composite number

en-noun

composite number (plural composite numbers)

It is evident, moreover, that if a composite number terminates in any one of the digits 1, 3, 7, 9, no one of its factors can be the number 5, or any number ending in 5.

1853, Edward Hinkley, Tables of the Prime Numbers and Prime Factors of the Composite Numbers from 1 to 100,000, page 13:

The above remark applies also to many composite numbers which are not Carmichael numbers, but which are still not shown to be composite by Fermat's theorem for a specific base a.[…]Therefore, using Euler's criterion or a strong primality test with enough bases will finally reveal any composite number or, alternatively, prove the primality of any prime N.

1994, Hans Riesel, Prime Numbers and Computer Methods for Factorization, 2nd edition, Springer (Birkhäuser), →ISBN, page 91:

2006, Sze Kui Ng, Quantum Invariant of 3-Manifolds, Samuel F. Neilson (editor), New Research on Three-manifolds and Mathematics, Nova Science Publishers, page 47,
It is interesting that in each interval composite numbers are one-to-one assigned to the comparable composite knots while prime numbers are one-to-one assigned to prime knots.

(number theory) A (nonzero) natural number that is expressible as the product of two (or more) natural numbers other than itself and 1.

عَدَد غَيْر أَوَّلِيّ

number that is the product of two natural numbers other than itself and 1


FS

(cryptography) Initialism of forward secrecy.

first success distribution
first success distribution#English

(probability theory) Initialism of first success distribution.


antichain

First of all, Zorn's Lemma implies that every uncountable antichain in T is contained in a maximal uncountable antichain. So it suffices to make sure that T has no maximal uncountable antichains.

1997, Winfried Just, Martin Weese, Discovering Modern Set Theory II: Set-Theoretic Tools for Every Mathematician, American Mathematical Society, page 140:

2013, Vijay K. Garg, Maximal Antichain Lattice Algorithms for Distributed Computations, Proceedings, Davide Frey, Michel Raynal, Saswati Sarkar, Rudrapatna K. Shyamasundar, Prasun Sinha (editors), Distributed Computing and Networking: 14th International Conference, ICDCN, Springer, LNCS 7730, page 245,
We first define three different but isomorphic lattices: the lattice of maximal antichain ideals, the lattice of maximal antichains and the lattice of strict ideals.

2014, Martin Aigner, Günter M. Ziegler, Proofs from THE BOOK, Springer, 5th Edition, page 199,
In 1928 Emanuel Sperner asked and answered the following question: Suppose we are given the set N=1,2,3,…,n. Call a family ℱ of subsets of N, which has partial order ⊆]) an antichain if no set of ℱ contains another set of the family ℱ. What is the size of a largest antichain? Clearly, the family ℱₖ of all k-sets satisfies the antichain property with |ℱₖ|=\binomnk. Looking at the maximum of the binomial coefficients (see page 14) we conclude that there is an antichain of size \binomn[n/2]= max ₖ\binomnk. Sperner's theorem now asserts that there are no larger ones.

partially ordered set
partially ordered set

(set theory, order theory, graph theory) A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤.


hypohamiltonian

(graph theory) Of a graph, not containing a Hamiltonian cycle but such that the removal of any single vertex produces a Hamiltonian graph.


Hamiltonian path

Hamiltonian path (plural Hamiltonian paths)

Named after William Rowan Hamilton (1805-1865), Irish mathematician.

(graph theory) A path through a graph which visits each vertex exactly once.

Hamiltonpad

path which visits each vertex exactly once


Hamiltonian cycle

Hamiltonian cycle (plural Hamiltonian cycles)

(graph theory) A Hamiltonian path with an additional connection between the first and last vertices visited, forming a cycle.

hamiltonkreds

graph theory: a cycle visiting all vertices once


Hamiltonian graph

Hamiltonian graph (plural Hamiltonian graphs)

(graph theory) A graph for which there is a Hamiltonian cycle.


polegada

From Portuguese polegada (“inch”), from Vulgar Latin *pollicāta, from Latin pollicāris (“of or related to a thumb”), from pollex (“thumb”) + -āris (“-ary: forming adjectives”).

der

(historical, measure) A traditional Portuguese unit of length, usually about equal to 2.8 cm.


superfactorial

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Coined by Neil Sloane and Simon Plouffe in 1995, from super- + factorial.

(mathematics) A product of factorials, such that the superfactorial of a number n is 1! × 2! × 3! × ... × n!.


amicable number

en-noun

amicable number (plural amicable numbers)

The factors of 220, excluding 220 itself, are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110 and sum to 284; the factors of 284, excluding 284 itself, are 1, 2, 4, 71, and 142, and sum to 220; hence 220 and 284 are amicable numbers.

(number theory) One of a pair of numbers having the property that the sum of the divisors of each, excluding itself, is equal to the other number.


harmonic number

harmonic number (plural harmonic numbers)

The fourth harmonic number has a value of H_3=∑ₖ₌₁³1/k=1/1+1/2+1/3=1 5/6.

(number theory) Any of a series of numbers formed from the sum of the reciprocals of consecutive natural numbers


automorphic number

automorphic number (plural automorphic numbers)

5 is an automorphic number because 5² = 25, which ends in 5.

(mathematics) A number whose decimal representation of its square ends in itself.


Fibonacci number

Fibonacci number (plural Fibonacci numbers)

(mathematics) Any number in a Fibonacci sequence (being the sum of the preceding two numbers)


Fibonacci sequence

Fibonacci sequence (plural Fibonacci sequences)

Named after the Italian mathematician later known as Fibonacci (c.1175 – c.1250), who introduced the sequence to a European readership in his 1202 book Liber Abaci.

If the Fibonacci sequence is chosen for the quasiperiodic direction of a 1D QC,^([quasicrystal]) it may simply be called a Fibonacci phase.

1999, Walter Steurer, Torsten Heibach, “3. Crystallography of Quasicrystals”, in Zbigniew M. Stadnik, editor, Physical Properties of Quasicrystals, Springer, page 60:

The number of adult rabbit pairs being present in consecutive months is then given by the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, ... (every term is the sum of its two predecessors). This work can be seen as the very beginning of mathematical biology, though one has to admit that the Fibonacci sequence exerts a greater fascination for number theorists than for reproductive biologists.

2000, Martin Nowak, Robert M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, page 6:

In a well-known chapter on phyllotaxis, Coxeter (1969) calls the appearance of the Fibonacci sequence in botany a "fascinatingly prevalent tendency," called by Cook (1914) the "Law of Wiesner." The prevalence of the Fibonacci sequence in phyllotactic patterns is often referred to as “the mystery of phyllotaxis,” and “the bugbear of botanists.”

2009, Roger V. Jean, Phyllotaxis: A Systemic Study in Plant Morphogenesis, Cambridge University Press, page 1:

(mathematics) The sequence of integers, each of which is the sum of the preceding two, the first and second numbers both being 1.

Indeed, these pairs belong to a Fibonacci sequence of what are called Lucas numbers that begins 2, 1, 3, 4, 7, 11,...

1977, Scientific American, volume 236, page 137:

2007, Anthony Nicolaides, Make The Grade At GCSE Mathematics, Higher Tier, P.A.S.S. Publications, 3rd Edition, page 169,
19. The first two terms of a Fibonacci sequence are a and b. Write out a few terms.

(mathematics) Any sequence of numbers such that each is the sum of the preceding two.


pyramidal number

pyramidal number (plural pyramidal numbers)

(mathematics) A number that represents the number of items in a pyramid having a given number of sides and layers


practical number

practical number (plural practical numbers)

(mathematics) Any positive integer having the property that all smaller integers can be represented as sums of distinct divisors of it


triangular number

triangular number (plural triangular numbers)

Ten is a triangular number being the sum of 1, 2, 3, and 4.

(mathematics) Any integer that is the sum of n natural numbers from 1 to n.

三角形數 /三角形数

an integer which is the sum of n natural numbers


sine ratio

right-angled triangle
right-angled triangle

(trigonometry) The ratio of the side of a right-angled triangle opposite to a specified angle to the hypotenuse; when expressed as a real number between 0 and 1, it defines the sine of the angle.


memoryless

probability distribution
probability distribution

(probability theory) Of a probability distribution, such that any derived probability from a set of random samples is distinct and has no information (i.e. "memory") of earlier samples.


memorylessness

(probability theory) The property of being memoryless.


packetize

en-verb

packetize (third-person singular simple present packetizes, present participle packetizing, simple past and past participle packetized)

packetizes (present singular third-person)
packetizing (participle present)
packetized (participle past)
packetized (past)

(signal processing) To form data into packets, or bundled units, according to a specific protocol


packetization

en-noun

packetization (countable and uncountable, plural packetizations)

(signal processing) The act or process of bundling data into packets according to a specific protocol


autocorrelation

autocorrelation (countable and uncountable, plural autocorrelations)

Dividing the covariances by the variance gives the autocorrelations.

1990, K. Holden, D. Peel, John L. Thompson, Economic Forecasting, →ISBN, page 67:

(statistics, signal processing) The cross-correlation of a signal with itself: the correlation between values of a signal in successive time periods.

自相關 /自相关

statistics, signal processing: the cross-correlation of a signal with itself


DFT

DFT (countable and uncountable, plural DFTs)

discrete Fourier transform
discrete Fourier transform#English

(mathematics) Initialism of discrete Fourier transform.


discrete Fourier transform

discrete Fourier transform (plural discrete Fourier transforms)

(mathematics) The process of converting a discrete time-based function into its frequency-based representation.


interframe

Each keyframe becomes a reference for all the following interframes.

2003, Dan Livingston, Carlos Justiniano, Advanced Macromedia Flash MX, →ISBN, page 356:

(signal processing) A video frame which is compressed to express only the change from a reference frame.


intraframe

The frequency of intraframes determines the frequency of random access points for non-linear playback or editing.

1999, Francis Botto, Dictionary of Multimedia and Internet Applications, page 156:

(signal processing) A video frame that does not depend on any other frame for rendering, but simply presents a fixed image. Usually subject to spatial compression.


deshuffle

en-verb

deshuffle (third-person singular simple present deshuffles, present participle deshuffling, simple past and past participle deshuffled)

deshuffles (present singular third-person)
deshuffling (participle present)
deshuffled (participle past)
deshuffled (past)

Upon reception, the data packets are deshuffled by the deshuffler.

(signal processing) To restore shuffled data to its original ordered state.


eigenspace

(linear algebra) The linear subspace consisting of all eigenvectors associated with a particular eigenvalue, together with the zero vector.

特徵空間 /特征空间

set of the eigenvectors associated with a particular eigenvalue


ignorable

en-adj

ignorable (comparative more ignorable, superlative most ignorable)

more ignorable (comparative)
most ignorable (superlative)

Although there is an abundance of statistical literature describing (complicated) methods that can be used to investigate whether or not one is dealing with ignorable or informative missing data in a longitudinal study (see, for instance, Diggle, 1989; Ridout, 1991; Diggle et al., 1994), it is basically quote easy to investigat this matter.

2003, Jos W. R. Twisk, Applied Longitudinal Data Analysis for Epidemiology, →ISBN:

Another pertinent distinction in Rubin's missing data classification system is whether the missing data mechanism is ignorable.

2007, Patrick E. McKnight, Katherine M. McKnight, Souraya Sidani, Missing Data: A Gentle Introduction, →ISBN, page 50:

If θ and φ are not functionally related to each other (or that the knowledge of one does not provide any information about the other) then the parameters are called “distinct,” and the missing data mechanism is ignorable.

2015, Trivellore Raghunathan, Missing Data Analysis in Practice, →ISBN, page 6:

(statistics, of missing data) Unrelated to the parameters being estimated


B-frame

(signal processing) A compressed video frame which is reconstructed based on its differences from both the previous and the subsequent frame.


macroblock

(signal processing, video compression) A block of adjacent pixels, typically a rectangular 16×16 block


D-frame

(signal processing, video compression) A low-quality intraframe containing only DC components, used for high-speed previews.


I-frame

(signal processing, video compression) Abbreviation of intraframe.


P-frame

(signal processing, video compression) A video frame which contains only information on the differences from previous frames


crisping

For two vague regions, one topological relation exists between any pair of crispings. There are a number of relations possible between the members of the sets of crisp regions on which the vague regions stand.

2003, Wenzhong Shi, Peter Fisher, Michael F. Goodchild, Spatial Data Quality:

(topology) A crisp, clearly-defined object that exists within a more vaguely defined object.


Z-transform

(mathematics) A transform that converts a discrete time-domain signal into a complex frequency-domain representation.


equiprobable

The random number generator is designed to generate random numbers with an equiprobable law of distribution with the limits +1 to -1.

1964, I. A. Turyev et al., A Laboratory computer for joint operation with a simulator:

(mathematics, logic) Having equal probability, such as any number from 1 to 6 being the equiprobable outcome of the fair toss of fair dice.


onza

From Spanish onza (“ounce, Spanish ounce”), from Latin ū̆ncia. Doublet of a, one, inch, uncia, onça, oka, ouguiya, and awqiyyah.

doublet

(historical) A traditional Spanish unit of mass, equivalent to about 28.76 g.


exanewton

(metrology) An SI unit of force equal to 10¹⁸ newtons.


figurate number

en-noun

figurate number (plural figurate numbers)

(mathematics, number theory) A number equal to the number of dots in a geometric figure formed of dots. The series begins with unity and is formed so that subtracting each from the following, and treating the series so formed in the same way, by a continuation of the process, yields equal differences.


conchoidal

en-adj

conchoidal (comparative more conchoidal, superlative most conchoidal)

more conchoidal (comparative)
most conchoidal (superlative)

c. 1695, Isaac Newton, 1976, D. T. Whiteside (editor), The Mathematical Papers of Isaac Newton, Volume 7: 1691-1695, page 621,
[…] a conchoidal hyperbola with an oval at its convexity.

(mathematics) Of or pertaining to a conchoid; that may be defined as a conchoid.


nonconvexity

en-noun

nonconvexity (usually uncountable, plural nonconvexities)

(mathematics) The state of not being mathematically convex.


arcsecant

(trigonometry) function that is the compositional inverse of the secant function. Symbol: arcsec


arccosecant

(trigonometry) function that is the compositional inverse of the cosecant function. Symbol: arccsc


headgroup

(mathematics) The group of instances at the head (high end) of a distribution curve


sinistrorse

en-adj

sinistrorse (comparative more sinistrorse, superlative most sinistrorse)

more sinistrorse (comparative)
most sinistrorse (superlative)

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subsequence

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(mathematics) A sequence that is contained within a larger one.


equinumerosity

(mathematics) The state or quality of being equinumerous.


resplendency

en-noun

resplendency (countable and uncountable, plural resplendencies)

Latin, from resplendere (“to shine brightly”).

(mathematics) A property of the truth of sentence structures in Peano arithmetic


antidifferentiation

antidifferentiation (usually uncountable, plural antidifferentiations)

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(calculus) The process of finding the antiderivative.

integração

the process of finding the antiderivative


concyclic

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(geometry, of a set of points) Lying on a common circle.


barycenter

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(geometry) The centroid, the geometric center of a plane figure


correlator

correlation function
correlation function

(statistics, quantum mechanics) A correlation function

(optics, signal processing) A type of device used to compare two signals


covariate

On the basis of these analogies, any inference of a population structure driven by selective sweeps would require good longitudinal data from natural bacterial populations, as well as observations of episodic crashes in diversity causally associated with genetic changes and not associated with changes in ecological covariates.

2009 February 6, Christophe Fraser et al., “The Bacterial Species Challenge: Making Sense of Genetic and Ecological Diversity”, in Science, volume 323, number 5915, →DOI, pages 741–746:

(statistics) A variable that is possibly predictive of the outcome under study.


paraxial

paraxial rectangle

(mathematics) Parallel to one or more axes of the coordinate system.


nonperturbative

(mathematics, physics) Beyond the scope of perturbation theory


discretization

discretization (countable and uncountable, plural discretizations)

Analyses all required a planar mathematical discretization of a region containing a prescribed number of cells with prescribed orientations.

BLAZE Multiphysics has many features from: discretation, temporal resolution, user modification and post processing.

For extensional-stress resolving 'shelfy stream' models, differences between model results were mainly due to the choice of spatial discretization.

2013, Issues in Earth Sciences, Geology, and Geophysics, page 34:

(mathematics, computing, cognitive science) The act of discretizing, or dividing a continuous object or spectrum into a finite number of discrete elements


triaxial

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


preordered

Most of the theory of this section on linear order spaces (and cones) can be generalized to preordered linear spaces (and wedges).

1980, Johann Schröder, Operator Inequalities, Academic Press, page 8:

It can be proved [see Herden (1989a,c, 1990, 1993a,b) and Herden and Mehta (1997a) that a continuous isotone (or strictly isotone) function defined on a closed subset K of a preordered topological space X has a continuous isotone (or strictly isotone) extension to a function g on X if and only if there is a separable system on X which satisfies certain "separation" conditions.

1998, Ghanshyam B. Mehta, “Chapter 1: Preference and Utility”, in Salvador Barbera, Peter Hammond, Christian Seidl, editors, Handbook of Utility Theory, Volume 1: Principles, Springer, page 30:

We remind the reader that the barycentric subdivision sd(P) of a preordered set P is the poset of chains in P, ordered by inclusion.

1999, Rafael Villarroel-Flores, Equivariant Homotopy Type of Categories and Preordered Sets, University of Minnesota, page 24:

(set theory, order theory, of a set) Equipped with a preorder.


semirounded

Neither fully rounded nor angular; somewhat rounded


detrend

en-verb

detrend (third-person singular simple present detrends, present participle detrending, simple past and past participle detrended)

detrends (present singular third-person)
detrending (participle present)
detrended (participle past)
detrended (past)

(transitive, statistics, economics) To manipulate (data) to remove overall long-term trends in order to emphasise other patterns.


antiholomorphic

(mathematics) Describing any function in the complex plane whose derivative with respect to the complex conjugate exists at all points of an open set


superhelix

en-noun

superhelix (plural superhelices or superhelixes)

superhelices (plural)
superhelixes (plural)

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(molecular biology) The shape formed by a helix which in turn is twisted into a larger helix


detrended

(statistics, said of data) having long-term trends removed in order to emphasise short-term changes.


transversality

transversality (countable and uncountable, plural transversalities)

(mathematics) A property of two intersecting submanifolds, where at every intersection point, their separate tangent spaces at that point together generate the tangent space of the ambient manifold at that point.


microtesla

magnetic flux density
magnetic flux density#English

(metrology) An SI unit of magnetic flux density equal to 10⁻⁶ teslas. Symbol: μT


nonlinearly

The probability of a mistake rises nonlinearly with the number of steps.

1996, Craig Loehle, Thinking Strategically, →ISBN, page 56:

(mathematics) In a nonlinear fashion; often specifically exponentially


eigenproblem

(mathematics) A mathematical problem involving eigenvalues.

zadanie matematyczne z wartościami własnymi


eigendecomposition

(linear algebra) The factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.


chorded

a chorded cycle


anisotopic

an anisotopic distribution


hectobecquerel

(metrology) An SI unit of radiation equal to 10² becquerels. Symbol: h


attohertz

(metrology) An SI unit of frequency equal to 10⁻¹⁸ hertz.


picosiemens

electrical conductance
electrical conductance

(metrology) An SI unit of electrical conductance equal to 10⁻¹² siemens.


petabecquerel

(metrology) An SI unit of radioactivity equal to 10¹⁵ becquerels. Symbol: P


transvection

transvection (countable and uncountable, plural transvections)

From transvect + -ion. Coined in the genetic sense by Edward B. Lewis in 1954.

a projective transvection

(mathematics) A kind of linear mapping which leaves all points on one axis fixed, while other points are shifted parallel to the axis by a distance proportional to their perpendicular distance from the axis


isosurface

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an isosurface representing a concentration of 10 grams per cubic meter

(computer graphics, geometry) A surface that represents points of a constant value within a volume of space


yoctokatal

catalytic activity
catalytic activity#English

(metrology) An SI unit of catalytic activity equal to 10⁻²⁴ katals. Symbol: y


exakatal

(metrology) An SI unit of catalytic activity equal to 10¹⁸ katals. Symbol: E


gigakatal

(metrology) An SI unit of catalytic activity equal to 10⁹ katals. Symbol: G


kilokatal

(metrology) An SI unit of catalytic activity equal to 10³ katals. Symbol: k


hectokatal

(metrology) An SI unit of catalytic activity equal to 10² katals. Symbol: h


decakatal

(metrology) An SI unit of catalytic activity equal to 10¹ katals. Symbol: da


decikatal

(metrology) An SI unit of catalytic activity equal to 10⁻¹ katals. Symbol: d


centikatal

(metrology) An SI unit of catalytic activity equal to 10⁻² katals. Symbol: c


millikatal

(metrology) An SI unit of catalytic activity equal to 10⁻³ katals. Symbol: m


microkatal

(metrology) An SI unit of catalytic activity equal to 10⁻⁶ katals. Symbol: μ


nanokatal

(metrology) An SI unit of catalytic activity equal to 10⁻⁹ katals. Symbol: n


picokatal

(metrology) An SI unit of catalytic activity equal to 10⁻¹² katals. Symbol: p


attokatal

(metrology) An SI unit of catalytic activity equal to 10⁻¹⁸ katals. Symbol: a


femtokatal

(metrology) An SI unit of catalytic activity equal to 10⁻¹⁵ katals. Symbol: f


ill-defined

en-adj

ill-defined (comparative more ill-defined, superlative most ill-defined)

more ill-defined (comparative)
most ill-defined (superlative)

(mathematics) Defined in an inconsistent way.


microkelvin

thermodynamic temperature
thermodynamic temperature#English

(metrology) An SI unit of thermodynamic temperature equal to 10⁻⁶ kelvins. Symbol: μK


semimajor

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a semimajor radius

(geometry) Of or pertaining to the semimajor axis, the long axis of an ellipse


horopter

* From Ancient Greek ὅρος (hóros, “boundary”) + ὀπτήρ (optḗr, “observer”).

For any system of binocular vision, a three-dimensional curve containing all points from which the light will converge into a single image.


milha

From Portuguese milha (“Portuguese mile”), from Latin mīlia (“Roman mile”), plural of mīlle (“thousand”) from its length of 1000 Roman paces, from Proto-Indo-European *(sm̥-)ǵʰéslo-. Doublet of mile and milla.

(historical) A traditional Portuguese unit of distance, equivalent to about 1481.5, 1851.9, or 2057.6 m depending on the league used.


fingerbreadth

From finger + breadth. Compare Middle English fynger brede, fyngerbrede, fyngyrbrede.

A (usually approximate and informal) unit of measurement based upon the radial width of the human finger.


computable function

en-noun

computable function (plural computable functions)

(computer science) A mathematical function that can be computed using an abstract computation machine such as Turing machine.


nonoutlier

(statistics) A value which is not an outlier; a value within the general pattern of data


connectance

(mathematics) The fraction of all possible links in a network that are realized.


holomorph

(mathematics) The group formed by taking the semidirect product of a group by its automorphism group


contravariance

contravariance (countable and uncountable, plural contravariances)

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(category theory) A functor which reverses composition.

(linear algebra) Of vectors, the property of scaling inversely with a change of basis, as opposed to covariance.


autoregressive

en-adj

autoregressive (comparative more autoregressive, superlative most autoregressive)

more autoregressive (comparative)
most autoregressive (superlative)

An autoregressive model was used.

(statistics) Employing autoregression, using a weighted sample of past data to predict future results


bimodality

Frequency distributions of some of the variables indicate the existence of bimodalities.

1966, Zenon S. Zannetos, The Theory of Oil Tankship Rates, page 227:


PCC

Pearson correlation coefficient
w:Pearson correlation coefficient

(statistics) Initialism of Pearson correlation coefficient.


semicontinuous

upper semi-continuous
upper semi-continuous

lower semi-continuous
lower semi-continuous

(mathematics) (of a function) That it is continuous almost everywhere, except at certain points at which it is either upper semi-continuous or lower semi-continuous.


grav

A starship thundered invisibly close overhead, its gravs at full lift-off power.

The orbot was a speck, a clot, a ball, a toy. It was gliding silently in on gravs, directly overhead.

1992, Gardner Dozois, Geodesic Dreams: The Best Short Fiction Of Gardner Dozois, →ISBN, page 83:

Air cars include any vehicle which are grav powered and are capable of flying, but unlike aeroplanes they handle similar to normal ground cars.

2008, Martin Rait, FSpace Roleplaying Conspiracy Convention Skills Guide v1.1, →ISBN, page 7:

I set things up for the grav sled support and the Averonian operation.

2011, R Richard, Second Chance King of Avuls, →ISBN, page 7:

With the gravs, I can land in ten seconds and be cutting a door for you at the same time.

2011, J. E. Murphy, Sanctuary, →ISBN, page 317:

(science fiction) An anti-gravity device.


codifferentiation

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From co- + differentiation or codifferentiate + -ion.

In addition, a is called a co-exact form if the r-form a can be written as codifferentiation of a (r + l)-form β, ie, a = δβ.

1997, Bo-Yu Hou, Bo-Yuan Hou, Differential Geometry for Physicists, →ISBN, page 113:

(calculus) The act or process of obtaining the codifferential of a function, or a function which obtains the codifferential


cuboidal

cuboidal (comparative more cuboidal, superlative most cuboidal)

more cuboidal (comparative)
most cuboidal (superlative)

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A cuboidal block was formed.

(geometry) Of, pertaining to, or having the shape of a cuboid


megapascal

(metrology) An SI unit of pressure equal to 10⁶ pascals. Symbol: MPa


proba

(statistics) Abbreviation of probability.


multitaper

(signal processing) A technique to estimate the power spectrum of a stationary ergodic finite-variance random process, using several different data tapers which are orthogonal to each other.


quadrivalent

In graph theory terms, a regular projection of a knot, or knot diagram is thus a quadrivalent planar graph with over/under-decorated vertices.

2020 January 3, Wikipedia contributors, “Knot (mathematics)”, in English Wikipedia, Wikimedia Foundation:

(graph theory) Said of a graph: that all of its vertices have degree four.


invariant section

en-noun

invariant section (plural invariant sections)

* (law): Coined by Free Software Foundation in free software copyright licenses.

(mathematics) A section that will not vary through changing state.


RSA number

(mathematics) Any of the large semiprime numbers to be factored in the RSA Factoring Challenge, a competition from 1991 to 2007 encouraging research into computational number theory.


semiprime

Again, to be perfectly clear, we are looking for c values that produce a low density of semiprimes when employing Euler's basic polynomial but changing the c values, in the range of x=1 to 10000. Some very early standouts are: c=4 which produces 799 semiprimes; c=6 which produces 532 semiprimes; c=12 which produces only 431 semiprimes; c=18 which produces 364 semiprimes, and c=30 which produces only 320 semiprimes.

2010, Jason Earls, The Lowbrow Experimental Mathematician, Lulu.com, page 145:

2015, Jie Wang, Zachary A. Kissel, Introduction to Network Security: Theory and Practice, Wiley [under licence from Higher Education Press], page 113,
Firstly, we should change semiprimes from time to time, where a particular semiprime should only be used in a time interval shorter than the time required to factor an RSA challenge number of a similar length. Secondly, we should use semiprimes that consist of more than 200 decimal digits.

In this paper I will define four sequences of numbers obtained through concatenation, definitions which also use the notion of “sum of the digits of a number”, sequences that have the property to produce many primes, semiprimes and products of very few prime factors.

2015, Marius Coman, Two Hundred and Thirteen Conjectures on Primes: Collected Papers, Education Publishing, page 46:

(number theory) A natural number that is the product of two (not necessarily distinct) prime numbers.

puolialkuluku

number that is the product of two primes

biprime

product of two primes, not necessarily distinct


semiprime

The final part of the semiprime-semisimple analogy is given by
Proposition 4.4. A ring #92;mathbf#123;R#125; is semiprime if and only if #92;mathbf#123;R#125; is isomorphic to a subdirect product of prime rings.

1974, Thomas W. Hungerford, Algebra, Springer, page 446:

In this chapter we shall study the structure of semiprime alternative algebras.

1982, K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, A. I. Shirshov, translated by Harry F. Smith, Rings That Are Nearly Associative, Academic Press, page 176:

Let f be a semiprime fuzzy ideal of S and x#92;inS.

2003, John N. Mordeson, Davender S. Malik, Nobuaki Kuroki, Fuzzy Semigroups, Springer, page 213:

(mathematics) That has properties derived directly or by extension from a semiprime.


subrange

We are concerned with the subrange of integers between a and b.

The program defines two subrange types.

(mathematics, programming) A subset of a given range or numeric set.


additive function

additive function (plural additive functions)

(mathematics) A unary function that preserves the addition operation; a unary function f such that for any x and y: f(x + y) = f(x) + f(y).


hectopascal

(metrology) An SI unit of pressure equal to 10² pascals. Symbol: hPa


refactorization

refactorization (countable and uncountable, plural refactorizations)

(mathematics) A second or subsequent factorization.


femtobecquerel

radioactive activity
radioactive activity#English

(metrology) An SI unit of radioactive activity equal to 10⁻¹⁵ becquerels. Symbol: f


femtofarad

electrical capacitance
electrical capacitance#English

(metrology) An SI unit of electrical capacitance equal to 10⁻¹⁵ farads. Symbol: fF


femtocoulomb

(metrology) An SI unit of electric charge equal to 10⁻¹⁵ coulombs. Symbol: f


femtocandela

luminous intensity
luminous intensity#English

(metrology) An SI unit of luminous intensity equal to 10⁻¹⁵ candelas. Symbol: fcd


femtobel

(metrology) An SI unit of relative power equal to 10⁻¹⁵ bels. Symbol: f


femtojoule

energy, work, and heat
energy, work, and heat#English

(metrology) An SI unit of energy, work, and heat equal to 10⁻¹⁵ joules. Symbol: fJ


pseudovector

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(mathematics, physics) A quantity that transforms like a vector under a proper rotation but gains an additional change of sign under an improper rotation


pseudotensor

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(mathematics, physics) A quantity that transforms like a tensor under a proper rotation but gains an additional change of sign under an improper rotation.


teralumen

(metrology) An SI unit of luminous flux equal to 10¹² lumens. Symbol: T


megahenry

(metrology) An SI unit of electrical inductance equal to 10⁶ henrys. Symbol: M


overmatching

overmatching (usually uncountable, plural overmatchings)

(statistics) Matching for an apparent mediator that actually is a result of the exposure.


equifacial

(mathematics, of a polyhedron) Having equal faces.


tesseral

Blend of tessara + numeral, used in 1983 to describe such systems over various isohedral tilings of the plane.

(mathematics) Describing number systems, algebras, and algorithms over labeled hierarchical subdivisions of space.


pseudoreplication

pseudoreplication (countable and uncountable, plural pseudoreplications)

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There are two kinds of pseudoreplication: / temporal pseudoreplication, involving repeated measurements from the same individual, and / spatial pseudoreplicaiton, involving several measurements taken from the same vicinity.

2005, Michael J. Crawley, Statistics: an introduction using R, page 13:

(statistics, especially in, biology, ecology) The exaggeration of the statistical significance of a set of measurements resulting from treating the data as independent observations when they are in fact interdependent.


antiphase

(physics, mathematics) A difference in phase (of two waves) of 180°

contrafase

a difference in phase (of two waves) of 180°


zeptoliter

(metrology) An SI unit of volume equal to 10⁻²¹ liters. Symbol: z


hypergeometry

hypergeometry (countable and uncountable, plural hypergeometries)

A geometry in more than three dimensions.


foom

There are some scenarios in which private AI research wouldn't be nationalized: •An unexpected AI foom before anyone realizes what was coming.

2013, Brian Tomasik, International Cooperation vs. AI Arms Race, page 2:

Some advocates of this foom scenario say that there is an as-yet-undiscovered but very powerful set of related architectural innovations for AI system design, a set that one team could find first and then keep secret from others for long enough.

2016, Robin Hanson, The Age of Em: Work, Love, and Life when Robots Rule the Earth, →ISBN:

Though the programs will surely get better, there are no signs of foom.

2018, Steven Pinker, Enlightenment Now: The Case for Reason, Science, Humanism, and Progress, →ISBN:

artificial intelligence
artificial intelligence

A sudden increase in artificial intelligence such that an AI system becomes extremely powerful.


Turing test

Named after English mathematician, logician, and cryptographer Alan Turing (1912–1954). Turing himself used the term imitation game.

named-after

The Turing test used to be the gold standard for proving machine intelligence. This generation of bots is racing past it. We need to stay calm — and develop a new test.

2023 January 20, Cade Metz, “The Chatbots Can’t Outsmart You. Yet.”, in The New York Times, →ISSN:

(artificial intelligence) A test of a computer's ability to demonstrate intelligence, as measured by whether a human judge can reliably distinguish the computer from another human being by conversing with both entities in written natural language over a terminal.


coplanarity

en-noun

coplanarity (countable and uncountable, plural coplanarities)

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(geometry, of at least two things, usually lines) The state or characteristic of being within the same plane.


Minkowski spacetime

Minkowski spacetime (plural Minkowski spacetimes)

Named after German mathematician Hermann Minkowski (1864–1909).

named-after

(mathematics, relativity) A geometrically flat spacetime, i.e. one with zero curvature.


doubleton

(mathematics, rare) A set containing precisely two elements.


subcountable

(mathematics) Being the target (codomain) of a partial surjection from the natural numbers.


eigenstructure

(mathematics) The set of eigenvalues of a matrix.


(cryptography) Having had its MD5 checksum computed.


isochron

The entire plane is foliated by isochrons.

2007, Eugene M. Izhikevich, Dynamical Systems in Neuroscience, The MIT Press, page 446:

(mathematics, dynamical systems) A collection of points (such as a manifold), each point representing a set of initial conditions for a given dynamical system, such that every set results in the same long-term behaviour of the system.

Isochrone

collection of points representing initial conditions of a dynamical system


compositionality

Coordinate term: (in pragmatics) contextuality

(especially logic, semantics, mathematics) The property of being compositional.


LTO

en-noun

LTO (countable and uncountable, plural LTOs)

Coordinate term: DLT

(computing) Initialism of Linear Tape-Open, an open standard computer storage tape format having a single spooled cartridge with half-inch tape.

Linear Tape-Open

(software compilation) Initialism of link-time optimization.

Coordinate term: TLI

lunar transfer orbit
lunar transfer orbit#English

(space science, countable) Initialism of lunar transfer orbit.

lithium titanate oxide
lithium titanate oxide#English

(electrochemistry, uncountable) Initialism of lithium titanate oxide (“Li₄Ti₅O₁₂”).


LTO

w:Land Transportation Office (Philippines)

(Philippines) Initialism of Land Transportation Office.


magic circle

(mathematics) An arrangement of natural numbers on circles such that the sum of the numbers on each circle and the sum of numbers on diameter are identical.


determinacy

determinacy (countable and uncountable, plural determinacies)

(mathematics) (game theory) The study of the circumstances under which a game has a winning strategy.


microgeneration

microgeneration (countable and uncountable, plural microgenerations)

The elderly are market segments, by generations or microgenerations within age cohorts or by historical experience as personality types.

2002, Merry White, Perfectly Japanese: Making Families in an Era of Upheaval, page 169:

(countable, demography) A demographic or cohort similar to a generation but covering a shorter timespan.


resampling

(statistics) Any technique or instance of generating a new sample from an existing dataset.


bootstrapper

To a nonparametric bootstrapper, simulation might consist in resampling to obtain the 95% confidence interval of the correlation coefficient […]

2009, James R. Thompson, Simulation: A Modeler's Approach, page xi:

(statistics) One who uses bootstrap methods.


monogonal

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(geometry) Of or pertaining to a monogon.


monogonal

(geometry, of a line) That passes through exactly one vertex (of a polygon or polyhedron).


subminimum

subminimum (plural subminimums or subminima)

(mathematics) A point or value below a minimum.


cartesian

Following the approach adopted in [2, 3], two orthogonal cartesian reference systems are considered: […].

2009 January, Alfio Quarteroni, “Mathematical Models in Science and Engineering”, in Notices of the American Mathematical Society, volume 56, number 1, page 18:

(mathematics) Alternative spelling of Cartesian


quotient space

Thus if #92;mathfrak#123;D#125; is an arbitrary decomposition of a space X into mutually disjoint subsets, then the corresponding quotient space is obtained by 'shrinking' or 'identifying' each member of #92;mathfrak#123;D#125; to a single point. For this reason, the quotient spaces are sometimes called identification spaces and quotient maps as^([sic]) identification maps.

1983, K. D. Joshi, Introduction to General Topology, New Age International, page 129:

1989, unnamed translator, Nicolas Bourbaki, Elements of Mathematics: General Topology: Chapters 1-4, [1971, N. Bourbaki, Éléments de Mathématique: Topologie Générale 1-4, Masson], Springer, page 110,
PROPOSITION 6. Every quotient space of a connected space is connected.

The quotient space obtained from such a relation is called extended Reeb (ER) quotient space. Moreover, the ER quotient space, which is an abstract sub-space of M* and is independent from the geometry, may be represented as a traditional graph, which is called the extended Reeb graph (ERG).

2004, Silvia Biasotti, Bianca Falcidieno, Michela Spagnuolo, “6: Surface Shape Understanding Based on Extended Reeb Graphs”, in Sanjay Rana, editor, Topological Data Structures for Surfaces: An Introduction to Geographical Information Science, Wiley, page 96:

equivalence relation
equivalence relation

(topology and algebra) A space obtained from another by identification of points that are equivalent to one another in some equivalence relation.

identification space

space composed of points equivalent to each other in some relation


extremal

Tutorials provide an introduction to several major research topics in modern discrete mathematics, including probabilistic methods, extremal problems for graphs and set systems, Ramsey theory, additive number theory, combinatorial geometry, discrete harmonic analysis and more.

2009 January, “Mathematics Calendar”, in Notices of the American Mathematical Society, volume 56, number 1, page 73:

(mathematics) Relating to extrema (maximal or minimal).

extremal clause

in a w:en:Recursive definition; recursive definition


extremal

calculus of variations
calculus of variations

(mathematics) Any solution to a variety of equations in the calculus of variations.


groupoid

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(algebra) A magma: a set with a total binary operation.

[...] A category in which every morphism is an isomorphism is called a groupoid.
 This means that a group is a groupoid with only one object. [...]

(algebra and category theory) A set with a partial binary operation that is associative and has identities and inverses.

groupoïde

a set with a partial binary operation...


indecomposable

(mathematics) A vector space that cannot be decomposed.


indicable

(mathematics, of a group) Such that there exists a homomorphism from it to ℤ, the integers.


integrability

integrability (usually uncountable, plural integrabilities)

mathematical analysis
mathematical analysis

(mathematical analysis) The quality of being integrable (having an antidifference or antiderivative).


multivariable

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nonassociative

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This book has been written about associative algebras. However, there is an analogous “PI-theory” that can be carried out for nonassociative rings, which is outlined here.

1980, Lewis Halle Rowen, Polynomial Identities in Ring Theory, Academic Press, page 327:

1996, E. G. Goodaire, E. Jespers, C. Polcino Milies, Alternative Loop Rings, Elsevier, page 5,
Two important functions in nonassociative ring theory are the commutator and associator which, for elements a, b, c in a ring are defined respectively by
[a, b] = ab − ba
and
[a, b, c] = a(bc) − (ab)c.

2012, W. B. Vasantha Kandasamy, Florentin Smarandache, Non Associative Algebraic Structures Using Finite Complex Numbers, Zip Publishing, page 5,
Authors in this book for the first time have constructed nonassociative structures like groupoids, quasi loops, non associative semirings and rings using finite complex modulo integers.

(algebra, of an algebraic structure) Whose multiplication operation is not assumed to be associative for all elements.


nonconnected

(mathematics) Not connected: having more than one connected component.


conjugacy

conjugacy (countable and uncountable, plural conjugacies)

Because the gamma distribution is the conjugate prior for the precision parameter (#92;tau#61;1#47;#92;sigma²) of a univariate normal distribution, the Wishart distribution (as its multivariate generalization) extends conjugacy to the multivariate normal distribution.

2012 May 25, Steven W. Nydick, The Wishart and Inverse Wishart Distributions:

(mathematics) The condition or state of being conjugate.


decodable

en-adj

decodable (comparative more decodable, superlative most decodable)

more decodable (comparative)
most decodable (superlative)

[dɪˈkəʊdəbəɫ]

(information theory) Of a code, having a non-singular extension; being a lossless encoding.


fmole

(chemistry) (metrology) Symbol for femtomole, an SI unit of amount of substance equal to 10⁻¹⁵ moles.


hindcast

(mathematics) A test of a mathematical model by using data from a past event.


kiloparsec

(astronomy) A unit of distance equal to one thousand parsecs.


piconewton

(metrology) An SI unit of force equal to 10⁻¹² newtons. Symbol: pN


symplectic

A calque of complex, coined by Hermann Weyl in his 1939 book The Classical Groups: Their Invariants and Representations. From Ancient Greek συμπλεκτικός (sumplektikós), from συμ (sum) (variant of σύν (sún)), + πλεκτικός (plektikós) (from πλέκω (plékō)); modelled on complex (from Latin complexus (“braided together”), from com- (“together”) + plectere (“to weave, braid”)).
The symplectic group has previously been called the line complex group.

der

συμπλεκτικός

symplectic invariant

structure that is invariant under a symplectic form (regarded as a mapping)

(group theory, of a group) Whose characteristic abelian subgroups are cyclic.

(mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate.

(mathematics, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form.

There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.

1995, V. I. Arnold, “Some remarks on symplectic monodromy of Milnor fibrations”, in Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder, editors, The Floer Memorial Volume, Birkhäuser Verlag, page 99:

1997, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau, Structure of Dynamical Systems: A Symplectic View of Physics, Springer Science & Business Media (Birkhäuser).

2003, Fabrizio Catanese, Gang Tian (editors), Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E Summer School, Springer, Lecture Notes in Mathematics No. 1938.

2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde, editors, Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society:

In symplectic geometry, there is a notion of fibrations #92;pi#58;P#92;rightarrowM with a symplectic manifold F as fiber, where the structure group is the group of (exact) Hamiltonian symplectomorphisms of the fiber. These are called symplectic fibrations. If the base manifold (M,#92;omega#95;M) is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space P.

2003, Maung Min-Oo, “The Dirac Operator in Geometry and Physics”, in Steen Markvorsen, Maung Min-Oo, editors, Global Riemannian Geometry: Curvature and Topology, Springer, page 72:

(mathematics) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.


symplectic

συμπλεκτικός

The structure of stable symplectics on finite dimensional spaces has been studied by Krein [8], Gelfand & Lidskii [9], and Moser [10] in work of considerable practical importance.

1967, Journal of Mathematics and Mechanics, volume 16, number 1, Indiana University, page 339:

(mathematics) A symplectic bilinear form, manifold, geometry, etc.


anticorrelation

en-noun

anticorrelation (countable and uncountable, plural anticorrelations)

(statistics) Negative or inverse correlation, a relationship in which one value increases as the other decreases.


antidiagonal

(linear algebra) The diagonal of a matrix that leads from top-right towards bottom-left.

αντιδιαγώνιος

the diagonal of a matrix that leads from top-right towards bottom-left


normalizer

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In symbols, the normalizer of some subset S of group G is the subset N(S)=g∈G|g⁻¹Sg=S, so that S would be a normal subgroup if N(S) were the whole group.

(algebra) The subset of elements of some group which leave some given subset invariant when conjugating it.

Normalisator

set of group elements leaving a given subset invariant under conjugation


deconvolute

en-verb

deconvolute (third-person singular simple present deconvolutes, present participle deconvoluting, simple past and past participle deconvoluted)

deconvolutes (present singular third-person)
deconvoluting (participle present)
deconvoluted (participle past)
deconvoluted (past)

(mathematics) To invert a convolution equation


MLE

en-noun

MLE (countable and uncountable, plural MLEs)

maximum likelihood estimation
w:maximum likelihood estimation

(statistics) Initialism of maximum likelihood estimation.


tolbot

(obsolete, dialectal) A measure of capacity, possibly a bushel.


permutohedron

(mathematics) A polytope with n-1 dimensions that is embedded in an n-dimensional space, its vertices formed by permuting the coordinates of the vector (1, 2, 3, ..., n).


associahedron

(associativity rule), associate + -hedron

(mathematics) A convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a word of n letters and the edges correspond to a single application of the associativity rule.


horocycle

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(geometry) A curve in hyperbolic geometry whose normals all converge asymptotically.


horoball

Coined by William Thurston (1946-2012), American mathematician. See horosphere and ball.

(hyperbolic geometry) A horosphere together with the space above it.


hypergraph

(graph theory) A generalization of a graph, in which edges can connect any number of vertices.


geocomplexity

(mathematics, geology) The use of mathematical techniques to model complex geological systems (such as earthquakes)


five lemma

(singular only, mathematics) A particular lemma that claims the existence of a particular isomorphism in a commutative diagram given certain other homomorphisms in the diagram.


line integral

(mathematics) An integral whose integrand's domain is a curve.


developable

en-adj

developable (comparative more developable, superlative most developable)

more developable (comparative)
most developable (superlative)

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(geometry, of a surface) Described by a moving right line, and such that consecutive positions of the generator intersect each other, allowing the surface to be developed into a plane.


linearization

From linear + -ization or linearize + -ation.

(mathematics) A linear approximation of a non-linear system


refactorable

(mathematics, of an integer) Divisible by the count of its divisors.


tiddler

(British, informal) A small fish, especially a stickleback.


order tree

(topology) A set that is the union of subsets (called segments), each of which is totally ordered, such that the segments fit together a certain way.


ℝ-order tree

(topology) An order tree whose segments are homeomorphic to segments of the real line and that is the union of countably many segments.


trigonometric series

en-noun

trigonometric series (plural trigonometric series)

(mathematics) Any series of the form 1/2A_o+ displaystyle ∑ₙ₌₁ ᪲(A_n cos nx+B_n sin nx).


mathematical analysis

mathematical analysis (countable and uncountable, plural mathematical analyses)

(mathematics) The mathematical study of functions, sequences, series, limits, derivatives and integrals.


conditionalization

conditionalization (countable and uncountable, plural conditionalizations)

Such agents […] always update their opinions via conditionalization, and they never suffer information loss.

2025 September 30, (Please provide the book title or journal name), volume 138, number 3, →DOI:

(Bayesian statistics) An updating of one's belief state based on new information


radix point

Generalization of the term decimal point.

(mathematics) The character used to separate the integer and fractional part of a number in a digital representation of a number, regardless of the base used.


commutant

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The basic mathematical entity to be used here in elucidating the different senses of superselection rules is a von Neumann algebra #123;#92;mathfrak#123;M

2008 September 27, John Earman, “Superselection Rules for Philosophers”, in Erkenntnis, volume 69, number 3, →DOI:

(algebra, logic) The subset of all elements of a semigroup that commute with the elements of a given subset


quadratically

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In this work we show that, in presence of another nonminimally coupled scalar field, that is both quadratically and quartically coupled to the Ricci scalar, inflation naturally ends, representing an elegant solution to the graceful exit problem of topological inflation.

2015, Anja Marunović, Tomislav Prokopec, “Topological inflation with graceful exit”, in arXiv:


milliradian

An SI unit of plane angular measure equal to one thousandth of a radian


piecewise

Coordinate term: systemically

Coordinate term: locally

automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data

1994 July 24, Hugues Hoppe, Tony DeRose, Tom Duchamp, Mark Halstead, Hubert Jin, John McDonald, Jean Schweitzer, Werner Stuetzle, “Piecewise smooth surface reconstruction”, in Proceedings of the 21st annual conference on Computer graphics and interactive techniques (SIGGRAPH '94), New York, NY, USA: Association for Computing Machinery, →DOI, →ISBN, pages 295–302:

theory of piecewise differentiable functions and, specifically, piecewise differentiable equations

2012, Stefan Scholtes, Introduction to Piecewise Differentiable Equations (SpringerBriefs in Optimization), New York: Springer, →ISBN:

piecewise linear model which can serve as the base of any other

2013 March 9, Domine Leenaerts, Wim M. G. van Bokhoven, Piecewise Linear Modeling and Analysis, Springer Science & Business Media, →ISBN:

(especially mathematics) Throughout separate parts, but not necessarily throughout the whole.

paloittain

mathematics: throughout separate parts but not necessarily throughout the whole


piecewise

en-adj

piecewise (comparative more piecewise, superlative most piecewise)

more piecewise (comparative)
most piecewise (superlative)

Our formula is not defined as a piecewise function, but rather as a single closed-form expression

2018 April 1, Ivan Matić, Radoš Radoičić, Dan Stefanica, “A sharp Pólya-based approximation to the normal cumulative distribution function”, in Applied Mathematics and Computation, volume 322, →DOI, →ISSN, pages 111–122:

is a piecewise function but not a PLQ function

2019 September 1, Deepak Kumar, Yves Lucet, “Computation of the Epsilon-Subdifferential of Convex Piecewise Linear-Quadratic Functions in Optimal Worst-Case Time”, in Set-Valued and Variational Analysis, volume 27, number 3, →DOI, →ISSN, pages 623–641:

a piecewise function that consists of a single quadratic term and a constant term

2022, Ethan T. Wang, “Efficient Quantum State Preparation for the Cauchy Distribution Based on Piecewise Arithmetic”, in IEEE Transactions on Quantum Engineering, volume 3, →DOI, →ISSN, pages 1–9:

(mathematics) Defined by subfunctions and subdomains

In piecewise regression we replace the concept

1970 September, Victor E. McZgee, Willard T. Carleton, “Piecewise Regression”, in Journal of the American Statistical Association, volume 65, number 331, →DOI, →ISSN, pages 1109–1124:

we can get arbitrarily close to any piecewise function with knot locations satisfying

2000 July, J. Pittman, C.A. Murthy, “Fitting optimal piecewise linear functions using genetic algorithms”, in IEEE Transactions on Pattern Analysis and Machine Intelligence, volume 22, number 7, →DOI, pages 701–718:

In essence, a piecewise function over an interval

2016 November, Daniel Berjon, Guillermo Gallego, Carlos Cuevas, Francisco Moran, Narciso Garcia, “Optimal Piecewise Linear Function Approximation for GPU-Based Applications”, in IEEE Transactions on Cybernetics, volume 46, number 11, →DOI, →ISSN, pages 2584–2595:

piecewise linear
piecewise linear#English

(mathematics) Clipping of piecewise linear.


sublinear

The sublinear dependence of blue straggler number on core mass is interesting.

2009 January 15, Christian Knigge, Nathan Leigh, Alison Sills, “A binary origin for ‘blue stragglers’ in globular clusters”, in Nature, volume 457, number 7227, →DOI:

(mathematics) Describing a function that grows more slowly than a linear one.


semiregular

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A space is semiregular iff the regularly open sets (3D) form a base for the topology.[…]Every space X can be embedded in a semiregular space.

1970, Stephen Willard, General Topology, published 2004, page 98:

(topology, of a topological space) Whose regular open sets form a base.

It will be seen below that this semiregular polyhedron is of importance in its relationship to periodic minimal surfaces serving as a conceptual reference.

1993, H. Terrones, A. L. MacKay, “The Geometry of Hypothetical Curved Graphite Structures”, in H. W. Kroto, J.E. Fischer, Deann Cox, editors, The Fullerenes, page 115:

In a semiregular tessellation, there is an isometry of the plane carrying any vertex to any other vertex.

1998, David A. Singer, Geometry: Plane and Fancy, page 35:

While one of the semiregular polyhedra was mentioned by Plato, their first serious study is attributed to Archimedes.

2003, Saul Stahl, Geometry from Euclid to Knots, published 2010, page 272:

One that we will consider here is the semiregular tessellation—a tessellation of two or more regular polygons that are arranged so that the same polygons appear in the same order around each vertex point. The tessellation at the left in Figure 9.38 is a semiregular tessellation because the two figures are a square and a regular octagon. The tessellation at the right in Figure 9.38 is not a semiregular tessellation because the two figures are a square and a nonregular octagon.[…]There are only eight possible semiregular tessellations.

2011, Tom Bassarear, Mathematics for Elementary School Teachers, page 583:

(geometry, of a polyhedron or tessellation of the plane) Uniform (isogonal and isotoxal) with regular faces of two or more types, such that each vertex is surrounded by the same polygons in the same order.


spherical angle

en-noun

spherical angle (plural spherical angles)

(geometry) A particular dihedral angle, the angle between two intersecting arcs on a sphere, measured by the angle between the planes containing the arcs.


orthoradial

(mathematics) Relative to a grid of circles surrounding a point and lines starting at that point; such a graph has alternate circular and radial components


cotyle

cotyle (plural cotyles or cotylae or cotylai)

cotyles (plural)
cotylae (plural)
cotylai (plural)

From Latin cotylē and Ancient Greek κοτύλη (kotúlē, “cup, half-pint”). Doublet of kotyle and kotylos.

der

Again, they give the patient a cotyle of hulwort, clary seed, or caper root with half a drachm of squill; or an acetabulum of germander or thyme in three cyathi of oxymel; or two cotylae of alexanders seed with three cyathi of wine; or a cotyle of fennel seed and libanotis (Latin rosmarinum, ‘rosemary’) mixed with wine; or a drachm of gum ammoniac with three cyathi of oxymel.

1950, Caelius Aurelianus, translated by Israel Edward Drabkin, On Acute Diseases and On Chronic Diseases, University of Chicago Press, page 749:

(historical) Synonym of hemina (“a unit of Roman liquid measure”)


methuselah

en-noun

methuselah (plural methuselahs or methuselae)

methuselahs (plural)
methuselae (plural)

The first known methuselah was the r pentomino, but even longer lasting ones have been found by enumerating and testing small patterns. The following, called "rabbits," takes over 10000 generations to stabilize.

1996 December 16, Paul Callahan, “Need help in finding topic for research project”, in comp.theory.cell-automata (Usenet):

Is there somewhere a list of n-cell methuselah patterns in Conway's Life? (assuming some reasonable limits on the bounding box)

2003 February 24, Michael Hedera, “Methuselahs in Conway's Life”, in comp.theory.cell-automata (Usenet):

The pattern below seems to take about 30000 generations to stabilize. The initial population is 20. Is this methuselah a known one?

2008 June 29, Andrzej Megier, “Game of life methuselah?”, in comp.theory.cell-automata (Usenet):

(cellular automata) A small pattern that takes many generations to stabilize.


monoexponential

(mathematics) Involving the exponent of a single variable


monoexponential

(mathematics) The exponent of a single variable


habitable zone

The zone around a star where a planet could experience temperatures like those on Earth, allowing for the possible existence of liquid water and of life.

zona d'habitabilitat

the planetary zone that could sustain life


Goldilocks zone

Goldilocks zone (plural Goldilocks zones)

So called because, like the third of the three bowls of porridge in the fairy tale Goldilocks, it is neither too hot nor too cold, but just right.

This plot may be a map of another type of Goldilocks zone for habitable ocean worlds—one base on composition.

2021, Kevin Hand, Alien Oceans: The Search for Life in the Depths of Space, Princeton University Press, →ISBN, page 43:


hexecontahedron

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From Ancient Greek ἑξήκοντα (hexḗkonta, “60”) + -hedron, from Ancient Greek ἕδρα (hédra, “geometric face”).


icosidodecahedron

en-noun

icosidodecahedron (plural icosidodecahedra or icosidodecahedrons)

icosidodecahedra (plural)
icosidodecahedrons (plural)

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[…]together to form not only regular polyhedrons but rhombicosidodecahedrons, truncated icosidodecahedrons, and such.

1961, The New Yorker, Volume 37, Part 4, page 172:

1992, Jean-Louis Verger-Gaugry, Quasicrystals and the Concept of Interpenetration in m35-approximant Crystals with Long-range Icosahedral Atomic Clustering, A. R. Yavari, Ordering and Disordering in Alloys, Elsevier Applied Science, page 498,
A succession of 10 concentric icosidodecahedra centered at (0, 0, 0), forming a geometric sequence (the nᵗʰ one is τⁿ larger than the first one), is also put into evidence.

The edges of the octahedron form three squares; the edges of the cuboctahedron form four hexagons, and the edges of the icosidodecahedron form six decagons.

2004, David Darling, The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes, page 263:

Thus, there is a star octahedron, three star dodecahedrons, and fifty-nine star icosidodecahedrons.

2004, Marc-Alain Ouaknin, The Mystery of Numbers, unnumbered page:

The dark-gray (online: red) icosahedra are part of the B clusters, the light-gray dodecahedra of the B’ clusters, and the (online: blue) icosidodecahedra of the M clusters.

2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 306:

Polyhedrons include prisms; pyramids; the Platonic solids, including tetrahedrons, cubes, octahedrons, dodecahedrons, and icosahedrons; the Archimedean solids, such as cuboctahedrons and icosidodecahedrons; and the Johnson solids, such as square pyramids and triangular cupolas (dome-shape).

2010, Debra Ann Ross, Master Math: Geometry, Cengage Learning, page 306:

An Archimedean solid with thirty-two regular faces (twelve pentagons and twenty triangles).


zonohedron

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(geometry) A special case of convex polyhedron, in which every face of the polyhedron is a polygon with point symmetry.

chamfered cube
rhombic dodecahedron
zonohedron


zonotope

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(geometry) A polytope formed by the Minkowski sum of a zonohedron's line segments in any dimension.


Cantorian

en-adj

Cantorian (comparative more Cantorian, superlative most Cantorian)

more Cantorian (comparative)
most Cantorian (superlative)

(set theory, New Foundations) Smaller than its own power set; satisfying Cantor's theorem.


inscribable

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(geometry) That can be inscribed; whose vertices all lie on a sphere.


tetrahedralizable

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(geometry) That can be divided into tetrahedra.


DDE

delay differential equation
delay differential equation#English

(calculus) Initialism of delay differential equation.


delay differential equation

en-noun

delay differential equation (plural delay differential equations)

differential equation
differential equation

(calculus) a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times


stochastic differential equation

stochastic differential equation (plural stochastic differential equations)

stochastic differential equations (plural)

(calculus) a type of differential equation in which one or more of the terms is a stochastic process resulting in a solution which is itself a stochastic process

стохастическое дифференциальное уравне́ние


SDE

SDE (countable and uncountable, plural SDEs)

(calculus) Initialism of stochastic differential equation.


separatrix

separatrix (plural separatrixes or separatrices)

separatrixes (plural)
separatrices (plural)

Borrowed from Latin separatrix, the feminine form of separator (originally owing to an implied līnea (“line”)), from sēparāre (“to divide; to separate”) + -trix (forming female agents); equivalent to separate + -trix. First developed as a decimal mark among the medieval Arab mathematicians, whence a shorter variant gave rise to the decimal comma employed by many European countries and their former colonies.

(mathematics) The boundary separating two modes of behavior in a differential equation.


picomole

(chemistry, physics) A unit of substance equal to one trillionth (10⁻¹²) of a mole


poloid

(mathematics) A closed loop that has been twisted in a third dimension.


tweakable

en-adj

tweakable (comparative more tweakable, superlative most tweakable)

more tweakable (comparative)
most tweakable (superlative)

(cryptography, not comparable) Of a block cipher: accepting a second input (the "tweak"), used in conjunction with the key to select the permutation computed by the cipher.


locally indicable

(algebra, of a group) Such that each of its nontrivial, finitely generated subgroups maps homomorphically onto ℤ.


homomorphically

(mathematics) By means of a homomorphism.


antisymmetrizer

(mathematics, physics) A linear operator that makes a wave function of N identical fermions antisymmetric under the exchange of the coordinates of any pair of fermions.

operador antissimetrizador

a linear operator that makes a wave function of N identical fermions antisymmetric


covary

en-verb

covary (third-person singular simple present covaries, present participle covarying, simple past and past participle covaried)

covaries (present singular third-person)
covarying (participle present)
covaried (participle past)
covaried (past)

More specifically, to say that there is an informative criterion of diachronic identity is to say that facts of diachronic identity covary with facts about continuants’ instantaneous qualitative profiles […].

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

The participants certainly differ in how their practice is distributed (1, 2, or 3 days), but they also differ in how much total practice they get (3, 6, or 9 hours). This is a perfect example of a confound—it is impossible to tell if the results are due to one factor (distribution of practice) or the other (total practice hours); the two factors covary perfectly.

2009, C. James Goodwin, Research In Psychology: Methods and Design, John Wiley & Sons, →ISBN, page 175:

(statistics) To vary together with another variable, particularly in a way that may be predictive


correlogram

(mathematics) A graph that shows the correlation between two variables.


strange attractor

en-noun

strange attractor (plural strange attractors)

The term was coined by David Ruelle and Floris Takens.

(mathematics) An attractor that has a non-integer dimension or whose dynamics on it are chaotic.


eigenbasis

(mathematics) A basis for a vector space consisting entirely of eigenvectors.

Eigenbasis

basis of a vector space consisting entirely of eigenvectors


immanant

(linear algebra) A function or property of a matrix, defined as a generalization of the concepts of determinant and permanent.


microinch

A unit of measurement, the length of one one-millionth of an inch, equivalent to 25.4 nanometers. Symbol: µin


vorticity

vorticity (countable and uncountable, plural vorticities)

It might sound puzzling that the ageostrophic geopotential (or the ageostrophic pressure in z-coordinate) has no impact on the evolution of the vorticity of a quasi-geostrophic disturbance and yet it affects the perturbation kinetic energetics (not globally but locally).

2004, Zhu Xun, Li Xiaofan, Cai Ming, Observation, Theory And Modeling Of Atmospheric Variability, →ISBN, page 13:

This results from the vorticity component of shear, whereas elongated cells would further be affected by the rate of strain component.

2009 February 20, William M. Durham et al., “Disruption of Vertical Motility by Shear Triggers Formation of Thin Phytoplankton Layers”, in Science, volume 323, number 5917, →DOI, pages 1067–1070:

An extreme version of vorticity is a vortex. The vortex is a spinning, cyclonic mass of fluid, which can be observed in the rotation of water going down a drain, as well as in smoke rings, tornados and hurricanes.

2013 March, Frank Fish, George Lauder, “Not Just Going with the Flow”, in American Scientist, volume 101, number 2, archived from the original on 2013-05-01, page 114:

(mathematics, fluid dynamics) A property of a fluid flow related to local angular rotation; defined as the curl of the flow's velocity field.


alternative algebra

alternative algebra (plural alternative algebras)

(algebra) An algebra such that every subalgebra generated by two elements is associative.


power-associative algebra

power-associative algebra (plural power-associative algebras)

(algebra) An algebra such that every subalgebra generated by one element is associative.


sigmoidal

en-adj

sigmoidal (comparative more sigmoidal, superlative most sigmoidal)

more sigmoidal (comparative)
most sigmoidal (superlative)

The requirement […] typically results in a sigmoidal dependence on [ATP] 38 —the hallmark of binding cooperativity.

2009 January 7, Jeffrey R. Moffitt et al., “Intersubunit coordination in a homomeric ring ATPase”, in Nature, volume 457, number 7228, →DOI:

(statistics) Characterized by a sigmoid curve or function


predictand

(mathematics) That which is to be predicted.


osculator

(Vedic arithmetic) An algorithm for performing osculation.

(rare, mathematics) A circle of osculation.


starlike

starlike (comparative more starlike, superlative most starlike)

more starlike (comparative)
most starlike (superlative)

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

the growth theorem for holomorphic starlike mappings

(geometry) Convex; having the property that any line segment joining any mapped point to a specified point in the domain lies entirely in the domain.


fat tail

probability distribution
probability distribution

(statistics, probability) A tail of a probability distribution with significantly higher kurtosis than a normal distribution (which has kurtosis = 0).

leptokurtosis

tail of distribution with positive kurtosis

(statistics, probability) A tail of a probability distribution with infinite variance.


keyspace

en-noun

keyspace (countable and uncountable, plural keyspaces)

(cryptography) The notional space that contains all possible cryptographic keys.


teraelectron volt

teraelectron volt (plural teraelectron volts)

10¹² electron volts, as a unit of energy (TeV).


whiskering

natural transformation
natural transformation

(mathematics, category theory) The act of composing a natural transformation and a functor to produce another natural transformation.


quartic function

quartic function (plural quartic functions)

(mathematics) Any function of a polynomial whose greatest exponent is 4.


quintic function

quintic function (plural quintic functions)

(mathematics) Any function of a polynomial whose greatest exponent is 5.


eigenspectrum

(mathematics) The set of all eigenvalues of a linear operator.


antipole

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A line drawn from a point on a circle to its antipole will cross through the center.

(geometry) A position directly opposite (possibly also used figuratively).


megagon

Find the constant of proportionality for a decagon, kilogon, and megagon.

1999, Mark Dugopolski, College Algebra and Trigonometry, page 505:

There can exist a regular polygon with 1000 sides (this might be called a "regular kilogon"), 1,000,000 sides (a "regular megagon"), or 1,000,000,000 sides (a "regular gigagon").

2003, Stan Gibilisco, Geometry Demystified:

A megagon is close to the perfection of a circle — a kind of generational transmutation.

2007, Arthur Greenberg, From Alchemy to Chemistry in Picture and Story:

(geometry) A polygon with one million sides.


prototile

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(geometry) Any of the minimal set of non-congruent shapes from which a larger set of shapes, some of which may be congruent, can be produced.


ANN

(machine learning) Initialism of artificial neural network.


attoliter

(US) (metrology) An SI unit of fluid measure equal to 10⁻¹⁸ liters; alternative spelling of attolitre.


attolitre

(metrology) An SI unit of fluid measure equal to 10⁻¹⁸ litres; alternative spelling of attoliter.


chemical structure

chemical structure (plural chemical structures)

(physical chemistry) The arrangement of chemical bonds between atoms in a molecule (or in an ion or radical with multiple atoms), specifically which atoms are chemically bonded to what other atoms with what kind of chemical bond, together with any information on the geometric shape of the molecule needed to uniquely identify the type of molecule.


nonsingular

(linear algebra, of a matrix) Invertible.


corner solution

corner solution (plural corner solutions)

(mathematics, economics) A solution to a minimization or maximization problem where an interior solution is infeasible.


postmillennial

en-adj

postmillennial (comparative more postmillennial, superlative most postmillennial)

more postmillennial (comparative)
most postmillennial (superlative)

“I want to get into the heads of people younger than me, to be postmillennial,” she says. “I look at different Instagram influencers, at the music and the music scene, to try to understand it all.”

2020 February 7, Melanie Gerlis, quoting Avery Singer, “Avery Singer: the artist breathing fresh life into painting”, in Financial Times:

Following the millennial generation; relating to Generation Z.


subexpression

The third part of the regular expression, \1, is the backreference and tells ColdFusion to refer back to the first subexpression[…]

2003, Rob Brooks-Bilson, Programming ColdFusion MX:

Something to note that's shared between all subexpressions (as well as scriptblocks) is that the end of a line does not terminate the subexpression.

2020 February 24, “Handling PowerShell's Versatile Subexpressions”, in Clear-Script:

(mathematics, programming) An expression that is a part of a larger expression.

podvýraz

expression that is a part of a larger one


wlog

without loss of generality
without loss of generality#English

(mathematics) Initialism of without loss of generality.


lateral area

(geometry) The sum of the areas of the lateral (vertical) faces of a cylinder, cone, frustum, or the like.


superatomic

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(mathematics) Describing a Boolean algebra in which each subalgebra is atomic.


interquartile range

en-noun

interquartile range (plural interquartile ranges)

(statistics) The difference between the first and third quartiles; a robust measure of sample dispersion.


box plot

(statistics) A graphical summary of a numerical data sample through five statistics: median, lower quartile, upper quartile, and some indication of more extreme upper and lower values.


maneh

An obsolete Middle Eastern unit of weight, the mina.


cross-validation

cross-validation (usually uncountable, plural cross-validations)

(statistics) Any technique or instance of assessing how the results of a statistical analysis will generalize to an independent dataset.


distribution-free

(statistics) Free of specific assumptions about the shape of the probability distribution generating the sample.


signum function

signum function (plural signum functions)

(mathematics) The function that determines the sign of a real number, yielding −1 if negative, +1 if positive, or otherwise zero.


completable

(mathematics, of a partial algebra) That can be expanded to a total algebra.


tetrakis

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

bor

(mathematics, chemistry) Having four identical units


unkeyed

an unkeyed hash function

(computing, cryptography) Without a key.


Shannon entropy

en-noun

Shannon entropy (countable and uncountable, plural Shannon entropies)

Named after Claude Shannon, the "father of information theory".


negentropy

negentropy (countable and uncountable, plural negentropies)

/ˌnɛɡˈɛntɹɒpi/

/ˌnɛɡˈɛntɹəpi/

Erwin Schrödinger
Léon Brillouin
What is Life?

From nega- + entropy.
A blend of negative + entropy, coined by the French physicist Léon Brillouin (1889–1969). The term negative entropy was introduced by the Austrian physicist Erwin Schrödinger (1887–1961) in his book What is Life? (1944, based on lectures delivered in February 1943).

Brillouin (1956) made an attempt to link thermodynamic notions to the notions of information theory. To this end he employs the idea of bound information or information consistent with some microstates of a physical system. […] Brillouin has shown that bound information is equal to entropy decrease or negentropy increase. This is a so called negentropy principle of information, according to which negentropy can be turned into information and vice versa as follows from (1.103).

1990, Aleksandr I. Zotin, “Thermodynamics of Nonequilibrium Processes”, in Thermodynamic Bases of Biological Processes: Physiological Reactions and Adaptations, Berlin, New York, N.Y.: Walter de Gruyter, →ISBN, section 1.3.2 (Maxwell’s Demon and Negentropy Effects), page 46:

(information theory) The difference between the entropy of a probability distribution and the maximum possible entropy of the same probability distribution.


hendecagonal

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(geometry) Having eleven sides and angles; similar to a hendecagon


tridecagonal

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(geometry) Having thirteen sides and angles, similar to a tridecagon.

13-kulmion muotoinen

having thirteen sides and thirteen angles


umol

Derived from the similarity between the letter u and the Greek letter µ.


Reuleaux triangle

Reuleaux triangle (plural Reuleaux triangles)

Named after Franz Reuleaux, 19th-century German engineer, who used Reuleaux triangles in his machine designs.

(geometry) A figure consisting of three circular arcs, each centered on the intersection of the other two.


treelength

(mathematics) A measure of the size or complexity of a tree.


hyperellipse

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The hyperellipse is defined by (x/a)ⁿ + (y/b)ⁿ = 1 with b ≤ a, where n is the shape parameter and a and b are the axes along the x and y axes, respectively.

2003, M. M. Yovanovich and E. E. Marotta, "Thermal Spreading and Contact Resistances", chapter 4 of Adrian Bejan and Allan D. Kraus (editors), Heat Transfer Handbook, Wiley-IEEE, page 286

(geometry) A superellipse: a curve in two dimensions of a certain type, a generalization of the ellipse.

(geometry) Specifically, a superellipse with an exponent (shape parameter) greater than that of the ellipse (two).

This algorithm extends the model of RNS by incorporating multiple hypershape (hypersphere, hyperrectangle, or hyperellipse) detector representation in the unit hypercube [0, 1]ⁿ (Balachandran et al., 2007).

2008, Dipankar Dasgupta, Luis Fernando Niño, Immunological Computation: Theory and Applications, CRC Press, →ISBN, page 97:

(geometry) A multi-dimensional manifold of a certain type, a generalization of the ellipse and ellipsoid.


perfect set

The Cantor set is perfect.

(mathematical analysis) A set which is equal to its set of limit points. That is, a set A is perfect if A'=A.


unipotent

(mathematics) Having a single idempotent element.


conj

(mathematics) Abbreviation of (complex) conjugate.


blockwise

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(geometry) Allowing movement vertically or horizontally only, as if navigating the edges of a grid pattern.


keyphrase

(cryptography) A phrase used in encryption as a key, like a single keyword (password).


EVT

EVT (countable and uncountable, plural EVTs)

extreme value theory
w:extreme value theory

(statistics) Initialism of extreme value theory.


tractrix

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(geometry) A curve that satisfies the following property: that segment of the tangent line that lies between the point of tangency and a fixed line has length independent of the point of tangency chosen.


fourth dimension

(algebraic geometry) The fourth coordinate indicating a position along the fourth axis.


ungula

Borrowed from Latin ungula (“claw, hoof”), from unguis (“nail, claw, hoof”).

(geometry) A section of a cylinder, cone, or other solid of revolution, cut off by a plane oblique to the base; so called from its resemblance to the hoof of a horse.


superficies

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Borrowing from Latin superficiēs (“top, surface”), from super- (“above, over”) + faciēs (“form, configuration, shape”). Doublet of surface.

af

(geometry) A two-dimensional magnitude that has length and breadth; especially such a surface that forms the boundary of a solid.

The Superficies was compoſed of ſeveral bits of Wood, about the bigneſs of a Dye, but ſome larger than others.

1726 October 28, [Jonathan Swift], “The Author Permitted to See the Grand Academy of Lagado. […]”, in Travels into Several Remote Nations of the World. […] [Gulliver’s Travels], volume II, London: […] Benj[amin] Motte, […], →OCLC, part III (A Voyage to Laputa, Balnibarbi, Glubbdubdribb, Luggnagg, and Japan), page 72:

The visible, external surface of a body.


leptokurtotic

en-adj

leptokurtotic (comparative more leptokurtotic, superlative most leptokurtotic)

more leptokurtotic (comparative)
most leptokurtotic (superlative)


fat-tailed

fat-tailed (comparative more fat-tailed, superlative most fat-tailed)

more fat-tailed (comparative)
most fat-tailed (superlative)

(statistics) Having a fat tail; leptokurtic.


heavy-tailed

heavy-tailed (comparative more heavy-tailed, superlative most heavy-tailed)

more heavy-tailed (comparative)
most heavy-tailed (superlative)

(statistics) Having a heavy tail; leptokurtic.


Proth number

After French mathematician François Proth (1852-1879).

2006, B. Grégoire, L. Théry, B. Werner, A Computational Approach to Pocklington Certificates, Masami Hagiya, Philip Wadler (editors), Functional and Logic Programming: 8th International Symposium, Proceedings, Springer, LNCS 3945, page 109,
To generate Pocklington certificates for Proth number we add a new entry to the oracle: pocklington -proth k p.

Suppose that a Proth number n#61;k2ʳ#43;1 satisfies the condition that a#123;(n-1)#47;2#125;#92;equiv-1#92;pmodn for some integer a. Prove that n is prime.

2016, Abhijit Das, Computational Number Theory, Taylor & Francis (CRC Press / Chapman & Hall), page 295:

If a Proth number is prime, we call it a Proth prime.

2014, Adam Spencer, Adam Spencer's Big Book of Numbers, Brio Books, page 388:

(number theory) Any number of the form k·2ⁿ + 1, where k is odd, n is a positive integer, and 2ⁿ > k.


RCT

(statistics) Initialism of randomized controlled trial.


memberless

(set theory) Without members; empty or null.


random sequence

en-noun

random sequence (plural random sequences)

(statistics, probability theory) A sequence of identically distributed random variables.


CDF

Initialism of cumulative distribution function.


iid

(statistics, probability theory) Initialism of independent and identically distributed.


stemplot

(statistics) A means of displaying data used especially in exploratory data analysis.


stem-and-leaf

(statistics) Alternative spelling of stem and leaf


overfit

en-verb

overfit (third-person singular simple present overfits, present participle overfitting, simple past and past participle overfitted)

overfits (present singular third-person)
overfitting (participle present)
overfitted (participle past)
overfitted (past)

In all modeling techniques, and neural networks in particular, care must be taken not to overtrain or overfit the model. If possible, models should be interpreted in terms of their mechanistic meaning.

2004, Mark T.D. Cronin, Predicting Chemical Toxicity and Fate, CRC Press, →ISBN, page 169:

If your strategy is to always fit and use the global model, you will probably overfit the model (i.e., include unnecessary variables).

2007, Kenneth P. Burnham, David R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer Science & Business Media, →ISBN, page 250:

(statistics) To use a statistical model that has too many parameters relative to the size of the sample leading to a good fit with the sample data but a poor fit with new data.

過度擬合 /过度拟合

statistics: to use a statistical model that has too many parameters


parallelizable

(mathematics, of a manifold) Whose tangent bundle is a trivial bundle.


pseudocubic

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(geometry) describing a rhombohedral structure that is almost cubic


subequal

(mathematics) Describing a set of numbers, none of which is as great as the sum of all the rest


unbinned

(mathematics) Not divided into bins (intervals into which data is placed)


monoalphabetic

(cryptography) Of a substitution cipher, using the same fixed mappings from plaintext to cipher letters across the entire text.


fanega

From Spanish fanega, from Andalusian Arabic فَنِيقَة (faníqa, “sack”), from Arabic فَنِيقَة (fanīqa).

der

(historical) A traditional Spanish unit of dry measure, chiefly used for grain and roughly equivalent to a bushel.

cuartillo (1⁄120 Galician fanega or 1⁄48 Castilian fanega)


cilly

Uncertain; possibly a pun on silly and the letters CIL used as a cryptographic key.

Another type of cilly was the repeated use of the same message key, perhaps the initials of the operator's girlfriend […]

Answer c is a reference to a cilly, which was a three-character message key used in the German Enigma machine.

2002, Ronald L Krutz, Russell Dean Vines, The CISSP Prep Guide: Gold Edition:

Taunt describes the work involved in breaking Enigma messages, cribs, cillies, the Herivel tip, help from Bombes and more.

2005, Brian J Winkel, Cipher A Deavours, David Kahn, Louis Kruh, The German Enigma cipher machine:

By 1944, cillies had already become rare; hence, Bletchley Park had already found other breaks into the Enigma nets.

2006, Rebecca Ann Ratcliff, Delusions of intelligence: Enigma, Ultra and the end of secure ciphers:

Cillies resulted from a combination of two different mistakes in a multi-part message by some Enigma operators.

2007, Friedrich Ludwig Bauer, Decrypted secrets: methods and maxims of cryptology:

(cryptography, historical) Any predictable facet of the Enigma Machine cipher due to operator error or laziness, whose existence helped the Allies to break the code.


factorially

The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F₁) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore.

1974, Stanisław Lem, translated by Michael Kandel, The Cyberiad:

(mathematics) According to a factorial series or ratio.


Bayesian

en-adj

Bayesian (comparative more Bayesian, superlative most Bayesian)

more Bayesian (comparative)
most Bayesian (superlative)

(probability, statistics) Of or pertaining to Bayes' theorem and its applications.


Bayesian

(statistics) A proponent of Bayesianism.


zetetics

(mathematics) A branch of algebra which relates to the direct search for unknown quantities.


sequential compactness

(mathematical analysis) The property of a topological space that every sequence has a convergent subsequence.


sequential continuity

(mathematical analysis) The property of a function f between metric spaces, that given a convergent sequence x_n→x^*, then f(x_n)→f(x^*), i.e. the property of a function that it preserves sequential convergence.


discrete metric

en-noun

discrete metric (plural discrete metrics)

(mathematical analysis) a metric d such that for any pair of points x and y, d(x,y)=0 if x=y and d(x,y)=1 if x ne y.


Hausdorff space

Hausdorff space (plural Hausdorff spaces)

Named after German mathematician Felix Hausdorff (1868–1942).

named-after

More generally, each compact subset of a Hausdorff space is closed.[…]Metric spaces and compact Hausdorff spaces enjoy an even stronger separation property; in either case, disjoint closed sets can always be separated by disjoint open sets.

2005, N. L. Carothers, A Short Course on Banach Space Theory, Cambridge University Press, page 167:

In 1953, Grothendieck [G] characterized locally convex Hausdorff spaces which have the Dunford-Pettis property and used this property to characterize weakly compact operators u : C(K) → F, where K is a compact Hausdorff space and F is a locally compact Hausdorff space (briefly, lcHs) which is complete.

2008, Thiruvaiyaru V. Panchapagesan, The Bartle-Dunford-Schwartz Integral, Springer (Birkhäuser), page ix:

Our construction of βD is a special case of more general constructions in which compact Hausdorff spaces are obtained using sets which are maximal subject to having certain algebraic properties.

2012, Neil Hindman, Dona Strauss, Algebra in the Stone-Cech Compactification: Theory and Applications, 2nd edition, Walter de Gruyter, page 83:

(topology) A topological space in which for any two distinct points x and y, there is a pair of disjoint open sets U and V such that x∈U and y∈V.

T₂ space

topological space in which distinct points are contained in distinct open sets


Hausdorff metric

en-noun

Hausdorff metric (plural Hausdorff metrics)

The Hausdorff metric topology was first discovered by D. Pompeiu and by F. Hausdorff in 1927. This topology has been used in a number of areas such as function space topologies, approximation theory, and optimisation (see, e.g., 22).

2014, James F. Peters, Topology of Digital Images: Visual Pattern Discovery in Proximity Spaces, Springer Science & Business Media, →ISBN, page 195:

(mathematical analysis) In the abstract metric space of all compact subsets of ℝⁿ, given a pair of compact sets A and B, the Hausdorff metric is h(A,B)= mbox maxρ(A,B),ρ(B,A) where ρ(A,B)= sup _(a∈A) inf _(b∈B),d(a,b), where d is the Euclidean metric in ℝⁿ.


Euclidean metric

Euclidean metric (plural Euclidean metrics)

(mathematical analysis) In the space ℝⁿ, the metric d(⃑x,⃑y)=√ where ⃑x=(x_1,...,x_n) and ⃑y=(y_1,...,y_n).

Euklidovská metrika

(analysis) the metric that defines the "ordinary" distance between two points


uniform metric

(mathematical analysis) The metric ρ(f,g)= sup _(x∈X)|f(x)-g(x)| where f and g are functions on X.


supermodular

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

(mathematics, said of a function) having the property that f(x∨y)+f(x∧y)≥f(x)+f(y) for all x, y isin Rᵏ, where x ∨ y denotes the componentwise maximum and x ∧ y the componentwise minimum of x and y.


polychoron

polychoron (plural polychorons or polychora)

From poly- (“many”) + -choron (“room”), from Ancient Greek πολύς (polús, “many, much”) and χῶρος (khôros, “room”).

uder

(mathematics) A four-dimensional polytope


completely metrizable

(mathematical analysis) Of a set, that it is metrizable and, under such given metric, complete.


Polish space

They were first extensively studied by Polish topologists and logicians, such as Sierpiński, Kuratowski, and Tarski.

ℝⁿ is a Polish space

completely metrizable
completely metrizable

(topology) A separable, completely metrizable topological space


Cantor-Bendixson theorem

Named after Georg Cantor (1845–1918), a German mathematician who invented set theory, and Ivar Otto Bendixson (1861–1935), a Swedish mathematician.

(set theory) A theorem which (in a simpler formulation) states that a closed uncountable set in Euclidean n-space is equal to the disjoint union of a perfect set and a countable set.

Georg Cantor
Ivar Otto Bendixson
Perfect set property


limit point

is an example of a function having infinitely many essential singularities with a limit point at z=0. It is an easy matter to give examples of "elementary" functions whose singularities have a countable number of limit points.

1962 [Ginn and Company], Einar Hille, Analytic Function Theory, Volume 2, 2005, American Mathematical Society, page 19, The function sin ( cot 1/z)

If z_0 is a limit point of S, then every ϵ-neighborhood of z_0 must contain infinitely many points of S.

1970 [Macmillan], John W. Dettman, Applied Complex Variables, 1984, Dover, unnumbered page, Let S' be the set of limit points of a set S. Then the closure ◌̅S of S is S∪S'. […]

As the next example shows, the set of zeros may well have a limit point not belonging to the domain.

2006, Ivan Francis Wilde, Lecture Notes on Complex Analysis, Imperial College Press, page 153:

(topology) Given a subset S of a given topological space T, any point p whose every neighborhood contains some point, distinct from p, which belongs to S.

verdichtingspunt

point whose every neighborhood contains a point in a given subset


continuum hypothesis

In other words, it is consistent with the axioms^([of set theory]) to suppose that the continuum hypothesis is false. (It had been known for some time — see below — that it is consistent with the axioms of set theory to suppose that CH is true.)

2002, Steven G. Krantz, Handbook of Logic and Proof Techniques for Computer Science, Springer (Birkhäuser), page 65:

2013, Kenneth Reinhard, Introduction, Susan Spitzer (translator), Alain Badiou, The Incident at Antioch: A Tragedy in Three Acts / L’Incident d’Antioche: Tragédie en trois actes, Columbia University Press, page xxxiii,
After all, when Paul Cohen sent his proof of the undecidability of the continuum hypothesis (which Badiou considers an “event”) to Kurt Gödel in 1963, Gödel wrote back that “reading your proof had a similarly pleasant effect on me as seeing a good play."

In the end, it turned out that Cantor was unable to prove his continuum hypothesis precisely because it is unprovable.

2015, R. Bruce Elder, DADA, Surrealism, and the Cinematic Effect, Wilfrid Laurier University Press, page 582:

(set theory) The hypothesis which states that any infinite subset of ℝ must have the cardinality of either the set of natural numbers or of ℝ itself.

continuümhypothese

hypothesis that there is no cardinality between that of ℤ and that of ℝ


generalized continuum hypothesis

Generalization of the continuum hypothesis.

(set theory) The hypothesis that, for each ordinal α, there is no cardinal number strictly between א_α and 2^(א_α), i.e. 2^(א_α)=א_(α+1).


homothecy

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

Let us determine the center and the ratio of this homothecy.

1950, Duke Mathematical Journal, Duke University Press, page 76:

The restriction of B to S_b is a homothecy of scale b.

1981, Kenneth Joseph Arrow, Michael D. Intriligator, Handbook of Mathematical Economics, North-Holland, page 1720:

Proposition 7.4 Homothecies preserve circles. That is, for any homothecy h and any circle C, h(C) is a circle as well.[…]Were we willing to do the same with homothecies, we would meet an obstruction: the composition of two homothecies is not necessarily a homothecy.

2013, Felipe Cucker, Manifold Mirrors: The Crossing Paths of the Arts and Mathematics, Cambridge University Press, page 161: