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Mathematical function used in cryptography
In cryptography, a T-function is a bijective mapping that updates every bit of the state in a way that can be described as x i ′ = x i + f ( x 0 , ⋯ ,
T-function
In mathematics, Owen's T function T(h, a), named after statistician Donald Bruce Owen, is defined by T ( h , a ) = 1 2 π ∫ 0 a e − 1 2 h 2 ( 1 + x 2 )
Owen's_T_function
Extension of the factorial function
}t^{z-1}e^{-t}\,dt,\ \qquad \Re (z)>0.} The gamma function then is defined in the complex plane as the analytic continuation of this integral function:
Gamma_function
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
Mathematical function with no sudden changes
In mathematics, a continuous function is a function such that a small variation of its argument induces at most a small variation of its value. This implies
Continuous_function
Function whose graph is 0, then 1, then 0 again, in an almost-everywhere continuous way
normalized boxcar function) is defined as rect ( t T ) = Π ( t T ) = { 0 , if | t | > T 2 1 2 , if | t | = T 2 1 , if | t | < T 2 . {\displaystyle
Rectangular_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
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
Hyperbolic analogues of trigonometric functions
hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin
Hyperbolic_functions
Probability distribution
cumulative distribution function (CDF) can be written in terms of I, the regularized incomplete beta function. For t > 0 , F ( t ) = ∫ − ∞ t f ( u ) d u =
Student's_t-distribution
Economic model which weighs rewards based on when they are received
the discount function f(t) having a negative first derivative and with ct (or c(t) in continuous time) defined as consumption at time t, total utility
Discount_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
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
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)
Maximized objective function of an optimization problem
value function represents the optimal payoff of the system over the interval [ t , t 1 ] {\displaystyle [t,t_{1}]} when started at the time- t {\displaystyle
Value_function
Mathematical function
the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined
Z_function
actuarial mathematics, the accumulation function a(t) is a function of time t expressing the ratio of the value at time t (future value) and the initial investment
Accumulation_function
Genetically engineered T cell
activating functions into a single receptor. CAR T cell therapy is a cell therapy that uses T cells engineered with CARs to treat cancer. T cells are modified
CAR_T_cell
Type of white blood cell
On the other hand, CD4+ T cells function as "helper cells." Unlike CD8+ killer T cells, the CD4+ helper T (TH) cells function by further activating memory
T_cell
probability density function, Φ ( x ) = ∫ − ∞ x φ ( t ) d t = 1 2 [ 1 + erf ( x 2 ) ] {\displaystyle \Phi (x)=\int _{-\infty }^{x}\varphi (t)\,dt={\frac
List of integrals of Gaussian functions
List_of_integrals_of_Gaussian_functions
mimic function changes a file A {\displaystyle A} so it assumes the statistical properties of another file B {\displaystyle B} . That is, if p ( t , A )
Mimic_function
Special mathematical function
mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only for special
Polylogarithm
Effect in signal processing
The Fourier transform of a function of time, s ( t ) {\displaystyle s(t)} , is a complex-valued function of frequency, S ( f ) {\displaystyle S(f)} ,
Spectral_leakage
Model of thermodynamic properties
specified temperature T and pressure P. Common departure functions include those for enthalpy, entropy, and internal energy. Departure functions are used to calculate
Departure_function
Scorer's functions can also be defined in terms of Airy functions: G i ( x ) = B i ( x ) ∫ x ∞ A i ( t ) d t + A i ( x ) ∫ 0 x B i ( t ) d t , H i ( x
Scorer's_function
Class of mathematical functions
Intuitively, subharmonic functions are related to convex functions of one variable as follows. If the graph of a convex function and a line intersect at
Subharmonic_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
Mathematical function relating circular and hyperbolic functions
{gd} \psi } . The Gudermannian function reveals a close relationship between the circular functions and hyperbolic functions. It was introduced in the 1760s
Gudermannian_function
Medical condition
T cell deficiency is a deficiency of T cells, caused by decreased function of individual T cells. It causes an immunodeficiency of cell-mediated immunity
T_cell_deficiency
mathematics the synchrotron functions are defined as follows (for x ≥ 0): First synchrotron function F ( x ) = x ∫ x ∞ K 5 3 ( t ) d t {\displaystyle F(x)=x\int
Synchrotron_function
Function of propagation delay and Doppler frequency
function is given by χ ( τ , f ) = ∫ − ∞ ∞ s ( t ) s ∗ ( t − τ ) e i 2 π f t d t {\displaystyle \chi (\tau ,f)=\int _{-\infty }^{\infty }s(t)s^{*}(t-\tau
Ambiguity_function
First known wavelet basis
wavelet function ψ ( t ) {\displaystyle \psi (t)} can be described as ψ ( t ) = { 1 0 ≤ t < 1 2 , − 1 1 2 ≤ t < 1 , 0 otherwise. {\displaystyle \psi (t)={\begin{cases}1\quad
Haar_wavelet
Special case of the polylogarithm
dilogarithm function is sometimes defined as ∫ 1 v ln t 1 − t d t = Li 2 ( 1 − v ) . {\displaystyle \int _{1}^{v}{\frac {\ln t}{1-t}}dt=\operatorname
Dilogarithm
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
Method of solution to differential equations
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with
Green's_function
Conjecture on zeros of the zeta function
Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics
Riemann_hypothesis
Zeta-like functions approximate arbitrary holomorphic functions
universality of zeta functions is the remarkable ability of the Riemann zeta function and other similar functions (such as the Dirichlet L-functions) to approximate
Zeta_function_universality
Periodic distribution ("function") of "point-mass" Dirac delta sampling
as sha function, impulse train or sampling function) is a periodic generalized function with the formula Ш T ( t ) := ∑ k = − ∞ ∞ δ ( t − k T ) {\displaystyle
Dirac_comb
Complex-differentiable (mathematical) function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood
Holomorphic_function
Mathematical function
Debye functions is defined by D n ( x ) = n x n ∫ 0 x t n e t − 1 d t . {\displaystyle D_{n}(x)={\frac {n}{x^{n}}}\int _{0}^{x}{\frac {t^{n}}{e^{t}-1}}\
Debye_function
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
Mathematical function
In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: ψ ( z ) = d d z ln Γ ( z ) = Γ ′ ( z ) Γ ( z )
Digamma_function
Theorem of convex functions
convex function (for t ∈ [0,1]), t f ( x 1 ) + ( 1 − t ) f ( x 2 ) , {\displaystyle tf(x_{1})+(1-t)f(x_{2}),} while the graph of the function is the convex
Jensen's_inequality
Statistical function that defines the quantiles of a probability distribution
the quantile function of a probability distribution is the inverse of its cumulative distribution function. That is, the quantile function of a distribution
Quantile_function
mathematics, the Toronto function T(m,n,r) is a modification of the confluent hypergeometric function defined by Heatley (1943), Weisstein, as T ( m , n , r ) =
Toronto_function
Function in condensed matter physics
scattering function is the spatial Fourier transform of the van Hove function G ( r → , t ) {\displaystyle G({\vec {r}},t)} : F ( k → , t ) ≡ ∫ G ( r → , t ) exp
Dynamic_structure_factor
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 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
Dynamical system whose system function is not directly dependent on time
time-dependent output function y ( t ) {\displaystyle y(t)} , and a time-dependent input function x ( t ) {\displaystyle x(t)} , the system will
Time-invariant_system
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Type of function in mathematics
an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex function is analytic at
Analytic_function
Symbol representing a mathematical concept
Similarly, if T {\displaystyle T} is some term in the language, F ( T ) {\displaystyle F(T)} is also a term. As such, the interpretation of a function symbol
Function_symbol
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_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
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
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
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
Function that only depends on time
for each value of t. In the more general case, any nonhomogeneous source function in any variable can be described as a forcing function, and the resulting
Forcing function (differential equations)
Forcing_function_(differential_equations)
Integral transform useful in probability theory, physics, and engineering
transform that converts a function of a real variable (usually t {\displaystyle t} , in the time domain) to a function of a complex variable s {\displaystyle
Laplace_transform
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Function with a repeating pattern
A 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
Functions in mathematics
the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R {\displaystyle f\colon U\to \mathbb
Harmonic_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
Nowhere analytic, infinitely differentiable function
the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by Jaap Fabius (1966). This function satisfies
Fabius_function
Mathematical function
function is a generalization of the reciprocal gamma function of the Laplace transform. Formally, it can be defined as ν ( x ) ≡ ∫ 0 ∞ x t d t Γ ( t +
Nu_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
Hardy–Littlewood maximal function. They play an important role in understanding, for example, the differentiability properties of functions, singular integrals
Maximal_function
Concept in mathematics
In mathematics, the K-function, typically denoted K(z), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of
K-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
Special mathematical function defined as sin(x)/x
In mathematics, physics and engineering, the sinc function (/ˈsɪŋk/ SINK), denoted by sinc(x), is defined as either sinc ( x ) = sin x x . {\displaystyle
Sinc_function
Mathematical finite graph-associated function
mathematics, the Ihara zeta function is a zeta function associated with a finite graph. It closely resembles the Selberg zeta function, and is used to relate
Ihara_zeta_function
Concept in the analysis of dynamical systems
ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of
Lyapunov_function
Asymmetric sigmoid function
or 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
Gompertz_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
Mathematical function
Kummer's function is defined by Λ n ( z ) = ∫ 0 z log n − 1 | t | 1 + t d t . {\displaystyle \Lambda _{n}(z)=\int _{0}^{z}{\frac {\log ^{n-1}|t|}{1+t}}\;dt
Kummer's_function
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Parameter in atmospheric modeling
The Exner function is a parameter used in atmospheric modeling. Depending on the application, the Exner function may be defined as Π = c p ( p p 0 ) R
Exner_function
Practice and study of secure communication techniques
cryptographic hash function is computed, and only the resulting hash is digitally signed. Cryptographic hash functions are functions that take a variable-length
Cryptography
Real function with secant line between points above the graph itself
function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph of the function
Convex_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
Mathematical function
Riemann–Siegel theta function is defined in terms of the gamma function as θ ( t ) = arg ( Γ ( 1 4 + i t 2 ) ) − log π 2 t {\displaystyle \theta (t)=\arg \left(\Gamma
Riemann–Siegel_theta_function
Theory of cryptography
In cryptography, a sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any
Sponge_function
Mathematical function
the Chebyshev function is either a scalarising function (Tchebycheff function) or one of two related functions. The first Chebyshev function ϑ(x) or θ(x)
Chebyshev_function
of functions on the unit interval of the following form: { t ↦ r n ( t ) = sgn ( sin 2 n + 1 π t ) ; t ∈ [ 0 , 1 ] , n ∈ N } . {\displaystyle \{t\mapsto
Rademacher_system
characteristic function φ ( t ) {\displaystyle \varphi (t)} . The empirical characteristic function (ECF) defined as φ n ( t ) = 1 n ∑ j = 1 n e i t X j , {\displaystyle
Empirical characteristic function
Empirical_characteristic_function
Electrical engineering concept
real-valued function s(t), it is determined from the function's analytic representation, sa(t): φ ( t ) = arg { s a ( t ) } = arg { s ( t ) + j s ^ ( t ) }
Instantaneous phase and frequency
Instantaneous_phase_and_frequency
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
Cryptography algorithm
internal IV using the pseudorandom function S2V. S2V is a keyed hash based on CMAC, and the input to the function is: Additional authenticated data (zero
Block cipher mode of operation
Block_cipher_mode_of_operation
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
Special function defined by an integral
d t ln t . {\displaystyle \operatorname {li} (x)=\int _{0}^{x}{\frac {dt}{\ln t}}.} Here, ln denotes the natural logarithm. The function 1/(ln t) has
Logarithmic_integral_function
Mathematical function such that every output has at least one input
surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's codomain, there
Surjective_function
Special function defined by an integral
Fresnel integrals S(x) and C(x), and their auxiliary functions F(x) and G(x) are transcendental functions named after Augustin-Jean Fresnel that are used in
Fresnel_integral
Mathematical relation consisting of a multi-variable function equal to zero
multivariable functions that are continuously differentiable. A common type of implicit function is an inverse function. Not all functions have a unique
Implicit_function
Extension of superfactorials to the complex numbers
the double gamma function, is log G ( 1 + z ) = z 2 log ( 2 π ) + ∫ 0 ∞ d t t [ 1 − e − z t 4 sinh 2 t 2 + z 2 2 e − t − z t ] {\displaystyle \log
Barnes_G-function
_{+}.} It is called super regressive if and only if the time reversed function f(−t) is progressive, or equivalently, if s u p p f ^ ⊆ R − . {\displaystyle
Progressive_function
Class of generalisations of the derivative
value ( D + f ( t ) = D + f ( t ) = D − f ( t ) = D − f ( t ) {\displaystyle D^{+}f(t)=D_{+}f(t)=D^{-}f(t)=D_{-}f(t)} ) then the function f is differentiable
Dini_derivative
Special case of the short-time Fourier transform
analysis. The window function means that the signal near the time being analyzed will have higher weight. The Gabor transform of a signal x(t) is defined by
Gabor_transform
Limiting a position to an area
offers the clip function. In the Wolfram Language, it is implemented as Clip[x, {minimum, maximum}]. In OpenGL, the glClearColor function takes four GLfloat
Clamp_(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
Negative of a convex function
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to
Concave_function
T FUNCTION
T FUNCTION
Female
Egyptian
, the daughter of King Snefru.
Female
Egyptian
, the name of several Egyptian ladies.
Male
Czechoslovakian
, given.
Male
Hungarian
Hungarian form of Old High German Bernhard, BERNÃT means "bold as a bear."
Female
Egyptian
, the daughter of Osirtesen.
Surname or Lastname
English, French, German, Hungarian (Donát), Polish, and Czech (Donát)
English, French, German, Hungarian (Donát), Polish, and Czech (Donát) : from a medieval personal name (Latin Donatus, past participle of donare, frequentative of dare ‘to give’). The name was much favored by early Christians, either because the birth of a child was seen as a gift from God, or else because the child was in turn dedicated to God. The name was borne by various early saints, among them a 6th-century hermit of Sisteron and a 7th-century bishop of Besançon, all of whom contributed to the popularity of the baptismal name in the Middle Ages, which was not checked by the heresy of a 4th-century Carthaginian bishop who also bore it. Another bearer was a 4th-century gramMarian and commentator on Virgil, widely respected in the Middle Ages as a figure of great learning.
Female
Egyptian
, a sister of the prince Ra-hotep.
Female
Norse
Old Norse name composed of the elements bjarga "to rescue" and ljótr "bright, light," hence "rescue light."Â
Female
Egyptian
, The Good Companion.
Female
Egyptian
, the goddess of darkness.
Male
Hungarian
Czech and Hungarian form of Latin Donatus, DONÃT means "given (by God)."
Female
Egyptian
, The Most Powerful of Beings.
Female
Icelandic
Icelandic form of Latin Margarita, MARGRÉT means "pearl."
Female
Egyptian
, a daughter of Rameses II; & a wife of Rameses II.
Female
Egyptian
, the wife of Toti.
Male
Czechoslovakian
, earnest, serious.
Female
Egyptian
, the goddess of time.
Male
Czechoslovakian
, living.
Female
Egyptian
, the mother of the priest Fai-iten-hemh-bai.
Female
Egyptian
, an Egyptian lady, the wife of Antefaker.
T FUNCTION
T FUNCTION
Female
German
Feminine form of German Hermann, HERMINE means "army man."
Boy/Male
English French Teutonic
auburn-haired.
Boy/Male
Hindu
Brightness
Surname or Lastname
English
English : from a personal name equivalent to Severin.English : topographic name from the river Severn, which flows from Wales through much of western England to the Bristol Channel. The river name is recorded as early as the 2nd century ad in the form Sabrina. This is one of Britain’s most ancient river names; the original meaning is uncertain, but it may have been ‘slow-moving’.
Female
English
Variant spelling of English Pearlie, PERLIE means "pearl."
Boy/Male
American, Australian, Chinese, Christian, German, Scandinavian, Swedish
Grim Bear; Bear; Courageous; Brave Like a Bear; Form of Bernard
Surname or Lastname
English (Kent)
English (Kent) : probably a variant of Scottish Roxburgh.
Biblical
passage; revolution; heap
Boy/Male
English
From the people's meadow. From a surname and place name derived from the Old English, meaning...
Girl/Female
Hindu
Lamp
T FUNCTION
T FUNCTION
T FUNCTION
T FUNCTION
T FUNCTION
v. t.
See Kiddy, v. t.
v. t.
See Kittle, v. t.
v. t.
See Haze, v. t.
v. t.
See Bromate, v. t.
v. t.
See Agast, v. t.
v. t.
See Forcarve, v. t.
v. t.
See Chivy, v. t.
v. t.
See Cob, v. t.
v. t.
See Entail, v. t.
v. t.
See Roust, v. t.
v. t.
See Reenforce, v. t.
v. t.
See Buttweld, v. t.
v. t.
See Leach, v. t.
v. t.
See Jam, v. t.
v. t.
See Feeze, v. t.