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Function that can be written as a sum over prime factors
theory, an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied
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)
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
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
Z-module homomorphism
In algebra, an additive map, Z {\displaystyle \mathbb {Z} } -linear map or additive function is a function f {\displaystyle f} that preserves the addition
Additive_map
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
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
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 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
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
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
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
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
Value that makes no change when added
In mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the
Additive_identity
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
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
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
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
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
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
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
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
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
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
Process of calculating the causal factors that produced a set of observations
L^{2}} . 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
Multiplicative function Additive function Dirichlet convolution Erdős–Kac theorem Möbius function Möbius inversion formula Divisor function Liouville function Partition
List_of_number_theory_topics
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
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
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
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
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
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
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
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
Generalization of a measure
of a measure: while the latter must be countably additive, the former must only be finitely additive. In many important applications the A {\displaystyle
Content_(measure_theory)
Theorem in number theory
In 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 f(mn)=f(m)+f(n)}
Erdős–Wintner_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
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
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
Substance introduced to reduce friction between surfaces in mutual contact
to 350 °C and chemical inertness make it a useful additive in special greases, where it can function both as a thickener and a lubricant. Under extreme
Lubricant
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
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
Design pattern in functional programming to build generic types
analogous to the corresponding functions of the same name. In fact, int * string, bind, and return form a monad. An additive monad is a monad endowed with
Monad (functional programming)
Monad_(functional_programming)
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
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
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)
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
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
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
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
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
Unsolved problem in number theory
conjecture is an old unsolved problem in additive number theory posed by Paul Erdős and Pál Turán in 1941. It concerns additive bases, subsets of natural numbers
Erdős–Turán conjecture on additive bases
Erdős–Turán_conjecture_on_additive_bases
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
Fundamental theorem of probabilistic number theory
_{a}^{b}e^{-t^{2}/2}\,dt.} More generally, if f(n) is a strongly additive function ( f ( p 1 a 1 ⋯ p k a k ) = f ( p 1 ) + ⋯ + f ( p k ) {\displaystyle
Erdős–Kac_theorem
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
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
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
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
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)
Equation whose unknown is a function
f(xy)=f(x)+f(y)} , satisfied by all logarithmic functions and, over coprime integer arguments, additive functions f ( x y ) = f ( x ) f ( y ) {\displaystyle
Functional_equation
Number
number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers
0
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
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
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
Subject in mathematics
{\displaystyle \nu :{\mathcal {E}}(X,G)\to \mathbb {R} +} is a σ-additive function, i.e. ν {\displaystyle \nu } is a measure. Let Γ ⊂ X ∗ {\displaystyle
Measure theory in topological vector spaces
Measure_theory_in_topological_vector_spaces
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
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
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
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
Property of certain measures on topological spaces
field of measure theory, τ-additivity is a certain property of measures on topological spaces. A measure or set function μ {\displaystyle \mu } on a
Tau_additivity
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
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
Fundamental principle of physics
{\displaystyle \phi } is a nonlinear function. By the additive state decomposition, the system can be additively decomposed into x ˙ 1 = A x 1 + B u 1
Superposition_principle
Exploring properties of the integers with complex analysis
prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem)
Analytic_number_theory
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
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
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
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
In geometry, a valuation is a finitely additive function from a collection of subsets of a set X {\displaystyle X} to an abelian semigroup. For example
Valuation_(geometry)
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
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
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)
Description of particle density in statistical mechanics
unique up to an additive constant, if it exists. In recent years, some attention has been given to develop pair correlation functions for spatially-discrete
Radial_distribution_function
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 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
} (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
Type of noise in signal processing
channel testing and modelling, Gaussian noise is used as additive white noise to generate additive white Gaussian noise. In telecommunications and computer
Gaussian_noise
mathematics, a Schwartz–Bruhat function, named after Laurent Schwartz and François Bruhat, is a complex valued function on a locally compact abelian group
Schwartz–Bruhat_function
Material to reduce fecal sludge build-up
Pit additives is a commercially produced material that aims to reduce fecal sludge build-up and control odor in pit latrines, septic tanks and wastewater
Pit_additive
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
Fairness notion in fair item allocation
lexicographic potential function that strictly increases at each step and guarantees termination. The argument makes heavy use of the additive structure of the
Envy-freeness_up_to_any_item
Water-soluble food coloring
during food processing and storage. The use of caramel color as a food additive in the brewing industry in the 19th century is the first recorded instance
Caramel_color
Sweetener and sugar substitute
local teas, and as a "sweet treat". The legal status of stevia as a food additive or dietary supplement varies from country to country. Stevia has been widely
Stevia
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
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
Generalizations of '"`UNIQ--math-00000046-QINU`"' 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
Antioxidant
categories in catalogues and databases, such as food additive, household product ingredient, industrial additive, personal care product and cosmetic ingredient
Butylated_hydroxytoluene
ADDITIVE FUNCTION
ADDITIVE FUNCTION
Girl/Female
Arabic, Muslim
Addition; Surplus; Increase; Growth
Male
Croatian
, addition, or, Jehovah will add.
Boy/Male
Arabic, Muslim
Increase; Addition; Surplus; Plenty
Boy/Male
Biblical American Hebrew
Increase; addition.
Male
Dutch
, addition, or, he will add.Â
Female
Swiss
, addition.
Male
Swiss
, addition.
Male
Dutch
, addition, or, he will add.
Male
Dutch
, addition; or, he will add.
Male
Dutch
, addition, or, he will add.Â
Male
Dutch
, addition; or, he will add.
Boy/Male
Tamil
Born after or in addition to
Male
Dutch
, addition; or, he will add.
Male
Croatian
, addition, or, Jehovah will add.
Boy/Male
Hindu
Born after or in addition to
Male
Dutch
, addition, or, he will add.
Male
Swiss
, addition.
Female
Czechoslovakian
, addition, or, he will add.
Female
Swiss
, addition.
Male
Chamoru
, Joseph; addition; he will add.
ADDITIVE FUNCTION
ADDITIVE FUNCTION
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from either of two places in northern France: Coignières in Seine-et-Oise or Cogners in Sarthe. This surname is well established in the southern states, where it is now borne mainly by African Americans.
Girl/Female
Danish, French, German, Swedish
Battle Maiden
Girl/Female
Indian, Tamil
Gold Like
Girl/Female
Tamil
Ahilya | அஹிலà¯à®¯à®¾
Maiden
Girl/Female
Tamil
Boy/Male
Hindu
Benediction of God, Pleased by gods
Girl/Female
Hindu, Indian
Shining Jewel
Boy/Male
Tamil
Desire, Lovely, Spring, Lover, Beautiful, Husband, Moon, A precious stone, Vishnu
Boy/Male
Indian, Punjabi, Sikh
Servant of God's Feet
Boy/Male
Tamil
Unique, No one like him, Non duality
ADDITIVE FUNCTION
ADDITIVE FUNCTION
ADDITIVE FUNCTION
ADDITIVE FUNCTION
ADDITIVE FUNCTION
a.
Proper to be added; positive; -- opposed to subtractive.
n.
Increase; addition; surplus.
n.
A title annexed to a man's name, to identify him more precisely; as, John Doe, Esq.; Richard Roe, Gent.; Robert Dale, Mason; Thomas Way, of New York; a mark of distinction; a title.
n.
That part of arithmetic which treats of adding numbers.
a.
Adaptive.
n.
A dot at the right side of a note as an indication that its sound is to be lengthened one half.
n.
An addition.
prep.
Addition; union; accumulation.
a.
Suited, given, or tending, to adaptation; characterized by adaptation; capable of adapting.
a.
Answering to an interrogative or inquiry; conveying a reply; as, redditive words.
adv.
Likewise; also; in addition.
n.
Something added to a coat of arms, as a mark of honor; -- opposed to abatement.
a.
Adaptive.
a.
Having the quality of hiding.
a.
Additive.
a.
Pertaining to adoption; made or acquired by adoption; fitted to adopt; as, an adoptive father, an child; an adoptive language.
a.
Of or pertaining to hearing; auditory.
n.
The act of adding two or more things together; -- opposed to subtraction or diminution.
n.
Anything added; increase; augmentation; as, a piazza is an addition to a building.
a.
Adducing, or bringing towards or to something.