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Function that can be written as a sum over prime factors
In number theory, an additive function is an arithmetic function f {\displaystyle f} on the natural numbers such that for all coprime a {\displaystyle
Additive_function
Mapping function
In mathematics, an additive set function is a function μ \mu mapping sets to numbers, with the property that its value on a union of two disjoint sets
Sigma-additive_set_function
Generalization of mass, length, area and volume
instance, a countably additive set function with values in the (signed) real numbers is called a signed measure, while such a function with values in the
Measure_(mathematics)
Functional equation
{\displaystyle f(x+y)=f(x)+f(y).} A function f {\displaystyle f} that solves this equation is called an additive function. Over the rational numbers, it can
Cauchy's_functional_equation
Function which is not continuous at any point of its domain
\}} is a continuous function. Thus if f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } is a non-linear additive function then for every point
Nowhere_continuous_function
Method for nonparametric multiple regression
Jerome H. Friedman and Werner Stuetzle that extends additive models. This model adapts the additive models in that it first projects the data matrix of
Projection_pursuit_regression
Property of some mathematical functions
particularly norms and square roots. Additive maps are special cases of subadditive functions. A subadditive function is a function f : A → B {\displaystyle f\colon
Subadditivity
Topics referred to by the same term
Look up additive in Wiktionary, the free dictionary. Additive may refer to: Additive function, a function in number theory Additive map, a function that
Additive
Z-module homomorphism
In algebra, an additive map or additive function is a function f {\displaystyle f} that preserves the addition operation: f ( x + y ) = f ( x ) + f (
Additive_map
Function defined on integers in number theory
\mid \,x}{p\in \mathbb {P} }}{\frac {\nu _{p}(x)}{p}}} is a totally additive function: ld ( x ⋅ y ) = ld ( x ) + ld ( y ) . {\displaystyle \operatorname
Arithmetic_derivative
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
Number of prime factors of a natural number
prime-factor-counting functions have many important number theoretic relations. The function ω ( n ) {\displaystyle \omega (n)} is additive and Ω ( n ) {\displaystyle
Prime_omega_function
Function whose domain is the positive integers
is no prime number that divides both of them. Then an arithmetic function a is additive if a(mn) = a(m) + a(n) for all coprime natural numbers m and n;
Arithmetic_function
Additives for lubricants to prevent metal-to-metal contact
controversial. Many AW additives function as EP additives, for example organophosphates or sulfur compounds. The mechanism of function of TCP and ZDDP is
Antiwear_additive
Sound synthesis technique
Additive synthesis example A bell-like sound generated by additive synthesis of 21 inharmonic partials Problems playing this file? See media help. Additive
Additive_synthesis
Function on an integer n which is log(p) if n equals p^k and zero otherwise
important arithmetic function that is neither multiplicative nor additive. The von Mangoldt function, denoted by Λ ( n ) {\displaystyle \Lambda (n)} , is defined
Von_Mangoldt_function
Moment of inertia of diff geometric shapes
calculating moments of inertia, it is useful to remember that it is an additive function and exploit the parallel axis and the perpendicular axis theorems
List_of_moments_of_inertia
Preference ranking
then it can be represented by an additive utility function. If the preferences are represented by an additive function, then a simple arithmetic calculation
Ordinal_utility
Function from sets to numbers
F\in {\mathcal {F}}.} Every finitely additive function on a field of sets is modular. In geometry, a set function valued in some abelian semigroup that
Set_function
Value that makes no change when added
the ring of functions from R → R {\displaystyle \mathbb {R} \to \mathbb {R} } , the function mapping every number to 0 is the additive identity. In
Additive_identity
Group homomorphism up to bounded error
quasimorphism (or quasi-morphism) is a function f : G → R {\displaystyle f:G\to \mathbb {R} } which is additive up to bounded error, i.e. there exists
Quasimorphism
Number that, when added to the original number, yields the additive identity
mathematics, the additive inverse of an element x, denoted −x, is the element that when added to x, yields the additive identity. This additive identity is
Additive_inverse
Theorem in number theory
probabilistic number theory, a real-valued function f ( n ) {\displaystyle f(n)} on the integers is additive if f ( m n ) = f ( m ) + f ( n ) {\displaystyle
Erdős–Wintner_theorem
f} is subadditive. The maximum of additive set functions is subadditive (dually, the minimum of additive functions is superadditive). Formally, for each
Subadditive_set_function
it with a knife. A possible utility function for this case is given at the right. A utility function is additive if and only if it is both submodular
Utility functions on indivisible goods
Utility_functions_on_indivisible_goods
Fundamental color in color mixing
can match another monochromatic light under additive mixing so at least one of the color matching functions is negative for each wavelength. A negative
Primary_color
Generalization of finite measure to Banach spaces
Banach space X , {\displaystyle X,} a finitely additive vector measure (or measure, for short) is a function μ : F → X {\displaystyle \mu :{\mathcal {F}}\to
Vector_measure
Cadlag in probability theory
An additive process, in probability theory, is a cadlag, continuous in probability stochastic process with independent increments. An additive process
Additive_process
Multiplicative function Additive function Dirichlet convolution Erdős–Kac theorem Möbius function Möbius inversion formula Divisor function Liouville function Partition
List_of_number_theory_topics
Extension of the factorial function
point of view, the Legendre normalization of the gamma function is the integral of the additive character e − x {\displaystyle e^{-x}} against the multiplicative
Gamma_function
Statistics models class
generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some
Generalized_additive_model
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
Subfield of number theory
results include the Erdős–Wintner theorem, the Erdős–Kac theorem on additive functions and the DDT theorem. Number theory Analytic number theory Areas of
Probabilistic_number_theory
Open cover in mathematical analysis
general form of the covering principle and relative differentiation of additive functions, I", Mathematical Proceedings of the Cambridge Philosophical Society
Besicovitch_covering_theorem
Conditions for switching order of integration in calculus
be constructed by applying Carathéodory's extension theorem to the additive function μ such that μ(A × B) = μ1(A)μ2(B) on the ring of sets generated by
Fubini's_theorem
Mathematical function, denoted exp(x) or e^x
\exp(y)} and maps the additive identity 0 to the multiplicative identity 1. The same equation is satisfied by other continuous functions f ( x ) = b x {\displaystyle
Exponential_function
Form of the utility function
e − a c {\displaystyle u(c)=1-e^{-ac}} . Note that the additive term 1 in the above function is mathematically irrelevant and is (sometimes) included
Exponential_utility
Mathematical and computational problem
S2CID 15905063. Hoberg, Rebecca; Rothvoss, Thomas (2017), "A Logarithmic Additive Integrality Gap for Bin Packing", Proceedings of the Twenty-Eighth Annual
Bin_packing_problem
Additive process used to make a 3D object
3D printing, also called additive manufacturing, is the construction of a three-dimensional object from a CAD model or a digital 3D model. It can be done
3D_printing
Integer
(negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative
−1
Mathematical relation assigning a probability event to a cost
particular, Andranik Tangian showed that the most usable objective functions — quadratic and additive — are determined by a few indifference points. He used this
Loss_function
abelian group G a homomorphism from G to the additive group of the complex numbers is called an additive function, and a homomorphism to the multiplicative
Exponential_polynomial
American mathematician (1956–2023)
Integral-Valued, Prime-Independent, Multiplicative or Additive Function of n Divides a Polynomial Function of n. After finishing up the work for her PhD in
Claudia_Spiro
Oscillatory error in Fourier series
differentiable periodic function around a jump discontinuity. The N {\textstyle N} th partial Fourier series of the function (formed by summing the N
Gibbs_phenomenon
function is affected by arithmetic operations on its argument. The following are special examples of a homomorphism on a binary operation: Additive function:
List_of_types_of_functions
Fundamental theorem of probabilistic number theory
defined as Φ(a,b)=12π∫abe−t2/2dt. More generally, if f(n) is a strongly additive function (f(p1a1⋯pkak)=f(p1)+⋯+f(pk)) with |f(p)|≤1 for all prime p, then
Erdős–Kac_theorem
Process of calculating the causal factors that produced a set of observations
of L2. Thus any solution of this equation is determined up to an additive function in the null-space and, in the case of infinity of singular values
Inverse_problem
Loss function used in robust regression
generalization of L {\displaystyle L} . The Huber loss function is used in robust statistics, M-estimation and additive modelling. Winsorizing Robust regression M-estimator
Huber_loss
Function equal to the product of its values on coprime factors
ω ( n ) {\displaystyle \gamma (n)=(-1)^{\omega (n)}} , where the additive function ω ( n ) {\displaystyle \omega (n)} is the number of distinct primes
Multiplicative_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
Statistical model extension
the predictor functions are modeled as function of the functional principal component scores of the predictor function in an additive structure. This
Functional_additive_model
Point where function's value is zero
{R} } is a real-valued function (or, more generally, a function taking values in some additive group), its zero set is f − 1 ( 0 ) {\displaystyle f^{-1}(0)}
Zero_of_a_function
Design pattern in functional programming to build generic types
are analogous to the corresponding functions of the same name. int * string, bind, and return form a monad. An additive monad is a monad endowed with an
Monad (functional programming)
Monad_(functional_programming)
Concept in pharmacology and biochemistry
remaining function would be at (1-60%)×(1-60%)=16%, meaning the additive inhibitory effect would be 84%. Since the application of additive effect is commonly
Additive_effect
Abelian group extending a commutative monoid
only group homomorphism that does that. Examples of additive functions are the character function from representation theory: If R {\displaystyle R} is
Grothendieck_group
Property of a number
which the operation no longer alters the number. Usually, this involves additive or multiplicative persistence of a non-negative integer, which is how often
Persistence_of_a_number
cardinal number) is additively indecomposable. The class of additively indecomposable numbers is closed and unbounded. Its enumerating function is normal, given
Additively indecomposable ordinal
Additively_indecomposable_ordinal
Number which when multiplied by x equals 1
multiplicative is often omitted and then tacitly understood (in contrast to the additive inverse). Multiplicative inverses can be defined over many mathematical
Multiplicative_inverse
Theorem in order theory and lattice theory
pertains to monotone functions on complete lattices), this result is often attributed to Alfred Tarski who proves it for additive functions. Moreover, the Kleene
Kleene_fixed-point_theorem
Number property of being positive or negative
phrase "change of sign" is associated with exchanging an object for its additive inverse (multiplication with −1, negation), an operation which is not restricted
Sign_(mathematics)
Set-to-real map with diminishing returns
linear function. Additionally if ∀ i , w i ≥ 0 {\displaystyle \forall i,w_{i}\geq 0} then f is monotone. Budget-additive functions Any function of the
Submodular_set_function
Flavor enhancer (621 or E621)
broth in large concentrations. The European Union classifies it as a food additive permitted in certain foods and subject to quantitative limits. MSG has
Monosodium_glutamate
A set function is called fractionally subadditive, or XOS (not to be confused with OXS), if it is the maximum of several non-negative additive set functions
Fractionally subadditive valuation
Fractionally_subadditive_valuation
Function which is integrable on its domain
sets of finite measure μ {\textstyle \mu } , then, in order that an additive function of a set X {\textstyle {\boldsymbol {\mathfrak {X}}}} on E {\textstyle
Locally_integrable_function
Functions such that f(–x) equals f(x) or –f(x)
notion of additive inverse. This includes abelian groups, all rings, all fields, and all vector spaces. Thus, for example, a real function could be odd
Even_and_odd_functions
Fundamental principle of physics
x˙=Ax+B(u1+u2)+ϕ(c𝖳x),x(0)=x0, where ϕ is a nonlinear function. By the additive state decomposition, the system can be additively decomposed into x˙1=Ax1+Bu1+ϕ(yd),x1(0)=x0
Superposition_principle
Properties of mathematical relationships
In mathematics, a linear map or linear function f(x) is a function that satisfies the two properties: Additivity: f(x + y) = f(x) + f(y). Homogeneity of
Linearity
The AU extension is based on the notion of an additive utility function. Many different utility functions are compatible with a given ordering. For example
Responsive_set_extension
In additive number theory, an additive basis is a set S {\displaystyle S} of natural numbers with the property that, for some finite number k {\displaystyle
Additive_basis
Function used in computer cryptography
science Do one-way functions exist? More unsolved problems in computer science In computer science, a one-way function is a function that is easy to compute
One-way_function
Whole number
number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, complex numbers
0
Hypothesis in evolutionary biology
the production of offspring, this is a multiplicative rather than additive function of reproductive success. Further game theoretical models demonstrated
Handicap_principle
Statistical regression model
In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an
Additive_model
Algebraic structure with addition, multiplication, and division
⋅ b = b ⋅ a. Additive and multiplicative identity: there exist distinct elements 0 and 1 in F such that a + 0 = a and a ⋅ 1 = a. Additive inverses: for
Field_(mathematics)
Basic noise model used in information theory
Additive white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature
Additive_white_Gaussian_noise
Stochastic process
up to a certain time. When analyzing sums, random walks, or other additive functions of independent random variables, one can often apply the central limit
Doob_martingale
Process of mapping a continuous set to a countable set
produces a sequence of quantization errors, which is sometimes modeled as an additive random signal called quantization noise because of its stochastic behavior
Quantization (signal processing)
Quantization_(signal_processing)
Lubricant used for internal combustion engines
typically consist of base oils enhanced with various additives, particularly antiwear additives, detergents, dispersants, and, for multi-grade oils, viscosity
Motor_oil
Set of cryptographic hash functions
SHA-512 are hash functions whose digests are eight 32-bit and 64-bit words, respectively. They use different shift amounts and additive constants, but their
SHA-2
Machine learning technique
That is, algorithms that optimize a cost function over function space by iteratively choosing a function (weak hypothesis) that points in the negative
Gradient_boosting
Chemicals that improve oil performance
choose different additives for each use. Additives comprise up to 5% by weight of some oils. Nearly all commercial motor oils contain additives, whether the
Oil_additive
Chemical compound
food additive, dipotassium phosphate is used in imitation dairy creamers, dry powder beverages, mineral supplements, and starter cultures. It functions as
Dipotassium_phosphate
the sum of primes dividing n, counted with multiplicity. It is an additive function. A Ruth-Aaron pair is a pair of two consecutive numbers (n,n+1) with
Table_of_prime_factors
Non-sinusoidal waveform
of triangle wave at 220 Hz Problems playing this file? See media help. Additive Triangle wave sound sample After each second, a harmonic is added to a
Triangle_wave
Function with a multiplicative scaling behaviour
mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by
Homogeneous_function
Class of statistical models
response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized
Generalized_linear_model
only for σ-additive measures. There are two equivalent ways to define a cylinder set measure. One way is to define it directly as a set function on the cylindrical
Cylinder_set_measure
To like one thing more than another
quadratic or additive functions — laid down by Gérard Debreu enabled Andranik Tangian to develop methods for their elicitation. In particular, additive and quadratic
Preference
Zero in algebraic structures
to the same thing, depending on the context. An additive identity is the identity element in an additive group or monoid. It corresponds to the element
Zero_element
Function in decision theory
individual attribute utility functions, b) the aggregating constants' values, and c) whether the attribute utility functions are additive, these terms being addressed
Multi-attribute_utility
Process for fairly dividing resources
required that the preferences of the agents are represented by an additive function. The main concept in the proof is the simplex of partitions. Suppose
Envy-free_cake-cutting
Concept in economics
In economics, additive utility is a cardinal utility function with the sigma additivity property. Additivity (also called linearity or modularity) means
Additive_utility
Any real function on R admits a continuous restriction on a dense subset of R
\mathbb {Q} } of irrational numbers is continuous. Similarly, every additive function R → R {\displaystyle \mathbb {R} \to \mathbb {R} } that is not linear
Blumberg_theorem
American automotive oil additive
founded by Burt Pierce in 1923. It is used as a fuel additive and oil additive, purportedly to function as a corrosion inhibitor, penetrating oil, transmission
Marvel_Mystery_Oil
} (normalization) Let f be a function on positive integers that satisfies the above three properties. From the additive property, we can show that for
Hartley_function
Chemistry of wine
to wine Gum arabic has been used in the past as fining agent. List of additives permitted for use in the production of wine under European Union law:
Wine_chemistry
Distributional regression model
The generalized additive model for location, scale and shape (GAMLSS) is a distributional regression model in which a parametric statistical distribution
Generalized additive model for location, scale and shape
Generalized_additive_model_for_location,_scale_and_shape
Mathematical function with convex lower level sets
quasiconvex, h(x,y)=f(x)+g(y)) need not be quasiconvex. Such functions are called "additively decomposed" in economics and "separable" in mathematical optimization
Quasiconvex_function
Hilbert function, the Hilbert–Samuel function is not additive on an exact sequence. However, it is still reasonably close to being additive, as a consequence
Hilbert–Samuel_function
Mathematical function that outputs real values
In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each
Real-valued_function
travel, tourism, insurance
ADDITIVE FUNCTION
ADDITIVE FUNCTION
Boy/Male
Hindu
Born after or in addition to
Male
Swiss
, addition.
Male
Dutch
, addition, or, he will add.Â
Boy/Male
Arabic, Muslim
Increase; Addition; Surplus; Plenty
Male
Chamoru
, Joseph; addition; he will add.
Female
Czechoslovakian
, addition, or, he will add.
Female
Swiss
, addition.
Male
Dutch
, addition; or, he will add.
Male
Swiss
, addition.
Male
Croatian
, addition, or, Jehovah will add.
Boy/Male
Biblical American Hebrew
Increase; addition.
Male
Dutch
, addition, or, he will add.Â
Male
Dutch
, addition; or, he will add.
Male
Dutch
, addition; or, he will add.
Male
Dutch
, addition, or, he will add.
Boy/Male
Tamil
Born after or in addition to
Male
Dutch
, addition, or, he will add.
Female
Swiss
, addition.
Male
Croatian
, addition, or, Jehovah will add.
Girl/Female
Arabic, Muslim
Addition; Surplus; Increase; Growth
ADDITIVE FUNCTION
ADDITIVE FUNCTION
ADDITIVE FUNCTION
ADDITIVE FUNCTION
ADDITIVE FUNCTION
ADDITIVE FUNCTION
ADDITIVE FUNCTION
travel, tourism, insurance