Dirac delta

Named after English theoretical physicist Paul Dirac (1902–1984); the notation was chosen because the symbol behaves analogously to the Kronecker delta.

named-after

(mathematics) A function-like symbol denoted as δ, with the property ∫f(t)δ(x-t)dt=f(x), informally understood as a function with an infinite value at 0 and zero elsewhere, and formally as a distribution or a measure.


pmf

probability mass function
probability mass function#English

Initialism of probability mass function.


pdf

probability density function
probability density function#English

Initialism of probability density function.


cumulative distribution function

en-noun

cumulative distribution function (plural cumulative distribution functions)

cumulative distribution functions (plural)

A function which at each point t of the sample space has as its value the probability that a given random variable is less than (or equal) t. In symbols, F_X(t)=Pr(X<t).


hyperfactorial

(mathematics) The result of multiplying a given number of consecutive integers from 1 to the given number, each raised to its own power.

The result of multiplying a given number of consecutive integers from 1 to the given number, each raised to its own power.
For example, the hyperfactorial of 3 is 1¹ * 2² * 3³ = 1 * 4 * 27 = 108


K-function

mathematical analysis
mathematical analysis

(mathematical analysis) A generalization of the hyperfactorial function in mathematics to real and complex numbers.


beta function

Considering the equation of the binomial coefficient n choose k described in terms of the factorial, replacing n with p + q and k with p, turning the RHS upside-down and replacing factorials with the Gamma function, then replacing (p + q) choose p with Β(p, q) yields Euler's equation for the Beta function.

Euler integral of the first kind
Euler integral of the first kind

(mathematical analysis) A mathematical function that is also called the Euler integral of the first kind; it is a symmetric special function.

Betafunktion

function which generalizes the notion of a factorial


convex function

convex function (plural convex functions)

(computer science) A mathematical function where the line segment between any two points on the graph of the function lies above the graph in a vector space of at least two dimensions.


concave function

concave function (plural concave functions)

(computer science) The negative of the convex function.


set function

(computer science) A mathematical function whose input is a set (usually of real numbers or a set of points in the Euclidean or some measure space), and whose output is usually a number.


density function

density function (plural density functions)

(probability theory) Clipping of probability density function.


stress function

stress function (plural stress functions)

(physics) A function that finds a more tractable method for the elastic equations that describe the deformation of an elastic body subject only to boundary surface forces.


number-theoretic function

number-theoretic function (plural number-theoretic functions)

(mathematics) a real or complex valued function of n defined on the set of natural numbers that expresses some arithmetical property of n.


mass function

(astronomy, mathematics) A relationship that describes the mass distribution.


distribution function

distribution function (plural distribution functions)

(mathematics, physics) A function of seven variables of the form f(x,y,z,t;v_x,v_y,v_z) that gives the number of particles per unit volume in single-particle phase space.


unit function

multiplicative function
multiplicative function

(mathematics) a completely multiplicative function on the positive integers that is defined as equal to one for a special value and zero otherwise:


zeta function

(mathematics) function of the complex variable s that analytically continues the sum of the infinite series ∑ₙ₌₁ ᪲1/(nˢ) that converges when the real part of s is greater than 1.


correlation function

correlation function (plural correlation functions)

(mathematics) function giving the statistical correlation between random variables at two different points in space or time


partition function

partition function (plural partition functions)

(mathematics) generalization of the definition of a partition function in statistical mechanics


stream function

stream function (plural stream functions)

(mathematics) A function used to plot streamlines that represent the trajectories of particles in a steady flow.


discriminant function

discriminant function (plural discriminant functions)

(mathematics) A function used to predict a categorical dependent variable by one or more continuous or binary independent variables.


distance function

distance function (plural distance functions)

(mathematics) a function used to calculate the distance between two points.


Hankel function

Hankel function (plural Hankel functions)

(mathematics) Either of two functions that are solutions to Bessel's equation.


Dirac comb

Named after English physicist Paul Dirac. The functions, when plotted visually, resemble the teeth of a comb.

named-after

tempered distribution
tempered distribution

Dirac delta function
Dirac delta function

(mathematics) A periodic tempered distribution constructed from Dirac delta functions for some given period. It allows both continuous and discrete phenomena to be represented in a single framework.


modular form

analytic function
analytic function#English

functional equation
functional equation#English

(mathematics) A complex analytic function satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.


Dickman function

(number theory) A function, denoted by ρ, used to estimate the proportion of smooth numbers up to a given bound.


波函數

/pu̯ɔ⁵⁵ xän³⁵ ʂu⁵¹/

/pɔː⁵⁵ haːm²¹ sou̯³³/

/pu̯ɔ⁵⁵ xän³⁵ ʂu⁵¹/

/pɔː⁵⁵ haːm²¹ sou̯³³/


quasicircle

We then use a limiting Cauchy integral along level curves of Green's function to show that the Plemelj-Sokhotski jump formula holds on quasicircles with boundary data in the Douglas-Osborn space, which also enable us to prove the well-posedness of a Riemann-Hilbert problem with boundary data in Douglas-Osborn space on quasicircles.

2016, Eric Schippers, Wolfgang Staubach, “Harmonic reflection in quasicircles and well-posedness of a Riemann-Hilbert problem on quasidisks”, in arXiv:

(mathematics) A Jordan curve in the complex plane that is the image of a circle under a quasiconformal mapping of the plane onto itself.


polygamma function

en-noun

polygamma function (plural polygamma functions)

(mathematics) A meromorphic function on ℂ, defined as the (m+1)-th derivative (for a given order m) of the logarithm of the gamma function.


digamma function

digamma function (plural digamma functions)

(mathematics) The first of the polygamma functions, being the logarithmic derivative of the gamma function.


trigamma function

trigamma function (plural trigamma functions)

(mathematics) The second of the polygamma functions, after the digamma function.


circle inversion

circle inversion (plural circle inversions)

The first of these is obtained by the method of circle inversion first discovered by Peaucellier.

1875, A. B. Kempe, On Some New Limkages: Messenger of Mathematics, volume 4, page 121:

Nikolai Joukowski (1847-1921) was a Russian mathematician who did research in aerodynamics (James and James, 1992). He used circle inversion in the complex number plane to study airfoil shapes.

1997, Mathematical Association of America, MAA Notes, numbers 41-42, page 169:

As is common with nonlinear projections, it is possible to come up with many variants of circle inversions.[…]An obvious (but perhaps not very useful) extension of circle inversion is sphere inversion, where the spaces inside and outside a sphere are swapped.

2011, David Salomon, The Computer Graphics Manual, page 88:

(geometry, inversive geometry, for a given circle with centre O and radius r) A transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the point at infinity.


differential operator

differential operator (plural differential operators)

Define P(D) to be the differential operator given by P(D)#61;D²#43;5D#43;6, where D is the differentiation operator. Then P(D)(#92;sin(x))#61;-#92;sin(x)#43;5#92;cos(x)#43;6.

[…]these conditions appeared in the very first papers on ordinary differential operators.

2000, S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, page 328:

A differential operator P#92;left(D#92;right) is hypoelliptic if for any domain ⊂ #92;mathbb#123;R#125;ⁿ any solution u of the equation P#92;left(D#92;right)u#61;0 from the class #92;mathfrak#123;D#125;'#92;left(#92;Omega#92;right) is a function from C#92;infty(ω) for any open set ω ⊂⊂ #92;Omega.
A complete algebraic description of all hypoelliptic differential operators has been obtained by Hörmander in [H1].

2012, Youri Egorov, Bert-Wolfgang Schulze, Pseudo-Differential Operators, Singularities, Applications, page 27:

Secondly, differential operators and to some extent their fundamental solutions are local even with respect to the wave front set.

1998, L. Hörmander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, page 251:

(mathematics, mathematical analysis) An operator defined as a function of the differentiation operator (the operator which maps functions to their derivatives).

微分算子

mathematics: an operator defined as a function of the differentiation operator


colog

(mathematics) Abbreviation of cologarithm.


Brillouin function

Brillouin function (plural Brillouin functions)

Named after the physicist Léon Brillouin (1889–1969).

statistical mechanics
statistical mechanics

A special function that appears when studying an idealized paramagnetic material in statistical mechanics.


smooth function

smooth function (plural smooth functions)

Any ANALYTIC FUNCTION is smooth. But a smooth function is not necessarily analytic.

2003, Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, →ISBN, page 419:

(mathematics) a function that has derivatives of all finite orders everywhere in its domain.


functionhood

He did not distill the essential idea of functionhood: that to each x in the domain there corresponds a unique y in the range.

1999, William Dunham, Euler: The Master of Us All, The Mathematical Association of America, published 1999, page 17:

(mathematics, logic, grammar) The state or quality of being a function.


原函數

/ɥɛn³⁵ xän³⁵ ʂu⁵¹/

ㄩㄢˊ ㄏㄢˊ ㄕㄨˋㄦ

/ɥɛn³⁵ xän³⁵ ʂuɻʷ⁵¹/

/ɥɛn³⁵ xän³⁵ ʂu⁵¹/

/ɥɛn³⁵ xän³⁵ ʂuɻʷ⁵¹/

(calculus) primitive function; antiderivative


exponential decay

exponential decay (countable and uncountable, plural exponential decays)

The service value of the capital stock, i.e. the product of its price and quantity component, is decomposed into a depreciation component and an interest component, similar to the decomposition which holds under exponential decay.

2017, E. Biørn, Taxation, Technology, and the User Cost of Capital, →ISBN, page 239:

A decrease where the rate of decrease is proportional to the amount remaining.


special function

special function (plural special functions)

Any of various specific mathematical functions that have more or less established names and notations due to their importance.


偶函數

/ˀoʊ̯²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/ŋɐu̯¹³ haːm²¹ sou̯³³/

/ˀoʊ̯²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/ŋɐu̯¹³ haːm²¹ sou̯³³/


奇函數

/t͡ɕi⁵⁵ xän³⁵ ʂu⁵¹/

/t͡ɕi⁵⁵ xän³⁵ ʂu⁵¹/


反函數

/fän²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

ㄈㄢˇ ㄏㄢˊ ㄕㄨˋㄦ

/fän²¹⁴⁻²¹ xän³⁵ ʂuɻʷ⁵¹/

/fän²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/fän²¹⁴⁻²¹ xän³⁵ ʂuɻʷ⁵¹/


凹函數

/ˀɑʊ̯⁵⁵ xän³⁵ ʂu⁵¹/

/ˀɑʊ̯⁵⁵ xän³⁵ ʂuɻʷ⁵¹/

/ˀɑʊ̯⁵⁵ xän³⁵ ʂu⁵¹/

/ˀɑʊ̯⁵⁵ xän³⁵ ʂuɻʷ⁵¹/


凸函數

/tʰu⁵⁵ xän³⁵ ʂu⁵¹/

/tʰu⁵⁵ xän³⁵ ʂuɻʷ⁵¹/

/tʰu⁵⁵ xän³⁵ ʂu⁵¹/

/tʰu⁵⁵ xän³⁵ ʂuɻʷ⁵¹/


指數函數

ㄓˇ ㄕㄨˋ ㄏㄢˊ ㄕㄨˋ

ㄓˇ ㄕㄨˋ ㄏㄢˊ ㄕㄨˋ

чжишу ханьшу

/ʈ͡ʂʐ̩²¹⁴⁻²¹ ʂu⁵¹ xän³⁵ ʂu⁵¹/

/ʈ͡ʂʐ̩²¹⁴⁻²¹ ʂu⁵¹ xän³⁵ ʂu⁵¹/

exponential function
exponential function


線性函數

ㄒㄧㄢˋ ㄒㄧㄥˋ ㄏㄢˊ ㄕㄨˋ

ㄒㄧㄢˋ ㄒㄧㄥˋ ㄏㄢˊ ㄕㄨˋ

сяньсин ханьшу

/ɕi̯ɛn⁵¹⁻⁵³ ɕiŋ⁵¹ xän³⁵ ʂu⁵¹/

/siːn³³ sɪŋ³³ haːm²¹ sou̯³³/

/ɕi̯ɛn⁵¹⁻⁵³ ɕiŋ⁵¹ xän³⁵ ʂu⁵¹/

/siːn³³ sɪŋ³³ haːm²¹ sou̯³³/


Dirichlet eta function

Named after German mathematician Peter Gustav Lejeune Dirichlet (1805–1859).

named-after

Riemann zeta function
Riemann zeta function

(mathematics, mathematical analysis) The alternating sum of the Dirichlet series expansion of the Riemann zeta function:η(s)=∑ₙ₌₁ ᪲(-1)ⁿ⁻¹/nˢ=1/(1ˢ)-1/(2ˢ)+1/(3ˢ)-1/(4ˢ)+⋯.


logarithmic derivative

en-noun

logarithmic derivative (plural logarithmic derivatives)

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

From this Coulomb function, we can then calculate the logarithmic derivative of U²(r) at the eigenvalue for any value of r outside the core. If there exists a radius R lying in the Coulomb region and sufficiently small that the logarithmic derivative at R is a smooth function of the energy, we can obtain the logarithmic derivative for arbitrary energies within a reasonable range by interpolating it between the eigenvalues.

1955, Frank S. Ham, “The Quantum Defect Method”, in Frederick Seitz, David Turnbull, editors, Solid State Physics, Volume 1, Academic Press, page 138:

In economics, it is popular to consider the logarithmic derivative (#92;ln#92;varphi(t))'#61;#92;varphi'(t)#47;#92;varphi(t), as a convenient growth measure.

1994, Bjarne S. Jensen, The Dynamic Systems of Basic Economic Growth Models, Kluwer Academic, page 329:

In this section we consider the R-matrix method in which a solution is first found in an inner region 0 ≤ r ≤ a by expanding in a basis set yielding the logarithmic derivative of the wave function on the boundary r = a.

1995, Philip G. Burke, Charles J. Joachain, Theory of Electron-Atom Collisions: Part 1: Potential Scattering, Plenum Press, page 86:

(calculus, mathematical analysis) Given a real or complex function f, the ratio of the value of the derivative to the value of the function, (f')/f, regarded as a function.

логаритмична производна

ratio of the value of the derivative to the value of the function, regarded as a function


Borel transform

Borel transform (plural Borel transforms)

(mathematics) A generalization of this in Nachbin's theorem.


sigmoid function

sigmoid function (plural sigmoid functions)

1995, Jun Han, Claudio Moraga, The Influence of the Sigmoid Function Parameters on the Speed of Backpropagation Learning, José Mira, Francisco Sandoval (editors), From Natural to Artificial Neural Computation: International Workshop on Artificial Neural Networks, Proceedings, Springer, LNCS 930, page 195,
[The] [s]igmoid function is the most commonly known function used in feed forward neural networks because of its nonlinearity and the computational simplicity of its derivative.

The first significant new insight from gamma spatial analysis emerged on re-examination of the sigmoid function representing bilateral saturation.

2012, Walter Freeman, Neurodynamics: An Exploration in Mesoscopic Brain Dynamics, Springer, page 241:

2016, Roumen Anguelov, Svetoslav Markov, Hausdorff Continuous Interval Functions and Applications, Marco Nehmeier, Jürgen Wolff von Gudenberg, Warwick Tucker (editors), Scientific Computing, Computer Arithmetic, and Validated Numerics: 16th International Symposium, SCAN 2014, Springer, LNCS 9553, page 10,
Sigmoid functions find multiple applications to neural networks and cell growth population models [14,20]. A sigmoid function on R with a range [a,b] is defined as a monotone function s(t): R →[a,b] such that lim _(t→-∞)s(t)=a, and lim _(t→∞)s(t)=b.

(mathematical analysis, statistics) Any of various real functions whose graph resembles an elongated letter "S"; specifically, the logistic function y=(eˣ)/(eˣ+1)=1/(1+e⁻ˣ).


Smarandache function

Named after Florentin Smarandache, who rediscovered the function in 1980.

(number theory) A function, denoted by S(n) for some positive integer n, that yields the smallest number s such that n divides the factorial s!. For example, the number 8 does not divide 1!, 2!, 3!, but does divide 4!, so S(8) = 4.


witch of Agnesi

witch of Agnesi (plural witches of Agnesi)

Named after Italian mathematician Maria Gaetana Agnesi, who wrote about such curves, and from a mistranslation of Italian versiera, the term she used for them which means "rope", but which is spelled the same as versiera (“witch”).

(geometry) A cubic plane curve defined from two diametrically opposite points of a circle.


common logarithm

common logarithm (plural common logarithms)


Napierian logarithm

Napierian logarithm (plural Napierian logarithms)

Napierian logarithms (plural)
Naperian logarithm (alternative)

(mathematics) The logarithm to the base e, named after John Napier.


Walsh function

Named after the American mathematician Joseph L. Walsh.

(mathematics) In harmonic analysis, any of a complete orthogonal set of functions that can be used to represent any discrete function.


Möbius function

Named after August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer who introduced it in 1832.

(combinatorics) A function from the natural numbers to the set {−1, 0, 1} which maps perfect squares to 0, prime numbers to −1, and is multiplicative.


Baire function

(mathematics) A function obtained from a continuous function by transfinite iteration of the operation of forming pointwise limits of sequences of functions.


功函數

/kʊŋ⁵⁵ xän³⁵ ʂu⁵¹/

/kʊŋ⁵⁵ haːm²¹ sou̯³³/

/kʊŋ⁵⁵ xän³⁵ ʂu⁵¹/

/kʊŋ⁵⁵ haːm²¹ sou̯³³/


對數函數

ㄉㄨㄟˋ ㄕㄨˋ ㄏㄢˊ ㄕㄨˋ

ㄉㄨㄟˋ ㄕㄨˋ ㄏㄢˊ ㄕㄨˋ

/tu̯eɪ̯⁵¹⁻⁵³ ʂu⁵¹ xän³⁵ ʂu⁵¹/

/tɵy̯³³ sou̯³³ haːm²¹ sou̯³³/

/tu̯eɪ̯⁵¹⁻⁵³ ʂu⁵¹ xän³⁵ ʂu⁵¹/

/tɵy̯³³ sou̯³³ haːm²¹ sou̯³³/

logarithmic function
logarithmic function


二次函數

ㄦˋ ㄘˋ ㄏㄢˊ ㄕㄨˋ

ㄦˋ ㄘˋ ㄏㄢˊ ㄕㄨˋ

/ˀɤɻ⁵¹⁻⁵³ t͡sʰz̩⁵¹ xän³⁵ ʂu⁵¹/

/jiː²² t͡sʰiː³³ haːm²¹ sou̯³³/

/ˀɤɻ⁵¹⁻⁵³ t͡sʰz̩⁵¹ xän³⁵ ʂu⁵¹/

/jiː²² t͡sʰiː³³ haːm²¹ sou̯³³/


有理函數

ㄧㄡˇ ㄌㄧˇ ㄏㄢˊ ㄕㄨˋ

ㄧㄡˇ ㄌㄧˇ ㄏㄢˊ ㄕㄨˋ

/joʊ̯²¹⁴⁻³⁵ li²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/jɐu̯¹³ lei̯¹³ haːm³³ sou̯³³/

/joʊ̯²¹⁴⁻³⁵ li²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/jɐu̯¹³ lei̯¹³ haːm³³ sou̯³³/


超越函數

ㄔㄠ ㄩㄝˋ ㄏㄢˊ ㄕㄨˋ

ㄔㄠ ㄩㄝˋ ㄏㄢˊ ㄕㄨˋ

чаоюэ ханьшу

/ʈ͡ʂʰɑʊ̯⁵⁵ ɥɛ⁵¹ xän³⁵ ʂu⁵¹/

/ʈ͡ʂʰɑʊ̯⁵⁵ ɥɛ⁵¹ xän³⁵ ʂu⁵¹/

transcendental function
transcendental function


代數函數

ㄉㄞˋ ㄕㄨˋ ㄏㄢˊ ㄕㄨˋ

ㄉㄞˋ ㄕㄨˋ ㄏㄢˊ ㄕㄨˋ

дайшу ханьшу

/taɪ̯⁵¹⁻⁵³ ʂu⁵¹ xän³⁵ ʂu⁵¹/

/taɪ̯⁵¹⁻⁵³ ʂu⁵¹ xän³⁵ ʂu⁵¹/


單調函數

ㄉㄢ ㄉㄧㄠˋ ㄏㄢˊ ㄕㄨˋ

ㄉㄢ ㄉㄧㄠˋ ㄏㄢˊ ㄕㄨˋ

даньдяо ханьшу

/tän⁵⁵ ti̯ɑʊ̯⁵¹ xän³⁵ ʂu⁵¹/

/tän⁵⁵ ti̯ɑʊ̯⁵¹ xän³⁵ ʂu⁵¹/


初等函數

ㄔㄨ ㄉㄥˇ ㄏㄢˊ ㄕㄨˋ

ㄔㄨ ㄉㄥˇ ㄏㄢˊ ㄕㄨˋ

чудэн ханьшу

/ʈ͡ʂʰu⁵⁵ tɤŋ²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/ʈ͡ʂʰu⁵⁵ tɤŋ²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/


TREE

Kruskal's tree theorem
Kruskal's tree theorem

(mathematics) An extremely fast-growing function based on Kruskal's tree theorem.


橢圓函數

ㄊㄨㄛˇ ㄩㄢˊ ㄏㄢˊ ㄕㄨˋ

ㄊㄨㄛˇ ㄩㄢˊ ㄏㄢˊ ㄕㄨˋ

тоюань ханьшу

/tʰu̯ɔ²¹⁴⁻²¹ ɥɛn³⁵ xän³⁵ ʂu⁵¹/

/tʰɔː¹³ jyːn²¹ haːm²¹ sou̯³³/

/tʰu̯ɔ²¹⁴⁻²¹ ɥɛn³⁵ xän³⁵ ʂu⁵¹/

/tʰɔː¹³ jyːn²¹ haːm²¹ sou̯³³/


d'Alembert operator

d'Alembert operator (plural d'Alembert operators)

Named after Jean le Rond d'Alembert (1717–1783), a French mathematician, mechanician, physicist, philosopher, and music theorist.

differential operator
differential operator

(physics) A differential operator which may be expressed as ∂_μ∂^μ=∑_(μ=0)³∂/∂x^μ∂/∂x_μ; it is the four-dimensional (Minkowski space) equivalent of the three-dimensional Laplace operator.

Jean le Rond d'Alembert
d'Alembert operator


導函數

/tɑʊ̯²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/tɑʊ̯²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/


週期函數

ㄓㄡ ㄑㄧ ㄏㄢˊ ㄕㄨˋ

ㄓㄡ ㄑㄧˊ ㄏㄢˊ ㄕㄨˋ

чжоуци ханьшу

/ʈ͡ʂoʊ̯⁵⁵ t͡ɕʰi⁵⁵ xän³⁵ ʂu⁵¹/

/ʈ͡ʂoʊ̯⁵⁵ t͡ɕʰi³⁵ xän³⁵ ʂu⁵¹/

/ʈ͡ʂoʊ̯⁵⁵ t͡ɕʰi⁵⁵ xän³⁵ ʂu⁵¹/

/ʈ͡ʂoʊ̯⁵⁵ t͡ɕʰi³⁵ xän³⁵ ʂu⁵¹/


增函數

/t͡sɤŋ⁵⁵ xän³⁵ ʂu⁵¹/

/t͡sɤŋ⁵⁵ xän³⁵ ʂu⁵¹/


遞增函數

ㄉㄧˋ ㄗㄥ ㄏㄢˊ ㄕㄨˋ

ㄉㄧˋ ㄗㄥ ㄏㄢˊ ㄕㄨˋ

дицзэн ханьшу

/ti⁵¹ t͡sɤŋ⁵⁵ xän³⁵ ʂu⁵¹/

/ti⁵¹ t͡sɤŋ⁵⁵ xän³⁵ ʂu⁵¹/


遞減函數

ㄉㄧˋ ㄐㄧㄢˇ ㄏㄢˊ ㄕㄨˋ

ㄉㄧˋ ㄐㄧㄢˇ ㄏㄢˊ ㄕㄨˋ

дицзянь ханьшу

/ti⁵¹ t͡ɕi̯ɛn²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/ti⁵¹ t͡ɕi̯ɛn²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/


減函數

ㄐㄧㄢˇ ㄏㄢˊ ㄕㄨˋ

ㄐㄧㄢˇ ㄏㄢˊ ㄕㄨˋ

/t͡ɕi̯ɛn²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/t͡ɕi̯ɛn²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/


狄利克雷函數

ㄉㄧˊ ㄌㄧˋ ㄎㄜˋ ㄌㄟˊ ㄏㄢˊ ㄕㄨˋ

ㄉㄧˊ ㄌㄧˋ ㄎㄜˋ ㄌㄟˊ ㄏㄢˊ ㄕㄨˋ

Диликэлэй ханьшу

/ti³⁵ li⁵¹⁻⁵³ kʰɤ⁵¹ leɪ̯³⁵ xän³⁵ ʂu⁵¹/

/ti³⁵ li⁵¹⁻⁵³ kʰɤ⁵¹ leɪ̯³⁵ xän³⁵ ʂu⁵¹/


常函數

/ʈ͡ʂʰɑŋ³⁵ xän³⁵ ʂu⁵¹/

/ʈ͡ʂʰɑŋ³⁵ xän³⁵ ʂu⁵¹/


常數函數

ㄔㄤˊ ㄕㄨˋ ㄏㄢˊ ㄕㄨˋ

ㄔㄤˊ ㄕㄨˋ ㄏㄢˊ ㄕㄨˋ

чаншу ханьшу

/ʈ͡ʂʰɑŋ³⁵ ʂu⁵¹ xän³⁵ ʂu⁵¹/

/ʈ͡ʂʰɑŋ³⁵ ʂu⁵¹ xän³⁵ ʂu⁵¹/


空間波函數

ㄎㄨㄥ ㄐㄧㄢ ㄅㄛ ㄏㄢˊ ㄕㄨˋ

ㄎㄨㄥ ㄐㄧㄢ ㄅㄛ ㄏㄢˊ ㄕㄨˋ

кунцзянь боханьшу

/kʰʊŋ⁵⁵ t͡ɕi̯ɛn⁵⁵ pu̯ɔ⁵⁵ xän³⁵ ʂu⁵¹/

/kʰʊŋ⁵⁵ t͡ɕi̯ɛn⁵⁵ pu̯ɔ⁵⁵ xän³⁵ ʂu⁵¹/

spatial wave function
spatial wave function


Gaussian function

Gaussian function (plural Gaussian functions)

(mathematics) A function of the form f(x)=a· exp (-((x-b)²)/(2c²)) for arbitrary real-number constants a, b and non-zero c; used in statistics, signal processing, etc.


Barnes integral

Barnes integral (plural Barnes integrals)

They were introduced by Ernest William Barnes.

(mathematics) A contour integral involving a product of gamma functions, closely related to generalized hypergeometric series.


busy beaver function

busy beaver function (plural busy beaver functions)

(mathematics, computing theory) The mathematical function, denoted by Σ(n), that maps each positive integer n to the number of steps required for the busy beaver among machines with two colors and n states to terminate.


隱函數

/in²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/in²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

(mathematical analysis, algebraic geometry) implicit function


Nullstelle

de-noun

Nullstelle f (genitive Nullstelle, plural Nullstellen)

Nullstelle (genitive)
Nullstellen (plural)
Nullstelle (nominative singular)
Nullstellen (definite nominative plural)
Nullstelle (genitive singular)
Nullstellen (definite genitive plural)
Nullstelle (dative singular)
Nullstellen (dative definite plural)
Nullstelle (accusative singular)
Nullstellen (accusative definite plural)

/ˈnʊlˌʃtɛlə/

(mathematics) zero, root (value of the independent variables of a function, for which the function is equal to zero)


貝塞爾函數

ㄅㄟˋ ㄙㄞˋ ㄦˇ ㄏㄢˊ ㄕㄨˋ

ㄅㄟˋ ㄙㄞˋ ㄦˇ ㄏㄢˊ ㄕㄨˋ

Бэйсайэр ханьшу

/peɪ̯⁵¹⁻⁵³ saɪ̯⁵¹ ˀɤɻ²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/peɪ̯⁵¹⁻⁵³ saɪ̯⁵¹ ˀɤɻ²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/


antylogarytm

antylogarytm (nominative singular)
antylogarytmy (nominative plural)
antylogarytmu (genitive singular)
antylogarytmów (genitive plural)
antylogarytmowi (dative singular)
antylogarytmom (dative plural)
antylogarytm (accusative singular)
antylogarytmy (accusative plural)
antylogarytmem (instrumental singular)
antylogarytmami (instrumental plural)
antylogarytmie (locative singular)
antylogarytmach (locative plural)
antylogarytmie (singular vocative)
antylogarytmy (plural vocative)


coordinate chart

en-noun

coordinate chart (plural coordinate charts)

A set S#92;subset#92;mathbb#123;R#125;³ is called a regular surface if each of its points has a neighborhood in S that is diffeomorphic to an open set in #92;mathbb#123;R#125;². That is, for every p#92;inS, there exists a neighborhood, V, of p in S, an open set U#92;subset#92;mathbb#123;R#125;², and a diffeomorphism #92;sigma#58;U#92;rightarrowV. Such a diffeomorphism #92;sigma is called a surface patch or a coordinate chart. A collection of surface patches that together cover all of the points of S is called an atlas for S.

2016 September 30, Kristopher Tapp, Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics), Springer, →ISBN, →OCLC, page 125:

differential geometry
differential geometry

(differential geometry) A homeomorphism from a local neighborhood around a point on a topological n-manifold in a Banach space to an n-dimensional Banach space (typically a subspace of the space the manifold is embedded in).


coordinate map

Let (W#95;0,#92;psi) be a smooth coordinate chart for P, and let (E#95;1,#92;dots,E#95;#123;n-p#125;) be a local orthonormal frame for the normal bundle NP; by shrinking W#95;0 if necessary, we can assume that the coordinates and the local frame are defined on the same open subset W#95;0#92;subseteqP. Let #92;hat#123;W#125;#95;0#61;#92;psi(W#95;0)#92;subseteq#92;mathbb#123;R#125;ᵖ, and let NP#92;vert#95;#123;W#95;0#125; be the portion of the normal bundle over W#95;0. The coordinate map #92;psi and frame (E#95;j) yield a diffeomorphism #92;hat#123;W#125;#95;0#92;times#92;mathbb#123;R#125;#123;n-p#125;#92;rightarrowNP#92;vert#95;#123;W#95;0#125; defined by[…]

2019 January 2, John M. Lee, Introduction to Riemannian Manifolds (Graduate Texts in Mathematics), Springer, →ISBN, →OCLC, page 135:

coordinate chart
coordinate chart#English

(differential geometry) Synonym of coordinate chart.


Weierstrass function

Weierstrass function (plural Weierstrass functions)

(mathematics) A real-valued function that is continuous everywhere but differentiable nowhere.


超橢圓函數

ㄔㄠ ㄊㄨㄛˇ ㄩㄢˊ ㄏㄢˊ ㄕㄨˋ

ㄔㄠ ㄊㄨㄛˇ ㄩㄢˊ ㄏㄢˊ ㄕㄨˋ

чаотоюань ханьшу

/ʈ͡ʂʰɑʊ̯⁵⁵ tʰu̯ɔ²¹⁴⁻²¹ ɥɛn³⁵ xän³⁵ ʂu⁵¹/

hyperelliptic function
hyperelliptic function


一次函數

ㄧ ㄘˋ ㄏㄢˊ ㄕㄨˋ

ㄧ ㄘˋ ㄏㄢˊ ㄕㄨˋ

/i⁵⁵ t͡sʰz̩⁵¹ xän³⁵ ʂu⁵¹/

/jɐt̚⁵ t͡sʰiː³³ haːm²¹ sou̯³³/

/i⁵⁵ t͡sʰz̩⁵¹ xän³⁵ ʂu⁵¹/

/jɐt̚⁵ t͡sʰiː³³ haːm²¹ sou̯³³/


隸屬函數

ㄌㄧˋ ㄕㄨˇ ㄏㄢˊ ㄕㄨˋ

ㄌㄧˋ ㄕㄨˇ ㄏㄢˊ ㄕㄨˋ

/li⁵¹ ʂu²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/li⁵¹ ʂu²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

(fuzzy logic, set theory) membership function


surjective function

surjective function (plural surjective functions)


funkcja liniowa

funkcja liniowa (nominative singular)
funkcje liniowe (nominative plural)
funkcji liniowej (genitive singular)
funkcji (genitive plural)
funkcyj  liniowych (archaic genitive plural)
funkcji liniowej (dative singular)
funkcjom liniowym (dative plural)
funkcję liniową (accusative singular)
funkcje liniowe (accusative plural)
funkcją liniową (instrumental singular)
funkcjami liniowymi (instrumental plural)
funkcji liniowej (locative singular)
funkcjach liniowych (locative plural)
funkcjo liniowa (singular vocative)
funkcje liniowe (plural vocative)

(functional analysis, linear algebra) linear function (linear map)


funkcja kwadratowa

funkcja kwadratowa (nominative singular)
funkcje kwadratowe (nominative plural)
funkcji kwadratowej (genitive singular)
funkcji (genitive plural)
funkcyj  kwadratowych (archaic genitive plural)
funkcji kwadratowej (dative singular)
funkcjom kwadratowym (dative plural)
funkcję kwadratową (accusative singular)
funkcje kwadratowe (accusative plural)
funkcją kwadratową (instrumental singular)
funkcjami kwadratowymi (instrumental plural)
funkcji kwadratowej (locative singular)
funkcjach kwadratowych (locative plural)
funkcjo kwadratowa (singular vocative)
funkcje kwadratowe (plural vocative)


funkcja sześcienna

funkcja sześcienna (nominative singular)
funkcje sześcienne (nominative plural)
funkcji sześciennej (genitive singular)
funkcji (genitive plural)
funkcyj  sześciennych (archaic genitive plural)
funkcji sześciennej (dative singular)
funkcjom sześciennym (dative plural)
funkcję sześcienną (accusative singular)
funkcje sześcienne (accusative plural)
funkcją sześcienną (instrumental singular)
funkcjami sześciennymi (instrumental plural)
funkcji sześciennej (locative singular)
funkcjach sześciennych (locative plural)
funkcjo sześcienna (singular vocative)
funkcje sześcienne (plural vocative)


SFT

sparse Fourier transform
w:sparse Fourier transform

(mathematics) Initialism of sparse Fourier transform.


STFT

short-time Fourier transform
w:short-time Fourier transform

(mathematics) Initialism of short-time Fourier transform.


本徵函數

ㄅㄣˇ ㄓㄥ ㄏㄢˊ ㄕㄨˋ

ㄅㄣˇ ㄓㄥ ㄏㄢˊ ㄕㄨˋ

бэньчжэн ханьшу

bɛnʹčžɛn xanʹšu

/pən²¹⁴⁻²¹ ʈ͡ʂɤŋ⁵⁵ xän³⁵ ʂu⁵¹/

/pən²¹⁴⁻²¹ ʈ͡ʂɤŋ⁵⁵ xän³⁵ ʂu⁵¹/


mantysa

mantysa (nominative singular)
mantysy (genitive singular)
mantysie (dative singular)
mantysę (accusative singular)
mantysą (instrumental singular)
mantysie (locative singular)
mantyso (singular vocative)

(arithmetic) mantissa (part of a logarithm after the decimal point)


відображення

uk-noun

відобра́ження<loci:ju>

відобра́ження • (vidobrážennja) n inan (genitive відобра́ження, nominative plural відобра́ження, genitive plural відобра́жень)

відобра́ження (canonical)
vidobrážennja (romanization)
відобра́ження (genitive)
відобра́ження (nominative plural)
відобра́жень (genitive plural)
відобра́ження (nominative singular)
відобра́ження (nominative plural)
відобра́ження (genitive singular)
відобра́жень (genitive plural)
відобра́женню (dative singular)
відобра́женням (dative plural)
відобра́ження (accusative singular)
відобра́ження (accusative plural)
відобра́женням (instrumental singular)
відобра́женнями (instrumental plural)
відобра́женні (locative singular)
відобра́женню (locative singular)
відобра́женнях (locative plural)
відобра́ження (singular vocative)
відобра́ження (plural vocative)

uk-ndecl

відобра́ження<loci:ju>

Uk-відображення.ogg

From the відобра́ж- (vidobráž-) stem of відобрази́ти (vidobrazýty) + -ення (-ennja). Compare Russian отображе́ние (otobražénije)

af

відобрази́ти

cog

отображе́ние

(mathematics) mapping (a function that maps every element of a given mathematical structure (eg: a set) to a unique element of another structure; a correspondence)


funkcja pierwotna

funkcja pierwotna (nominative singular)
funkcje pierwotne (nominative plural)
funkcji pierwotnej (genitive singular)
funkcji (genitive plural)
funkcyj  pierwotnych (archaic genitive plural)
funkcji pierwotnej (dative singular)
funkcjom pierwotnym (dative plural)
funkcję pierwotną (accusative singular)
funkcje pierwotne (accusative plural)
funkcją pierwotną (instrumental singular)
funkcjami pierwotnymi (instrumental plural)
funkcji pierwotnej (locative singular)
funkcjach pierwotnych (locative plural)
funkcjo pierwotna (singular vocative)
funkcje pierwotne (plural vocative)


funkcja pochodna

funkcja pochodna (nominative singular)
funkcje pochodne (nominative plural)
funkcji pochodnej (genitive singular)
funkcji (genitive plural)
funkcyj  pochodnych (archaic genitive plural)
funkcji pochodnej (dative singular)
funkcjom pochodnym (dative plural)
funkcję pochodną (accusative singular)
funkcje pochodne (accusative plural)
funkcją pochodną (instrumental singular)
funkcjami pochodnymi (instrumental plural)
funkcji pochodnej (locative singular)
funkcjach pochodnych (locative plural)
funkcjo pochodna (singular vocative)
funkcje pochodne (plural vocative)


logarytm naturalny

logarytm naturalny (nominative singular)
logarytmy naturalne (nominative plural)
logarytmu naturalnego (genitive singular)
logarytmów naturalnych (genitive plural)
logarytmowi naturalnemu (dative singular)
logarytmom naturalnym (dative plural)
logarytm naturalny (accusative singular)
logarytmy naturalne (accusative plural)
logarytmem naturalnym (instrumental singular)
logarytmami naturalnymi (instrumental plural)
logarytmie naturalnym (locative singular)
logarytmach naturalnych (locative plural)
logarytmie naturalny (singular vocative)
logarytmy naturalne (plural vocative)

(mathematics) natural logarithm (logarithm in base e)


експонента

uk-noun

експоне́нта<>

експоне́нтний

експоне́нта • (eksponénta) f inan (genitive експоне́нти, nominative plural експоне́нти, genitive plural експоне́нт, relational adjective експоне́нтний)

експоне́нта (canonical)
eksponénta (romanization)
експоне́нти (genitive)
експоне́нти (nominative plural)
експоне́нт (genitive plural)
експоне́нтний (adjective relational)
експоне́нта (nominative singular)
експоне́нти (nominative plural)
експоне́нти (genitive singular)
експоне́нт (genitive plural)
експоне́нті (dative singular)
експоне́нтам (dative plural)
експоне́нту (accusative singular)
експоне́нти (accusative plural)
експоне́нтою (instrumental singular)
експоне́нтами (instrumental plural)
експоне́нті (locative singular)
експоне́нтах (locative plural)
експоне́нто (singular vocative)
експоне́нти (plural vocative)

uk-ndecl

експоне́нта<>

показнико́ва фу́нкція
показникова функція#Ukrainian

(mathematics) synonym of показнико́ва фу́нкція f (pokaznykóva fúnkcija, “exponential function, exponential”)


показникова функція

uk-noun

показнико́ва<+> фу́нкція<>

показнико́ва фу́нкція • (pokaznykóva fúnkcija) f inan (genitive показнико́вої фу́нкції, nominative plural показнико́ві фу́нкції, genitive plural показнико́вих фу́нкцій)

показнико́ва фу́нкція (canonical)
pokaznykóva fúnkcija (romanization)
показнико́вої фу́нкції (genitive)
показнико́ві фу́нкції (nominative plural)
показнико́вих фу́нкцій (genitive plural)
показнико́ва фу́нкція (nominative singular)
показнико́ві фу́нкції (nominative plural)
показнико́вої фу́нкції (genitive singular)
показнико́вих фу́нкцій (genitive plural)
показнико́вій фу́нкції (dative singular)
показнико́вим фу́нкціям (dative plural)
показнико́ву фу́нкцію (accusative singular)
показнико́ві фу́нкції (accusative plural)
показнико́вою фу́нкцією (instrumental singular)
показнико́вими фу́нкціями (instrumental plural)
показнико́вій фу́нкції (locative singular)
показнико́вих фу́нкціях (locative plural)
показнико́ва фу́нкціє (singular vocative)
показнико́ві фу́нкції (plural vocative)

uk-ndecl

показнико́ва<+> фу́нкція<>

(mathematics) exponential function, exponential (any function in which an independent variable is in the form of an exponent: f(x) = aˣ)


rocket equation

The equation for how much delta-v a rocket produces: Δv = vₑ ln(m₀/m₁); where Δv is delta-v, vₑ is effective exhaust velocity, ln is the natural log function, m₀ is initial mass of the rocket, and m₁ is final mass of the rocket.


자연로그

[ˈt͡ɕa̠(ː)jʌ̹ɭɭo̞ɡɯ]

Compound of 자연(自然) (jayeon, “natural”) + 로그 (rogeu, “log”).


kalagmitaning pamamahagi

tl-noun

kalagmitaning pamamahagi (Baybayin spelling ᜃᜎᜄ᜔ᜋᜒᜆᜈᜒᜅ᜔ ᜉᜋᜋᜑᜄᜒ)

ᜃᜎᜄ᜔ᜋᜒᜆᜈᜒᜅ᜔ ᜉᜋᜋᜑᜄᜒ (Baybayin)

From kalagmitan (“probability (neologism)”) + -in + -g + pamamahagi (“distribution”).

af

probability distribution
probability distribution


傳遞函數

ㄔㄨㄢˊ ㄉㄧˋ ㄏㄢˊ ㄕㄨˋ

ㄔㄨㄢˊ ㄉㄧˋ ㄏㄢˊ ㄕㄨˋ

чуаньди ханьшу

/ʈ͡ʂʰu̯än³⁵ ti⁵¹ xän³⁵ ʂu⁵¹/

/ʈ͡ʂʰu̯än³⁵ ti⁵¹ xän³⁵ ʂu⁵¹/


fonction de transfert

fr-noun

fonction de transfert f (plural fonctions de transfert)

LL-Q150 (fra)-Lepticed7-fonction de transfert.wav


Übertragungsfunktion

de-noun

Übertragungsfunktion f (genitive Übertragungsfunktion, plural Übertragungsfunktionen)

Übertragungsfunktion (genitive)
Übertragungsfunktionen (plural)
Übertragungsfunktion (nominative singular)
Übertragungsfunktionen (definite nominative plural)
Übertragungsfunktion (genitive singular)
Übertragungsfunktionen (definite genitive plural)
Übertragungsfunktion (dative singular)
Übertragungsfunktionen (dative definite plural)
Übertragungsfunktion (accusative singular)
Übertragungsfunktionen (accusative definite plural)


newidyn dibynnol

cy-noun

newidyn dibynnol m (plural newidynnau dibynnol, not mutable)

(sciences, statistics) dependent variable


newidyn annibynnol

newidyn annibynnol m (plural newidynnau annibynnol, not mutable)

independent variable
independent variable

(sciences, statistics) independent variable


newidyn rheolydd

newidyn rheolydd m (plural newidynnau rheolydd, not mutable)


surjekcja

pl-noun

surjekcja f (related adjective surjekcyjny)

surjekcyjny (adjective)
surjekcja (nominative singular)
surjekcje (nominative plural)
surjekcji (genitive singular)
surjekcji (genitive plural)
surjekcyj (archaic genitive plural)
surjekcji (dative singular)
surjekcjom (dative plural)
surjekcję (accusative singular)
surjekcje (accusative plural)
surjekcją (instrumental singular)
surjekcjami (instrumental plural)
surjekcji (locative singular)
surjekcjach (locative plural)
surjekcjo (singular vocative)
surjekcje (plural vocative)
suriekcja (alternative)

(set theory) surjection (function for which every element of the codomain is mapped to by some element of the domain)


absolútna hodnota

singular
plural
nominative
absolútna hodnota
absolútne hodnoty
genitive
absolútnej hodnoty
absolútnych hodnôt
dative
absolútnej hodnote
absolútnym hodnotám
accusative
absolútnu hodnotu
locative
absolútnych hodnotách
instrumental
absolútnou hodnotou
absolútnymi hodnotami


zérushely

zérushelyek (plural)
zérushely (nominative singular)
zérushelyek (nominative plural)
zérushelyet (accusative singular)
zérushelyeket (accusative plural)
zérushelynek (dative singular)
zérushelyeknek (dative plural)
zérushellyel (instrumental singular)
zérushelyekkel (instrumental plural)
zérushelyért (causal-final singular)
zérushelyekért (causal-final plural)
zérushellyé (singular translative)
zérushelyekké (plural translative)
zérushelyig (singular terminative)
zérushelyekig (plural terminative)
zérushelyként (essive-formal singular)
zérushelyekként (essive-formal plural)
zérushelyül (essive-modal singular)
zérushelyben (inessive singular)
zérushelyekben (inessive plural)
zérushelyen (singular superessive)
zérushelyeken (plural superessive)
zérushelynél (adessive singular)
zérushelyeknél (adessive plural)
zérushelybe (illative singular)
zérushelyekbe (illative plural)
zérushelyre (singular sublative)
zérushelyekre (plural sublative)
zérushelyhez (allative singular)
zérushelyekhez (allative plural)
zérushelyből (elative singular)
zérushelyekből (elative plural)
zérushelyről (delative singular)
zérushelyekről (delative plural)
zérushelytől (ablative singular)
zérushelyektől (ablative plural)
zérushelyé (singular)
zérushelyeké (plural)
zérushelyéi (singular)
zérushelyekéi (plural)
zérushelyem (first-person possessed-single possessive singular)
zérushelyeim (first-person possessed-many possessive singular)
zérushelyed (possessed-single possessive second-person singular)
zérushelyeid (possessed-many possessive second-person singular)
zérushelye (possessed-single possessive singular third-person)
zérushelyei (possessed-many possessive singular third-person)
zérushelyünk (first-person plural possessed-single possessive)
zérushelyeink (first-person plural possessed-many possessive)
zérushelyetek (plural possessed-single possessive second-person)
zérushelyeitek (plural possessed-many possessive second-person)
zérushelyük (plural possessed-single possessive third-person)
zérushelyeik (plural possessed-many possessive third-person)


miejsce zerowe

miejsce zerowe (nominative singular)
miejsca zerowe (nominative plural)
miejsca zerowego (genitive singular)
miejsc zerowych (genitive plural)
miejscu zerowemu (dative singular)
miejscom zerowym (dative plural)
miejsce zerowe (accusative singular)
miejsca zerowe (accusative plural)
miejscem zerowym (instrumental singular)
miejscami zerowymi (instrumental plural)
miejscu zerowym (locative singular)
miejscach zerowych (locative plural)
miejsce zerowe (singular vocative)
miejsca zerowe (plural vocative)