monotone function

monotone function (plural monotone functions)

monotone Funktion

order theory: function such that either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x)

Where defined, the first derivative of a monotone function never changes sign, although it may be zero.

Section 1 contains Lebesgue's main tool, a theorem saying that monotone functions on the line are differentiable almost everywhere.

2005, Anthony W. Knapp, Basic Real Analysis, Springer, page 357:

Monotone functions on #91;a,b#93; have nice properties. For example, they are integrable on #91;a,b#93; and have only a countable number of jump discontinuities. In this section, we shall also show that every monotone function is a function of bounded variation, and hence the class #92;mathit#123;BV#125;(#91;a,b#93;) contains the class of monotone functions on #91;a,b#93;.

2011, Saminathan Ponnusamy, Foundations of Mathematical Analysis, Springer, page 469:

We saw in the previous section that monotone functions have some nice properties. For example, a monotone function is continuous except possibly on a countable set. They are also closed under scalar multiplication, and the sum of two increasing functions is increasing. (Exercise (4) on page 103). However, the difference and product of two monotone functions are not necessarily monotone (Exercise (5) on page 103).

2013, Donald Yau, A First Course in Analysis, World Scientific, page 104:

(calculus) A function f : X→R (where X is a subset of R, possibly a discrete set) that either never decreases or never increases as its independent variable increases; that is, either x ≤ y implies f(x) ≤ f(y) or x ≤ y implies f(y) ≤ f(x).

monotone Funktion

calculus: real function that either never decreases or never increases

nondecreasing function

function that never decreases as its independent variable increases

nonincreasing function

function that never increases as its independent variable increases

mathematical analysis
mathematical analysis

(order theory, mathematical analysis) A function f : X→Y (where X and Y are posets with partial order "≤") with either: (1) the property that x ≤ y implies f(x) ≤ f(y), or (2) the property that x ≤ y implies f(y) ≤ f(x).


rectilinear

en-adj

rectilinear (comparative more rectilinear, superlative most rectilinear)

more rectilinear (comparative)
most rectilinear (superlative)

/ˌɹɛktɪˈlɪniɚ/

/ˌɹɛktɪˈlɪnɪə/

From post-Classical Latin; either from rectilīneāris or from rectilīneus (whence rectiline) + -ar, in both cases ultimately deriving from rectus (“straight”) + līnea (“line”).

(geometry, art) Formed from straight lines.


nilpotent

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From nil (“not any”) + potent (“having power”) with literal meaning “having zero power” - bearing Latin roots nil and potens.
Coined in 1870, along with idempotent, by American mathematician Benjamin Peirce to describe elements of associative algebras.

compound

If a square matrix is upper triangular, then it is nilpotent (under the usual matrix multiplication).

The rest of this book is devoted to determining the conjugacy classes and centralizers of nilpotent elements in L(G) and unipotent elements in G, where G is an exceptional algebraic group of type E₈,E₇, E₆, F₄ or G₂ over an algebraically closed field K of characteristic p. This chapter contains statements of the main results for nilpotent elements.

2012, Martin W. Liebeck, Gary M. Seitz, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, American Mathematical Society, page 129:

(mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.

linear transformation
linear transformation

(mathematics, algebra) In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.

(Lie theory, of an element x of a Lie algebra L) Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).

lower central series
lower central series

(Lie theory, of a Lie algebra) Such that the lower central series terminates.

(group theory, of a group) Admitting a central series of finite length.

(ring theory, of an ideal I) Such that there exists a natural number k with Iᵏ = 0.

(semigroup theory, of a semigroup with zero) Containing only nilpotent elements.

(of an algebra over a commutative ring) Such that there exists some natural number n (called the index of the algebra) such that all products (of elements in the given algebra) of length n are zero.


nilpotent

The so-called spinor algebra of C(2), the language of the quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra of space, including its beautiful representation on the Riemann sphere, and a new proof of the Heisenberg uncertainty principle.

2015, Garret Sobczyk, “Part I: Vector Analysis of Spinors”, in arXiv:


CSPRNG

pseudorandom number generator
pseudorandom number generator#English

(cryptography) Initialism of cryptographically secure pseudorandom number generator.


codebook

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In the 19th century codebooks were used not so much for secrecy as for compression, to bring down the prohibitive cost of telegraph communication. […] But when Dr. Bellovin hunted though the card catalog, his interest was piqued by an 1882 codebook whose title included the word “secrecy.”

2011 July 25, John Markoff, “Codebook Shows an Encryption Form Dates Back to Telegraphs”, in The New York Times:

(cryptography) A book, table, database, or other object that stores the mapping between plaintext words or phrases and their equivalents in a code.

salakirjoitusavain

cryptography: mapping between plaintext and code


ECC

en-noun

ECC (countable and uncountable, plural ECCs)

(cryptography) Initialism of elliptic curve cryptography.


globoid

A globoid is always round.

(mathematics) A spherical representation or projection of a sphere or ellipsoid.


globoid

It's presented in globoid form.

(mathematics) Of, or pertaining to, a globe


twotino

This provides a possible explanation for the low fraction of twotinos compared to plutinos in the Kuiper belt.

2009, A. C. Quillen, “Resonances in Galactic and Circumstellar Disks”, in G. Contopoulos, P. A. Patsis, editors, Chaos in Astronomy: Conference 2007, Springer, page 199:

Plutinos are Kuiper belt objects in a 2:3 resonance (a = 39.4 AU) with Neptune and are named after Pluto since these bodies have orbits similar to Pluto. Twotinos are objects that are in a 1:2 resonance (a = 47.8 AU) with Neptune.

2017, Thomas H. Burbine, Asteroids, Cambridge University Press, page 234:

These objects have been given the name of twotinos (rhymes with "plutinos").
Interestingly, there are very few low-eccentricity TNOs beyond the twotinos.

2021, Barbara Ryden, Bradley M. Peterson, Foundations of Astrophysics, Cambridge University Press, page 276:

(astronomy) Any astronomical object, on the apparent outer edge of the Kuiper Belt, whose orbit has a 1:2 resonance with the planet Neptune.

Resonant trans-Neptunian object#1:2 resonance ("twotinos", period ~330 years)


significant digit

significant digit (plural significant digits)

significant figure
significant figure#English

(mathematics) Synonym of significant figure


canonical form

canonical form (countable and uncountable, plural canonical forms)

A canonical form is an element of a set of representatives of equivalence classes of forms such that there is a function or procedure which projects every element of each equivalence class onto that one element, the canonical form of that equivalence class. The canonical form is expected to be simpler than the rest of the forms in some way. For example, for cubic polynomials acted upon by the group of translations along the abscissa, the canonical forms are cubic polynomials without a quadratic term.

(mathematics, computing) A standard or normal presentation of a mathematical entity or a text string, etc.


(geometry) Synonym of pentacontagon: A 50-sided polygon.


rigidification

/ɹɪˌd͡ʒɪdɪfɪˈkeɪʃən/

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(geometry) A form of isomorphism applied between line bundles.


maund

From Hindi मन (man) / Urdu من (man), and their source, Persian من, from Middle Persian, from Akkadian 𒈠𒉡𒌑 (manû). The -d is probably from assimilation with Etymology 1 above, or from comparison with pound.

Now the rail has come, and the fire-carriage says buz-buz-buz, and a hundred lakhs of maunds slide across that big bridge.

1888, Rudyard Kipling, “In Flood Time”, in In Black and White, Folio Society, published 2005, page 410:

One mann or maund is approximately 37.32 kilograms.

2023, Radhika Iyengar, Fire on the Ganges, Fourth Estate, page 146:

A unit of weight in south and west Asia, whose value varies widely by location.


descriptive statistics

(statistics) A branch of statistics dealing with summarization and description of collections of data—data sets, including the concepts of arithmetic mean, median, mode, and quantile.


nominal variable

nominal variable (plural nominal variables)

(statistics, metrics) A variable with values which have no numerical value, such as gender or occupation.


ratio variable

(statistics) A variable with the features of interval variable and, additionally, whose any two values have meaningful ratio, making the operations of multiplication and division meaningful.


interval variable

interval variable (plural interval variables)

(statistics) An ordinal variable with the additional property that the magnitudes of the differences between two values are meaningful.


ordinal variable

ordinal variable (plural ordinal variables)

(statistics) A variable with values whose order is significant, but on which no meaningful arithmetic-like operations can be performed.


binomial distribution

binomial distribution (plural binomial distributions)

The first two have long histories in statistical theory, the binomial distribution having been discovered by James Bernoulli about 1700 and the Poisson distribution, which is a limiting form of the binomial distribution, by S. D. Poisson in 1837.

1979, M. G. Bulmer, Principles of Statistics, Dover, page 81:

The number of hits by a player in a given number of at-bats can be represented by a binomial distribution where the probability of a hit is the player's "true" batting average.

2003, Jim Albert, Teaching Statistics Using Baseball, Mathematical Association of America, page 263:

In any application of the binomial distribution, we must clearly specify which outcome is the success and which is the failure. The binomial distribution model allows us to compute the probability of observing a specified number of successes when the process is repeated a specific number of times (e.g., in a set of patients) and the outcome for a given patient is either a success or a failure.

2008, Lisa Marie Sullivan, Essentials of Biostatistics, Jones and Bartlett Publishers, page 67:

probability distribution
probability distribution

(probability theory, statistics) The discrete probability distribution of the number of successes in a sequence of n independent trials, each of which yields success with probability p.


binomial coefficient

binomial coefficient (plural binomial coefficients)

(combinatorics) a coefficient of any of the terms in the expansion of the binomial (x+y)ⁿ, defined by n choose k=(n!)/(k!(n-k)!), read as "n choose k"


differential geometry

differential geometry (usually uncountable, plural differential geometries)

1945, Eric Temple Bell, The Development of Mathematics, 2nd Edition, 1992 Republication, page 358,
[…] projective differential geometries of the American and Italian schools do not seem to have attracted physicists.

1962, I. M. James, The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry, page 189,
The general theory of manifolds of class 2 is a sub-class of differential geometries, which contain the theory of affine connections, curvature and osculating sub-spaces.

Note that projective differential geometry is a basis for Euclidean and non-Euclidean differential geometries since metric properties of submanifolds of Euclidean and non-Euclidean spaces should only be added to their projective properties.

1993, M. A. Akivis, V. V. Goldberg, Projective Differential Geometry of Submanifolds, page v:

In this sense, C#123;k#95;0#125; is the natural hypothesis of differentiability in the particular question of differential geometry.

2012, Heinrich W. Guggenheimer, Differential Geometry, page 145:

differentiable manifold
differentiable manifold

(geometry, mathematical analysis) The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra.


differential topology

(mathematics) Field dealing with differentiable functions on differentiable manifolds.


number field

algebraic number field
algebraic number field

(algebra, field theory) algebraic number field


nonidentity

Moreover, in a group of prime order p, every non-identity element (i.e. every element other than 1) has period p.

1995, Thomas A. Whitelaw, Introduction to Abstract Algebra, →ISBN, page 99:

(mathematics) An operator which modifies its operand, and which therefore is not the identity.


objective function

objective function (plural objective functions)

(mathematics) A function to be maximized or minimized in optimization theory.


saw tooth

(mathematics, engineering) Describing a function or waveform that consists of repeated triangular transitions when graphed.


sawtooth

(cellular automata) A pattern whose living cell population reaches new peaks infinitely many times before dropping to a fixed value after each peak.


Markovian

From Markov + -ian, named for the Russian mathematician Andrey Markov.

It is not immediately obvious that a random variable with distribution f(x) can be produced by the Gibbs sequence of (2.3) or that the sequence even converges. That this is so relies on the Markovian nature of the iterations, which we now develop in detail for the simple case of a 2 × 2 table with multinomial sampling.

1992, Casella and George, Explaining the Gibbs Sampler, in: The American Statistician 46(3) 167–174

AR(p) models are simple univariate devices to capture the often-observed Markovian nature of financial and macroeconomic data […]

2018, Guidolin and Pedio, Essentials of Time Series for Financial Applications, Academic Press:

(statistics, of a process) Exhibiting the Markov property, in which the conditional probability distribution of future states of the process, given the present state and all past states, depends only upon the present state and not on any past states.


uniformize

en-verb

uniformize (third-person singular simple present uniformizes, present participle uniformizing, simple past and past participle uniformized)

uniformizes (present singular third-person)
uniformizing (participle present)
uniformized (participle past)
uniformized (past)

It is clear that these functions are also the only ones to be uniformized by the simple mapping of the Riemann surface, for of course any function that is single-valued in t must have been, before the mapping, a single-valued function on the Riemann surface.

2000, Ludwig Bieberbach, Conformal Mapping, →ISBN, page 198:

(mathematics) To carry out a process of uniformization, by which a multiple-valued function on a Riemann surface is converted to a single-valued function.


healthy participant effect

(medicine, statistics) A skewing of data in randomized medical studies that occurs when healthy participants are less likely to drop out of the study than sicker patients.


Basel problem

Named after Basel, the home town of Euler and of the Bernoulli family who unsuccessfully attacked the problem.

As noted, some of Euler's contemporaries, while accepting his answer to the Basel Problem, wondered about the validity of the argument that got him there.

1999, William Dunham, Euler: The Master of Us All, Mathematical Association of America, →ISBN, page 55:

Solving the Basel problem was one of the early triumphs of L. Euler (1707–1783)... .

2005, Rajendra Bhatia, Fourier Series, Mathematical Association of America, →ISBN, section 3.10, page 75:

And so ends one of Euler's most famous papers. We see that Euler actually solves the Basel problem three times and that he does much more.

2007, Charles Edward Sandifer, The Early Mathematics of Leonhard Euler, Mathematical Association of America, →ISBN, page 165:

(mathematics) The question as to the value of ∑ₙ₌₁ ᪲1/(n²), the sum of the reciprocals of the squares of the positive integers.


Riemann zeta function

en-noun

Riemann zeta function (usually uncountable, plural Riemann zeta functions)

Named after German mathematician Bernhard Riemann.

named-after

It is straightforward to show that the Riemann zeta function has zeros at the negative even integers and these are called the trivial zeros of the Riemann zeta function.

2004, Paula B. Cohen, “Interactions between number theory and operator algebras in the study of the Riemann zeta function (d'apres Bost-Connes and Connes)”, in David Chudnovsky, Gregory Chudnovsky, Melvyn Bernard Nathanson, editors, Number Theory: New York Seminar 2003, Springer,, page 87:

The Riemann zeta-function (which has no relation to the Weierstrass function of Chapter 8, and must not be confused with it) was originally of interest because of its connection with number theory. Since then it has served as the model for a proliferation of "zeta-functions" throughout mathematics. Some mention of the Riemann zeta-function, and treatment of the prime number theorem as an asymptotic result have become a topic treated by writers of introductory texts in complex variables.

2008, Sanford L. Segal, Nine Introductions in Complex Analysis, Revised edition, Elsevier (North-Holland), page 397:

2009, Arthur T. Benjamin, Ezra Brown (editors), Biscuits of Number Theory, Mathematical Association of America, page 195,
The Riemann zeta function is the function ζ(s)=∑ₙ₌₁ ᪲n⁻ˢ for s a complex number whose real part is greater than 1. […] The historical moments include Euler's proof that there are infinitely many primes, in which he proves
ζ(s)=∏ₚₚᵣᵢₘₑ(1-1/(pˢ))⁻¹
as well as Riemann's statement of his hypothesis and several others. Beineke and Hughes then define the moment of the modulus of the Riemann zeta function by
I_k(T)=1/T∫₀ ᪲|ζ(1/2+it)|²ᵏdt
and take us through the work of several mathematicians on properties of the second and fourth moments.

analytic continuation
analytic continuation

(number theory, analytic number theory, uncountable) The function ζ defined by the Dirichlet series ζ(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1.

Riemann-zeta-functie

analytic continuation of a function defined as the sum of a Dirichlet series


collider

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(graph theory) A node in a causal graph that has at least two incoming edges.


U-shaped

en-adj

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

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

http://www.nps.gov/archive/olym/uv.htm,
After the ice melts away, the valley appears U-shaped.

Shaped like the letter U; bent such that the two ends are parallel.

A-shaped - B-shaped - C-shaped - D-shaped - E-shaped - F-shaped - G-shaped - H-shaped - I-shaped - J-shaped - K-shaped - L-shaped - M-shaped - N-shaped - O-shaped - P-shaped - Q-shaped - R-shaped - S-shaped - T-shaped - U-shaped - V-shaped - W-shaped - X-shaped - Y-shaped - Z-shaped


nonempty

(mathematics) Of a set, containing at least one element, thereby being distinct from the empty set.


homographic

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From homo- + -graphic; alternatively, homograph + -ic.


nummular

nummular (comparative more nummular, superlative most nummular)

more nummular (comparative)
most nummular (superlative)

From Latin nummulus (“(small amount of) money”) + English -ar (suffix forming adjectives with the sense ‘of, pertaining to, or near’). Nummulus is the diminutive of nummus (“a coin; piece of money”) + -ulus (diminutive suffix); while nummus is from Doric Greek νοῦμμος (noûmmos), from Ancient Greek νόμος (nómos, “kind of coin”), from νέμω (némō, “to deal out, dispense, distribute”) (from Proto-Indo-European *nem- (“to distribute; to give; to take”)) + -ος (-os, suffix forming nouns).

硬幣形的 /硬币形的

flattened with a rounded form; coin-shaped

NUMMULAR […] An epithet applied to the sputa in phthisis, when they flatten at the bottom of the vessel, like a piece of money.

[1839, Robley Dunglison, “NUMMULAR”, in Medical Lexicon. A New Dictionary of Medical Science, […], 2nd edition, Philadelphia, Pa.: Lea and Blanchard, successors to Carey and Co., →OCLC, page 421, column 2:

(by extension) Flattened with a rounded form, as a disc; coin-shaped.

(pathology, obsolete) Of sputum: forming flat, round shapes (formerly thought to be a symptom of tuberculosis).


MRP

en-noun

MRP (countable and uncountable, plural MRPs)

MRP stands for Multilevel Regression Post-stratification.

2024 June 28th, “A Different Bias” (channel name of Phil Moorhouse), What is an MRP Election Poll?, via YouTube, 2:11–2:14:

(statistics) Initialism of multilevel regression and poststratification (“a technique for estimating public opinion within a specific subgroup”).


Dehn surgery

Dehn surgery (countable and uncountable, plural Dehn surgeries)

(topology) The removal of a solid torus from a 3-dimensional manifold, followed by its being replaced via a homeomorphism of its boundary.

(topology, specifically) The same, but with the manifold in question being the 3-dimensional sphere.


solid torus

(topology) The topological space that is a Cartesian product of the two-dimensional disk and the circle.

(mathematics) The standard representation of that topological space within Euclidean 3-dimensional space.


incompressible

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From French incompressible, from in- + compressible.

(calculus, of a vector field) Having a divergence equal to zero.


Pareto distribution

Pareto distribution (plural Pareto distributions)

(statistics) A probability distribution such that for a random variable X with that distribution holds that the probability that X is greater than some number x is given by

A probability distribution such that for a random variable X with that distribution holds that the probability that X is greater than some number x is given by
 Pr (X>x)=(x/(x_m))⁻ᵏ
for all x ≥ xₘ, where xₘ is the (necessarily positive) minimum possible value of X, and k is a positive parameter.


simply connected

(topology, of a topological space) Having its fundamental group a singleton.

单连通的

in topology, having its fundamental group a singleton


simple connectivity

(topology) The state of being simply connected.


countably

(mathematics) In a way that can be put into one-to-one correspondence with the natural numbers or any subset thereof.


supersolid

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(mathematics) An analogue in a space of four or more dimensions of a solid in three dimensions.


tonelada

From Portuguese and Spanish tonelada, from tonel (“tun”) + -ada (“-ful”), from Old French tonel (“little tun, cask”), from tone + -el (“-elle: forming diminutives”), from Late Latin tunna (“tun”), from Proto-Celtic *tunna (“hide, skin”).

(historical) A traditional Spanish unit of mass, equivalent to about 920 kg.


Augean

en-adj

Augean (comparative more Augean, superlative most Augean)

more Augean (comparative)
most Augean (superlative)

/ɔːˈd͡ʒiːən/

From Latin Augeas + -an. Augeas is a figure in Greek mythology whose stables were never cleaned until Hercules was given the task of cleaning them.

an Augean task


senary

From the Latin sēnārius (“consisting of six each”), from sēnī (“six each, six at a time”) + -ārius (whence the English suffix -ary).

der

The senary fraction 0.2 is one-third, i.e. two-sixths.

(arithmetic) Of, pertaining to, or based on six.


senary

(arithmetic) The numeral system which uses six as the base.


cleartext

en-noun

cleartext (countable and uncountable, plural cleartexts)

(cryptography) The unencrypted form of an encrypted text; plain text


icositetrahedron

icositetrahedron (plural icositetrahedrons or icositetrahedra)

icositetrahedrons (plural)
icositetrahedra (plural)

(mathematics) Any of several solids having twenty-four faces.


first-passage time

first-passage time (plural first-passage times)

(mathematics) The time taken for a random walker to reach a specified target.


random walker

(mathematics) An object taking a random walk.


random walk

(mathematics) A stochastic path consisting of a series of sequential movements, the direction (and sometime length) of which is chosen at random.


quadrate

From Middle English quadrat, quadrate, from Latin quadrātum. Doublet of quadrat; compare also quadrant (“square or quadrangle”).

At which command, the powers militant
That stood for heav'n, in mighty quadrate joyn'd.

1667, John Milton, “Book V”, in Paradise Lost. […], London: […] [Samuel Simmons], and are to be sold by Peter Parker […]; [a]nd by Robert Boulter […]; [a]nd Matthias Walker, […], →OCLC; republished as Paradise Lost in Ten Books: […], London: Basil Montagu Pickering […], 1873, →OCLC, lines 61-62:

(geometry) A plane surface with four equal sides and four right angles; a square; hence, figuratively, anything having the outline of a square.


payoff function

payoff function (plural payoff functions)

(game theory) A mathematical function describing the award given to a single player at the outcome of a game.


utility function

utility function (plural utility functions)

(game theory) A mathematical function that assigns a real number to every element of the outcome space in a way that captures the agent's preferences over both simple and compound lotteries.


nonconstructive

(mathematics) That proves the existence of something without demonstrating a method of construction.


lugeon

(geology) A unit of measurement of permeability, equal to one foot per year.


stochastically

en-adv

stochastically (comparative more stochastically, superlative most stochastically)

more stochastically (comparative)
most stochastically (superlative)

That is when we have no clear and distinct conception of the truth of a proposition (which is the knowledge of it and can never be false) we may notwithstanding, extend our assents further and judge stochastically, that is opine, this way or that way concerning it, and that sometimes with a great deal of confidence and assurance too.

1838, Ralph Cudworth, edited by John Allen, A Treatise of Freewill, … Now First Edited, from the Original MS., and with Notes, London: John W[illiam] Parker, West Strand, →OCLC, pages 39–40:

In the table the scores from group A are stochastically smaller than those for B, C, or D because group A always has at least as many scores at or below a particular number as any of the other groups. Similarly, the scores from group B are stochastically smaller than those from group C.

1954, Gordon W[illard] Allport, “Selective Quantitative Techniques”, in Gardner Lindzey, editor, Handbook of Social Psychology, volumes 1 (Theory and Method), Reading, Mass.: Addison-Wesley, →OCLC, page 317, column 2:

In still other cases, the state of the system is stochastically determined or else assumed to be stochastically determined, that is, determined by a random factor.

1973 October, J[ames] C[lement] I. Dooge, “Lecture 1. Hydrologic Systems.”, in Linear Theory of Hydrologic Systems (Technical Bulletin; no. 1468), Washington, D.C.: Agricultural Research Service, United States Department of Agriculture, →OCLC, page 8:

In a stochastic manner; by means of a process involving a randomly determined sequence of events.


LLM

Some skeptics argue that the software is capable only of blind mimicry — that it’s imitating the syntactic patterns of human language but is incapable of generating its own ideas or making complex decisions, a fundamental limitation that will keep the L.L.M. approach from ever maturing into anything resembling human intelligence.

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

Currently, large language models (LLM) are the base model for creating more specific natural language producers, like chatbots or personal assistants. BERT, GPT-3, and other LLM can be used to program all kinds of “semantic machines”, to create machines for almost any kind of linguistic purpose.

2022, Hendrik Kempt, Synthetic Friends: A Philosophy of Human-Machine Friendship, Springer Nature, →ISBN, page 22:

We design WikiChat (Figure 1) to ground LLMs using Wikipedia to achieve the following objectives. While LLMs tend to hallucinate, our chatbot should be factual.

2023, Sina J. Semnani, Violet Z. Yao, Heidi C. Zhang, Monica S. Lam, “WikiChat: A Few-Shot LLM-Based Chatbot Grounded with Wikipedia”, in arXiv:

large language model
large language model#English

(machine learning) Initialism of large language model.

logic learning machine
w:logic learning machine

(machine learning) Initialism of logic learning machine.


common multiple

en-noun

common multiple (plural common multiples)

120 and all its multiples are common multiples of 60, 8 and 15.

(mathematics) A number which may be divided by any of a given set of numbers without a remainder.


spherule

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From Latin sphērula, sphaerula, from sphēra, sphaera (“sphere”) + -ula (diminutive suffix).


histogram

/ˈhɪstəˌɡɹæm/

Probably from Ancient Greek ἱστός (histós, “mast”) + -γραμμα (-gramma), although it is sometimes claimed to have been derived from historical + diagram; coined in 1891 by English mathematician Karl Pearson.

Such distinctions, however, require detailed information, such as histograms of the distribution of energy use among residential customers, both by month and by year.

1983, Alan Meier, Janice Wright, Arthur H. Rosenfeld, Supplying Energy Through Greater Efficiency: The Potential for Conservation, University of California Press, page 39:

The use of the piecewise linear frequency polygon (FP) in place of the underlying histogram would seem mainly a graphical advantage.

2005, D. W. Scott, S. R. Sain, “Multidimensional density estimation”, in C. R. Rao, E. J. Wegman, J. L. Solka, editors, Data Mining and Data Visualization, Elsevier, page 237:

A histogram is constructed by placing the variable of interest on the horizontal axis and the frequency, relative frequency or percent frequency on the vertical axis.[…]Histograms for data found in applications are never perfectly symmetric, but the histogram for many applications may be roughly symmetric.

2017, David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran, Essentials of Statistics for Business and Economics, Cengage Learning, page 44:

(statistics) A graphical display of numerical data in the form of upright bars, with the area of each bar representing frequency.


nonfunctional

(mathematics, of a relation) Not a function in the mathematical sense.


NOT

(mathematics, logic) A unary operation on logical values that changes true to false, and false to true.


spiral of Archimedes

spiral of Archimedes (plural spirals of Archimedes)

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


Archimedean spiral

Archimedean spiral (plural Archimedean spirals)

Named after Archimedes of Syracuse (c. 287 – c. 212 BC), a Greek mathematician, physicist, engineer, inventor, and astronomer.

Max flees and tries to visit Sol, only to find that he has died. Max searches his house and finds mathematical scribblings similar to his own. On a Go board, with its pieces arranged in an Archimedean spiral, Max finds a piece of paper with the 216-digit number.

2010 November 16, Wikipedia contributors, “Pi (film)”, in English Wikipedia, Wikimedia Foundation:

Archimedean spiral
Archimedes of Syracuse

Archimédova spirála

a spiral that increases in distance from the point of origin at a constant rate


preorder

The relation of logical implication over sentences is an example of a preorder.

Example 436 For each set A, the relation #92;subseteq is a preorder on #92;mathcal#123;P#125;(A).

2002, Yves Nievergelt, Foundations of Logic and Mathematics, Springer (Birkhäuser), page 152:

Let us first compare S#95;1, S#95;2 and S#95;3 w.r.t. the partial preorder #92;succeq.

2010, S. Kaci, “Refined Preference-Based Argumentation Frameworks”, in Pietro Baroni, F. Cerutti, M. Giacomin, G. R. Simari, editors, Computational Models of Argument: Proceedings of COMMA 2010, IOS Press, page 306:

2000, Jean-Charles Pomerol, Sergio Barba-Romero, Multicriterion Decision in Management: Principles and Practice, Springer, Softcover, page 58,
It can easily be verified that the above relation is a preorder, i.e. that it is reflexive and transitive.

(set theory, order theory) A binary relation that is reflexive and transitive.


irreflexive

(set theory) Of a binary relation R on X: such that no element of X is R-related to itself.


structurality

structurality (countable and uncountable, plural structuralities)

(mathematics, logic) A property satisfied by structural translations from sequents into equations or from equations into sequents.


attractor

(mathematics, physics) A set of points or states to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed.


compactify

en-verb

compactify (third-person singular simple present compactifies, present participle compactifying, simple past and past participle compactified)

compactifies (present singular third-person)
compactifying (participle present)
compactified (participle past)
compactified (past)

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(mathematics, transitive) To enlarge (a topological space) in order to render it compact.


regression to the mean

en-noun

regression to the mean (plural regressions to the mean)

(statistics) The phenomenon by which extreme examples from any set of data are likely to be followed by examples which are less extreme; a tendency towards the average of any sample. For example, the offspring of two very tall individuals tend to be tall, but closer to the average (mean) than either of their parents.


PWA

PWA (countable and uncountable, plural PWAs)

PWA functions

(mathematics) Initialism of piecewise affine.


semimajor axis

Coordinate term: semiminor axis

(geometry) Half of the major axis of a circle or ellipse.

半長軸 /半长轴

half of the major axis of a circle or ellipse

(geometry) Half of the distances between the two branches of a hyperbola.


major axis

halkaisija

diameter of a circle — see also diameter

(geometry) The longest diameter of an ellipse, running through the center and foci, with its ends being the widest points of the shape.


division ring

multiplicative inverse
multiplicative inverse

(algebra) A ring with 0 ≠ 1, such that every non-zero element a has a multiplicative inverse, meaning an element x with ax = 1.


multiset

Coined by Nicolaas Govert de Bruijn, multi- + set.

Two words are anagrams if they are made up of the same multiset of letters.

Membrane computing essentially deals with multisets, which are sets with multiplicities associated with their elements.

2002, Gheorghe Pǎun, Membrane Computing: An Introduction, Springer, page 49:

2006, Xin Chen, Lan Liu, Zheng Liu, Tao Jiang, On the Minimum Common Integer Partition Problem, Tiziana Calamoneri, Irene Finocchi, Giuseppe F. Italiano (editors), Algorithms and Complexity: 6th Italian Conference CIAC 2006, Proceedings, Springer, LNCS 3998, page 236,
A partition of a positive integer n is a multiset of positive integers that add up to exactly n, and an integer partition of a multiset S of integers is defined as the multiset union of partitions of integers in S.

2012, Edward A. Scheinerman, Mathematics: A Discrete Introduction Brooks/Cole (Cengage Learning), page 102,
Two multisets are the same provided they contain the same elements with the same multiplicities. For example, {1, 2, 3, 3} = {3, 1, 3, 2}, but {1, 2, 3, 3} ≠ {1, 2, 3, 3, 3}.

(set theory) A generalized type of set in which multiple occurrences of an element are permitted.

多重集

generalized type of set that may contain multiple occurrences of elements


WordNet

Copycat uses a network of concepts, called a Slipnet, to find correspondences between nonidentical objects, just as ARCS uses WordNet-style semantic information to find similar concepts.

1996, Keith J. Holyoak, Paul Thagard, Mental Leaps: Analogy in Creative Thought, page 259:

Recently the Group started a project of creating a thesaurus of the WordNet type for Estonian.

1997, Josephine A. Edwards, Geoffrey Kingscott, Language Industries Atlas, page 334:

By (partly) mirroring one another, general servers would probably share a similar general WordNet-like or CYC-like ontology […].

2001, Philippe Martin and Peter Eklund, "Large-scale cooperatively built KBs", Harry S. Delugach, Gerd Stumme, Conceptual Structures: Broadening the Base : 9th International Conference on, page 232

One very interesting possibility seems to be to complement WordNet-style lexicons with the SIMPLE design, thereby trying to get at a more comprehensive and coherent architecture for the development of semantic lexical resources.

2002, Nicoletta Calzolari et al., "Towards a Standard for a Multilingual Lexical Entry: The EAGLES/ISLE Initiative", in Alexander Gelbukh, ed., Computational Linguistics and Intelligent Text Processing: Third, page 270

Chai (2000) uses WordNet for information extraction, ie the identification and extraction of domain specific target information from a document [....]

2003, Piet Van Sterkenburg, editor, A Practical Guide to Lexicography, page 198:

For conference, which has 3 senses in WordNet, we get the following candidate taxonomic relations: [....]

2005, Paul Buitelaar, Philipp Cimiano, Bernardo Magnini, Ontology Learning from Text: Methods, Evaluation And Applications, page 64:

artificial intelligence
artificial intelligence

(linguistics, artificial intelligence) A particular wordnet, a semantically structured lexical database, for the English language at Princeton University.


orbital plane

The plane of ecliptic is the orbital plane of the earth and the other planets in the solar system.

(astronomy) The surface (plane) that contains an orbit.


taxicab distance

taxicab distance (countable and uncountable, plural taxicab distances)

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

Suggesting the route taken by a taxi through a grid of intersecting streets.

The taxicab distance between (0,0) and (3,4) is 7.

(mathematics) The distance between two points located on a grid, where the only path allowed is vertical and horizontal lines.


pentahedron

pentahedron (plural pentahedrons or pentahedra)

pentahedrons (plural)
pentahedra (plural)

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Their tent was too small for them to stand, a long but low pentahedron, in shape like the triangular glass prism Saeed used to have as a child, with which he would refract sunlight into little rainbows.

2017, Mohsin Hamid, Exit West, Hamish Hamilton, page 106:

(geometry) A polyhedron with five faces.


PRP

(mathematics) Initialism of probable prime.


zettameter

On the other extreme, our galaxy (we call it the Milky Way) is about 0.9 Zm (Zettameters, 100 million trillion meters) in diameter.

2015, Claude Phipps, No Wonder You Wonder!: Great Inventions and Scientific Mysteries, →ISBN:

What is the speed of light in Zm (zettameters) per second?

2016, Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Mathematical Excursions, →ISBN, page 364:

The size scale for the nuclear chemistry laboratory ranges from zeptometers (10⁻²¹ m) to zettameters (10²¹ m).

2017, Walter D. Loveland, David J. Morrissey, Glenn T. Seaborg, Modern Nuclear Chemistry, →ISBN, page 2:


yoctometer

Sheldon Cooper: My hair is growing at the rate of 4.6 yoctometers per femtosecond.

2012, Mark Cendrowski, The Big Bang Theory, Season 5, Episode 18, "The Werewolf Transformation"


yottameter

No longer do they have to say the visible universe is 1,000 yottameters in diameter. Now it's just 1 ronnameter, give or take a yottameter.

2023 January 10, Adam Rogers, “Move over, megatons”, in Business Insider:


chatbot

From chat + -bot, from earlier chatterbot.

The chatbot was quite simple yet informative.

To deal with a large number of typical queries, “chatbots” technology should be considered. A chatbot can be defined as an intelligent evolution of email. The chatbot categorizes messages on the fly and provides answers to questions accordingly. As such, it can be used as a customer support tool.

2000, Handbook on Electronic Commerce, Springer, →ISBN, page 59:

Wolfram Alpha researcher and chatbot author Robert Lockhart describes the chatbot community as being split between two competing approaches, what he calls “pure semantics” and “pure empiricism.”

2012, Brian Christian, The Most Human Human […] , Anchor Books, →ISBN, page 29:

Chatbot technology, of course, dates back to Weizenbaum’s early experiments with his Eliza program.

2015, John Markoff, Machines of Loving Grace […] , New York: Ecco Press, →ISBN, page 221:

Mr. Aumann confronted his student over whether he had written the essay himself. The student confessed to using ChatGPT, a chatbot that delivers information, explains concepts and generates ideas in simple sentences — and, in this case, had written the paper.

2023 January 16, Kalley Huang, “Alarmed by A.I. Chatbots, Universities Start Revamping How They Teach”, in The New York Times, →ISSN:

Generative AI won’t be the end of employment, we are told, only “boring work” – with chatbots helpfully doing all the soul-destroying, repetitive tasks and humans merely supervising them.

2023 May 8, Naomi Klein, “AI machines aren’t ‘hallucinating’. But their makers are”, in The Guardian, →ISSN:

(Internet, artificial intelligence) A computer program that holds conversations through a chat room.


algebraic number theory

Blend of algebraic number + number theory. Possibly (alternatively or also) a calque of German algebraische Zahlentheorie.

blend

As is well-known in algebraic number theory, there is a far-reaching analogy between number fields and algebraic function fields in one variable with finite constant field.

1998, Norbert Klingen, Arithmetical Similarities: Prime Decomposition and Finite Group Theory, Oxford University Press (Clarendon Press), page 241:

The field of mathematics that these generalize to is known as algebraic number theory. As a matter of historical fact, our development here parallels the development of algebraic number theory.

2008, Steven H. Weintraub, Factorization: Unique and Otherwise, CRC Press, page 143:

Elementary arithmetic studies divisibility and factorization of ordinary integers, Algebraic number theory considers the same questions for algebraic numbers, solutions to polynomial equations with integer coefficients. In this setting, (un)fortunately, the uniqueness of prime factorization no longer holds. Remedying and measuring its failure is the starting point of algebraic number theory.

2013, Mak Trifković, Algebraic Theory of Quadratic Numbers, Springer, page v:

(mathematics, number theory) The branch of number theory in which number-theoretic questions are expressed in terms of properties of algebraic number fields or related objects, and studied using techniques from algebra.

հանրահաշվական թվերի տեսություն

branch of number theory concerning algebraic number fields


number-theoretically

(mathematics) By means of, or in terms of, number theory.


graph-theoretically

(mathematics) In a manner which uses graph theory

(mathematics) In the sense of graph theory


set theoretically

(mathematics) In a manner which uses set theory

but see w sposób używający teorii mnogości

(mathematics) In the sense of set theory


wordnet

Bilingual corpora can be used for synset validation in a more fruitful way, especially having in mind the request that all synsets from a wordnet for a language other than English have to be associated, if possible, with an English synset using ILI.

2003, Cvetana Krstev, "Corpora Issues in Validation of Serbian Wordnet", in Václav Matoušek, Pavel Mautner, eds., Text, Speech and Dialogue: 6th International Conference, TSD 2003, České, page 133

(if a document mentions dogs, a wordnet allows the inference it is about animals)

2004, Helge Dyvik, "Translations as Semantic Mirrors: from parallel corpus to wordnet", in Karin Aijmer, Bengt Altenberg, eds., Advances in Corpus Linguistics: Papers from the 23rd International, page 312

This trimmed wordnet was used in a cross-retrieval test environment and compared with the generic wordnet and no wordnet.

2006, Paul Buitelaar et al., "Domain-Specific WSD", in Eneko Agirre, Philip Edmonds, eds., Word Sense Disambiguation: Algorithms And Applications, page 290

(artificial intelligence, linguistics) A semantically structured lexical database.


TU

University of Tulsa
w:University of Tulsa


Herschel

(Uranus): after its discoverer, William Herschel.

This Herschel could be sent through stages of Buckingham's components, producing an arbitrary excess of gliders along a variety of different paths.

1996 November 16, Paul Callahan, “Still-life glider reflector found”, in comp.theory.cell-automata (Usenet):

This uses Paul Callahan's catalysis of a glider into a Herschel and a glider, followed by David Buckingham's 77, 64, 64, 77, and 77 gen Herschel moves.

1999 October 7, Mirek Wojtowicz, “Conway's Life: Glider reflector?”, in comp.theory.cell-automata (Usenet):

In Conway's Life, for example, a surprising number of small patterns serendipitously create R-pentominos and/or B-heptominos, which are "tamable" and happen to travel very well; this is what allows Herschel circuitry to be built.

2007 May 12, Dave Greene, “Wanted: 2D CA, "as complex" but "denser" than Life”, in comp.theory.cell-automata (Usenet):

(cellular automata) A heptomino shaped like the lowercase letter h, critical as a methuselah.


communality

en-noun

communality (countable and uncountable, plural communalities)

(mathematics) A measure of variance in factor analysis.


centiampere

electric current
electric current#English

(metrology) An SI unit of electric current equal to 10⁻² amperes. Symbol: cA


picoampere

(metrology) An SI unit of current equal to 10⁻¹² amperes. Symbol: pA


femtoampere

A billionth of a millionth (10⁻¹⁵) of an ampere. Symbol: fA


zero tensor

A generalization of the zero vector to tensor space.


subconical

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(geometry, mycology) Shaped somewhat like a cone.


apolar

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(geometry) Orthogonal under the polar pairing between the symmetric algebra of a vector space and its dual.


with respect to

To calculate acceleration, you need to differentiate velocity with respect to time.

independent variable
independent variable

(mathematics) Taking as the independent variable.


missingness

In large scale surveys the assumption of missingness at random is untenable.

1992, Arijit Chaudhuri, Horst Stenger, Survey Sampling: Theory and Methods, page 282:

These methods are very sensitive to assumptions made about the missingness mechanism or about the distributions of the variables with missing data.

2002, Paul D. Allison, Missing Data, Sage Publications, →ISBN, page 86:

Some imputation models require the data to have a certain distribution of their missing values, their missingness pattern.

2006, Mamdouh Refaat, Data Preparation for Data Mining Using SAS, page 180:

(statistics) The manner in which data are missing from a sample of a population.


pigeonhole principle

pigeonhole principle (countable and uncountable, plural pigeonhole principles)

From the commonly used expository example that if n+1 pigeons are placed in n pigeonholes, at least one pigeonhole must contain two (or more) pigeons.

The pigeonhole principle is usually stated as follows.
(16.43) If more than n pigeons are placed in n holes, at least one hole will contain more than one pigeon.
The pigeonhole principle is obvious, and one may wonder what it has to do with computer science or mathematics.

1993, David Gries, Fred B. Schneider, A Logical Approach to Discrete Math, Springer, page 355:

1. κ is a regular cardinal.
2. If we put κ pigeons into λ < κ pigeonholes, then some pigeonhole must contain κ pigeons.

2009, John Harris, Jeffry L. Hirst, Michael Mossinghoff, Combinatorics and Graph Theory, Springer, page 313, Of course our list of pigeonhole principles is not all inclusive. For example, more set theoretic pigeonhole principles are given in [72]. Corollary 3.31 (Ultimate Pigeonhole Principle). The following are equivalent

2012, Dov M. Gabbay, Akihiro Kanamori, John Woods (editors), Handbook of the History of Logic: Volume 6: Sets and Extensions in the Twentieth Century, Elevier (North-Holland), page 325,
As we turn to look at various pigeonhole principles and how they are used to prove partition theorems, particularly for pairs, we keep in mind the slogan that is embedded in the Motzkin quote: complete disorder is impossible.

(mathematics) The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence).


endofunction

(mathematics) A function whose codomain is equal to its domain.


ensmallen

en-verb

ensmallen (third-person singular simple present ensmallens, present participle ensmallening, simple past and past participle ensmallened)

ensmallens (present singular third-person)
ensmallening (participle present)
ensmallened (participle past)
ensmallened (past)

From small + en- -en, by analogy with embiggen. Attested from 2002.
Logical antonym of "embiggen," a humorous neologism popularized by television writer David X. Cohen; see 1996 quotation.


capacitate

capacitate (third-person singular simple present capacitates, present participle capacitating, simple past and past participle capacitated)

capacitates (present singular third-person)
capacitating (participle present)
capacitated (participle past)
capacitated (past)

(transitive, mathematics) To reach maximum throughput on at least part of a constrained network.


phone survey

(statistics) An opinion poll or survey conducted through the use of calling people on their telephones to gather information relating to the public.


polygonization

(mathematics) The subdivision of a plane into polygons


polygonize

polygonize (third-person singular simple present polygonizes, present participle polygonizing, simple past and past participle polygonized)

polygonizes (present singular third-person)
polygonizing (participle present)
polygonized (participle past)
polygonized (past)

(mathematics) To subdivide a plane into polygons.


symmetric matrix

en-noun

symmetric matrix (plural symmetric matrixes or symmetric matrices)

symmetric matrixes (plural)
symmetric matrices (plural)

(mathematics) A square matrix that is its own transpose, and is thereby symmetric about the main diagonal

symmetrinen matriisi

a square matrix that is its own transpose, and is thereby symmetric about the main diagonal


polyalgorithm

(mathematics, computing) A set of algorithms together with rules for choosing when to use each one.


quintale

Alternative form of quintal, particularly in Italian contexts.


uncountably

From uncountable + -ly or un- + countably.

If a set is neither finite nor countably infinite, it is said to be uncountably infinite or simply uncountable.

2004, Jayant V. Deshpande, Mathematical Analysis And Applications: An Introduction, page 55:

(mathematics) In a way that is incapable of being put into one-to-one correspondence with the natural numbers or any subset thereof.


homogeneous space

homogeneous space (plural homogeneous spaces)

A manifold or topological space X on which G acts by symmetry in a transitive way.

einsleitt rúm

manifold or topological space on which G acts by symmetry in a transitive way


aliasing

(signal processing, graphics, sound recording) Distortion caused by a low sampling rate, such as a moiré effect or jaggies.

graphics; sound recording; graphics; sound recording

grajneco

distortion caused by a low sampling rate


osculating

en-adj

osculating (comparative more osculating, superlative most osculating)

more osculating (comparative)
most osculating (superlative)

(mathematics, of a curve) Having three or more points coincident with another


octonion

Blend of Latin octō (“eight”) + quaternion.

blend

According to the logic of doubling the dimensions on which Cayley–Dickson algebra is built, after quaternions the so-called 8D octonions (#92;mathbbO—Octonions) can be obtained, followed by 16D sedenions, 32D pathions, 64D chingons, 128D routons, and 256D voudons.

2022, Zlatka Valkova-Jarvis, Vladimir Poulkov, Viktor Stoynov, Dimitriya Mihaylova, Georgi Iliev, “A Method for the Design of Bicomplex Orthogonal DSP Algorithms for Applications in Intelligent Radio Access Networks”, in Symmetry, volume 14, number 3, MDPI AG, →DOI, →ISSN:

There is no theoretical limit to multispace dimensional numbering as there are definitions for octonion (8D), sedenion (16D), pathion (32D), chingon (64D), routon (128D), and voudon (256D) numbered space.

2023, Melanie Swan, Renato P. dos Santos, “Quantum Intelligence: Responsible Human-AI Entities”, in AAAI 2023 Spring Symposia, Socially Responsible AI for Wellbeing, March 27–29, 2023, USA, CEUR Workshop Proceedings, →DOI:

(mathematics) An 8-dimensional nonassociative extension of a quaternion with a real part and 7 imaginary parts (each a real multiple of a distinct square root of −1).


(topology, of a topological space) Having a singleton as its fundamental group.


fundamental group

en-noun

fundamental group (plural fundamental groups)

From the definition it will be clear the group is a topological invariant of X; i.e., if two spaces are homeomorphic, their fundamental groups are isomorphic.

1991, William S. Massey, A Basic Course in Algebraic Topology, Springer, page 35:

Therein came into focus the far-reaching vision that the perspective of non-abelian fundamental groups could lead to a fundamentally new understanding of deep arithmetic phenomena, including the arithmetic theory of moduli and Diophantine finiteness on hyperbolic curves.

2011, John Coates, Minhyong Kim, Florian Pop, Mohamed Saïdi, Peter Schneider, editors, Non-abelian Fundamental Groups and Iwasawa Theory, Cambridge University Press, page vii:

During the more than 100 years of its existence, the notion of the fundamental group has undergone a considerable evolution.

2012, Jakob Stix, editor, The Arithmetic of Fundamental Groups: PIA 2010, Springer, page ix:

(topology) For a specified topological space, the group whose elements are homotopy classes of loops (images of some arbitrary closed interval whose endpoints are both mapped to a designated point) and whose group operation is concatenation.

grup fonamental

group of equivalence classes of the homotopies of loops in a given topological space


four-vector

(mathematics) A vector in four-dimensional vector space, especially one having three spatial dimensions and one temporal dimension.


summable

(mathematics, of a function) Having a Lebesgue integral.


vectorial

(mathematics) Of or pertaining to a vector.


adelic

(mathematics) Of or pertaining to an adele ring.


quasilinear

en-adj

quasilinear (comparative more quasilinear, superlative most quasilinear)

more quasilinear (comparative)
most quasilinear (superlative)

(mathematics) Having some properties of linearity.


quasiperiodic

quasiperiodic (comparative more quasiperiodic, superlative most quasiperiodic)

more quasiperiodic (comparative)
most quasiperiodic (superlative)

(mathematics, of a function) Such that an increment of a variable leads to a multiplication by some function.


tex

A milligram per meter, a unit of linear mass density for thread or fiber.


hectowatt-hour

(physics) A measure of energy, one hundred watt-hours, or one-tenth of a UK "unit" of electricity.


schlicht

(mathematics) univalent (analytic and one-to-one) in a given region, sometimes qualified with the stipulation that the function is 0 at 0 and has a slope there equal to 1 (see Koebe function)


parameterization

en-noun

parameterization (countable and uncountable, plural parameterizations)

(design, engineering) The representation of physical characteristics or properties by parameters rather than as sui generis instances; usually and especially:

(computing) Such parameterized representation in a computer model.

The representation of a curve or surface in terms of a parametric equation.


acre foot

(US, engineering, agriculture) A unit of measure, used for volumes of water, equal to one acre times one foot (that is, to the amount of water required to cover one acre of land to a depth of one foot), which is 43,560 cubic feet, 325,851 gallons, 1,233 cubic meters.


fuzzy logic

fuzzy logic (countable and uncountable, plural fuzzy logics)

(mathematics) A form of reasoning, derived from fuzzy set theory, whereby a truth value need not be exactly zero (false) or one (true), but rather can be zero, one, or any value in between.


rhombitruncated icosidodecahedron

rhombitruncated icosidodecahedron (plural rhombitruncated icosidodecahedrons)

(geometry) An Archimedean solid composed of 122 faces, 120 vertices, and 240 edges.


equivariant

f:S→T is equivariant with respect to g,!: for every s,! in S,!, g_T,!f(s)=f(g_S,!s), where g_S,! and g_T,! are actions on different sets of the same group.

(mathematics, of a function) Not affected by a specified group action.


stellate

en-verb

stellate (third-person singular simple present stellates, present participle stellating, simple past and past participle stellated)

stellates (present singular third-person)
stellating (participle present)
stellated (participle past)
stellated (past)

From stell(a) + -ate (verb-forming suffix).

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

(geometry) To extend the edges or planes of a polyhedron to form a new shape.


sail curve

(geometry) A catenary-generated curve in the form of a cross-section of a sail filled by wind.


septagon

From Latin septem (“seven”) + Ancient Greek γωνία (gōnía, “angle”), equivalent to septa- + -gon.

(proscribed) A polygon with seven sides and seven angles.


cwt.

Short for centum weight, from Latin centum + weight.


totient

From Latin totiēns (“so many times, so often”). Coined by English mathematician James Joseph Sylvester in 1879.

coin

(mathematics) The number of positive integers not greater than a specified integer that are relatively prime to it.


Heron's formula

The formula A=√, where a, b, and c are the sidelengths of a triangle, s is its semiperimeter, and A is its area.


sidelength

(mathematics) The length of a side (of a polygon).


semiperimeter

cyclic quadrilateral
cyclic quadrilateral

(mathematics) Half of the perimeter (sum of the lengths of the sides) of a polygon. The term is typically applied to triangles, cyclic quadrilaterals, and regular polygons.


Euler characteristic

en-noun

Euler characteristic (plural Euler characteristics)

A polygon's or polyhedron's Euler characteristic is just the number of corners minus the number of edges plus the number of faces.

(topology, of a topological space) The sum of even-dimensional Betti numbers minus the sum of odd-dimensional ones.


cyclic-inscriptable

All triangles, all rectangles, and all cyclic quadrilaterals are cyclic-inscriptable.

(mathematics) Able to be inscribed in a circle; able to be circumscribed.


relatively prime

keskenään jaottomia

(of two or more positive integers) having no factors in common

keskenään jaoton ... kanssa

(of a positive integer) having no factor in common with...

24 and 35 are relatively prime.

[Nicomachus] sets up three classes, and designates them as prime, composite and relatively prime; the latter are pairs of composite numbers that are prime to each other.

1926, Nicomachus of Gerasa, Frank Egleston Robbins, Louis Charles Karpinski, chapter VIII, in Martin Luther D'Ooge, transl., Introduction to Arithmetic, New York: The Macmillan Company, page 121:

(mathematics, of two or more numbers) having no factors (except the number 1) in common.

24 is relatively prime to 35.

(mathematics, of a number) having no factors (except the number 1) in common with a specified other number or numbers.


coprime

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24 and 35 are coprime.

(number theory, of two or more positive integers) Having no positive integer factors in common, aside from 1.

24 is coprime to 35.

(number theory, of a positive integer) Having no positive integer factors, aside from 1, in common with one or more specified other positive integers.

greatest common divisor
greatest common divisor

(algebra, by extension, of two or more polynomials) Whose greatest common divisor is a nonzero constant (i.e., polynomial of degree 0).


aperiodic

en-adj

aperiodic (comparative more aperiodic, superlative most aperiodic)

more aperiodic (comparative)
most aperiodic (superlative)

(mathematics, stochastic processes, of a state) for which any return to it may occur at irregular times; not periodic.


moving average

(statistics) A weighted average that is determined for a given data point based on its value and the past values.


RW

(mathematics, probability) Initialism of random walk.


MCT

mathematical analysis
mathematical analysis

monotone convergence theorem
monotone convergence theorem#English

(mathematical analysis) Initialism of monotone convergence theorem.


law of averages

... as they will not have sufficient distribution of risk to permit the law of averages to play its part and a severe total loss may ...

1919, William David Winter, Marine Insurance: Its Principles and Practice, McGraw-Hill, page 96:

Second Law - The Law of Averages. Whenever something (such as throwing a die) can have more than one result, if all the possible results have an equal chance ...

1971, Russell Langley, Practical Statistics Simply Explained, Courier Dover Publications, →ISBN, page 22:

It is upon the ideas of 'repeated experimentation' and the law of averages that many of our notions of chance are founded.

1986, Geoffrey Grimmett, Dominic Welsh, Probability: An Introduction, OUP, →ISBN, page 124:

law of large numbers
law of large numbers

(statistics) The statistical tendency toward a fixed proportion in the results when an experiment is repeated a large number of times; the law of large numbers.


law of large numbers

(statistics) The statistical tendency toward a fixed ratio in the results when an experiment is repeated a large number of times; law of averages.


sublevel

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(mathematics) Having a lesser constant value than a related level set


swingeing

swingeing (comparative more swingeing, superlative most swingeing)

more swingeing (comparative)
most swingeing (superlative)

/ˈswɪnd͡ʒɪŋ/

/ˈswɪnd͡ʒɪŋ/

From swinge + -ing. Swinge is derived from Middle English swengen (“to strike”), from Old English swengan (“to dash, strike; to cause to swing”).

swinger

one who swinges; anything very large, forcible, or astonishing

And when Occaſion did require, / In midſt of Houſe a mighty Fire, / Of black dry'd Earth and ſwingeing Blocks / Was made, enough to roaſt an Ox; […]

1716, W[illiam] M[offat], Hesperi-neso-graphia: Or, A Description of the Western Isle. In Eight Canto’s, 4th edition, London: Printed and sold by J. Baker, at the Black-Boy in Pater-Noster-Row, →OCLC, canto II, page 7:

"Let him pursue his own course," said Diggs, taking up a pen, and making some hasty memoranda on a sheet of paper. "We shall have swingeing damages—swingeing damages."

1855, William Harrison Ainsworth, “Abel’s Interview with the Miser—Unexpected Appearance of Randulph and Cordwell Firebras—Result of the Meeting”, in The Miser’s Daughter: A Tale, London, New York, N.Y.: G[eorge] Routledge & Co., Farringdon Street; New York, 18, Beekman Street, →OCLC, page 123:

A shock for passengers by the Dover-Dunkerque "Night Ferry" is the swingeing increases in berth rates for those who are not travelling in the sleeping cars.

1962 December, “Beyond the Channel: European timetables: The winter train services”, in Modern Railways, page 413:

Every day produces more evidence that this hard Tory Brexit is a disaster in the making. Carmakers and other export manufacturers, fearing swingeing tariffs, are demanding special protections and exemptions or else they leave.

2017 March 27, “The Observer view on triggering article 50: As Britain hurtles towards the precipice, truth and democracy are in short supply”, in The Observer, London, archived from the original on 2017-05-17:

After petrol rationing ended in 1952, the BTC was aware that more swingeing cuts had to be made, and a sinister message was conveyed by the loss of the meandering 38-mile route from Blisworth to Stratford-upon-Avon in April 1952, and the 25-mile Abergavenny-Merthyr Heads of the Valleys line in January 1958.

2023 March 8, Howard Johnston, “Was Marples the real railway wrecker?”, in RAIL, number 978, page 51:


explanator

From Latin explānātor, from explānō (“to flatten out, make plain, explain”).

(statistics) A variable that predicts or explains the variation in another variable; an explanatory variable.


flag complex

(topology) A simplicial complex where every collection of pairwise adjacent vertices spans a simplex.


simplicial complex

en-noun

simplicial complex (plural simplicial complexes)

(topology) A collection of simplices of various dimensions, connected to one another according to certain rules.


oblatum

From Late Latin oblātus (oblatus), from Latin ob (“in front of, before”) + lātus (“broad, wide”), (modelled after and contrasting with prolatus (“extended, lengthened”)).

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(geometry) An oblate spheroid; a figure described by the revolution of an ellipse about its minor axis.


multivaluedness

(mathematics) The property of being multivalued.


countably infinite

1953 [Addison-Wesley], Bruce Elwyn Meserve, Fundamental Concepts of Algebra, 1982, Dover, page 36,
This one-to-one correspondence between the set of positive integers and the set of pairs of positive integers indicates that the set of pairs is countably infinite. Since the set of positive rational numbers is a subset of the set of all pairs of positive integers, the set of positive rational numbers is at most countably infinite. Then, since it is also at least countably infinite, the set of positive rational numbers is countably infinite.

Instead of saying that the aggregate of natural numbers is countably infinite (see Chapter 24), one can use Cantor's symbolism and state that its cardinal number is #92;aleph#95;0 (read aleph null).[…]Now the range of a random variable may be a finite set, a countably infinite set, or a continuum.

1970, Edna E. Kramer, “The Nature and Growth of Modern Mathematics”, in Paperback, Princeton University Press, published 1982, page 332:

The term “countably infinite” would seem to suggest that such a set is infinite. However, the definitions of “countably infinite” and “infinite” were made separately, and so we have to prove that countably infinite sets are indeed infinite (otherwise our notation would be rather misleading).

2000, Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, Springer (Birkhäuser), page 211:

(set theory, of a set) That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection exists from ℕ to the set.


half-line

(geometry) ray; a line extending indefinitely in one direction from a point.


yoctoampere

However, in the IGZO-FET, heavy holes strongly suppress tunneling current, and at most yoctoampere off-state current is estimated which is dominated by thermally excited holes.

2012, Masakazu Murakami, Kiyoshi Kato, Ko Inada, Takanori Matsuzaki, Yasuyuki Takahashi, Shunpei Yamazaki, “Theoretical examination on a significantly low off-state current of a transistor using crystalline In-Ga-Zn-oxide”, in 19th International Workshop on Active-Matrix Flatpanel Displays and Devices (AM-FPD):

First, they are known to show an off-state current on the order of yoctoampere per micron (10⁻²⁴ A/µm) at room temperature (RT).

2016, Yoshinobu Asami, Motomu Kurata, Yutaka Okazaki, Eiji Higa, Daisuke Matsubayashi, Satoru Okamoto, Shinya Sasagawa, Tomoaki Moriwaka, Tetsuya Kakehata, Yuto Yakubo, “Properties of c-axis-aligned crystalline indium–gallium–zinc oxide field-effect transistors fabricated through a tapered-trench gate process”, in The Japan Society of Applied Physics, volume 55, number 4S:

For example, the off-state current per micrometer of the channel width at 85° C. is less than or equal to 100 yA (1 yA (yoctoampere) is 1×10⁻²⁴ A).

2018, Jun Koyama, Semiconductor device including refresh circuit for memory cell (UA Patent 9,922,692):

electrical current
electrical current#English

(metrology) An SI unit of electrical current equal to 10⁻²⁴ amperes. Symbol: yA


deciampere

(metrology) An SI unit of electrical current equal to 10⁻¹ amperes. Symbol: dA


integer factorization

integer factorization (plural integer factorizations)

(mathematics) The decomposition of a composite number into a product of smaller integers


discrete topology

discrete topology (plural discrete topologies)

In the discrete topology all sets are open (but they are also all closed).

An infinite set with discrete topology is not compact.

(topology) A topology on a set consisting of all subsets of that set.


sublemma

sublemma (plural sublemmas or sublemmata)

(mathematics) A statement proven for use in the proof of a more important statement, usually a lemma


nullhomotopic

(topology, of a map) Homotopic to a constant map.


homotopic

f and g are homotopic.

(topology, of two continuous maps) Such that there is a homotopy (a continuous deformation) taking one to the other.

homotopisch

(topology) such that there is a homotopy taking one to the other


Cayley complex

Cayley complex (plural Cayley complexes)

(mathematics) A 2-dimensional CW complex encoding information about a group and its presentation.


CW complex

The C stands for "closure-finite", and the W for "weak topology".

(topology) A collection of balls of various dimensions, with higher-dimensional ones mapped along their respective boundaries to lower-dimensional ones.


Cayley table

multiplication table
multiplication table

(algebra) The analogue for a group of a multiplication table.


quadrinomial

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(algebra) An expression consisting of four terms.


analytic geometry

Having thus noted the distinction between Analytic Geometry and Geometry, let us note in what way it differs from Algebra.

1889, Arthur Sherburne Hardy, Elements of Analytic Geometry, Ginn, published 1891, page 12:

1921, Claude Irwin Palmer, William Charles Krathwohl, Analytic Geometry, McGraw-Hill, page 261,
In plane analytic geometry, all the points and lines are confined to one plane.

2018, Peter Kuhfittig, Technical Calculus with Analytic Geometry, 5th Edition, Cengage Learning (BROOKS/COLE), page 1,
Analytic geometry may be defined as the study of classical geometry by means of algebra.

(geometry) The subbranch of geometry that investigates geometrical figures via the mathematical properties of their representations in a coordinate system.


p-adic number

The expansion (21)2121ₚ is equal to the rational p-adic number #92;textstyle#123;2p#43;1#92;overp²-1#125;.

In the set of 3-adic numbers, the closed ball of radius 1/3 "centered" at 1, call it B, is the set x|∃n∈ℤ.,x=3n+1. This closed ball partitions into exactly three smaller closed balls of radius 1/9: x|∃n∈ℤ.,x=1+9n, x|∃n∈ℤ.,x=4+9n, and x|∃n∈ℤ.,x=7+9n. Then each of those balls partitions into exactly 3 smaller closed balls of radius 1/27, and the sub-partitioning can be continued indefinitely, in a fractal manner.
Likewise, going upwards in the hierarchy, B is part of the closed ball of radius 1 centered at 1, namely, the set of integers. Two other closed balls of radius 1 are "centered" at 1/3 and 2/3, and all three closed balls of radius 1 form a closed ball of radius 3, x|∃n∈ℤ.,x=1+n/3, which is one out of three closed balls forming a closed ball of radius 9, and so on.

3. In his recent book Professor Hensel has developed a theory of logarithms of the rational p'''-adic numbers, and from this he has shown how all such numbers can be written in the form p#92;alpha#92;omega#92;betae#92;gamma.

1914, Bulletin of the American Mathematical Society, page 452:

p'''-Adic numbers were introduced in mathematics by K. Hensel, and this invention led to substantial developments in number theory, where p'''-adic numbers are now as natural as ordinary real numbers.[…]Bleher noticed in [19] that the set of purely fractional p'''-adic numbers is an example of hierarchical lattice.

1991, M. D. Missarov, “Renormalization Group and Renormalization Theory in p-Adic and Adelic Scalar Models”, in Ya. G. Sinaĭ, editor, Dynamical Systems and Statistical Mechanics: From the Seminar on Statistical Physics held at Moscow State University, American Mathematical Society, page 143:

#92;Q#95;p is called the p-adic number field, and its elements are called p-adic numbers. In this section we introduce the p'''-adic number fields, which are very important objects in number theory.
The p'''-adic numbers were originally introduced by Hensel around 1900.

2000, Kazuya Kato, Nobushige Kurokawa, Takeshi Saitō, Takeshi Saito, translated by Masato Kuwata, Number Theory: Fermat's dream, American Mathematical Society, page 58:

(number theory) An element of a completion of the field of rational numbers with respect to a p-adic ultrametric.

p進數 /p进数

element of a completion of the rational numbers with respect to a p-adic ultrametric


additivity

additivity (countable and uncountable, plural additivities)

(uncountable, mathematics) The property of being additive.


decimal system

(mathematics) A numerical system of counting in tens.


common knowledge

(logic, game theory) A special kind of knowledge for a group of agents, such that when all the agents in a group G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum.


pair of pants

A pair of pants . pair of pants (canonical)
pairs of pants (plural)

(topology) The orientable surface of genus zero having three boundary components.


nonorientable

The Möbius strip is a nonorientable surface.

Through every point of a nonorientable surface there passes a Möbius-like nonorientable strip (with an odd number of half-twists) which is part of that surface.


equipotential

A region whose every point has the same potential.


Keith number

(mathematics) A repetitive Fibonacci-like integer which appears in a linear recurrence relation.


repfigit number

repfigit number (plural repfigit numbers)


margin of error

margin of error (plural margins of error)

(statistics) An expression of the lack of precision in the results obtained from a sample.


binary logarithm

binary logarithm (plural binary logarithms)


structuralism

structuralism (countable and uncountable, plural structuralisms)

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(mathematics) In the philosophy of mathematics, a theory that holds that mathematical theories describe structures, and that mathematical objects are exhaustively defined by their place in such structures.


cosinus

Learned borrowing from New Latin cosinus, abbreviation of complementi sinus. Doublet of cosine.

lbor

When I came to these very buildings to pass my examination I knew far better the names of all the plants in this garden than the theory of the cubic roots or the long formulæ of the sum of two cosinus.

1884, A[lbert] A[ugustin] Fauvel, Chinese Plants in Normandy, Hong Kong: […], page 4, column 1:

So, in the helicopteron, as the helix is at the same time a sustaining plane, it should be likened to a surface moving horizontally, and in which, consequenty, the resistance to motion will be to the lifting power as the sinus is to the cosinus of the angle formed by such plane with the horizon.

1884 November 29, “Aerial Navigation”, in Scientific American: A Weekly Journal of Practical Information, Art, Science, Mechanics, Chemistry, and Manufactures, volume LI, number 22, New York, N.Y.: Munn & Co., translation of original by Victor Tatin in La Nature, page 342, column 1:

And according to our choice of a symmetrical conjunction or opposition, all the cosinuses are reduced to 1, namely to coefficients build up solely by scalar Keplerian elements a, e.

1949, Contributions from the Astronomical Institute of the Charles University Prague, page 38:

The variations are described in terms of cycles of sinuses and cosinuses.

1996, Pentti Zetterberg, Matti Eronen, Markus Lindholm, “Construction of a 7500-Year Tree-Ring Record for Scots Pine (Pinus sylvestris, L.) in Northern Fennoscandia and its Application to Growth Variation and Palaeoclimatic Studies”, in Heinrich Spiecker, Kari Mielikäinen, Michael Köhl, Jens Peter Skovsgaard, editors, Growth Trends in European Forests (European Forest Institute Research Report; No. 5), Springer-Verlag Berlin Heidelberg, →ISBN, page 15:

Basically, the rotation of the matrix of the factor loadings L represents its post-multiplication, i.e. L* = LO by the rotation matrix O, which itself resembles one of the matrices included in the classical rotational Lie groups SO(m) (containing the specific m–fold combination of sinuses and cosinuses.

2007, Vladimir G. Ivancevic, Tijana T. Ivancevic, “Introduction: Human and Computational Mind”, in Computational Mind: A Complex Dynamics Perspective (Studies in Computational Intelligence; 60), Springer-Verlag Berlin Heidelberg, →ISBN, →LCCN, section 1 (Natural Intelligence and Human Mind), pages 60–61:


trichotomy

en-noun

trichotomy (countable and uncountable, plural trichotomies)

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From Ancient Greek τριχοτομία (trikhotomía), from τρίχα (tríkha) + τόμος (tómos) + -ία (-ía).

affix

[A linear order] obeys the following trichotomy law[.]

Aliprantis, Border (2006), Infinite Dimensional Analysis: A Hitchhiker's Guide (3rd ed.), p. 6

(algebra) the property of an order relation whereby, given an ordered pair of elements (of a given algebraic structure), exactly one of these is true: the first element is 'less than' the second one, the second is 'less than' the first, or the two elements are equal.


circular sector

en-noun

circular sector (plural circular sectors)

(geometry) A portion of a circle enclosed by two radii and an arc.


abstract harmonic analysis

abstract harmonic analysis (uncountable)

1970, Edwin Hewitt, Kenneth A. Ross, Abstract Harmonic Analysis: Volume II: Structure and Analysis for Compact Groups; Analysis on Locally Compact Abelian Groups, Springer, 2nd reprint, 2002, page 547,
WIENER [1] goes well beyond analysis of periodic functions on R or even functions in 𝔏₂(R); this important paper has yet to be interpreted and assimilated into the standard repertory of abstract harmonic analysis.

The present book is a text book for a graduate course on abstract harmonic analysis and its applications.

2014, Anton Deitmar, Siegfried Echterhoff, Principles of Harmonic Analysis, 2nd edition, Springer, page v:

2015, Gerald B. Folland, A Course in Abstract Harmonic Analysis, 2nd edition, Taylor & Francis (CRC Press):

(harmonic analysis, representation theory, topology) A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups.

harmonic analysis; representation theory; harmonic analysis; representation theory


avoirdupois ounce

avoirdupois ounce (plural avoirdupois ounces)

A unit of weight in the avoirdupois system of units, equal to one sixteenth of a avoirdupois pound.


avoirdupois pound

avoirdupois pound (plural avoirdupois pounds)

A unit of weight in the avoirdupois system of weights, defined as 0.45359237 kg in most of the English-speaking world since 1959.


RDS

(statistics) Initialism of respondent-driven sampling.


expected value

expected value (countable and uncountable, plural expected values)

weighted average
weighted average#English

(probability theory) The weighted average of outcome values, using probability as the weighting function.


aliquant

(mathematics, dated) An integer that is less than another, but that does not divide the other integer into integral parts.

aliquanta

integer that does not divide another into integral parts


aliquant

5 is an aliquant part of 16.

(mathematics, dated) Less than another specified integer, but not dividing it into integral parts.


subnet

(topology) The abstraction of a sequence.


SNR

(electronics, communication, mathematics) signal-to-noise ratio


multilinear

(mathematics, of a function etc) That is linear in each variable separately.


hypergeometric

hypergeometric series
hypergeometric series

(mathematics) Pertaining to mathematical entities of different kinds (series, functions, equations, ...) but strictly related to hypergeometric series


hypergeometric

(mathematics) Such a function, series etc.


hypergeometric series

hypergeometric series (plural hypergeometric series)

(mathematics) Any power series such that the ratio of the (k+1)-th and the k-th terms is a rational function of the natural integer k.


radicate

en-verb

radicate (third-person singular simple present radicates, present participle radicating, simple past and past participle radicated)

radicates (present singular third-person)
radicating (participle present)
radicated (participle past)
radicated (past)

From Latin radicatus, past participle of radicari (“to take root”), from radix (“root”).

Numbers, arithmetically, can be added, subtracted, multiplied and divided, exponentiated and radicated, […]

1972, Patrick Meredith, Dyslexia and the individual, page 36:

(transitive, arithmetic, rare) To extract the root of a number.


graph toughness

(mathematics) A measure, expressed by a positive integer (with the exception of complete graphs), of the connectivity of a graph.


reweight

reweight (third-person singular simple present reweights, present participle reweighting, simple past and past participle reweighted)

reweights (present singular third-person)
reweighting (participle present)
reweighted (participle past)
reweighted (past)

(mathematics, statistics) To adjust the weighting given to a value.


tropical geometry

The adjective tropical was chosen by some French mathematicians in honor of the Brazilian pioneer of the field, Imre Simon.

(mathematics) A recent branch of geometry that can be described as a piecewise linear version of real algebraic geometry.


enneagram

(mathematics) A nine-pointed stellate polygon


continuant

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As a further point of clarification, notice that (C0) does not characterize a criterion for determining whether a continuant x of kind K that exists at t 1 is identical to a continuant y of kind K that exists at t 2 .

2007 July 18, Thomas Sattig, “Identity in 4D”, in Philosophical Studies, volume 140, number 2, →DOI:

(mathematics) A determinant formed from a tridiagonal matrix.


compactification

en-noun

compactification (countable and uncountable, plural compactifications)

(topology) Any of various procedures of enlarging a topological space to make it compact.

kompaktifikation

procedure of enlarging a topological space to make it compact

kompaktifikation

topological space enlarged to become compact

(topology) The space resulting from any such procedure.


real valued

(mathematics) Used to describe a mathematical entity, like a function, that takes values from the real numbers (as opposed to, for instance, from the complex numbers).


linha

From Portuguese linha (“line”), from Old Galician-Portuguese linha, from Latin līnea (“thread, line”), from līnum (“flax”), from Proto-Indo-European *līno- (“flax”).

(historical, measure) A traditional short Portuguese unit of length, usually about equal to 2.3 mm.


correlation coefficient

correlation coefficient (plural correlation coefficients)

(statistics) Any of the several measures indicating the strength and direction of a linear relationship between two random variables.


random variable

random variable (plural random variables)

probability distribution
probability distribution

(statistics, loosely) A quantity whose value is random and to which a probability distribution is assigned, such as the possible outcome of a roll of a dice.

Henceforth the symbol X(w) will be used for the random variable X#58;S#92;rightarrow#92;mathbb#123;R#125;.

1996, Ron C. Mittelhammer, Mathematical Statistics for Economics and Business, volume 78, Springer, page 45:

The particular example considered here is the Hilbert space of random variables.

2009, Christian Perwass, Geometric Algebra with Applications in Engineering, Springer, page 351:

A two-dimensional random variable is a mapping of the points in the sample space to ordered pairs {x, y}. Usually, when dealing with a pair of random variables, the sample space naturally partitions itself so that it can be viewed as a combination of two simpler sample spaces.

2012, Scott Miller, Donald Childers, Probability and Random Processes, 2nd edition, Elsevier (Academic Press), page 177:

(statistics, formally) A measurable function from a sample space to the measurable space of possible values of the variable.


skewness

skewness (countable and uncountable, plural skewnesses)

moment about the mean
moment about the mean

(statistics) A measure of the asymmetry of the probability distribution of a real-valued random variable; is the third standardized moment, defined as scriptstyle γ₁=(μ₃)/(σ³),! where μ₃ is the third moment about the mean and σ is the standard deviation.


cnoidal

Coined by Korteweg and de Vries in their paper in Philosophical Magazine (1895, series 5, vol. 39, pp. 422-443) to describe a class of solutions to the KdV equation which involve a Jacobi elliptic function. The Jacobi elliptic function involved is commonly written as cn(x|m), and the term cnoidal was designed to be analogous to sinusoidal, the word describing waves which involve the sine function.

(mathematics, physics) Describes a travelling wave whose amplitude is constricted; e.g. a wave in shallow water.

Jacobi elliptic function
en:Cnoidal wave


API unit

From API (“American Petroleum Institute”).

The radioactivity of a typical shale is 100 API units.

(oil industry) A unit of radioactivity used for measuring natural gamma rays in the ground.


API gravity

API gravity (countable and uncountable, plural API gravities)

(oil industry) A specific gravity scale measuring the relative density of various petroleum liquids, expressed in degrees.

grau API

density of petroleum liquid relative to water


factorable

(mathematics) Capable of being factored. For integers synonyms are composite, non-prime.


normal distribution

normal distribution (plural normal distributions)

φ_(μ,σ²)(x)=1/(σ√),e²)/(2σ²))=1/σφ((x-μ)/σ), x∈ℝ.

It begins with the normal distribution, which is the limiting form of the sample sum over an arbitrary population.

2008, James L. Johnson, Probability and Statistics for Computer Science, Wiley, page 437:

The normal distribution is the backbone of traditional statistics. We learn very early in our statistics training that the distribution of sample means, regardless of the shape of the parent distribution, approaches a normal distribution as the sample size increases.

2012, Larry Pace, Beginning R: An Introduction to Statistical Programming, Apress, page 103:

The development of the general theories of the normal distributions began with the work of de Moivre (1733, 1738) in his studies of approximations to certain binomial distributions for large positive integer n > 0.

2014, Mohammad Ahsanullah, B.M. Golam Kibria, Mohammad Shakil, Normal and Student's t Distributions and Their Applications, Springer (Atlantis Press), page 7:

probability density function
probability density function

(statistics) Any of a family of continuous probability distributions such that the probability density function is the Gaussian function


Gaussian distribution

Gaussian distribution (plural Gaussian distributions)


Cauchy distribution

Cauchy distribution (plural Cauchy distributions)

(statistics) A symmetric continuous probability distribution with fat tails, with probability density function that is


standard normal distribution

standard normal distribution (plural standard normal distributions)

(statistics) The normal distribution with a mean of zero and a variance of one.


information entropy

(information theory) A measure of the uncertainty associated with a random variable; a measure of the average information content one is missing when one does not know the value of the random variable (usually in units such as bits); the amount of information (measured in, say, bits) contained per average instance of a character in a stream of characters.


information theory

(mathematics) A branch of applied mathematics and engineering involving the quantification of information sent over a communication channel, disregarding the meaning of the sent messages, exemplified by the noisy-channel coding theorem.


monotonically

(mathematics) In a monotonic manner, of a function that either never decreases or never increases as its independent variable increases.


hectoampere

(metrology) An SI unit of electrical current equal to 10² amperes. Symbol: hA


hectoamp

(metrology) An SI unit of electrical current equal to 10² amps. Symbol: h


centiamp

(metrology) An SI unit of electric current equal to 10⁻² amperes. Symbol: cA


deciamp

(metrology) An SI unit of electrical current equal to 10⁻¹ amps. Symbol: d


decagramme

(British spelling) Alternative spelling of decagram


strongly connected component

strongly connected component (plural strongly connected components)

(graph theory) Given a directed graph, a maximal strongly connected subgraph.


strongly connected

(graph theory) Of a directed graph, such that for every pair of vertices u and v there is a path from u to v and a path from v to u.

(graph theory) Of a directed graph, such that for every pair of vertices u and v there is a directed path either from u to v or from v to u.


connected component

connected component (plural connected components)

(topology and graph theory) A connected subset that is, moreover, maximal with respect to being connected.


factorizable

(mathematics, of an integer or polynomial etc) Able to be factorized.


statistical significance

statistical significance (countable and uncountable, plural statistical significances)

(statistics) A measure of how unlikely it is that a result has occurred by chance.


significance level

significance level (plural significance levels)

(statistics) A measure of how likely it is to draw a false conclusion in a statistical test, when the results are really just random variations.

(statistics) The probability, usually expressed as a percentage, of making a decision to reject the null hypothesis when the null hypothesis is actually true; the probability of making a type I error.


central limit theorem

central limit theorem (plural central limit theorems)

(statistics and mathematics, singular only) The theorem that states that if the sum of independent identically distributed random variables has a finite variance, then it will be approximately normally distributed.

(mathematics, countable) Any of various similar theorems.


Bernoulli distribution

Bernoulli distribution (plural Bernoulli distributions)

After Swiss mathematician Jacob Bernoulli (1654—1705), one of many noted mathematicians of the Bernoulli family, who made important contributions to the field of probability.

1977 [Wiley], Jean Dickinson Gibbons, Ingram Olkin, Milton Sobel, Selecting and Ordering Populations, 1999, Society for Industrial and Applied Mathematics, Unabridged corrected republication, page 103,
Since both of these distributions involve the same parameter p, the problem under consideration here may be called either selection of the best Bernoulli distribution or selection of the best binomial distribution.

1985, R. R. Kinnison, Applied Extreme Value Statistics, Battelle Press, page 26,
A critical factor in the use of Bernoulli distributions is that the parameters of the distribution are known constants.

2000, A. Berny, Selection and Reinforcement Learning for Combinatorial Optimization, Marc Schoenauer, Kalyanmoy Deb, Günther Rudolph, Xin Yao, Evelynne Lutton, Juan Julian Merelo, Hans-Paul Schwefel (editors), Parallel Problem Solving from Nature-PPSN VI, 6th International Conference Proceedings, Springer, page 601,
In this paper however, we will only consider the family of Bernoulli distributions.

(statistics) A discrete probability distribution that represents the result of a single trial, taking value 1 with "success" probability p and value 0 with "failure" probability q=1-p.

Bernoulli distribution
Bernoulli family
Jacob Bernoulli


sample mean

mathbf ̄x=1/N∑ₖ₌₁ᴺ mathbf xₖ.

(statistics) Given a random sample mathbf x₁,…, mathbf x_N from an n-dimensional random variable mathbf X, a mean defined as


random sample

(statistics) A sample randomly taken from an investigated population.


dirigent

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From Latin dīrigēns, present participle of dīrigō.

The straight line in which the vertical polar plane cuts the plane of the circle of contact is called the dirigent. As there are in general two circles of contact, there are two dirigents, and they are parallel to the diretrices.

1877, James Booth, A Treatise on Some New Geometrical Methods, page 348:

In this case, to which Sphero-Cartesians, and all other sphero-quadrics, whose dirigents are small circles, are analogous in Spherics, the dirigent conic F must also have double contact with S.

1891, Proceedings of the London Mathematical Society, volume 21, page 308:

(dated, geometry) The line of motion of a describent line or surface that in so moving defines a plane or solid figure; a directrix.


coker

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multiring

(mathematics) A set containing multiple rings.


standardized variable

standardized variable (plural standardized variables)

(mathematics, statistics) The value of a variable minus its mean, divided by its standard deviation.


hyperhypercube

Extension of hypercube; hyper- + hypercube.

A five-dimensional shape, usually cube-like.


coproduct

Meronym: inclusion

The coproduct is a structure constructed from several similar structures, equipped with appropriate inclusion maps, which generalises the disjoint union of sets, of topological spaces and the free product of groups.

(mathematics) The colimit of two (or more) objects, without regard to any morphisms between them.


unimodal

(mathematics) Having a single mode (local maximum).

Having, or operating in, a single mode.
Having a single mode (local maximum).


kilogray

ionizing radiation
ionizing radiation#English

(metrology) An SI unit of absorbed energy from ionizing radiation equal to 10³ grays. Symbol: k


rel

Since M#95;0 and M#95;1 are cobordant rel boundary and f#95;0,f#95;1 are n-connected, the number #92;delta#58;#61;#92;frac12(#92;mathrm#123;rk#125;H#95;nM#95;0-#92;mathrm#123;rk#125;H#95;nM#95;1) is a nonnnegative integer.

1994, N[ikita] Netsvetaev, “Diffeomorphism Criteria for Simply Connected Even-Dimensional Manifolds”, in Oleg Viro, editor, Topology of Manifolds and Varieties (Advances in Soviet Mathematics [series] 18), American Mathematical Society, →ISBN, page 237:

The following notations are in common use: H#58;f#92;simeqg (rel A) means that H is a homotopy rel A from f to g....

1997, Paul Selick, Introduction to Homotopy Theory (Fields Institute Monographs), American Mathematical Society, →ISBN, page 15:

Then in n#92;gen', there is a map h#58;Z#92;toZ' such that h#124;A#61;g and gf#92;simeqf'h rel A, so the diagram above is commutative up to homotopy rel A.

2002, Allen Hatcher, Algebraic Topology, Cambridge, →ISBN, page 355:

(mathematics) Abbreviation of relative to.


NOT operator

(mathematics, logic) An operation on logical values that changes true to false, and false to true.


probability density

probability density (plural probability densities)

(probability theory) probability density function


bicapped

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(geometry, of a prism) Having a cap (in the shape of a pyramid) at each end


alternative hypothesis

alternative hypothesis (plural alternative hypotheses)

(statistics) A rival hypothesis to the null hypothesis. Their likelihoods are compared by a statistical hypothesis test.


statistical process control

statistical process control (uncountable)

(statistics) A method of monitoring a process through the use of control charts.


gigabarrel

A unit of volume equal to a thousand million barrels.


directrix

directrix (plural directrixes or directrices)

directrixes (plural)
directrices (plural)

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From Latin directrix; equivalent to direct + -trix.

(geometry) A line used to define a curve or surface; especially a line, the distance from which a point on a conic has a constant ratio to that from the focus.

richtlijn

a line used to define a curve or surface


millier

From French millier (“a thousand, a 1000ish, 1000 kg”), from mille (“thousand”) + -ier (“-er”).

bor

(archaic, rare) Synonym of metric ton, 1000 kg.


nanomole

(metrology) An SI unit of amount of substance equal to 10⁻⁹ moles. Symbol: nmol


henagon

From Ancient Greek: εἷς (heîs, “one”, accusative héna) + -gon.

A polygon having one edge and one angle.