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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 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 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
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
a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies
Continuous_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
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
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
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
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
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
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
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
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
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
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
White blood cells of the immune system
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
Statistical function that defines the quantiles of a probability distribution
probability distribution's quantile function is the inverse of its cumulative distribution function. That is, the quantile function of a distribution D {\displaystyle
Quantile_function
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
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
Genetically engineered T cell
antigen-binding and T cell activating functions into a single receptor. CAR T cell therapy uses T cells engineered with CARs to treat cancer. T cells are modified
CAR_T_cell
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
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
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
fields of group theory and representation theory of groups, a class function is a function on a group G that is constant on the conjugacy classes of G. In
Class_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)
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
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
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
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
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
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
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
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
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
Type of mathematical function
elementary function is a function of a single variable (real or complex) that is typically encountered by beginners. The basic elementary functions are polynomial
Elementary_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
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
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
Branch of mathematics
differential equation d f d t = − a f ( t ) {\displaystyle {\frac {df}{dt}}=-af(t)} is solved by a function f ( t ) {\displaystyle f(t)} that is proportional
Calculus
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
Integral transform and linear operator
singular integral that takes a function, u(t) of a real variable and produces another function of a real variable H(u)(t). The Hilbert transform is given
Hilbert_transform
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
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
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
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
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
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
mathematics, the local zeta function Z(V, s) (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as Z ( V , s ) =
Local_zeta_function
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
Smooth and compactly supported function
analysis, a bump function is a localized auxiliary function, usually chosen to be smooth and to have compact support. Bump functions are commonly used
Bump_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
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
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
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
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
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
Probability of survival beyond any specified time
function is: S ( t ) = ∫ t ∞ f ( u ) d u = Pr ( T > t ) = 1 − F ( t ) = 1 − ∫ 0 t f ( u ) d u {\displaystyle S(t)=\int _{t}^{\infty }f(u)\,du=\Pr(T>t)=1-F(t)=1-\int
Survival_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
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
Functions in mathematics
the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R {\displaystyle f:U\to \mathbb {R} }
Harmonic_function
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
American rapper and actor (born 1958)
Town to the humorous expositional nature of Ice-T's role on Special Victims Unit, saying that his function on the show is to be perpetually amazed by bad
Ice-T
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 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
Hardy–Littlewood maximal function. They play an important role in understanding, for example, the differentiability properties of functions, singular integrals
Maximal_function
color function. It maps places in P into colors in Σ. N is a node function. It maps A into (P × T) ∪ (T × P). E is an arc expression function. It maps
Coloured_Petri_net
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
Property of functions which is weaker than continuity
Briefly, a function on a domain X {\displaystyle X} is lower semi-continuous if its epigraph { ( x , t ) ∈ X × R : t ≥ f ( x ) } {\displaystyle \{(x,t)\in X\times
Semi-continuity
Meromorphic function
In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers C {\displaystyle \mathbb {C} } defined as the (m +
Polygamma_function
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
Summary of dynamics of a stochastic process
The Onsager–Machlup function is a function that summarizes the dynamics of a continuous stochastic process. It is used to define a probability density
Onsager–Machlup_function
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_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
Function used as a performance test problem for optimization algorithms
Himmelblau's function In mathematical optimization, Himmelblau's function is a multi-modal function, used to test the performance of optimization algorithms
Himmelblau's_function
the expenditure function represents the minimum amount of expenditure needed to achieve a given level of utility, given a utility function and the prices
Expenditure_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
Linear map or polynomial function of degree one
the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a
Linear_function
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)
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
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
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
Function whose actual domain of definition may be smaller than its apparent domain
In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that
Partial_function
Optimization performance test
Sphere function of two variables In mathematical optimization, the sphere function is a convex function used as a performance test problem for optimization
Sphere_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
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
Hash function that is suitable for use in cryptography
ISBN 978-3-642-17400-1. ISSN 0302-9743. Rogaway, P.; Shrimpton, T. (2004). "Cryptographic Hash-Function Basics: Definitions, Implications, and Separations for
Cryptographic_hash_function
Interrelated entities that form a whole
described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems
System
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
Endocrine gland
autoreactive T cells from maturing, was understood by 1994. In recent decades, advances in immunology have allowed the thymus's function in T-cell maturation
Thymus
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
Arithmetic function
Liouville function, named after French mathematician Joseph Liouville and denoted λ ( n ) {\displaystyle \lambda (n)} , is an important arithmetic function. Its
Liouville_function
characteristic function satisfies d 0 | t | β 0 exp ( − | t | β / γ ) ≤ | φ X ( t ) | ≤ d 1 | t | β 1 exp ( − | t | β / γ ) as t → ∞ {\displaystyle d_{0}|t|^{\beta
Smoothness (probability theory)
Smoothness_(probability_theory)
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
product's excess supply function is the negative of the excess demand function—it is the product's supply function minus its demand function. In most cases the
Excess_demand_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
Sum of a function's values every _P_ offsets
mathematics, any integrable function s ( t ) {\displaystyle s(t)} can be made into a periodic function s P ( t ) {\displaystyle s_{P}(t)} with period P by summing
Periodic_summation
T FUNCTION
T FUNCTION
Female
Norse
Old Norse name composed of the elements bjarga "to rescue" and ljótr "bright, light," hence "rescue light."Â
Female
Egyptian
, the daughter of King Snefru.
Male
Hungarian
Czech and Hungarian form of Latin Donatus, DONÃT means "given (by God)."
Female
Egyptian
, The Good Companion.
Male
Hungarian
Hungarian form of Old High German Bernhard, BERNÃT means "bold as a bear."
Female
Egyptian
, a sister of the prince Ra-hotep.
Male
Czechoslovakian
, living.
Female
Egyptian
, the daughter of Osirtesen.
Female
Egyptian
, a daughter of Rameses II; & a wife of Rameses II.
Female
Egyptian
, the goddess of time.
Male
Czechoslovakian
, given.
Female
Egyptian
, the mother of the priest Fai-iten-hemh-bai.
Female
Egyptian
, the goddess of darkness.
Female
Egyptian
, the name of several Egyptian ladies.
Female
Egyptian
, the wife of Toti.
Female
Egyptian
, The Most Powerful of Beings.
Female
Icelandic
Icelandic form of Latin Margarita, MARGRÉT means "pearl."
Male
Czechoslovakian
, earnest, serious.
Female
Egyptian
, an Egyptian lady, the wife of Antefaker.
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.
T FUNCTION
T FUNCTION
Girl/Female
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
Prosperous; Wife of the God Vishnu; Goddess Laxmi; Another Name of Goddess Parvati
Boy/Male
Indian, Telugu
Highest; Kingdom; Bigger
Girl/Female
Biblical
The fleece of them.
Boy/Male
American, British, English
Royal Ruler; King's Ruler
Boy/Male
Indian, Sanskrit
Beautiful Lord
Girl/Female
Australian, Hebrew
To Rest
Male
Irish
Variant spelling of Irish Gaelic Donnchadh, DONNACHAIDH means "brown warrior."
Girl/Female
Biblical
Fear, or throwing down, of the Lord.
Boy/Male
Teutonic
Wise protector.
Boy/Male
Welsh
Legendary son of Nwython.
T FUNCTION
T FUNCTION
T FUNCTION
T FUNCTION
T FUNCTION
v. t.
See Kittle, v. t.
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See Leach, v. t.
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See Roust, v. t.
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See Kiddy, v. t.
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See Bromate, v. t.