monogon

A geodesic with multiple points contains at least one simple monogon.

1955, Herbert Busemann, The Geometry of Geodesics, page 295:

There are no one-sided closed polygons on a plane. On the cube, however, monogons are a diverse and interesting class of figures.

1981, Harold Abelson, Andrea A. DiSessa, Turtle Geometry: The Computer As a Medium for Exploring Mathematics, →ISBN, page 262:

2003, Gordon Baker, translator and editor, Ludwig Wittgenstein and Friedrich Waismann, The Voices of Wittgenstein: The Vienna Circle, Routledge, →ISBN, page 409,
We explain to somebody what is a regular quadrilateral constructed within the circle; then a regular triangle and a regular bi-angle. Now we ask him to draw a regular monogon by analogy, and we probably think that he cannot do this. But what if he draws a point on the circle and says that it is a regular monogon?

(geometry) A one-dimensional object comprising one vertex and one (not necessarily straight) edge both of whose ends are that vertex.

According to Theorem 4.1.1, such a derived imbedding could be obtained from an imbedded voltage graph with one vertex, 6s#43;2 edges, and 4s#43;2 faces. Of these faces, 4s#43;1 should be 3-sided and satisfy KVL. The other face should be a monogon whose net voltage has order two.

1987, Jonathan L. Gross, Thomas W. Tucker, Topological Graph Theory, Dover Publications, published 2001, →ISBN, page 231:

2002, Tao Li, "Laminar Branched Surfaces in 3–manifolds", Geometry & Topology 6, page 158,
There is no monogon in M-int(N(B)), ie, no disk D⊂M-int(N(B)) with ∂D=D∩N(B)=α∪β, where α⊂∂_(vN)(B) is in an interval fiber of ∂_(vN)(B) and β⊂∂_(hN)(B).

a. 2006, Thilo Kuessner, "A survey on simplicial volume and invariants of foliations and laminations", in, Paweł Walczak, et al., editors, Foliations 2005, →ISBN, page 295,
An end-compressing monogon for F is a monogon properly embedded in the complimentary region C which is not homotopic (rel. boundary) into ∂C.

(geometry) A two-dimensional object comprising one vertex, one edge both of whose ends are that vertex, and one face filling in the hollow formed by that edge.


digon

From di- (prefix meaning ‘two’) + -gon (suffix forming the names of plane figures containing a given number of angles).

confix

monogon · digon · trigon · tetragon · pentagon · hexagon · heptagon · octagon · nonagon · decagon · undecagon · dodecagon · see also Category:English terms suffixed with -gon

They [the students] also came upon new and unusual mathematical figures: the digon, a two-sided polygon on a spherical space, and the apeirogon, an open polygon with infinitely many sides […]. All these discoveries brought up even more questions. Is a circle a polygon? What makes an octagon an octagon – its eight vertices, its eight sides, or both? Can a polygon cross itself? Does a polygon need to be closed?

2013, Brent Davis, Moshe Renert, chapter 6, in The Math Teachers Know: Profound Understanding of Emergent Mathematics, New York, N.Y., Abingdon, Oxfordshire: Routledge, →ISBN, page 102:

(geometry) A polygon having two edges and two vertices.

digono

A pair of parallel undirected edges in a multigraph.

A pair of antiparallel edges in a directed graph.


tridecagon

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(geometry) A polygon having thirteen sides and thirteen angles.


tetradecagon

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(geometry) A polygon having fourteen sides and fourteen angles.


tetrakaidecagon

a polygon having fourteen sides and fourteen angles


apeirogon

/əˈpiːɹɵɡɑn/

/əˈpeɪ̯ɹɵɡɑn/

Hence the regular polygon ABCD ... can either be a convex n-gon, a star n-gon, a horocylic^([sic – meaning horocyclic]) 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:

In geometry, an apeirogon is a limiting case of a regular polygon. The number of sides in an apeirogon is becoming infinite, so the apeirogon as a whole approaches a circle. A magnified view of a small piece of the apeirogon looks like a straight line.

1994, Steven Schwartzman, The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Washington, D.C.: Mathematical Association of America, →ISBN, page 27:

[A]n apeirogon (infinite regular polygon) is a linear one {∞}, a planar (skew) one (zigzag apeirogon), which is the blend {∞} # { } with a segment, or helix, which is a blend of {∞} with a bounded regular polygon.

2002, Peter McMullen with Egon Schulte, Abstract Regular Polytopes, Cambridge: Cambridge University Press, →ISBN, page 217:

There are exactly 12 regular apeirohedra that in some sense are reducible and have components that are regular figures of dimensions 1 and 2. These apeirohedra are blends of a planar regular apeirohedron, and a line segment { } or linear apeirogon {∞}. This explains why there are 12 = 6·2 blended (or non-pure) apeirohedra. For example, the blend of the standard square tessellation {4,4} and the infinite apeirogon {∞}, denoted {4,4}#{∞}, is an apeirohedron whose faces are helical apeirogons (over squares), rising above the squares of {4,4}, such that 4 meet at each vertex; the orthogonal projections of {4,4}#{∞} onto their component subspaces recover the original components, the square tessellation and the linear apeirogon.

2014, Daniel Pellicer with Egon Schulte, “Polygonal Complexes and Graphs for Crystallographic Groups”, in Robert Connelly, Asia Ivić Weiss, Walter Whiteley, editors, Rigidity and Symmetry, New York, N.Y.: Springer, →ISBN, page 331:

(mathematics, geometry) A type of generalised polygon with a countably infinite number of sides and vertices;

A type of generalised polygon with a countably infinite number of sides and vertices;
(in the regular case) the limit case of an n-sided regular polygon as n increases to infinity and the edge length is fixed; typically imagined as a straight line partitioned into equal segments by an infinite number of equally-spaced points.


zerogon

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(geometry) A circle visualized as a polygon having no edges or vertices.


polar equation

(mathematics) An equation defining a curve in terms of radius and angle.


asymptotically

The value grew asymptotically.

mathematical analysis
mathematical analysis

(mathematical analysis) In an asymptotical manner, in the way of an asymptote, toward an asymptote.

مُتَقَارِباً

(analysis) in an asymptotical manner, in the way of an asymptote


dynamical system

en-noun

dynamical system (plural dynamical systems)

(mathematics, physics) A system which is time-dependent.


onça

From Portuguese onça, from Latin uncia (“unit, ¹⁄₁₂ pound”), ultimately from Proto-Indo-European *óynos (“one”).

(historical) A traditional Portuguese unit of mass, usually equivalent to 28.7 g.


Markov process

Markov process (plural Markov processes)

Named after Russian mathematician Andrey Markov (Андре́й Андре́евич Ма́рков) (1856—1922), who researched the processes.

It has been remarked in 1 that a Markov process with time reversal is again a Markov process.

2007, N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edition, page 81:

The second part is written for probabilists and it studies the case where fast motions are certain Markov processes such as random evolutions and, in particular, diffusions.

2009, Yuri Kifer, “Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging”, in Memoirs of the American Mathematical Society, number 944, page vii:

2013, M. G. Shur, Markov Process, entry in Michiel Hazewinkel (editor), Encyclopaedia of Mathematics, Volume 6, page 102,
In the theory of Markov processes most attention is given to homogeneous (in time) processes.

conditional probability distribution
conditional probability distribution

(probability theory) Any stochastic process for which the conditional probability distribution of future states depends only on the current state (and not on past states).


algebraic structure

algebraic structure (plural algebraic structures)

(algebra, universal algebra) Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra.


Gaussian

en-adj

Gaussian (comparative more Gaussian, superlative most Gaussian)

more Gaussian (comparative)
most Gaussian (superlative)

The problem of inversion of the mgf/chf of a sum of lognormals to obtain the CDF/pdf is considered with special reference to methods related to Post Widder technique, Gaussian quadrature and the Fourier series method.

2016, N B Chakrabarti, “A Note on a Sum of Lognormals”, in arXiv:

(mathematics) Of or pertaining to Carl Friedrich Gauss.

The criterion for positivity was determined for each antigen of each species applying a mixture model to the PP data which assumed two inherent Gaussian distributions: a narrow distribution or seronegatives, and a broader distribution of seropositives.

2015 September 11, “Hotspots of Malaria Transmission in the Peruvian Amazon: Rapid Assessment through a Parasitological and Serological Survey”, in PLOS ONE, →DOI:


Gaussian

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

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


exponential equation

en-noun

exponential equation (plural exponential equations)

(mathematics) A type of equation which includes a variable located in the exponent; for example, eˣ=1,.


French curve

A drafting template having edges of various curvatures, used for drawing smoothly-curved lines.


inner product

(linear algebra) A generalization of the dot product for vectors of any dimensionality that may or may not be complex-numbered.


Riemann

(mathematics) Pertaining to the mathematician Bernhard Riemann.


basin of attraction

basin of attraction (plural basins of attraction)

(mathematics, physics) Informally, a set of points from which a dynamical system spontaneously moves to a particular attractor.


magic cube

(number theory) By analogy with magic square, an n-by-n-by-n arrangement of n³ numbers such that the numbers in each row, in all columns (horizontal and vertical) and in all main diagonals (of which there are 6*n+4) each have the same sum.


conjugator

Equation (10.9) represents the reflection coefficient of the phase conjugation and can be used to design phase conjugators.

1994, Chai Yeh, Applied Photonics, Academic Press, →ISBN, page 204:

Many different configurations of self-pumped phase conjugators relying on four-wave mixing to produce a phase-conjugate wave have been reported.

1995, Marvin J. Weber, CRC Handbook of Laser Science and Technology Supplement 2: Optical Materials, CRC Press, →ISBN, page 450:

Thus, for using such an attack, one should choose a good length function on Bₙ and run it iteratively until he gets the correct conjugator.

2010, David Garber, “Braid Group Cryptography”, in A. Jon Berrick, Frederick R. Cohen, Elizabeth Hanbury, Yan-Loi Wong, Jie Wu, editors, Braids: Introductory Lectures on Braids, Configurations and Their Applications (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore; 19), World Scientific, →ISBN, page 373:

(mathematics) A function g, such that there is a conjugation mapping x to gxg⁻¹.


(astrophysics) Abbreviation of Lagrange point 1, located between the larger and smaller objects along a line connecting the two.


Coordinate term: L1

That is, for almost all late second language (L2) learners, the phonetic realization of phonological structures in the L2 is markedly different from native-language patterns.

2008, Jette G. Hansen Edwards, Mary L. Zampini, Phonology and Second Language Acquisition, John Benjamins Publishing, →ISBN, page 153:

This advantage was pertinent in the Hong Kong context where English is largely an L2 language, although would not be expected to be as large in an L1 context.

2017, Di Zou, James Lambert, “Feedback methods for student voice in the digital age”, in British Journal of Educational Technology, volume 48, number 5, page 1085:

A second language (a language being learned, as opposed to a mother tongue).


machine learning

artificial intelligence
artificial intelligence

(artificial intelligence) The ability of computers to learn without being explicitly programmed.

Much of today’s AI-related technologies are powered by machine learning.
Audio (US): (file)

2019 February 3, “UN Study: China, US, Japan Lead World AI Development”, in Voice of America, archived from the original on 2019-02-07

(artificial intelligence) A field of study concerned with the design and development of algorithms and techniques that allow computers to learn.


computer vision

The single most popular AI technology identified in the report was computer vision.
Audio (US): (file)

(artificial intelligence) The science and technology of machines that see, concerned with the theory for building artificial systems that obtain information from images, such as a video sequence, views from multiple cameras, or multi-dimensional data from a medical scanner.


PSU

(statistics) Initialism of primary sampling unit, a sampling unit in the first stage of a polyetapic sampling.


weighted mean

Coordinate term: arithmetic mean

(arithmetic) An average calculated after biasing values according to agreed weightings.


tetrakis-

Borrowed from Ancient Greek τετράκις (tetrákis, “four times”).

bor

(mathematics) Synonym of tetra- used for multiplication with a second numerical prefix.


étale

First applied in a mathematical context (in French) by Alexander Grothendieck to étale morphisms, apparently with reference to the phrase mer étale ("the sea at high or low tide"), the connection being that étale morphisms are, in an intuitive sense, calmly behaved or "spread out."

Recall (Hartshorne [1977]) that a morphism ψ: U → V is called étale if it is étale at each point u ∈ U , where being étale at u means that the natural homomorphism of local ring completions ψ*: Ô_(ψ(u)) (V) → Ôᵤ(U) is an isomorphism.

1994, Aleksei Parshin, Igor Shafarevich, Algebraic Geometry IV: Linear Algebraic Groups Invariant Theory, page 278:

Because every Deligne-Mumford stack admits an étale cover π : U → 𝔛 by a scheme, to give a sheaf of sets F on the étale site of 𝔛 is equivalent to giving a sheaf F_U together with an isomorphism between the two pull-backs of F_U to U ×_𝔛 U satisfying the cocycle condition of [26] 12.2.1.

2009, Rob de Jeu, James Dominic Lewis, Motives and Algebraic Cycles: A Celebration in Honour of Spencer J. Bloch, page 96:

We will be interested in étale maps between stacks and étale covers of stacks.

2014, Christopher Douglas, John Francis, André Henriques, Michael Hill, Topological Modular Forms, page 53:

For a scheme X, let Ét(X) be the category of all étale morphisms from a scheme to X. An étale presheaf on X is a contravariant functor from Ét(X) to the category of sets.

2016, Thierry Vialar, Handbook of Mathematics, page 825:

(mathematics) Such that the natural homomorphism is an isomorphism.


superposition principle

(mathematics, physics) The principle stating that for a linear system, the net response is the sum of the response associated with each individual input.

principe de superposition

the principle stating that for a linear system, the net response is the sum of the response associated with each individual input


Brahmagupta's formula

(mathematics) A particular expression for the area of a quadrilateral.


mean

From Middle English meene, borrowed from Old French meien (French moyen), Late Latin mediānus (“that is in the middle, middle”), from Latin medius (“middle”). Cognate with mid. For the musical sense, compare the cognate Italian mezzano. Doublet of median and mizzen.

cog

(statistics) The average of a set of values, calculated by summing them together and dividing by the number of terms; the arithmetic mean.

Note that (1.41) is simply the probability-weighted mean without any explicit allowance for the stratification; each observation is weighted by its inflation factor and the total divided by the total of the inflation factors for the survey.

1997, Angus Deaton, The Analysis of Household Surveys: A Microeconometric Approach to Development Policy, World Bank Publications, page 51

Luckily, even though the arithmetic mean is unusable, both the harmonic and geometric means settle to precise values as the amount of data increases.

2002, Clifford A. Pickover, The Mathematics of Oz: Mental Gymnastics from Beyond the Edge, Cambridge University Press, →ISBN, page 246:

The generalized power means include power means, certain Gini means, in particular the counter-harmonic means.

2003, P. S. Bullen, Handbook of Means and Their Inequalities, Springer, →ISBN, page 251:

measure of central tendency
measure of central tendency

(mathematics) Any function of multiple variables that satisfies certain properties and yields a number representative of its arguments; or, the number so yielded; a measure of central tendency.

...if four numbers be in proportion, the product of the first and last, or of the two extremes, is equal to the product of the second and third, or of the two means.

1825, Silvestre François Lacroix, translated by John Farrar, An Elementary Treatise on Arithmetic, third edition, page 102:

Using the means-extremes property of proportions, you know that the product of the extremes equals the product of the means. The ratio t/4 = 5/2 can be rewritten as t:4 = 5:2, in which the extremes are t and 2, and the means are 4 and 5.

1999, Dawn B. Sova, How to Solve Word Problems in Geometry, McGraw-Hill,, →ISBN, page 85:

In #92;frac#123;18#125;#123;27#125;#61;#92;frac23, the product of the means is 2#92;cdot27, and the product of the extremes is 18#92;cdot3. Both products are 54.

2007, Carolyn C. Wheater, Homework Helpers: Geometry, Career Press,, →ISBN, page 99:

(mathematics) Either of the two numbers in the middle of a conventionally presented proportion, as 2 and 3 in 1:2=3:6.

keskimmäinen jäsen

mathematics: either of the two numbers in the middle of a conventionally presented proportion


fat

en-adj

fat (comparative fatter, superlative fattest)

fatter (comparative)
fattest (superlative)

Of sense: lean

carrying a larger than normal amount of fat; antonym(s) of

Sranan Tongo: fatu

From Middle English fat, from Old English fǣtt (“fatted, fat”), from Proto-West Germanic *faitid (“fatted”), originally the past participle of the verb *faitijan (“to make fat”), from *fait (“fat”).

chubby

fat client

a fat pointer

(computing) Carrying additional data or functionality.


fat

From Middle English fat, from Old English fæt (“vat, vessel, jar, cup, casket, division”), from Proto-Germanic *fatą (“vessel”), from Proto-Indo-European *pod- (“vessel”). Cognate with Dutch vat (“barrel, vessel”), German Fass (“barrel, drum”), Swedish fat (“barrel, dish, cask”). See vat.

inh

(obsolete) A dry measure, generally equal to nine bushels.


achiral

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(geometry, physical chemistry) superimposable on its mirror image; amphichiral


amphichiral

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(geometry, physical chemistry) superimposable on its mirror image; achiral


darcy

From the surname of the French scientist Henry Darcy.

A (non SI) unit of permeability used in measuring the permeability of porous mediums such as sand.


free group

Given a set S of "free generators" of a free group, let S⁻¹ be the set of inverses of the generators, which are in one-to-one correspondence with the generators (the two sets are disjoint), then let (S∪S⁻¹)^* be the Kleene closure of the union of those two sets. For any string w in the Kleene closure let r(w) be its reduced form, obtained by cutting out any occurrences of the form xx⁻¹ or x⁻¹x where x∈S. Noting that r(r(w)) = r(w) for any string w, define an equivalence relation ∼ such that u∼v if and only if r(u)=r(v). Then let the underlying set of the free group generated by S be the quotient set (S∪S⁻¹)^*/∼ and let its operator be concatenation followed by reduction.

A subset A of a free group F is called "separable" when there is a non-trivial free factorization F = F₁ * F₂ such that each element of A is conjugate to an element of F₁ or of F₂.

1999, John R. Stallings, “Whitehead graphs on handlebodies”, in John Cossey, Charles F. Miller, Michael Shapiro, Walter D. Neumann, editors, Geometric Group Theory Down Under: Proceedings of a Special Year in Geometric Group Theory, Walter de Gruyter, page 317:

2002, Gilbert Baumslag, B.9 Free and Relatively Free Groups, Alexander V. Mikhalev, Günter F. Pilz, The Concise Handbook of Algebra, Kluwer Academic, page 102,
The free groups in V then all take the form H/V(H), where H is a suitably chosen absolutely free group.

The context for generators and relations is that of a free group on the set of generators, and the relations indicate passage to a quotient of this free group by a normal subgroup.

2006, Anthony W. Knapp, Basic Algebra, Springer, page 303:

(group theory) A group that has a presentation without relators; equivalently, a free product of some number of copies of ℤ.

frjáls grúpa

group whose presentation consists of generators


free product

(mathematics) A group formed from others by concatenating their presentations (when those presentations are written with disjoint sets of generators).


relator

(group theory) An expression of the identity element of a group as a product of generators, used in a presentation (type of specification) of the group.


TEU

twenty-foot equivalent unit
twenty-foot equivalent unit#English

Initialism of twenty-foot equivalent unit.


homomorphic

en-adj

homomorphic (comparative more homomorphic, superlative most homomorphic)

more homomorphic (comparative)
most homomorphic (superlative)

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

Coordinate term: homologous

If it is necessary or desirable to preserve input or output port structure in homomorphic images, one must insist on a special case of homomorphism.

1993, A. Wayne Wymore, Model-Based Systems Engineering, CRC Press, →ISBN, page 182:

In this chapter two types of signature schemes satisfying homomorphic properties are presented. In the first section a description of the homomorphic signature schemes suitable in the single-user scenario is provided.

2016, Giulia Traverso, Denise Demirel, Johannes Buchmann, Homomorphic Signature Schemes: A Survey, Springer, →ISBN, page 11:

(algebra, biology) Of or pertaining to homomorphism; having a homomorphism.


age distribution

en-noun

age distribution (plural age distributions)

(statistics) The number of people in stated age ranges.

年齡分佈 /年龄分布

the number of people in stated age ranges


expander

(graph theory) A kind of sparse graph with strong connectivity properties.


Nash equilibrium

Nash equilibrium (plural Nash equilibria)

Named after American mathematician John Forbes Nash Jr.

named-after

(game theory) The set of choices of players' strategies for which no player can benefit by changing his or her strategy assuming that the other players keep theirs unchanged.


Pareto improvement

en-noun

Pareto improvement (plural Pareto improvements)

(game theory, economics) A change in the allocation of a resource to a set of individuals that is an improvement for at least one and no worse for any other.


Pareto efficient

en-adj

Pareto efficient (comparative more Pareto efficient, superlative most Pareto efficient)

more Pareto efficient (comparative)
most Pareto efficient (superlative)

(game theory, economics) Describing a situation in which the profit of one party cannot be increased without reducing the profit of another.


Pareto optimal

(game theory) Describing a strategy that cannot be made to perform better against one opposing strategy without performing less well against another.


Shapley value

Named in honour of Lloyd Shapley, who introduced it in 1953.

ϕᵢ(v)=∑_(S⊆N⧵i)(|S|!;(n-|S|-1)!)/(n!)(v(S∪i)-v(S)),

given a coalitional game with a set N of n players and a worth function v;:;𝒫(N);→ℜ.

(game theory) A real number determined for the player i as


normal form game

en-noun

normal form game (plural normal form games)

(game theory) Formally, a structure (P, mathbf S, mathbf F) where P = {1,2, ...,m} is a set of players, mathbf S=(S_1,S_2,…,S_m) is an m-tuple of pure strategy sets, one for each player, and mathbf F=(F_1,F_2,…,F_m) is an m-tuple of payoff functions.


extensive form game

extensive form game (plural extensive form games)

(game theory) Informally, a representation of a game as a tree of decision nodes, with the game beginning at a unique initial node, and flowing through the tree along a path determined by the players until a terminal node is reached, where play ends and payoffs are assigned to all players; each non-terminal node belongs to a player; that player chooses among the possible moves at that node, each possible move is an edge leading from that node to another node.


cooperative game

cooperative game (plural cooperative games)

characteristic function
characteristic function

(game theory) Informally, a game formalized using a function (called the characteristic function) that assigns to each coalition of players a real number representing the payoff that the coalition can gain if it is formed, without specifying how the outcome is divided among the participants of the coalition; upon the execution of the game, each player can be a member of at most one coalition.


biaxial

(mathematics, astronomy) Having two axes of rotation and two planes of symmetry (e.g. having the shape of a spheroid)


cylindrically

en-adv

cylindrically (comparative more cylindrically, superlative most cylindrically)

more cylindrically (comparative)
most cylindrically (superlative)

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


diagonalize

en-verb

diagonalize (third-person singular simple present diagonalizes, present participle diagonalizing, simple past and past participle diagonalized)

diagonalizes (present singular third-person)
diagonalizing (participle present)
diagonalized (participle past)
diagonalized (past)

(mathematics, transitive) To convert a square matrix into a diagonal matrix by multiplying it by a second matrix and its inverse.

diagonaliseren

convert square matrix into diagonal matrix


binary distribution

en-noun

binary distribution (plural binary distributions)

Bernoulli distribution
Bernoulli distribution

(statistics, probability theory) Bernoulli distribution.


microarcsecond

A unit of angle; one millionth (10⁻⁶) of an arcsecond.

mikrokaarisekunti

a unit of angle; one millionth (10−6) of an arcsecond


crossing number

crossing number (plural crossing numbers)

(mathematics) The minimum, taken over all planar representations of a link or graph, of the number of times it crosses itself.

Zarankiewicz's crossing number conjecture


cobordism

(mathematics) A connection between two manifolds of the same dimension n via a manifold of dimension n+1, where the smaller manifolds are included in the boundary of the larger manifold.

2008 April, John R. Harper, "Generalized cohomology, by Akira Kono and Dai Tamaki" (book review), Bulletin (New Series) of the American Mathematical Society volume 45 number 2, page 310,
Cobordism revives the intuitive idea of bounding harbored in the original work of Poincaré but later sacrificed in order to construct a viable theory based on simpicial complexes.

(mathematics) The theory and study of such objects.


Eilenberg-MacLane space

Eilenberg-MacLane space (plural Eilenberg-MacLane spaces)

After Samuel Eilenberg and Saunders Mac Lane (or MacLane), who invented the concept.

(mathematics) A topological space that has precisely one nontrivial homotopy group.


Fuchsian group

First studied by Henri Poincaré (1882), who was motivated by the work of Lazarus Fuchs (1880) and therefore named them after him.

(mathematics) Any discrete group of isometries of the hyperbolic plane.


hyperbolic plane

hyperbolic plane (plural hyperbolic planes)

(mathematics) A topological space homeomorphic to a plane (or open disk) and equipped with a hyperbolic metric.


isotopy

(mathematics) A form of homotopy that is always an embedding.


centrosymmetric

(mathematics) Having a centre of symmetry.


centre of symmetry

centre of symmetry (plural centres of symmetry)

(mathematics) A point, within an object or figure, through which any straight line also passes through two points on the edge of the figure at the same distance from the centre but on opposite sides.


diagonalized

(mathematics) Converted into a diagonal matrix


differentially

(mathematics) With regard to differentiation


orthogonality

In this chapter we develop one of the key concepts in the geometry of the vector space Rⁿ, namely, the concept of orthogonality of vectors.

1984, John Wesley Brown, Donald R. Sherbert, Introductory Linear Algebra with Applications, Prindle Weber & Schmidt, →ISBN:

Suppose we have an imaginary pair of axes with a set of comparable language entities on one and a set of attributes or capabilities on the other. When we talk of “orthogonality”, we usually mean that the space defined by these axes is as “full” as we can logically make it. Part of the Ruby way is to strive for this orthogonality.

2015, Hal Fulton, André Arko, The Ruby Way […] , Addison-Wesley Professional, →ISBN, page xl:

software engineering
software engineering

(mathematics, statistics, software engineering) The property of being orthogonal.


nonabsorbing

en-adj

nonabsorbing (comparative more nonabsorbing, superlative most nonabsorbing)

more nonabsorbing (comparative)
most nonabsorbing (superlative)

To interprest the results given by the fundamental matrix, recall that the nonabsorbing states are states 3 and 4.

1991, Robert E. Markland, Topics in Management Science, page 553:

A matrix C where C = NR determines the probability that the chain will enter a particular absorbing state having begun in a given nonabsorbing state.

2015, Carla C. Morris, Robert M. Stark, Finite Mathematics: Models and Applications, page 307:

Starting in a nonabsorbing state i, the chain will eventually be absorbed into absorbing state a if either (1) the chain transitions immediately into ''a, or (2) the chain transitions into any nonabsorbing state and then eventually is absorbed into state a.

2020, Matthew A. Carlton, Jay L. Devore, Probability with STEM Applications, page 453:

(mathematics) That permits a transition to a different state.


nondegenerate

In fanciful language, if our universe is nondegenerate, then so will be almost every world in it.

1995, Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green, Microeconomic Theory, Oxford University Press, page 595:


nondegenerate

(mathematics, physics) An instance or configuration that is not degenerate.


sinusoid

From the French sinusoïde, equivalent to sinus + -oid.

Temperature during the week can be represented with a sinusoid.

(mathematics) A curve having the shape of a sine wave.


sinusoid

sinusoid (comparative more sinusoid, superlative most sinusoid)

more sinusoid (comparative)
most sinusoid (superlative)


subindex

en-noun

subindex (plural subindexes or subindices)


CX

CX (countable and uncountable, plural CXes)

(cryptocurrencies) Abbreviation of cryptocurrency.


domain theory

partially ordered set
partially ordered set

(mathematics) A branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains.


coline

hyperplanes concurrent in a coline

1995, Ronald L. Graham, Martin Grötschel, László Lovász, Handbook of Combinatorics: Volume 1, page 831:


knotting

knotting (countable and uncountable, plural knottings)

(chiefly mathematics) The formation of a knot.


circumcenter

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(geometry) The center of a circumcircle (the circle that passes through every vertex of a given triangle or other cyclic polygon).


triangular prism

triangular prism (plural triangular prisms)


common denominator

common denominator (plural common denominators)

least common denominator

lowest common denominator

(mathematics) Any integer that is a common multiple of the denominators of two or more fractions.

ümumi məxrəc

any integer that is a common multiple of the denominators of two or more fractions


syndetic

asyndetic

antonym(s) of “grammar & library science”

From Latin syndeticus, from Ancient Greek συνδετικός (sundetikós), from σύνδετον (súndeton, “syndeton, use of conjunctions, a binding”) + -ικός (-ikós, “-ic: forming adjectives”), the neuter substantive of σῠ́νδετος (sŭ́ndetos, “bound, joined”), from συνδεῖν (sundeîn, “to join, to bind”), from σῠν- (sŭn-, “together”) + δεῖν (deîn, “to bind, to tie”). Equivalent to syndeton + -ic.

The gap between successive members of a syndetic set may vary but is always less than some specific value: i.e., there is an integer n such that {x,x+1,x+2,⋯,x+n}∩S≠∅ for any x∈N.

(mathematics) Having bounded gaps between its terms.


confounder

confounding variable
confounding variable

(mathematics) A factor, in data analysis, that causes the effects of two distinct processes to be indistinguishable; a confounding variable


biquadratic

(mathematics) Of a polynomial expression, involving only the zeroth, second, and fourth powers of a variable, as x⁴ + 3x² + 2. Sometimes extended to any expression involving the biquadrate or fourth power (but no higher powers), as x⁴ − 4x³ + 3x² − x + 1.


multifactorial

(mathematics) A generalization of a factorial in which each element to be multiplied differs from the next by an integer (e.g. n(n-3)(n-6)(n-9)...).


multivariate

(mathematics) A vector, each of whose elements is a variate.


nanosized

en-adj

nanosized (comparative more nanosized, superlative most nanosized)

more nanosized (comparative)
most nanosized (superlative)


probit

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Blend of probability + unit. Coined by Chester Ittner Bliss in 1934: “These arbitrary probability units have been termed ‘probits’…”

standard distribution
standard distribution

(statistics) A unit, derived from a standard distribution, used in measuring the responses to doses

The probit function, the inverse of the cumulative distribution function.


Xer

Many Xers sport piercings in their noses or navels.

We Xers have a love-hate relationship with our entertainment media.

1995, Kevin Graham Ford, Jim Denney, Jesus for a New Generation: Putting the Gospel in the Language of Xers:

Ellipsis of Gen-Xer.; a member of Generation X.


diverter

The diverter clearly gains from a successful diversion but pays a heavy price if caught.

2012, Morton D. Davis, Game Theory: A Nontechnical Introduction, page 47:

The game theory also requires a precise statement of all the conceivable moves the diverter might make and counter-moves available to the defender.

1980, LBL Newsmagazine, volumes 5-9, page 20:

(game theory) One who uses diversionary tactics.


geostatistics

(geology, mathematics) The application of statistics to geological observations


semivariance

(statistics) A measure of the dispersion of those values that fall below the mean or target value of a data set


semivariogram

(statistics) A function of the spatial dependence of semivariance; a graph of this function.


variogram

(statistics) A function of the spatial dependence of variance; a graph of this function

variograma

a function of the spatial dependence of variance; a graph of this function


uncorrelated

uncorrelated (comparative more uncorrelated, superlative most uncorrelated)

more uncorrelated (comparative)
most uncorrelated (superlative)

(statistics) Having a covariance of zero


timeweighted

(statistics) Describing a statistic (especially an average) in which some time periods are given more weight than others.


gyroid

Coordinate term: lattice

(mathematics) An infinitely connected periodic minimal surface containing no straight lines.


minimal surface

en-noun

minimal surface (plural minimal surfaces)

(mathematics) Any surface that has the least possible surface area of those into which it could transform; typically the shapes of soap bubbles that span wire frames

(mathematics) Any surface of vanishing mean curvature. Includes, but is not restricted to, surfaces of minimal area, as given by some boundary conditions.


mediatrix

mediatrix (plural mediatrices or mediatrixes)

mediatrices (plural)
mediatrixes (plural)

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From Late Latin mediātrīx, feminine of mediātor.

[…] the intersection of the normal at M to the parabola with the mediatrix of the line […]

2000, Jean H. Gallier, Curves and surfaces in geometric modeling, page 105:

(geometry, rare) A bisector, the line that is perpendicular to a line segment and intersects the line segment at its midpoint.


ellipticity

ellipticity (countable and uncountable, plural ellipticities)

(countable, mathematics) A measure of this flattening that is a function of the ellipse's equatorial and polar radii


pseudogroup

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(mathematics) An algebraic structure having elements that are homeomorphisms between subsets of a space


partition of unity

partition of unity (plural partitions of unity)

(mathematics) A collection of non-negative-valued functions defined on a topological space, such that every point has only finitely many nonzero values, and these sum to one.


meromorphic

Normal families of meromorphic functions are most naturally studied using the spherical metric (§1.2), an approach initiated by Ostrowski [1926]. Some results for meromorphic functions, such as the FNT, are immediate extensions from the analytic case, whereas others, such as Landau's or Julia's theorem are set in a much broader context than their analytic counterparts. Normality criteria pertinent to families of meromorphic functions, such as Marty's theorem, have not yet been encountered.

1993, Joel L. Schiff, Normal Families, Springer, page 71:

Note that such a transformation is holomorphic at the origin, but is essentially singular at infinity. However, since T(z) commutes with A(z), the transformed system has coefficient matrix A(z)-zq'(z)I and hence is again meromorphic at infinity.

2000, Werner Balser, Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations, Springer, page 39:

A point p#92;inP¹ is singular for #92;textstyle#92;frac#123;d#125;#123;dz#125;-A if the equation cannot be made regular at p with a local meromorphic transformation.

2012, Marius van der Put, Michael F. Singer, Galois Theory of Linear Differential Equations, Springer, page 147:

(complex analysis, of a function) That is the ratio of two holomorphic functions (and so possibly infinite at a discrete set of points).


holomorphic

1998, Stefan-M. Heinemann, Julia Sets in Cⁿ, Hartje Kriete, Progress in Holomorphic Dynamics, Addison Wesley Longman, page 159,
The iteration of holomorphic maps of one variable is one of the most lively fields of current mathematical research. Since its beginning in the twenties of this century, the theory of holomorphic endomorphisms of the Riemann sphere (= rational functions) has become well developed.

1998, Robert Friedman, Algebraic Surfaces and Holomorphic Vector Bundles, Springer, page 303,
A holomorphic 1-form on X is closed, and so
0=dη₁=df and η₂.

The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector field) acting on it.

2010, Graziano Gentili, Jacques Guenot, Giorgio Patrizio, Holomorphic Dynamical Systems: Lectures given at the C.I.M.E. Summer School, Springer, page v:

(complex analysis, of a complex function) Complex-differentiable on an open set around every point in its domain.


sublattice

(mathematics) A nonempty subset of a lattice.

hlutgrind

mathematics: nonempty subset of a lattice


oversample

(statistics) An additional sample of a subpopulation, above and beyond the portion of a main sample that already belongs to that subpopulation.


oversample

en-verb

oversample (third-person singular simple present oversamples, present participle oversampling, simple past and past participle oversampled)

oversamples (present singular third-person)
oversampling (participle present)
oversampled (participle past)
oversampled (past)

(statistics) To sample additional members of a subpopulation, above and beyond the members included in the main sample.


tricomponent

(graph theory) A component having three nodes.


cyclide

(mathematics) Any of a class of surfaces, described by quartic expressions, that are related to spherical surfaces


nonchiral

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(geometry, physical chemistry) Not chiral.


tensorial

en-adj

tensorial (comparative more tensorial, superlative most tensorial)

more tensorial (comparative)
most tensorial (superlative)

(mathematics) of or pertaining to a tensor


like terms

(mathematics) monomial expressions whose variable components are identical.

(mathematics) algebraic expressions whose literal coefficients represent the same value regardless of the numbers assigned to them.


multivariant

multivariant (comparative more multivariant, superlative most multivariant)

more multivariant (comparative)
most multivariant (superlative)


supermembrane

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theories of everything
theory of everything

(mathematics, physics) A multidimensional membrane (a brane) posited in some theories of everything.


FAI

friendly artificial intelligence
w:friendly artificial intelligence

(artificial intelligence) Initialism of friendly artificial intelligence.


Reebless

(topology) (of a foliation) Not containing a Reeb component.


Reeb component

Introduced by the French mathematician Georges Reeb (1920–1992).

(topology) A solid torus whose boundary is a leaf of a foliation of the ambient 3-dimensional manifold.


stellated

stellated (comparative more stellated, superlative most stellated)

more stellated (comparative)
most stellated (superlative)

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(geometry) Of a polyhedron, having its edges or planes extended to form a new shape.


multimodality

en-noun

multimodality (countable and uncountable, plural multimodalities)

(mathematics) The presence of multiple modes or maxima in a statistical distribution.


unblind

en-verb

unblind (third-person singular simple present unblinds, present participle unblinding, simple past and past participle unblinded)

unblinds (present singular third-person)
unblinding (participle present)
unblinded (participle past)
unblinded (past)

(cryptography, transitive) To convert (a blind signature) back to the unblinded state (as opposed to the blinded state).


supergroup

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Formally, a supergroup is a more general notion than group. We illustrate the difference between the two notions by a simple example.

2011, Alexander Kulikov, Nikolay Vereshchagin, editors, Computer Science – Theory and Applications […] , Springer, →ISBN, page 237:

(mathematics) The group to which a subgroup belongs.

Any group composed of other groups.
The group to which a subgroup belongs.


subsemigroup

(mathematics) Any subset of a semigroup that is closed under the semigroup operation.


semigroup

From semi- + group, reflecting the fact that not all the conditions required for a group are required for a semigroup. (Specifically, the requirements for the existence of identity and inverse elements are omitted.)

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

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

1988, A. Ya Aǐzenshtat, Boris M. Schein (translator), On Ideals of Semigroups of Endomorphisms, Ben Silver (editor), Nineteen Papers on Algebraic Semigroups, American Mathematical Society Translations, Series 2, Volume 139, page 11,
It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups.

If one considers the variety of semigroups, one has the binary operation of multiplication defined on every semigroup.

2012, Jorge Almeida, Benjamin Steinberg, “Syntactic and Global Subgroup Theory: A Synthesis Approach”, in Jean-Camille Birget, Stuart Margolis, John Meakin, Mark V. Sapir, editors, Algorithmic Problems in Groups and Semigroups, page 5:

(mathematics) Any set for which there is a binary operation that is closed and associative.

半群

set for which a closed associative binary operation is defined


attoampere

electric current
electric current#English

(metrology) An SI unit of electric current equal to 10⁻¹⁸ amperes. Symbol: aA


one-start

(mathematics, in two dimensions) Describing a simple spiral that starts at a point at the origin and does not divide the plane

(mathematics, in three dimensions) Describing a section of a simple helix


two-start

(mathematics, in two dimensions) Describing a double spiral that starts at the origin and divides the plane into two

(mathematics, in three dimensions) Describing a construction of two helices that wrap around the same cylinder; if infinite, would divide the surface of the cylinder into two


multi-start

(mathematics, in two dimensions) Describing a multiple spiral that starts at the origin and divides the plane into multiple regions

(mathematics, in three dimensions) Describing a construction of multiple helices that wrap around the same cylinder; if infinite, would divide the surface of the cylinder into multiple regions


isosceles trapezoid

en-noun

isosceles trapezoid (plural isosceles trapezoids)

A quadrilateral with two parallel sides and a separate pair of congruent sides which are not parallel.

等腰梯形

quadrilateral with two parallel sides and separate pair of congruent sides that are not parallel


semiautomaton

(mathematics, computer science) a multiplicative operation of a monoid on a set


antimatroid

(mathematics) a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included


matroid

From matrix + -oid. They were so named by Hassler Whitney in 1935 in an article titled “On the abstract properties of linear dependence”.

A matroid can be defined in terms of bases. A matroid consists of a ground set as well as a set of bases which is a nonempty subset of the power set of the ground set.

(combinatorics) A structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces and acyclicality in graphs.


cryptomorphic

Coined by Garrett Birkhoff before 1967, for use in the third edition of his book Lattice Theory.

Find them, and prove that an operation satisfying them provides another cryptomorphic version of topology 8.

1994, Michael Henle, A Combinatorial Introduction to Topology, page 269:

(mathematics) Two objects, especially systems of axioms or semantics for them, are called cryptomorphic if they are equivalent (possibly in some informal sense) but not obviously equivalent.


greedoid

From greed (from its applicability to problems that can be solved by greedy algorithms) and matroid.

(combinatorics) A particular type of set system.


polytree

(graph theory) a graph with at most one undirected path between any two vertices. In other words, a directed acyclic graph (DAG) for which there are no undirected cycles either.


pseudoforest

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(graph theory) an undirected graph in which every connected component has at most one cycle


coalgebra

(mathematics) a structure that is dual to unital associative algebras


unital

(mathematics) (of an algebra) containing a multiplicative identity element (or unit), i.e. an element 1 with the property 1x=x1=x for all elements x of the algebra.


rng

From ring, with i dropped to suggest the absence of the identity element.

(algebra) An algebraic structure satisfying the same properties as a ring, except that multiplication need not have an identity element.


semiring

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(algebra) An algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.


limit cycle

(systems theory) A closed trajectory in phase space of a dynamical system having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches minus-infinity.


algebraical

en-adj

algebraical (comparative more algebraical, superlative most algebraical)

more algebraical (comparative)
most algebraical (superlative)

From Latin algebraicus + -al or algebra + -ical.

(mathematics) Requiring a finite number of algebraic operations; the opposite of transcendental.

algebrallinen

requiring a finite number of algebraic operations


Lévy flight

Named after French mathematician Paul Pierre Lévy (1886–1971).

named-after

(mathematics) A type of random walk in which the increments are distributed according to a “heavy-tailed” distribution i.e. there are a significant number of large increments.


orthonormalization

en-noun

orthonormalization (countable and uncountable, plural orthonormalizations)

(mathematics) A form of orthogonalization in which the resulting vectors are all unit vectors

þverstöðlun

Form of orthogonalization in which the resulting vectors are all unit vectors


scalar field

(mathematics, physics) A function that assigns a scalar value to every point in space.

scalar multiplication
scalar multiplication

(mathematics, linear algebra) The field (algebraic structure) for which scalar multiplication is defined for a given vector space; field of scalars.


-sphere

n-sphere

(mathematics) Sphere of a certain dimensionality.


bimodal

(mathematics, of a distribution) Having two modes (local maxima)


long tail

In the marketing sense popularized by journalist Chris Anderson in 2004, alluding to the long tail of a power law distribution.

(mathematics, probability) Used other than figuratively or idiomatically: The tail of a distribution that represents the rare occurrence of extreme values.


momme

A unit of weight (3.75 grams) used for pearls, paper, and silk.


cisoid

(signal processing) Complex sinusoid or complex exponential.


SAE

(machine learning) Initialism of sparse autoencoder.


figural

en-adj

figural (comparative more figural, superlative most figural)

more figural (comparative)
most figural (superlative)

From Old French figural, from late Latin figūrālis, from figūra (“figure”).

(mathematics, obsolete) Of numbers, describing a geometrical figure.


self-organization

(cybernetics) A process of attraction and repulsion in which the internal organization of a system, normally an open system, increases in complexity without being guided or managed by an outside source.


optimization problem

en-noun

optimization problem (plural optimization problems)

(mathematics) The problem of finding the "best" solution from all feasible solutions, given constraints defining which of the solutions are feasible, and a goal function defining which of the feasible solutions is the best one.


rod-shaped

en-adj

rod-shaped (comparative more rod-shaped, superlative most rod-shaped)

more rod-shaped (comparative)
most rod-shaped (superlative)

Anthrax goes through two very different stages in its life cycle. One is a microscopic rod-shaped bacterium called bacillus anthracis, easy to grow in the lab but fragile and easily killed in the open.

S. pombe is a rod shaped organism, and during its cell cycle it grows mostly in length with little change in diameter.

1981, PCL John, The Cell Cycle, page 86:

The rod-shaped E. coli phages share a common host range with the RNA-containing E. coli phages, a coincidence which probably unites unrelated viruses.

1965, “Small Bacteriophages”, in Advances in Virus Research, volumes 1-11, pages 343–4:

(biology) Specifically, describing a form of bacterium.


electrolocation

(cybernetics) the ability of a robot to locate an object by detecting changes in its electric field.


complete lattice

en-noun

complete lattice (plural complete lattices)

(algebra) A partially ordered set in which all subsets have both a supremum (join) and an infimum (meet).


polytopal

en-adj

polytopal (comparative more polytopal, superlative most polytopal)

more polytopal (comparative)
most polytopal (superlative)

(mathematics) Of or pertaining to polytopes.


halfspace

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(geometry) Either of the two parts of a three-dimensional object cut by a two-dimensional plane


superposability

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trochoid

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From Ancient Greek τροχοειδής (trokhoeidḗs), from τροχός (trokhós, “wheel”) + εἶδος (eîdos, “form, image”).

(geometry) The curve traced by a point on a circle as it rolls along a straight line


monome

From mono- + -ome; compare binomial, polynomial.

(mathematics, logic, computing) An expression with a single term, such as a product of numeric variables (with no addition) or a conjunction of possibly negated Boolean variables (with no disjunction).


additive inverse

en-noun

additive inverse (plural additive inverses)

So called because the sum of a number and its additive inverse is the additive identity.

The additive inverse of 12 is −12.

(mathematics) The inverse with respect to addition; the opposite.


planimetry

planimetry (countable and uncountable, plural planimetries)

(mathematics) The measurement of distances, angles and areas on a plane, especially on a map or image


preimage

The preimage of #92;#123;4,9#92;#125; under the function f#58;#92;R#92;rightarrow#92;R#58;f(x)#61;x² is the set #92;#123;-3,-2,#43;2,#43;3#92;#125;.

1967 [Academic Press], Francois Treves, Topological Vector Spaces, Distributions and Kernels, 2006, Dover, page 22,
The preimage of a neighborhood U of 0 in E must be a neighborhood of (0,x), since (0,x) is mapped into 0.

Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.

2003, Sergei K. Lando, Alexander K. Zvonkin, Graphs on Surfaces and Their Applications, Springer, page 56:

Loosely speaking, saying that a function f is one-way implies that given y (in the range of f) it is infeasible to find a preimage of y under f.

2005, Oded Goldreich, Foundations of Cryptography: A Primer, now Publishers, page 24:

(mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ⁻¹(B) = {x ∈ X : ƒ(x) ∈ B}.

原像

set of all elements that map into a given subset of the codomain of a function


univariate

(mathematics) Having or involving a single variable

aonathráideach

mathematics: having or involving a single variable


univariate

(mathematics) A polynomial or function with only one variable

一元

mathematics: a polynomial or function with only one variable


bivariate

Our upper bound is the best possible, and it implies the existence of low-rank factorizations of positive semidefinite bivariate matrix polynomials and representations of biforms as sums of few squares.

2016, Grigoriy Blekherman, Daniel Plaumann, Rainer Sinn, Cynthia Vinzant, “Low-Rank Sum-of-Squares Representations on Varieties of Minimal Degree”, in arXiv:

(mathematics) Having or involving exactly two variables.


bivariate

(mathematics) A polynomial or function with exactly two variables.


sampling error

sampling error (countable and uncountable, plural sampling errors)

(statistics) The error caused by observing a sample instead of the whole population.


open set

(topology) Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.

(topology, mathematical analysis, restricted to metric spaces) A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set.

(topology) Most generally, a member of the topology of a given topological space.


closed set

Coordinate term: open set

(topology) A set whose complement is open.


expert system

“For each different kind of problem,” said Minsky, “the construction of expert systems had to start all over again, because they didn't accumulate common-sense knowledge.”

2003 May 13, Mark Baard, quoting Marvin Minsky, “AI Founder Blasts Modern Research”, in Wired, →ISSN:

artificially intelligent
artificial intelligence

(artificial intelligence) A type of artificially intelligent software system that stores expertise concerning some subject matter in a knowledge base and attempts to answer questions or solve problems in a manner which simulates the thought processes of a human expert.


bounded function

bounded function (plural bounded functions)

(mathematics) Any function whose values remain bounded by some constant.


commutate

en-verb

commutate (third-person singular simple present commutates, present participle commutating, simple past and past participle commutated)

commutates (present singular third-person)
commutating (participle present)
commutated (participle past)
commutated (past)

Back-formation from commutation (in the late 19th century), as is commutator (noun) too.

The match of two finite line segments in 2 dimensions requires 2 translations, 1 rotation, 1 scale transformation; the order is here important, and these operators cannot commutate.

2012, J. Kittler, V.W. Fu, L.F Pau, Pattern Recognition Theory and Applications, →ISBN, page 194:

(intransitive, mathematics) To commute; to be invariant under a reversal of the positions of operands.


cap off

cap off (third-person singular simple present caps off, present participle capping off, simple past and past participle capped off)

caps off (present singular third-person)
capping off (participle present)
capped off (participle past)
capped off (past)

a. 1997, Rob[ion] Kirby, "Problems in Low-Dimensional Topology", problem 3.21, in, 1997, William H[ilal] Kazez, editor, Geometric Topology, proceedings of the 1993 Georgia International Topology Conference, AMS/IP Studies in Advanced Mathematics 2, American Mathematical Society, →ISBN, part 2, page 163,
Let X be an acyclic 2-complex and M an abstract regular neighborhood of X; ∂M_0=S², so cap off to get a homology 3-sphere M³.

a. 1997, Michael T. Anderson, "Scalar Curvature and Geometrization Conjectures for 3-Manifolds", in, 1997, Karsten Grove and Peter Petersen, editors, Comparison Geometry, Mathematical Sciences Research Institute Publications 30, →ISBN, page 53,
Note, however, that when one cuts a 3-manifold along an incompressible torus, there is no canonical way to cap off the boundary components thus created, as is the case for spheres. For any toral boundary component, there are many ways to glue in a solid torus... .

Cap off, with discs just above the annulus, any circuits that bound in the annulus; then use annuli to cap off adjacent pairs of curves that encircle the annulus in opposite directions.

1997, W[illiam] B[ernard] Raymond Lickorish, An Introduction to Knot Theory, Graduate Texts in Mathematics 175, Springer, →ISBN, page 61:

(mathematics, transitive) To glue a relatively uncomplicated compact manifold to a manifold of the same dimension along (a component of the latter's boundary).


Hamiltonian

(mathematics) Of, attributed to or inspired by the Irish mathematician, astronomer and physicist William Rowan Hamilton (1805–1865).

(mathematics, graph theory, of a cycle/path) That visits each vertex exactly once.

Using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields, wa are able to describe a very large class of nonisochronous Hamiltonian system of even degree of degree arbitrary large.

2016, Jacky Cresson, Jordy Palafox, “Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat”, in arXiv:

(mathematics, graph theory, of a graph) Containing a Hamiltonian cycle.


coto

From Spanish coto (“half-span, quarter-cubit”), supposedly a variant of codo (“Spanish cubit”), from Vulgar Latin forms of Latin cubitum (“elbow, Roman cubit”), but more probably a development of or influenced by Latin quārtus (“a fourth”) from its use as a fourth of the cubit or Latin quattuor (“four”) from its approximation of the span across four fingers.

bor

(historical) A traditional Spanish unit of length, equivalent to about 10.4 cm.


tega

From Galician tega, variant of earlier talega, from Andalusian Arabic تَعْلِيقَة (taʕlíqa, “hanging thing”).

der

(historical) Synonym of ferrado, a traditional Galician unit of dry measure, mass, and land area


categorical variable

en-noun

categorical variable (plural categorical variables)


discrete variable

discrete variable (plural discrete variables)

(statistics) A variable that takes values from a finite or countable set, such as the number of legs of an animal.


continuous variable

continuous variable (plural continuous variables)

distribution function
cumulative distribution function

(statistics) A variable that has a continuous distribution function, such as temperature.


stereotomy

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From French stéréotomie, from Ancient Greek στερεός (stereós, “solid”) + -τομία (-tomía, “-cut”).

uder

Here your countenance brightened up, and, perceiving your lips move, I could not doubt that you murmured the word ‘stereotomy’, a term very affectedly applied to this species of pavement.

1841, Edgar Allan Poe, The Murders in the Rue Morgue:

(geometry, masonry) The cutting or dissection of solids.


osculatory

en-adj

osculatory (comparative more osculatory, superlative most osculatory)

more osculatory (comparative)
most osculatory (superlative)

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A circle may be osculatory with a curve, at a given point.

(geometry) Relating to, or having the properties of, an osculatrix; capable of osculation.


mathematical statistics

(statistics) The study of statistics from a purely mathematical standpoint, using probability theory, measure theory, linear algebra and analysis.

數理統計學 /数理统计学

study of statistics from math standpoint


inferential statistics

statistical inference
statistical inference

(statistics) A branch of statistics studying statistical inference—drawing conclusions about a population from a random sample drawn from it, or, more generally, about a random process from its observed behavior during a finite period of time.


statistical inference

en-noun

statistical inference (plural statistical inferences)

(statistics) Drawing conclusions about a population from a random sample drawn from it, or, more generally, about a random process from its observed behavior during a finite period of time.

inferència estadística

drawing conclusions from a random sample


applied statistics

Descriptive statistics
descriptive statistics

inferential statistics
inferential statistics

Descriptive statistics and inferential statistics.

應用統計學 /应用统计学

descriptive statistics and inferential statistics


totally ordered set

totally ordered set (plural totally ordered sets)

(set theory) A set having a specified total order.


confounding variable

confounding variable (plural confounding variables)

independent variable
independent variable

(statistics) An extraneous variable in a statistical model that correlates (positively or negatively) with both the dependent variable and the independent variable.


extraneous variable

extraneous variable (plural extraneous variables)

(statistics) A random variable that is not an independent variable and may bear any effect on the behaviour of the subject being studied.


point mass

probability distribution
probability distribution

(statistics) A probability distribution with unity probability mass at one specific outcome, and zero probability mass everywhere else.


half-open

(mathematics) (referring to an interval on the real line) containing only one of its endpoints

halvåben

mathematics: containing only one of its endpoints


traverse

From Middle English traversen, from Old French traverser, from Latin trans (“across”) + versus (“turned”), perfect passive participle of Latin vertere (“to turn”).

(geometry) A line lying across a figure or other lines; a transversal.


acre-foot

A unit of volume equal to an acre times a foot, equal to 43,560 cubic feet, or about 1233.5 cubic meters.


board foot

A board one square foot by one inch, about 2.36 liters.


US survey foot

A unit of length equal to ¹²⁰⁰⁄₃₉₃₇ of a meter, used in some states for measuring land.


sphericity

sphericity (countable and uncountable, plural sphericities)

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From spheric + -ity. In the geometrical sense, defined by the geologist Hakon Wadell in 1935.

(geometry, countable) The ratio of the surface area of a given particle to the surface area of a sphere with the same volume.

pallonmuotoisuus

ratio of particle surface area to sphere surface area


classifying space

classifying space (plural classifying spaces)

(mathematics) A topological space that is the quotient of a free action (of the specified group) on a weakly contractible space.


weakly contractible

(of a topological space) Having all its homotopy groups trivial.


NLQ

artificial intelligence
artificial intelligence

natural language
natural language#English

(artificial intelligence) Initialism of natural language query.


radial curve

(mathematics) Any of a family of curves that are the loci of points that have a defined relationship between a fixed point and the centre of curvature at each point on another curve


centre of curvature

centre of curvature (plural centres of curvature)

(mathematics, for any point on a curve) The centre of the osculating circle at the point on the curve.


radius of curvature

radius of curvature (plural radii of curvature)

(mathematics, for any point on a curve) The radius of the osculating circle at the point on the curve


osculating circle

osculating circle (plural osculating circles)

(geometry, for any point on a curve) The circle that has the same tangent, and the same curvature at the point on the curve.


leafspace

(mathematics) A topological space that is the quotient of a laminated or foliated manifold by identification of each leaf, and each closed complementary region, to a point.


covering space

Let (X, p) be a covering space of X such that X is simply connected.

2019, William S. Massey, A Basic Course in Algebraic Topology, page 132:

(topology) The domain of a covering of a topological space; the covering together with its domain. (See Usage notes at covering).


radical plane

(mathematics) The plane containing the circle formed by the intersection of two spheres (or whose points have equal power with respect to two non-intersecting spheres)


cluster analysis

cluster analysis (countable and uncountable, plural cluster analyses)

(artificial intelligence, statistics) The classification of objects into different groups, or more precisely, the partitioning of a data set into subsets (clusters), so that the data in each subset (ideally) share some common trait - often proximity according to some defined distance measure.


SWIFT

(mathematics) Acronym of Stored Waveform Inverse Fourier Transform.


birectangular

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Unlike a normal triangle, a spherical triangle can be birectangular because the sum of its angles is greater than 180 degrees.


compactum

(mathematics) A compact topological space.


well-order

1986, G. Richter, Noetherian semigroup rings with several objects, G. Karpilovsky (editor), Group and Semigroup Rings, Elsevier (North-Holland), page 237,
̲X is well-order enriched iff every morphism set ̲X(X,Y) carries a well-order ≤_(XY) such that
f≨_(XY)g⇒h•f≨_(XY)h•g
for every h:Y→Z.

2001, Robert L. Vaught, Set Theory: An Introduction, Springer (Birkhäuser), 2nd Edition, Softcover, page 71,
Some simple facts and terminology about well-orders were already given in and just before 1.8.4. Here are some more: In a well-order A, every element x is clearly of just one of these three kinds: x is the first element; x is a successor element - i.e., x has an immediate predecessor; or x is a limit element - i.e., x has a predecessor but no immediate predecessor. The structure (∅, ∅) is a well-order.

2014, Abhijit Dasgupta, Set Theory: With an Introduction to Real Point Sets, Springer (Birkhäuser), page 378,
Definition 1226 (Von Neumann Well-Orders). A well-order X is said to be a von Neumann well-order if for every x∈X, we have x=y∈X|y<x (that is x is equal to the set Pred(x) consisting of its predecessors).
Clearly the examples listed by von Neumann above, namely
empty , empty, empty ,empty, empty ,empty,empty ,empty, …
are all von Neumann well-orders if ordered by the membership relation "∈," and the process can be iterated through the transfinite. Our immediate goal is to show that these and only these are the von Neumann well-orders, with exactly one von Neumann well-order for each ordinal (order type of a well-order). This is called the existence and uniqueness result for the von Neumann well-orders.

(set theory, order theory) A total order of some set such that every nonempty subset contains a least element.


well-order

en-verb

well-order (third-person singular simple present well-orders, present participle well-ordering, simple past and past participle well-ordered)

well-orders (present singular third-person)
well-ordering (participle present)
well-ordered (participle past)
well-ordered (past)

The set of positive integers is well-ordered by the relation ≤.

1950, Frederick Bagemihl (translator), Erich Kamke, Theory of Sets, 2006, Dover (Dover Phoenix), page 111,
Starting from these special well-ordered subsets, it is then possible to well-order the entire set.

1975 [The Williams & Wilkins Company], Dennis Sentilles, A Bridge to Advanced Mathematics, Dover, 2011, page 182,
To carry the analogy a bit further, the axiom of choice implies the ability to well order any set.

Then #92;le#95;C is a well defined order on C, and (C,#92;le#95;C) belongs to #92;mathcal#123;X#125; (that is, #92;le#95;C well orders C) and is an upper bound for #92;mathcal#123;C#125;.

2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd edition, Springer, page 18:

(set theory, order theory, transitive) To impose a well-order on (a set).


cycler

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We took samples from the tubes in the cycler at regular intervals

(biochemistry) Ellipsis of thermal cycler.; a machine for creating multiple copies of DNA sequences.


Gudermannian

Named after Christoph Gudermann (1798–1852), + -ian.

(mathematics) A particular function, gd(x)=2 tan ⁻¹eˣ-π/2.


scientific calculator

en-noun

scientific calculator (plural scientific calculators)

(mathematics, computing) An electronic calculator that can handle trigonometric, exponential and often other advanced functions, and can show its output in scientific notation and sometimes in hexadecimal, octal or binary.


rationalize

en-verb

rationalize (third-person singular simple present rationalizes, present participle rationalizing, simple past and past participle rationalized)

tlb

(American spelling, Oxford British English)

rationalizes (present singular third-person)
rationalizing (participle present)
rationalized (participle past)
rationalized (past)

From French rationaliser. By surface analysis, rational + -ize.

(mathematics) To remove radicals, without changing the value of an expression or the roots of an equation.


cycloidal arch

en-noun

cycloidal arch (plural cycloidal arches)

(architecture) An arch that has a cycloidal shape, wherein the span of the arch is some factor of pi*rise.


connected graph

connected graph (plural connected graphs)

(graph theory) A graph in which there is a route of edges and nodes connecting any two nodes.


scatter plot

(statistics) A type of display using Cartesian coordinates to display values for two variables for a set of data.


dihedron

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(geometry) A polyhedron having two faces


cyclomatic

(graph theory) Used to describe the number of edges that must be removed from a graph to ensure that no graph cycle remains; equal to the number of edges, minus the number of nodes plus one.


MITM

Man-in-the-middle attack
Meet-in-the-middle attack

(cryptography) Initialism of meet-in-the-middle attack: Cryptographic attack that attempts to find a value in each of the ranges and domains of the composition of two functions such that the forward mapping of one through the first function is the same as the inverse image of the other through the second function


SRS

SRS (countable and uncountable, plural SRSes)

(statistics) Initialism of simple random sample, a sample chosen from a population so that any sample of the same size could have equally likely been chosen.


multigraph

(graph theory) A set V (whose elements are called vertices or nodes), taken together with a multiset E, each of whose elements (called an edge or line) is a cardinality-two multisubset of V.

(graph theory, less commonly) A set V (as before), taken together with a multiset E, each of whose elements is a cardinality-two subset of V.


astrodynamics

The study of the motion of rockets and spacecraft, usually from Newton's laws of motion, Newtonian gravity, and Kepler's laws


translogarithmic

en-adj

translogarithmic (comparative more translogarithmic, superlative most translogarithmic)

more translogarithmic (comparative)
most translogarithmic (superlative)

(mathematics) Describing functions that are both transcendental and logarithmic

translogaritmico

function which is trancendental and logarithmic


missing boundary

(of a compact topological space with boundary) Having had some but not all of its boundary removed.


homotope

en-verb

homotope (third-person singular simple present homotopes, present participle homotoping, simple past and past participle homotoped)

homotopes (present singular third-person)
homotoping (participle present)
homotoped (participle past)
homotoped (past)

(topology, transitive) To define or demonstrate a homotopy of (one map with another).

(topology, transitive) More loosely, to exhibit a homotopy equivalence between two spaces.


partial fraction

en-noun

partial fraction (plural partial fractions)

(mathematics) Any of several fractions to the sum of which a single fraction is equal.

كَسْرٌ جُزْئِيٌّ

mathematics: any of several fractions to the sum of which a single fraction is equal


Cauchy

A French surname; notably that of prolific mathematician Augustin-Louis Cauchy (1789-1857).


biostatistics

(biology, mathematics) The application of statistics to the study and analysis of biological and medical data


bocs

(mathematics) A BOCS representation of an algebraic structure


minimax

(decision theory, game theory) A decision rule used for minimizing the maximum possible loss, or maximizing the minimum gain.


maximin

(decision theory, game theory) A rule to identify the worst outcome of each possible option to find one's best (maximum payoff) play.


semiaxis

(mathematics) A line segment, joining the centre of a figure to an edge, that forms half of an axis of symmetry.


categorical product

categorical product (plural categorical products)

The categorical product generalises the Cartesian product of sets, product of topological spaces and direct product of groups.

(mathematics) The limit of two (or more) objects, considered without regard to any arrows between them.


categorical dual

categorical dual (plural categorical duals)

(category theory) For a given category C, its dual category Cᵒᵖ is obtained by reversing the direction of each one of the arrows of C.


pushout

* Deverbal from push out.
* (one who leaves school): Intended to avoid the negative implications of dropout.

(category theory) The colimit of a pair of morphisms which share the same domain.


initial object

In the category of sets, the initial object is the empty set, since there exists a unique function, namely the empty function, from the empty set into any other given set.

(category theory) An object within a category which sends out arrows to all other objects in that category, and such that each of these arrows is unique.


terminal object

terminal object (plural terminal objects)

In the category of sets, a terminal object is any singleton, since there exists a unique function, namely the constant function, from any given set into that singleton.

The terminal object is the limit over the empty diagram.

(category theory) An object within a category which receives arrows from all other objects in that category, and such that each of these arrows is unique.


exponential object

exponential object (plural exponential objects)

An exponential object generalizes its interpretation in category #92;mathbf#123;Set#125;; namely, that of as a function set or internal hom-set.

The pair Z^Y,#92;mbox#123;eval#125;#58;Z^Y#92;timesY#92;rightarrowZ is the terminal object of the comma category (-#92;timesY)#92;downarrowZ. Therefore the exponential object is a kind of universal morphism.

(category theory) An object which indexes a family of arrows between two given objects in a universal way, meaning that any other indexed family of arrows between the same given pair of objects must factor uniquely through this universally-indexed family of arrows.

currying ∼ exportation_(logic)

an instance of which is the transpositioning λ in the figure

modus ponens

homologous to the universal evaluation morphism, eval


galactic year

(astronomy) The time taken for the Solar System to orbit around the center of the Milky Way Galaxy, estimated to be from 225 to 250 million years.


flexagon

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(geometry) A flat model made from folded strips of paper that can be folded, or flexed, to reveal a number of hidden faces.

флексаго́н

a flat model made from folded strips of paper


circular segment

circular segment (plural circular segments)

(geometry) A region of a circle bounded by an arc and the chord connecting the endpoints of the arc.


BOMDAS

order of operations
order of operations#English

(mathematics, mnemonic) An acronym for arithmetic order of operations, with B first and AS last: Brackets, then order or 'of' in some curricula, then multiplication and division, then addition and subtraction.


BODMAS

order of precedence
order of precedence#English

(mathematics, mnemonic) An acronym for the arithmetic order of precedence, with the highest precedence first: Brackets, order, division, multiplication, addition, subtraction.


BEDMAS

(mathematics, mnemonic) An acronym for arithmetic order of precedence, with B first and AS last: Brackets, exponents, division, multiplication, addition, subtraction.


orthant

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Consider preferences defined over the nonnegative orthant by (x_1,x_2)≻(y_1,y_2) if x_1+x_2<y_1+y_2 […]

1992, Hal R. Varian, Microeconomic Analysis (3rd ed.), Norton, p. 114

(geometry) A n-dimensional generalization of the quadrant (in two-dimensional Cartesian space) and octant (in three-dimensional space).


cancellative

(mathematics) Said of a magma that has the cancellation property.


Fourier series

Named after French mathematician and physicist Joseph Fourier (1768-1830), who pioneered research into such series and their application to problems of heat transfer and vibration.

1951 [Blackie & Son], R. C. H. Young (translator), Konrad Knopp, Theory and Application of Infinite Series, [1947, Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, 4th Edition], 1990, Dover, Unabridged unaltered reprint of 2nd English Edition, page 493,
As we have seen (pp. 369—370), the question of the necessary and sufficient conditions under which the Fourier series of an integrable function converges and represents the given function is one which presents very great difficulties.

2001, David Cruz-Uribe (translator), Javier Duoandikoetxea Zuazo, Fourier Analysis, [1995, Javier Duoandikoetxea Zuazo, Análisis de Fourier], American Mathematical Society, page 20,
There are excellent discussions of Fourier series and integrals in Katznelson [10] and Dym and McKean [4]. The book by R. E. Edwards [5] is an exhaustive study of Fourier series from a more modern perspective.

Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable.

2006, K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering: A Comprehensive Guide, 3rd edition, Cambridge University Press, page 415:

mathematical analysis
mathematical analysis

(mathematics, mathematical analysis) Any series resulting from the decomposition of a periodic function into terms involving cosines and sines (or, equivalently, complex exponentials).

フーリエ級数

フーリエきゅうすう,fūrie kyūsū


yardland

From Middle English ȝerdelonde, yerdland, yerdlond, yertland, from Old English ġeardland, equivalent to yard (“unit”) + land.


epitrochoid

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A geometric curve traced by a fixed point on one circle which rotates around the perimeter of another circle. Examples include the shape of the Wankel engine


hypotrochoid

(geometry) A geometric curve traced by a fixed point on the radius line outside one circle which rotates inside the perimeter of another circle.


pomset

As usual, pomsets can be made setlike by requiring that the elements of the sets X should be chosen from a given set.


gsm

It produces grayback and whiteback coated duplex of 250-400 gsm.

Initialism of grams per square metre (unit for measuring the weight of paper).


algebraically closed

The fundamental theorem of algebra states that the field of complex numbers, #92;mathbb#123;C#125;, is algebraically closed.

Definition. A field is algebraically closed when it satisfies the equivalent conditions in Proposition 4.1. #92;square
For instance, the fundamental theorem of algebra (Theorem III.8.11) states that #92;Complex is algebraically closed. The fields #92;R, #92;Q, #92;Z#95;p, are not algebraically closed, but #92;R and #92;Q can be embedded into the algebraically closed field #92;Complex.

2007, Pierre Antoine Grillet, Abstract Algebra, 2nd edition, Springer, page 166:

In many ways #92;Q#95;p is analogous to #92;R. For example, #92;R is not algebraically closed. The exercises below show that #92;Q#95;p is not algebraically closed. However, by adjoining i#61;#92;sqrt#123;-1#125; to #92;R, we get the field of complex numbers, which is algebraically closed. In contrast, the algebraic closure #92;overline#92;Q#95;p of #92;Q#95;p is not of finite degree over #92;Q. Moreover, #92;Complex is complete with respect to the extension of the usual norm of #92;R. Unfortunately, #92;overline#92;Q#95;p is not complete with respect to the extension of the p-adic norm. So after completing it (via the usual method of Cauchy sequences) we get a still larger field, usually denoted by #92;Complex#95;p, and it turns out to be both algebraically closed and complete.

2008, M. Ram Murty, Problems in Analytic Number Theory, 2nd edition, Springer, page 155:

Definition 5.3.14. Let F be a field. A field extension P is called an algebraic closure of F if P is algebraically closed and every proper subfield of P containing F is not algebraically closed.
In other words, the algebraic closure of F is the minimal algebraically closed field containing F.

2015, Martyn R. Dixon, Leonid A. Kurdachenko, Igor Ya Subbotin, An Introduction to Essential Algebraic Structures, Wiley, page 195:

(algebra, field theory, of a field) Which contains as an element every root of every nonconstant univariate polynomial definable over it (i.e., over said field).

algébriquement clos

that contains among its elements every root of every nonconstant single-variable polynomial definable over it

(algebra, group theory, of a group) Such that any finite set of equations and inequations has a solution.


almost everywhere

Alternative form: a.e.

(measure theory) For all elements except those contained in some set of measure zero.

幾乎處處 /几乎处处

everywhere except at a set of measure zero


dodecadodecahedron

dodecadodecahedron (plural dodecadodecahedra or dodecadodecahedrons)

dodecadodecahedra (plural)
dodecadodecahedrons (plural)

/ˌdəʊdɛkəˈˌdəʊdɛkəˈhiːdɹən/

/ˌdəʊdɪkəˈˌdəʊdɪkəˈhiːdɹən/

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(geometry) A nonconvex polyhedron with twenty-four faces, thirty vertices, and sixty edges.


linea

From Latin līnea (“line, thread”), via Spanish línea in reference to the unit of length, from līnum (“flax”). Doublet of line.

(historical) A traditional Spanish unit of length, equivalent to about 1.9 mm.


AOP

AOP (countable and uncountable, plural AOPs)

all-one polynomial
all-one polynomial#English

(mathematics, countable) Initialism of all-one polynomial.


common antilog

From common + antilog, by analogy with common log.

This accordingly gives us another way of writing the exponential function, and also a way of calculating its value from a table of common antilogs.

1966, Cedric A. B. Smith, William Moses Feldman, Biomathematics: The Principles of Mathematics for Students of Biological and General Science, Charles Griffin, page 143:

common antilogarithm
common antilogarithm

(mathematics, rare) A common antilogarithm.


common antilogarithm

common antilogarithm (plural common antilogarithms)

(mathematics, rare) A base-ten antilogarithm; ten raised to a certain power.


pinch point

(mathematics) Cuspidal point, a type of singular point on an algebraic surface


emanant

(mathematics) The result of operating any number of times upon a quantic with the operator (x'd/dx + y'd/dy + ... + z'd/dz).


unvisited

en-adj

unvisited (comparative more unvisited, superlative most unvisited)

more unvisited (comparative)
most unvisited (superlative)

(not comparable, mathematics, of a node in a graph) Never visited.


true lover's knot

en-noun

true lover's knot (plural true lover's knots)

(mathematics) A particular knot of eight crossings.


algebraic topology

The basic goal of algebraic topology is to find algebraic invariants that classify topological spaces up to homeomorphism, although most usually classify up to homotopy (homeomorphism being a special case of homotopy).

Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.

1969, Emil Artin, Hel Braun, Introduction to Algebraic Topology, C. E. Merrill Publishing Company,
Professor Emil Artin lectured on algebraic topology during the winter semester of 1959–60.

The material in Chapters 7 (Obstruction Theory and Eilenberg-MacLane Spaces) and 8 (Bordism, Spectra, and Generalized Homology) introduces the student to the modern perspective in algebraic topology.

2001, James F. Davis, Paul Kirk, Lecture Notes in Algebraic Topology, American Mathematical Society, page xii:

2002, Allen Hatcher, Algebraic Topology, Cambridge University Press:

(mathematics) The branch of mathematics that uses tools from abstract algebra to study topological spaces.


quasiconvex

From quasi- (“to some degree”) + convex.

(mathematics) said of a function, if the inverse image of any set of the form (-∞,a) for that function is a convex set.


quasiconcave

From quasi- (“to some degree”) + concave.

(mathematics) said of a function, if the inverse image of any set of the form (a,∞) for that function is a convex set.


possibilistic

en-adj

possibilistic (comparative more possibilistic, superlative most possibilistic)

more possibilistic (comparative)
most possibilistic (superlative)

There are two types of inferences that can be made: possibilistic and probabilistic. In the possibilistic case, one is interested in the possibility or impossibility of certain events. In the probabilistic case, the actual probability of the events is also considered.

(mathematics) Of, pertaining to or derived using possibility.


hyperplane

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(geometry) An n-dimensional generalization of a plane; an affine subspace of dimension n − 1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)

nadrovina

an n-dimensional generalization of a plane


quadratrix

en-noun

quadratrix (plural quadratrices or quadratrixes)

quadratrices (plural)
quadratrixes (plural)

(mathematics) A curve having ordinates which are a measure of the area (or quadrature) of another curve.


arccotangent

(trigonometry) An inverse of the cotangent function. Symbol: arccot


nullipotent

Latin roots, nullus (“not any”) + potent (“having power”) – literally, “having no power”.

compound

(mathematics, computing) Describing an action which has no side effect. Queries are typically nullipotent: they return useful data, but do not change the data structure queried. Contrast with idempotent.


quintile

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


petahertz

(metrology) An SI unit of frequency equal to 10¹⁵ hertz.


zettahertz

(metrology) An SI unit of frequency equal to 10²¹ hertz.


PVR

(functional analysis) Initialism of peak-to-valley ratio.


conus

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bean curve

So called because the curve has a bean shape.

(mathematics) A curve with formula x⁴+x²ʸ²+y⁴=x(x²+y²),.


generant

en-adj

generant (comparative more generant, superlative most generant)

more generant (comparative)
most generant (superlative)

/ˈd͡ʒɛnəɹənt/

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generant

/ˈd͡ʒɛnəɹənt/


mesokurtic

(statistics) Of a distribution: having kurtosis equal to that of a normal distribution; equivalently, having zero excess kurtosis.


leptokurtic

leptokurtic (comparative more leptokurtic, superlative most leptokurtic)

more leptokurtic (comparative)
most leptokurtic (superlative)

(statistics) Of a distribution: having kurtosis greater than that of a normal distribution; equivalently, having positive excess kurtosis.


platykurtic

platykurtic (comparative more platykurtic, superlative most platykurtic)

more platykurtic (comparative)
most platykurtic (superlative)

(statistics) Of a distribution: having kurtosis less than that of a normal distribution; equivalently, having negative excess kurtosis.


platykurtosis

(statistics) The property of having kurtosis less than that of a normal distribution; equivalently, having negative excess kurtosis.


leptokurtosis

(statistics) The property of having kurtosis greater than that of a normal distribution; equivalently, having positive excess kurtosis.


mesokurtosis

(statistics) The property of having kurtosis equal to that of a normal distribution; equivalently, having zero excess kurtosis.


hyperbolike

hyperbolike (comparative more hyperbolike, superlative most hyperbolike)

more hyperbolike (comparative)
most hyperbolike (superlative)

(mathematics) Having topological properties that are equivalent to the existence of a hyperbolic structure.


superexponential

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From super- + exponential; so called because such a function approximates an exponential function from above.

(mathematics, of a real-valued function f on the non-negative real numbers) Having the properties that f(0) = 1 and ∀ g,h ≥ 0: f(g)f(h) ≤ f(g+h) .


IEO

en-noun

IEO (countable and uncountable, plural IEOs)

initial exchange offering
w:initial exchange offering

(cryptocurrencies) Initialism of initial exchange offering.


alternating knot

alternating knot (plural alternating knots)

(topology) A knot that has a knot diagram in which, in traveling along the knot, one passes through intersections alternatingly: over, under, over, under, etc.


knot diagram

(topology) A representation in the plane of a knot, with no triple points.


hillclimbing

(mathematics) A simple form of optimization that starts with an arbitrary solution to a problem, then attempts to find a better solution by incrementally changing a single element of the solution.


codeword

Bob cannot get any information out of the codeword since he doesn't know what transmission bases Alice used.

(cryptography) A string representing an encoded piece of text.


flype

(mathematics) A transformation of a knot involving a 180° rotation of a tangle


duplation

(mathematics) A historic form of multiplication based on doubling


disphenoid

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From di- (“twice, double”) + sphenoid (“wedge-shaped crystal or bone of the skull”).

prefix

The mineral chalcopyrite commonly crystallizes in disphenoids that are very difficult to distinguish from tetrahedrons.

1949, Edward Salisbury Dana, Minerals and How to Study Them, page 32:

1973, H. S. M. Coxeter, 3rd Edition, unnumbered page,
To make a model of a disphenoid, cut out an acute angled triangle and fold it along the joins of the mid-points of the sides. The disphenoid is said to be rhombic or tetragonal according as the triangle is isosceles or scalene.

If you rotate the [tetragonal] disphenoid 90° around its 2-fold axis and then perform the operation of inversion through the center-point of the object, it will occupy its original position again.

1977, Elizabeth A. Wood, Crystals and Light: An Introduction to Optical Crystallography, Revised edition, page 8:

In addition it should be remarked that there are two types of disphenoids, with different symmetries: the tetragonal disphenoid (having isosceles facets) and the rhombic one.

1993, Horst Martini, “A Hierarchical Classification of Euclidean Polytopes with Regularity Properties”, in Tibor Bisztriczky, Peter McMullen, Rolf Schneider, Asia Ivic Weiss, editors, Polytopes: Abstract, Convex and Computational, Proceedings of the NATO Advanced Study Institute, page 83:

(geometry) A non-regular tetrahedron whose four faces are congruent acute-angled triangles.

bisphenoid

non-regular tetrahedron with congruent faces


pointwise

(mathematics) Occurring or true for each point of a given set.


subtree

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(mathematics, computer science, graph theory) A tree wholly contained in another.

podstrom

mathematics, computer science: a tree wholly contained in another


bilinear

The function f(x,y)#61;xy is bilinear, because f(ax#43;bu,y)#61;af(x,y)#43;bf(u,y) and f(x,ay#43;bv)#61;af(x,y)#43;bf(x,v) for all values.

(linear algebra, of a function in two variables) Linear (preserving linear combinations) in each variable.

bilineární

(mathematics) linear in each of two variables

bilinear isotropic hardening

Möbius transformation
Möbius transformation

(complex analysis, physics, engineering) Of or pertaining to a Möbius transformation (type of conformal map representable as the ratio of two linear functions).


cuarta

From Spanish cuarta (“fourth”). Doublet of quart, quarter, and cuarto, &c.

(historical) A traditional Galician unit of dry measure, a quarter-ferrado equivalent to about 3–4.5 L depending on the substance measured.


diffeomorphism

(mathematics) A differentiable homeomorphism (with differentiable inverse) between differentiable manifolds.

微分同胚

mathematics: differentiable homeomorphism between differentiable manifolds


teleogenetic

en-adj

teleogenetic (comparative more teleogenetic, superlative most teleogenetic)

more teleogenetic (comparative)
most teleogenetic (superlative)

This is a teleogenetic system.


teleogenesis

(cybernetics) Autonomous setting of goals


polynomic

polynomic (comparative more polynomic, superlative most polynomic)

more polynomic (comparative)
most polynomic (superlative)


viss

Borrowed from Tamil வீசை (vīcai) and/or Telugu వీసె (vīse).

(Myanmar) A Burmese unit of measure for weight, approximately 1.63293 kilograms (3.6 pounds).

ပိဿာ

Burmese unit of weight, approximately 1.63293 kg


hyperboloid

A particular surface in three-dimensional Euclidean space, the graph of a quadratic with all three variables squared and their coefficients not all of the same sign.


Archimedes

är′kə-mēʹdēz

/ˌɑːɹkɪˈmiːdiːz/

Learned borrowing from Latin Archimēdēs, from Ancient Greek Ἀρχιμήδης (Arkhimḗdēs).

An Ancient Greek mathematician, physicist and engineer (c. 287–212 BCE).


fibration

(algebraic topology) A continuous mapping satisfying the homotopy lifting property with respect to any space.


n-ary

(mathematics) Of, or relating to, n entities (where n is an arbitrary or large number).


vigintile

From Latin viginti (“twenty”) + -ilis (adjective-forming suffix).

(statistics) Any of the values in a series that divides the distribution of individuals in that series into twenty groups of equal frequency.


param

(mathematics, programming, informal) Abbreviation of parameter.


overdispersion

(statistics) The presence of greater dispersion in a data set than would be expected according to the statistical model in use.