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In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, and extended
Describing_function
input describing functions (HOSIDF) were first introduced by dr. ir. P.W.J.M. Nuij. The HOSIDFs are an extension of the sinusoidal input describing function
Higher-order sinusoidal input describing function
Higher-order_sinusoidal_input_describing_function
Association of one output to each input
mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the
Function_(mathematics)
Reason for a change under natural selection; in physiology, what a system does
of describing function, even though its applicability is disputed. In contemporary philosophy of biology, there are three major accounts of function in
Function_(biology)
Function describing the effects of feedback on a control system
In control theory, a closed-loop transfer function is a mathematical function describing the net result of the effects of a feedback control loop on the
Closed-loop_transfer_function
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
Function specifying the behavior of a component in an electronic or control system
a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models
Transfer_function
Asymmetric sigmoid function
Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth
Gompertz_function
Extension of the factorial function
The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic
Gamma_function
Cybernetics. 7 (7): 567–568. doi:10.1109/TSMC.1977.4309773. "Counterexamples to Aizerman's and Kalman's conjectures and describing function method" (PDF).
Aizerman's_conjecture
Analytic function that does not satisfy a polynomial equation
mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable
Transcendental_function
Multivalued function in mathematics
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse
Lambert_W_function
Function modeling methodology for describing manufacturing functions
Function Modeling; where ICAM is Integrated Computer-Aided Manufacturing) is a function modeling methodology for describing manufacturing functions,
IDEF0
Control theory for nonlinear or time-variant systems
techniques for analyzing nonlinear feedback systems (see, e.g., and ): Describing function method Phase plane method Lyapunov stability analysis Singular perturbation
Nonlinear_control
Theory of language
defined six functions of language (or communication functions), according to which an effective act of verbal communication can be described. Each of the
Jakobson's functions of language
Jakobson's_functions_of_language
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Degree of differentiability of a function or map
In calculus and mathematical analysis, the smoothness of a function describes the number of times it can be differentiated without producing discontinuities
Smoothness
Sigmoid shape special function
mathematics, the error function (also called the Gauss error function), often denoted by e r f {\displaystyle \mathbf {erf} } , is the function erf ( z ) = 2
Error_function
Topics referred to by the same term
potential theory The potential function of a potential game In the potential method of amortized analysis, a function describing an investment of resources
Potential_function
Function with a repeating pattern
periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which are used to describe waves
Periodic_function
Mathematical function having a characteristic S-shaped curve or sigmoid curve
sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the
Sigmoid_function
Function describing equilibrium states of a system
state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the
State_function
Type of functional equation (mathematics)
{du}{dx}}=u^{2}+4.} Second-order nonlinear (due to sine function) ordinary differential equation describing the motion of a pendulum of length L: L d 2 u d x
Differential_equation
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Smooth approximation of one-hot arg max
The softmax function, also known as softargmax or normalized exponential function, converts a tuple of K real numbers into a probability distribution
Softmax_function
Quickly growing function
Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not
Ackermann_function
Branch of mathematics studying functions of a complex variable
holomorphic functions, which are differentiable functions of a complex variable. In contrast with a differentiable real function, a holomorphic function is always
Complex_analysis
Function that is continuous everywhere but differentiable nowhere
mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass function (nowhere-differentiable function)
Weierstrass_function_(nowhere-differentiable_function)
Mathematical function
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as
Jacobi_elliptic_functions
Mathematical function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}
Gaussian_function
Functions such that f(–x) equals f(x) or –f(x)
In mathematics, an even function is a real function such that f ( − x ) = f ( x ) {\displaystyle f(-x)=f(x)} for every x {\displaystyle x} in its domain
Even_and_odd_functions
Mathematical function
the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial
Beta_function
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given
Probability_density_function
Output of a dynamic system when given a brief input
equations describing such objects. Since the impulse function contains all frequencies (see the Fourier transform of the Dirac delta function, showing
Impulse_response
Hash functions intended for applications that do not need rigorous security
The non-cryptographic hash functions (NCHFs) are hash functions intended for applications that do not need the rigorous security requirements of the cryptographic
Non-cryptographic hash function
Non-cryptographic_hash_function
Relationship between electrical signal and light
transfer functions to describe the relationship between electrical signal, scene light and displayed light. The opto-electronic transfer function (OETF)
Transfer_functions_in_imaging
Representation on functions in computer engineering
concentrates on describing the dynamic process. The main concept in this modeling perspective is the process, this could be a function, transformation
Function_model
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) gives the relative merit of various statistical models for describing a data set. Often the
Likelihood_function
S-shaped curve
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac
Logistic_function
Mathematical description of quantum state
the name "wave function", and gives rise to wave–particle duality. However, whether the wave function in quantum mechanics describes a kind of physical
Wave_function
Computer science concept
into functions expecting either signed or unsigned chars, because it is compatible with both types. Intersection types are useful for describing overloaded
Type_system
Sequence of program instructions invokable by other software
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-formed
Function (computer programming)
Function_(computer_programming)
Mapping arbitrary data to fixed-size values
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support
Hash_function
Continuous function that is not absolutely continuous
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in
Cantor_function
Special functions of several complex variables
mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode the
Theta_function
Describes approximate behavior of a function
Big O notation is a mathematical notation that describes the approximate size of a function on a domain. Big O is a member of a family of notations invented
Big_O_notation
author of the edge-of-the-wedge theorem, Krylov–Bogolyubov theorem, describing function and multiple important contributions to quantum mechanics Vladimir
List of Russian mathematicians
List_of_Russian_mathematicians
Function in thermodynamics and statistical physics
partition function describes the statistical properties of a system in thermodynamic equilibrium.[citation needed] Partition functions are functions of the
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Mathematical function, inverse of an exponential function
to base b, written logb x = y, so log10 1000 = 3. As a single-variable function, the logarithm to base b is the inverse of exponentiation with base b.
Logarithm
Topics referred to by the same term
Internet services Spinal cord independence measure, a functional score describing function deficits of patients with a Spinal cord injury This disambiguation
SCIM
In physics, solution to Schrödinger equation
a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb. They are used to describe the behavior of
Coulomb_wave_function
Cryptographic hash function
Bruce Schneier, the Skein Hash Function". Slashdot. 2008-10-31. Retrieved 2008-10-31. "Paper describing the hash function, Version 1.3 (2010-10-01)" (PDF)
Skein_(hash_function)
Mathematical function characterizing set membership
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all
Indicator_function
Placeholder variables in programming
is to keep the foo counters turning." One book[which?] describing the MIT train room describes two buttons by the door labeled "foo" and "bar". These
Foobar
restriction theorem describes functions on a Lie algebra which are invariant under the action of a Lie group in terms of functions on a Cartan subalgebra
Chevalley_restriction_theorem
to proton ratio as a function of baryon density. Symmetry energy is an important parameter in the equation of state describing the nuclear structure
Symmetry_energy
Hash function that is suitable for use in cryptography
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with a fixed size of n {\displaystyle n}
Cryptographic_hash_function
Formal power series
generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often
Generating_function
Russian and Soviet mathematician
Princeton: Princeton University Press. ISBN 978-0-691-07985-1. Describing function Krylov–Bogolyubov theorem Krylov–Bogoliubov averaging method
Nikolay Krylov (mathematician, born 1879)
Nikolay_Krylov_(mathematician,_born_1879)
Special function in the physical sciences
mathematics, the Airy function (or Airy function of the first kind) A i ( x ) {\displaystyle \mathbf {Ai({\boldsymbol {x}})} } is a special function named after
Airy_function
Correlation as a function of distance
targets Correlation function (astronomy) – Function describing the distribution of galaxies in the universe Correlation function (statistical mechanics) –
Correlation_function
Type of functions, in mathematical analysis
holonomic function is an element of a holonomic module of smooth functions. Holonomic functions can also be described as differentiably finite functions, also
Holonomic_function
Graphical language for PLC design
The function block diagram (FBD) is a graphical language for programmable logic controller design, that can describe the function between input variables
Function_block_diagram
Scale to rate how well one is meeting various problems in living
The Global Assessment of Functioning (GAF) is a numeric scale used by mental health clinicians and physicians to rate subjectively the social, occupational
Global Assessment of Functioning
Global_Assessment_of_Functioning
System that regulates the formation of blocks on a blockchain
partial match of a hash function[citation needed] At the IACR conference Crypto 2022 researchers presented a paper describing Ofelimos, a blockchain protocol
Proof_of_work
Polynomial function of degree two
In mathematics, a quadratic function of a single variable is a function of the form f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c} with
Quadratic_function
Graphical depicture of loss
breakthrough in describing quality, and helped fuel the continuous improvement movement. The concept of Taguchi's quality loss function was in contrast
Taguchi_loss_function
Mathematical entity to describe the probability of each possible measurement on a system
the wave functions describing position and momentum, finite-dimensional vectors describing spin such as the singlet, and states describing many-body
Quantum_state
functions (PDFs), the hard scattering part, and fragmentation functions. The fragmentation functions, as are the PDFs, are non-perturbative functions
Fragmentation_function
Distance from origin of tangent hyperplanes
In mathematics, the support function hA of a non-empty closed convex set A in R n {\displaystyle \mathbb {R} ^{n}} describes the (signed) distances of supporting
Support_function
Unsolved problem in number theory
Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function. It was proposed
Manin_conjecture
Fundamental trigonometric functions
In mathematics, sine and cosine are trigonometric functions. The sine and cosine of an acute angle are defined in the context of a right triangle: the
Sine_and_cosine
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
Matrix of partial derivatives of a vector-valued function
matrix can also be thought of as describing the amount of "stretching", "rotating" or "transforming" that the function imposes locally near that point
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
All derivatives have the intermediate value property
analysis, Darboux's theorem states that the derivative of any real-valued function of a real variable has the intermediate value property, that is, that the
Darboux's_theorem_(analysis)
Patterns used in computer programming
glob() (/ɡlɒb/) is a POSIX C function for globbing, which is the archetypal use of pattern matching against the names in a filesystem directory such that
Glob_(programming)
Hash function without any collisions
In computer science, a perfect hash function h for a set S is a hash function that maps distinct elements in S to a set of m integers, with no collisions
Perfect_hash_function
Thesis on the nature of computability
definition of computable function, mathematicians often used the informal term effectively calculable to describe functions that are computable by paper-and-pencil
Church–Turing_thesis
Equations describing elastic deformation
In linear elasticity, the equations describing the deformation of an elastic body subject only to surface forces (or body forces that could be expressed
Stress_functions
Class of mathematical functions
elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions is also referred
Weierstrass_elliptic_function
Analytic function on the upper half-plane with a certain behavior under the modular group
type of function of a complex number variable that possesses a high degree of symmetry, of a certain kind. Similarly to a periodic function of a real
Modular_form
Property of some mathematical operations
François Servois in 1814, which used the word commutatives when describing functions that have what is now called the commutative property. Commutative
Commutative_property
Probability distribution
real-valued random variable. The general form of its probability density function is f(x)=12πσ2exp(−(x−μ)22σ2). The parameter μ is the mean or expectation
Normal_distribution
Loss function used in robust regression
used. The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by L δ ( a
Huber_loss
Type of energy
In solid-state physics, the work function is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the
Work_function
Point to which functions converge in analysis
mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which
Limit_of_a_function
Mathematical-logic system
calculi have been developed for describing communication and concurrency. The fact that lambda calculus terms act as functions on other lambda calculus terms
Lambda_calculus
Mathematical function
slightly different context, for the function describing the amount of the scatter (not scattered light), simply as a function of the incident light angle. An
Bidirectional scattering distribution function
Bidirectional_scattering_distribution_function
Process by which a quantum system takes on a definitive state
interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of
Wave_function_collapse
Concept in theoretical computer science
1962 paper, Radó defined two functions related to the busy beaver game: the score function Σ(n) and the shifts function S(n). Both take a number of Turing
Busy_beaver
Type of function in complex analysis
mathematics, plurisubharmonic functions (sometimes abbreviated as psh, plsh, or plush functions) form an important class of functions used in complex analysis
Plurisubharmonic_function
Software agent which acts autonomously
self-driving car's objective function might balance factors such as safety, speed, and passenger comfort. Different terms are used to describe this concept, depending
Intelligent_agent
Complex complementary error function
The Faddeeva function or Kramp function is a scaled complex complementary error function, w ( z ) := e − z 2 erfc ( − i z ) = erfcx ( − i z ) = e
Faddeeva_function
Objects extending the notion of functions
distributions. Generalized functions are especially useful for treating discontinuous functions more like smooth functions, and describing discrete physical phenomena
Generalized_function
Real function with finite total variation
In mathematical analysis, a function of bounded variation, also known as BV function, is a real-valued function whose total variation is bounded (finite):
Bounded_variation
Mathematical function, used to describe magnetization
Langevin function is derived using statistical mechanics and describes how magnetic dipoles are aligned by an applied field. The Brillouin function was developed
Brillouin and Langevin functions
Brillouin_and_Langevin_functions
American engineer and business executive (born 1975)
hardware engineering into prioritising function over form, marking a major departure from Jony Ive's form over function focus for Apple products. John Patrick
John_Ternus
Astronomical measure
Local Group. Note that the term "function" is slightly misleading, and the luminosity function might better be described as a luminosity distribution. Given
Luminosity function (astronomy)
Luminosity_function_(astronomy)
travel, tourism, insurance
DESCRIBING FUNCTION
DESCRIBING FUNCTION
Boy/Male
Arabic, Muslim
Describing
Male
Egyptian
, Functionary of the Interior.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Surname or Lastname
English
English : from the personal name Perceval, first found as the name of the hero of an epic poem by the 12th-century French poet Crestien de Troyes, describing the quest for the holy grail. The origin of the name is uncertain; it may be associated with the Gaulish personal name Pritorīx or it may be an alteration of the Celtic name Peredur (see Priddy). It seems to have been altered as the result of folk etymological association with Old French perce(r) ‘to pierce or breach’ + val ‘valley’.English : Norman habitational name from either of the two places in Calvados named Perceval.
Biblical
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Male
Egyptian
, a high Egyptian functionary.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English and North German
English and North German : occupational name for a maker of pins or pegs (or alternatively, in the case of the German name, a metonymic occupational name for a shoemaker), a derivative of Pinn, with the addition of the agent suffix -er.English : occupational name for a maker or user of combs, Anglo-Norman French peigner, an agent derivative of peigne ‘comb’.English : habitational name from Pinner, now part of northwest London, which derives its name from Old English pinn ‘pin’, ‘peg’ + Åra ‘slope’, ‘ridge’, describing a projecting hill spur.Jewish (Ashkenazic) : habitational name for someone from Pinne (Polish Pniewy) near PoznaÅ„.German : habitational name for someone from a place called Pinnan or Pinne.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a great functionary.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Girl/Female
Arabic, Muslim
Describing
Male
Celtic
, great justiciary, or functionary.
DESCRIBING FUNCTION
DESCRIBING FUNCTION
DESCRIBING FUNCTION
DESCRIBING FUNCTION
DESCRIBING FUNCTION
DESCRIBING FUNCTION
DESCRIBING FUNCTION
travel, tourism, insurance