resources, Future Development and Settlement, Springer, Praxis Publishing, page 57:

The $1.27-billion (1 billion euros) SOHO satellite was launched in 1995 and is flying a joint mission between NASA and the European Space Agency (ESA). It watches solar activity from an orbit about the Lagrange Point 1, a gravitationally stable spot between Earth and the sun that is about 932,000 miles (1.5 million kilometers) from our planet.

2013 July 28, Megan Gannon, “Spacecraft Sees Giant 'Hole' In the Sun”, in news.yahoo.com, retrieved 2013-07-29:

For science several of the Lagrange points are important. The question of access to Lagrange points or GSO slots emerges as these become congested.

2016, Francis Lyall, Paul B. Larsen, Space Law, Taylor & Francis (Routledge), page 247:

(astrophysics, orbital mechanics) A point in an orbital configuration of a two-body system where a small object affected only by gravity can theoretically be stationary relative to the two larger objects.


(astrophysics) Abbreviation of Lagrange point 5, located 60 degrees behind the smaller object along its orbit around the larger object.


cyclidic

(mathematics) of or pertaining to a cyclide


isocapacitary

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

(geometry) Having the same capacity; applied to the problem of finding an extremum for an integral over a space of a specified capacity.


capacitary

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


horocyclic

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

In two-dimensional Euclidean geometry using a polar coordinate system, horocyclic flow is either the circular convergence toward or away from a point or the rotational flow around a point.

Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic apeirogon or a hypercyclic apeirogon.

1984, Coxeter-Festschrift [Mitteilungen aus dem Mathem[atisches] Seminar Giessen], Giessen: Gießen Mathematischen Institut, Justus Liebig-Universität Gießen, page 247:

(geometry) Relating to a set of points that are all equidistant (keeping other coordinates constant) from some constant point.


Trojan point

point troyen

(astrophysics) any L4 and L5 Lagrange points

(astrophysics) the L4 and L5 Lagrange points of the Sun-Jupiter orbital configuration

point troyen

(astrophysics) by extension, any L4 and L5 Lagrange points


Trojan asteroid

Trojan asteroid (plural Trojan asteroids)

Derived from the names of the first three Trojan asteroids found (Achilles, Patroclus, Hektor)

(astrophysics) an asteroid occupying the Trojan points of the Sun-Jupiter system

(astrophysics) by extension, any asteroid occupying a Trojan point


Trojan moon

(astrophysics) A pseudo-moon that occupies a Trojan point of a system.


Trojan planet

(astrophysics) a planet that occupies a Trojan point of a star system


Lagrangian point

Lagrangian point (plural Lagrangian points)

(astrophysics) Alternative form of Lagrange point


lod

Some computer programs furnish p-values rather than maximum lod scores.

1999, Jurg Ott, Analysis of Human Genetic Linkage, →ISBN, page 66:

Markers were analysed in decreasing order of informativeness; a marker was only added to the map when it could be localized to a unique interval with a lod score of >= 3.0.

2001, Anatoly Ruvinsky, J. Sampson, The Genetics of the Dog, →ISBN, page 336:

Note that only recombinantion fractions between 0 and 0.5 are meaningful, and that all lod scores are zero at (theta)=0.5 (because they are then measuring the ratio of two identical probabilities, and log₁₀(1)=0).

2004, T. Strachan, Andrew P. Read, Human Molecular Genetics 3, →ISBN, page 406:

(statistics) Initialism of logarithm of odds. A measure of likelihood calculated by taking the log of the ratio of the probability of a hypothesis being true given the observed data over the probability that the hypothesis is false.


coquaternionic

(mathematics) Of or pertaining to coquaternions


coquaternion

(mathematics) Any of a group of elements of a type of four-dimensional vector space


hyperfunction

hyperfunction (countable and uncountable, plural hyperfunctions)

(mathematics, countable) A generalization of a function.


en-adj

3-dimensional (comparative more 3-dimensional, superlative most 3-dimensional)

more 3-dimensional (comparative)
most 3-dimensional (superlative)

Alternative spelling of three-dimensional.


4-dimensional (comparative more 4-dimensional, superlative most 4-dimensional)

more 4-dimensional (comparative)
most 4-dimensional (superlative)

Alternative spelling of four-dimensional.


2-dimensional (comparative more 2-dimensional, superlative most 2-dimensional)

more 2-dimensional (comparative)
most 2-dimensional (superlative)

Alternative spelling of two-dimensional.


polyspectrum

(mathematics) A higher-order spectrum of a multivariate stationary time series


axial point

(mathematics) Any point that lies on any of the axes of a coordinate system


biconditionality

(mathematics) The condition of being biconditional.


pseudoduality

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

(mathematics) The condition of being pseudodual


depth-first search

en-noun

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

Coordinate term: breadth-first search

(graph theory) An algorithm for traversing a tree or graph where one starts at the root and explores as far as possible along each branch before backtracking.

syvyyshaku

algorithm where one starts at the root and explores as far as possible down before going up


supertorus

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


supertoroid

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

(mathematics) Any of several surfaces related mathematically to a torus


octeract

(mathematics) An eight-dimensional hypercube


hexeract

(mathematics) A six-dimensional hypercube


hepteract

(mathematics) A seven-dimensional hypercube


enneract

(mathematics) A nine-dimensional hypercube


VSL

VSL (countable and uncountable, plural VSLs)

Forbes got more granular, contrasting the value of a statistical life (VSL) with the value of quality-adjusted life years (QALYs) to arrive at a more precise figure.

2021, Meghan O'Gieblyn, chapter 13, in God, Human, Animal, Machine […] , →ISBN:

Value of Statistical Life
w:value of life

(statistics, economics) Initialism of Value of Statistical Life, a measure of the monetary value of reducing the statistical likelihood of death in a population by a given amount.


infinite monkey theorem

(informal) The proposition that a monkey hitting typewriter keys at random is bound to produce meaningful text (such as a work by William Shakespeare), given an infinite amount of time. Often extended to a ludicrous number of monkeys, such as a thousand or an infinite number.


rule of three

(mathematics education) A rule stating that, if two ratios are equal, then the denominator of the second equals its numerator times the reciprocal of the first ratio: if a/b=c/d then d=(bc)/a.


cross-multiplication

cross-multiplication (countable and uncountable, plural cross-multiplications)

(mathematics) An instance, or the process, of cross-multiplying.

交叉相乘

an instance, or the process, or cross-multiplying


rhombicuboctahedron

rhombicuboctahedron (plural rhombicuboctahedra or rhombicuboctahedrons)

rhombicuboctahedra (plural)
rhombicuboctahedrons (plural)

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

From Latin rhombicuboctahaedron,
referring to the fact that the twelve of the square faces lie in the same planes as the twelve faces of the rhombic dodecahedron, the dual of the cuboctahedron. (See rhombicuboctahedron on Wikipedia.Wikipedia)

Therefore eight triangles and eighteen (that is, twelve and six) squares join up to make an icosihexahedron, which I call a truncated cuboctahedral rhombus or a rhombicuboctahedron.

1997, Johannes Kepler, E. J. Aiton, Alistair Matheson Duncan, Judith Veronica Field, transl., The harmony of the world, American Philosophical Society, page 119:

The gaps in a face-centered cubic packing of square sharing rhombicuboctahedra can be filled by cubes and tetrahedra (Fig. 2.4(h)).

2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 55:

So, for instance, covering up the right-hand side of our example (as in Figure 20.2(a)), we see that the rhombicuboctahedron does indeed have three types of face: two four-sided ones and one three-sided one.

2016, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 273:

small rhombicuboctahedron
small rhombicuboctahedron

(geometry) An Archimedean solid with eight triangular and eighteen square faces; the small rhombicuboctahedron.

rombikuboktaedri

polyhedron with 8 triangular and 18 square faces

斜方立方八面体

しゃほうりっぽうはちめんたい

菱形立方八面体

りょうけいりっぽうはちめんたい


gridpoint

(mathematics) Any point in the Cartesian plane with integer coordinates.


roundoff

(mathematics) The act of rounding off a number.


bicoherence

(mathematics) A squared normalised form of a bispectrum.


cutpoint

Every point of a line is a cutpoint, but no point of a circle is a cutpoint.

(topology) A point of a connected space whose removal causes the resulting space to be disconnected.


dictionary attack

dictionary attack (plural dictionary attacks)

/ˌdɪkʃənəɹi əˈtæk/

/ˌdɪkʃəˌnɛɹi əˈtæk/

Experts warn against using ordinary words as passwords as they are vulnerable to dictionary attacks.

(computing, cryptography) An attempt to illegally access a computer network, website, etc., that uses a list of words (from a dictionary) to try to guess decryption keys or passwords.

هجوم المعجم

attempt to illegally access a computer network, website, etc., that uses a list of words to try and guess decryption keys or passwords


long drink of water

long drink of water (plural long drinks of water)

/lɒŋ ˈdɹɪŋk əv ˈwɔːtə/

/lɔŋ ˈdɹɪŋk əv ˈwɔtɚ/

The term originated in the United States, and was presumably used in vaudeville performances. It was derived from earlier Scots lang drink.

Stair had grown up into a great lang drink, and would faukled, as Robin Cummell said, if he fell.

[1887, John Service, chapter XVI, in The Life and Recollections of Doctor Duguid of Kilwinning. Written by Himself, and Now First Printed from the Recovered Manuscript, Edinburgh: Young J. Pentland, →OCLC, page 103:

Other acts will include Klein, Abe and Nicholson, “the fat bellboy, the corpulent Scot and ‘the long drink of water,’” in a comedy of melody.

1915 August 1, “Photoplays, Vaudeville and outdoor amusements”, in The Washington Post, page 3, column 1:

Mr. [David] Kirkwood [Independent Labour Party member] addressed his reproof to Lord Winterton [Edward Turnour, 6th Earl Winterton], who, along with his colleagues, had protested against the defiance of the speaker's ruling. "Ye are not treating with Indians, ye big long drink of water," he shouted. Immediately the Speaker reproved the member for Dumbarton.

1924 May 10, “The Speaker defied”, in The Times, London, page 12:

American Dialect Society
Robert Wadlow
Stack Exchange


hexafoil

A design with six round semicircular petals stemming from a central circle.


empirical rule

(statistics, singular only) Synonym of the 68-95-99.7 rule


decycling

(mathematics) The removal of cycles from a graph


decycling

(mathematics) Describing the smallest number of vertices that can be removed from a graph such that no cycles remain


primorial

Blend of prime + factorial. Coined by American engineer and mathematician Harvey Dubner.

For example, up to 10⁹, every positive integer which is a multiple of a primorial and is less than the following primorial satisfies the given inequality. There has also been little discussion on which primorials qualify in the different situations when RH fails.

2017, Kevin Broughan, Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents, Cambridge University Press, page 97:

(number theory) Any number belonging to the integer sequence whose nth element is the product of the first n primes.

The primorial of 6 is #92;textstyle 6#92;#35;#61;2#92;times 3#92;times 5#61;30.

2020, Rong Pan, Qinheping Hu, Rishabh Singh, Loris D'Antoni, Solving Problem Sketches with Large Integer Values, Peter Müller (editor), Programming Languages and Systems: 29th European Symposium, Proceedings, Springer, LNCS 12075, page 587,
The following number theory result relates the primorial to the Chebyshev function.
θ(n)= log (n#)= log 2⁽¹⁺ᵒ⁽ⁿ⁾⁾ⁿ=(1+o(n))n

(number theory) A unary operation, denoted by the postfix symbol # and defined on the nonnegative integers, which maps 0 to 1, 1 to 1, and each subsequent number to the product of all primes less than or equal to it; the value mapped to by said operation for a given input.


SDG

SDG (countable and uncountable, plural SDGs)

synthetic differential geometry
w:synthetic differential geometry

(geometry) Initialism of synthetic differential geometry.


twattle

twattle (countable and uncountable, plural twattles)

Continue, if you choose, your twattle against Homœopathy; distort it, misinterpret it, calumniate and deride its author; the unprejudiced legions will soon be able to decide on which side is the truth.

1850 May, “Unjust Personalities”, in The American Journal of Homœopathy, volume 5, number 1, page 11:

It concedes too much to you Northern fellows; and all the old man said about magnanimity was mere twattle.

1860, Hezekiah Lord Hosmer, Adela, the Octoroon, page 91:

The penetrating power of that saying might atone for pages of twattle, and Carlyle has flashes of such tremendous insight as is only given to masters in literature.

1876 January, Francis Gerry Fairfield, “An Unconventional View of Herbert Spencer”, in Phrenological Journal, volume 65, number 1:

The lies, twattles, and contrivances about this affair, are innumerable.

1970, Lady Mary Wortley Montagu, James Archibald Stuart-Wortley-Mackenzie Wharncliffe (1st Baron), William Moy Thomas, The Letters and Works of Lady Mary Wortley Montagu, page 500:


distributionless

(mathematics) following no particular distribution


diperiodic

(mathematics, physics) Exhibiting two different periods simultaneously


subobject

equivalence relation
equivalence relation

(category theory) An object and a monomorphism from it to another object, which monomorphism is interpreted as an inclusion. Actually it is an equivalence class of monomorphisms to the same object, where the equivalence relation is the ability of a pair of monomorphisms to factor through each other.


pseudotriangulation

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

(mathematics) The partitioning of the plane into pseudotriangles


pseudotriangle

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

(mathematics) Any subset of a plane that lies between any three mutually tangent convex sets


convex set

(mathematics) A set which contains any convex combination of any (finite) subset of its points.


projectionless

(mathematics, of a C*-algebra) In which 0 and 1 are the only projections.


achronality

(mathematics, physics) The condition of being achronal.


regular prime

(mathematics) A prime number belonging to one of the two groups that prime numbers are divided into. The other group is the irregular primes.


irregular prime

irregular prime (plural irregular primes)

(mathematics) Any odd prime number that is not a regular prime.


geometricity

(mathematics) The condition of being geometric, or of having been geometricized.


hyperconifold

(mathematics, physics) A finite cyclic quotient of a conifold.


weighted graph

(graph theory) A graph that associates a weight (usually a real number) with every edge in the graph.


alles anderes ist Menschenwerk

A corruption of German mathematician Leopold Kronecker's finite dictum “die ganzen Zahlen hat Gott gemacht; alles andere ist Menschenwerk” : “God made the integers; everything else is the work of man”. The reason for the addition of an "s" to "andere" ("anderes" is grammatically incorrect and not present in the German phrase) is unclear.

Yet in its inadequate way it seems to gesture towards something which is closest of all to what has concerned many who have been worried about moral objectivity: the idea that there is no moral order ‘out there’ – out there, in the world, are only the sorts of things and the sorts of facts that science, and the more everyday processes of human enquiry of which science is a refinement, deal. Alles anderes ist Menschenwerk. Statement (c) [There are no moral facts; there are only the sorts of facts that science or common observation can discover, and the values that men place on those facts.] can be said – using the word in an unambitious way – to express a metaphysical view.

1972, Bernard Williams, Morality (1993 Canto edition, chapter 2: “Subjectivism: First thoughts”, pages 14–15

It would help overthrow the pernicious chauvinistic idea that, apart from certain elementary facts, Alles anderes ist Menschenwerk, all necessity, all intensionality, all value.

1980, Don S. Mannison, Michael A. McRobbie, R. Routley, Richard Sylvan, editors, Environmental Philosophy, Research School of Social Sciences Canberra Department of Philosophy, →ISBN, page 187, →ISBN:

‘Facts’ and ‘things’ are ‘out there’ in the world, alles anderes ist Menschenwerk.

1989, W. E. Morrow, Chains of Thought: Philosophical Essays in South African Education (Southern Book Publishers), page 41

“Everything else is the work of man.” “Everything else is a human construct.”


Bps

(computing) Initialism of byte per second.


convexification

convexification (countable and uncountable, plural convexifications)

(mathematics) The process of converting to convex form.


De Morgan's law

De Morgan's law (plural De Morgan's laws)

/dɨˈmɔɹɡɪnzˌlɔ/

Named after the British mathematician and logician Augustus De Morgan (1806–1871), who first formulated the laws in formal propositional logic.

Let ‘F’ stand for the state of affairs that consists in finite persons possessing and exercising free will. Let ‘p’ stand for ‘God exists’; ‘q’ for ‘F obtains’; ‘r’ for ‘F poses a serious risk of evil’; and ‘s’ for ‘There is no option available to God that counters F.’ With this in place, the argument may be formalized as follows:
(1) [(p & q) & r] → s Premiss
(2) ~s Premiss
(3) ~[(p & q) & r] 1, 2 MT
(4) ~(p & q) v ~r 3 DM
(5) r Premiss
(6) ~(p & q) 4, 5 DS
(7) ~p v ~q 6 DM
(3) follows from the conjunction of (1) and (2) by modus tollens; De Morgan’s law applied to (3) yields (4); (4) and (5) together lead to (6) by disjunctive syllogism; and another application of De Morgan’s law takes us from (6) to the final conclusion, according to which either God exists or there is free will (but not both).

2004 August, J. L. Schellenberg, “The Atheist’s Free Will Offence”, in International Journal for Philosophy of Religion, volume 56, № 1, pages 11-12:

(mathematics, logic) Either of two laws in formal logic which state that:

The negation of a conjunction is the disjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∧ 𝑞) ⇔ (¬ 𝑝) ∨ (¬ 𝑞)

The negation of a disjunction is the conjunction of the negations; expressed in propositional logic as: ¬ (𝑝 ∨ 𝑞) ⇔ (¬ 𝑝) ∧ (¬ 𝑞)

(mathematics) Either of two laws in set theory which state that:

The complement of a union is the intersection of the complements; as expressed by: (𝐴 ∪ 𝐵)′ = 𝐴′ ∩ 𝐵′

The complement of an intersection is the union of the complements; as expressed by: (𝐴 ∩ 𝐵)′ = 𝐴′ ∪ 𝐵′

(mathematics, loosely) Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀𝑥 𝑃(𝑥) ⇔ ∃𝑥 ¬𝑃(𝑥)


Game of Life

A cellular automaton devised by mathematician John Horton Conway, consisting of a grid of cells that are either "alive" or "dead" and grow or diminish based on the number of adjacent living cells.


law of cosines

(trigonometry) A generalization of the Pythagorean theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles.


ECM

ECM (countable and uncountable, plural ECMs)

elliptic curve method
elliptic curve method#English

(mathematics) Initialism of elliptic curve method.


geom.

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


coöriginal

/ˌkəʊəˈɹɪdʒənəl/

/ˌkoʊəˈɹɪd͡ʒənəl/

In operations on lines in space, it is convenient to substitute for some of the given lines other lines, equal, and therefore parallel, to the given ones, but passing through a point in space common to themselves and the other given lines; so that all the lines may be coöriginal.

1859 October (pub. 1860 October), John Daniel Runkle (editor), The Mathematical Monthly, volume II, № I, pages 29–31: W.P.G. Bartlett, “The Elements of Quaternions”, part I: “Lines”, § 4

(geometry, of a line) Originating from the same point in space.


supergeometry

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

differential geometry
differential geometry

(mathematics) A differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds


metaplectic

(mathematics) Describing a specific form of symplectic group.


orthochronous

Lorentz transformation
Lorentz transformation

Galilean transformation
Galilean transformation

(mathematics) Describing any Lorentz transformation or Galilean transformation which preserves the direction of time


homoeoid

From homoe- + -oid, from Ancient Greek: ὅμοιος (hómoios, “of like kind”, “similar”) in conjunction with εἶδος (eîdos, “form, likeness”).

(mathematics) A boundlessly thin shell constrained by a couple of similar surfaces with nearly identical orientations.


axiom of extensionality

(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements.


extensionality

extensionality (usually uncountable, plural extensionalities)

ekstensjonalność

the principle of distinguishing only by externally observable properties

(mathematics, functional analysis) The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same.

axiom of extensionality
axiom of extensionality

(mathematics, set theory) The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements.


peakon

(physics, mathematics) A soliton whose first derivative is discontinuous.


hendecahedron

hendecahedron (plural hendecahedrons or hendecahedra)

hendecahedrons (plural)
hendecahedra (plural)

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

(geometry) A polyhedron with eleven faces.


picoradian

(astronomy) A unit of solid angle equal to 10⁻¹² radians


Kronecker product

Kronecker product (plural Kronecker products)

From the surname of Leopold Kronecker (1823–1891), German mathematician.

(mathematics) The ⊗ operation (the tensor product) when applied to two matrices.


invex

Introduced by Morgan A. Hanson in 1981 as a generalization of convex.

(mathematics) Of a differentiable function f:ℝⁿ→ℝ, being such that there exists a vector valued function g such that f(x)-f(u)≥g(x,u)·∇f(u),, for all x and u.


pseudoconvex

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

(mathematics) Of a function: differentiable and increasing in any direction where it has a positive directional derivative.


pseudoconcave

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

(mathematics) (said of a function) differentiable and decreasing in any direction where it has a negative directional derivative.


coterminal

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

When you try to draw two coterminal angles on a circle, you will find that you only get one line.

(geometry, of two angles) Differing only by a whole number of complete circles.

coterminal

angle differing only by a whole number of complete circles

(category theory) Describing an object in a category, such that there is precisely one morphism that maps that object to every object in the category.


ENS

Coordinate term: DNS

The components involved in ENS loosely mimic those of DNS, with the difference that they are implemented as smart contracts within the Ethereum network.

2019, Santiago Palladino, Ethereum for Web Developers, Apress, →ISBN, page 267:

(cryptocurrencies) Initialism of Ethereum Name Service.


compositum

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

1998, Iain T. Adamson (translator), David Hilbert, The Theory of Algebraic Number Fields, [1897, D. Hilbert, Zahlbericht], Springer, page 98,
Of particular interest is the case in which the discriminants of the fields forming the compositum are relatively prime.

For #92;Q, we get the maximal abelian extension by adjoining all roots of unity, i.e., taking compositum of all m-th cyclotomic fields (this is the famous Kronecker-Weber theorem).

2004, Dinesh S. Thakur, Function Field Arithmetic, World Scientific, page 81:

This is then just the field compositum of all the quadratic extensions F(#92;sqrt#123;a#95;i#125;) in the algebraic closure of F.

2005, T. Y. Lam, Introduction to Quadratic Forms over Fields, American Mathematical Society, page 333:

(algebra, field theory) Given a field extension F/K and subextensions A and B, the smallest subextension that contains both A and B.

field compositum

smallest subextension of a given field extension that contains two given subextensions


Pepsi paradox

(rare) The statistical and psychological observation that a person is prone to prefer Coca-Cola over Pepsi when they have labels, but prone to prefer Pepsi over Coca-Cola when they are unlabelled.


contragredient

Neologism based on Latin contra and gradi.

(mathematics) Generally, denoting an object inversed and transposed (to another).

(mathematics) Of a representation in linear algebra: being the transpose of the former representation of an inverse object.

(mathematics) Of a matrix: being a transpose of an inverse matrix.


cryptoprocessor

(cryptography) A dedicated computer on a chip or microprocessor that carries out cryptographic operations.


erasure code

(information theory) A forward-error-correction (FEC) code for the binary erasure channel, which transforms a message of k symbols into a longer message with n symbols such that the original message can be recovered from a subset of the n symbols.


oblongum

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

(geometry, archaic) A prolate spheroid; a figure described by the revolution of an ellipse about its greater axis.


fixpoint

It feels like I've stepped through the looking glass and am wandering in a topsy-turvy world where the fixpoints we have lived with for decades have gone. Not just moved... gone.

2020 June 3, Stefanie Foster, “Comment: The recovery starts here”, in Rail, page 3:


subrepresentation

(mathematics, representation theory) Given a representation (W,ψ) of (say) a group G, a linear subspace of W which is preserved by the action of G in the sense that g · v ∈ V for all v ∈ V.


belinkedness

(mathematics) The number of times one branch of a link must be passed through the other in order to undo it.


coinitial

(mathematics, of a subset) Having an element b for each element a in the superset such that b is less than or equal to a.


glider gun

But in one position and phase of a 2-bee shuttle (the standard glider gun), the debris evolves into a glider and sails away before the bees return.

1989 October 31, Scott Huddleston, “life: glider guns”, in comp.theory.cell-automata (Usenet):

Alas this transformation by itself increases traversal length of the circuit because these new glider guns are much larger.

1998, M. Delorme, Jacques Mazoyer, Cellular automata: a parallel model, page 64:

In particular, since those two patterns extend their repetitions endlessly to the left and right, there is no need for a "glider gun" to provide a continuous supply of new patterns, as you suggest.

2005 January 2, Kent Dolan, “Re: Smaller UTM than Rule110”, in comp.theory.cell-automata (Usenet):

(cellular automata) In the Game of Life, any pattern that "fires" out gliders.


hemicube

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

(geometry) An abstract regular polyhedron containing half the faces of a cube.


pre-Hilbert space

pre-Hilbert space (plural pre-Hilbert spaces)

(mathematics) An incomplete metric space with an inner product.


jth

An arc labelled a over-crossing one labelled b has jᵗʰ coordinate (-1)#92;frac#123;a#43;b-j#125;#123;2#125;#92;Delta#95;j#92;theta(a,b,j)#123;-1#125;A#123;a#43;b-j#43;(a²#43;b²-j²)#47;2#125; with respect to base #92;#123;#91;(a,b)j(a,b)#93;#92;#125;.

2009 February, W. B. Raymond Lickorish, “WHAT IS... a Skein Module?”, in Notices of the American Mathematical Society, volume 56, number 2, →ISSN, page 242:

(mathematics) Occurring at position j in a sequence.


soficity

Description: This workshop will examine the influx of new ideas, trends, and advances in geometric group theory with focus on: (1) analysis (Baum-Connes conjecture, Kazhdan’s property, amenability, soficity, rapid decay); (2) statistics (random walks, random subgroups, percolation, generic properties of groups); and (3) geometry (Cannon conjecture, boundaries, BNS invariants, bounded (co)-homology of groups, isoperimetric functions).

2009 August 20, Notices of the American Mathematical Society, volume 56, number 7:

(mathematics) The quality of being sofic.


automorphy

Gisele Massengo Mophou*, Universit´e des Antilles et de la Guyanne (Campus de Fouillole), and Ousseynou Nakoulima, Universite des Antilles et de la Guyane (Campus de Fouillole) (1046-93-961) 10:00AM (1460) Stepanov-like almost automorphy and monotone evolution equations.

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

(mathematics) The property of being automorphic.


cross-ratio

(geometry) A special number associated with an ordered quadruple of collinear points, particularly points on a projective line, and preserved by the fractional linear transformations.

birapport

a special number associated with an ordered quadruple of collinear points, particularly points on a projective line, and preserved by the fractional linear transformations