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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
a theorem or an axiom asserts the existence of a function having some properties, without describing it more precisely. Often, the specification or description
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)
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
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
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
Field of medical research
Gain-of-function research (GoF research or GoFR) is medical research that genetically alters an organism in a way that may enhance the biological functions of
Gain-of-function_research
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
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
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
gamma function (represented by Γ {\displaystyle \Gamma } , capital Greek letter gamma) is the most common extension of the factorial function to complex
Gamma_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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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)
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
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
Mathematical functions
The hyperbolastic functions, also known as hyperbolastic growth models, are mathematical functions that are used in medical statistical modeling. These
Hyperbolastic_functions
A Chapman function, denoted ch, describes the integration of an atmospheric parameter along a slant path on a spherical Earth, relative to the vertical
Chapman_function
Mathematical function describing fluid motion
In applied mathematics, the Hough functions are the eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating sphere. As such
Hough_function
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
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
Mathematical concept in measure theory
measure theory, an approximately continuous function is a concept that generalizes the notion of continuous functions by replacing the ordinary limit with an
Approximately continuous function
Approximately_continuous_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
Degree of differentiability of a function or map
In mathematical analysis, the smoothness describes the number of times a function can be differentiated without producing discontinuities. The smoothness
Smoothness
Program function without side effects
In computer programming, a pure function is a function that has the following properties: the function return values are identical for identical arguments
Pure_function
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
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
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
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
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
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
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
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)
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
In number theory, the unit function is a completely multiplicative function on the positive integers defined as: ε ( n ) = { 1 , if n = 1 0 , if n ≠
Unit_function
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
functions (PDFs), the hard scattering part, and fragmentation functions. The fragmentation functions, as are the PDFs, are non-perturbative functions
Fragmentation_function
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability
Likelihood_function
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
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
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
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
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
Collection of tissues with similar functions
type cells to act together in a function. Tissues of different types combine to form an organ which has a specific function. The intestinal wall, for example
Organ_(biology)
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
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
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
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
Branch of mathematics studying functions of a complex variable
traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of a complex variable of
Complex_analysis
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
Shape descriptions in a geometrical/topological sense
Landi, Laura Papaleo, Michela Spagnuolo, Describing shapes by geometrical-topological properties of real functions ACM Computing Surveys, vol. 40 (2008)
Size_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
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)
algebra and in particular in algebraic combinatorics, the ring of symmetric functions is a specific limit of the rings of symmetric polynomials in n indeterminates
Ring_of_symmetric_functions
Design philosophy of 19th–20th centuries
Form follows function is a principle of design associated with late 19th- and early 20th-century architecture and industrial design in general, which states
Form_follows_function
Hash function that is suitable for use in cryptography
Whirlpool is a cryptographic hash function designed by Vincent Rijmen and Paulo S. L. M. Barreto, who first described it in 2000. Whirlpool is based on
Cryptographic_hash_function
Function for incompressible divergence-free flows in two dimensions
dynamics, two types of stream function (or streamfunction) are defined: The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange
Stream_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
Concept in dynamical systems
study of dynamical systems the term Feigenbaum function has been used to describe two different functions introduced by the physicist Mitchell Feigenbaum:
Feigenbaum_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
Operation on mathematical functions
two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new function f ∘ g {\displaystyle f\circ g} . When the composite function f ∘
Function_composition
Development phases of a computer-based system
information such as describing the major components of the system. The plan can include relatively low-level information such as describing functions, screen layout
Systems development life cycle
Systems_development_life_cycle
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
Mathematical function common in physics
by Rudolf Kohlrausch in 1854 to describe the discharge of a capacitor; thus it is also known as the Kohlrausch function. In 1970, G. Williams and D.C.
Stretched exponential function
Stretched_exponential_function
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
Function in computational chemistry
In computational chemistry, the Fukui function or frontier function is a function that describes the electron density in a frontier orbital, as a result
Fukui_function
Function returning one of only two values
switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the
Boolean_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
Solutions of Lamé's equation
In mathematics, a Lamé function, or ellipsoidal harmonic function, is a solution of Lamé's equation, a second-order ordinary differential equation. It
Lamé_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
Mathematical model describing how an output of a function is computed given an input
computation is a model that describes how an output of a mathematical function is computed given an input. A model of computation describes how units of computations
Model_of_computation
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
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
Function in probability theory
In probability theory and statistics, the covariance function describes how much two random variables change together (their covariance) with varying spatial
Covariance_function
Mathematical function relating circular and hyperbolic functions
Christoph Gudermann who also described the relationship between circular and hyperbolic functions in 1830. The Gudermannian function and its inverse were used
Gudermannian_function
Evaluation of a function on its argument
In mathematics, function application (or evaluation) is the act of taking a function and an input from its domain to obtain the corresponding value from
Function_application
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
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
Words supplying mainly grammatical information, rather than content information
but can describe only the general usages of function words. By contrast, grammars describe the use of function words in detail but treat lexical words only
Function_word
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