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Property of a function
extensions of Fekete's lemma that do not require the definition of superadditivity above to hold for all m {\displaystyle m} and n . {\displaystyle n
Superadditivity
Game where groups of players may enforce cooperative behaviour
{\displaystyle S\subseteq T\Rightarrow v(S)\leq v(T)} . This follows from superadditivity. i.e. if payoffs are normalized so singleton coalitions have zero value
Cooperative_game_theory
Photographic development agent
superadditivity holds without rate superadditivity. Note that the term superadditive development is usually not used to mean density superadditivity:
Superadditive_developer
the sets separately. This definition is analogous to the notion of superadditivity for real-valued functions. It is contrasted to subadditive set function
Superadditive_set_function
Subadditive or superadditive integral
their formulation of cumulative prospect theory. Nonlinear expectation Superadditivity Subadditivity Choquet, G. (1953). "Theory of capacities". Annales de
Choquet_integral
u(\{X,Y\})+u(\{Y,Z\})<u(\{X,Y\}\cup \{Y,Z\})+u(\{X,Y\}\cap \{Y,Z\}).} Superadditivity means that for every pair of disjoint sets A , B {\displaystyle A,B}
Utility functions on indivisible goods
Utility_functions_on_indivisible_goods
Lemma concerning the limit of subadditive sequences
{ a n } n = 1 ∞ {\displaystyle \{a_{n}\}_{n=1}^{\infty }} is called superadditive if and only if for all m , n ∈ N {\displaystyle m,n\in \mathbb {N} }
Fekete's_lemma
Principle in quantum information theory
1007/s00220-003-0981-7. S2CID 189829228. Hastings, M. B. (April 2009). "Superadditivity of communication capacity using entangled inputs". Nature Physics.
No-communication_theorem
Physiological capacity
compared to the sum of each single modality together, an effect called the superadditive effect of multisensory integration. Neurons that respond to both visual
Sense
Type of function in linear algebra
(mathematics) – Length in a vector space Seminorm – Mathematical function Superadditivity – Property of a function Proofs Let x ∈ X . {\displaystyle x\in X.}
Sublinear_function
In mathematics, invariant of square matrices
html Lin, Minghua; Sra, Suvrit (2014). "Completely strong superadditivity of generalized matrix functions". arXiv:1410.1958 [math.FA]. Paksoy;
Determinant
of fractionally-subadditive valuations. When agents' utilities are superadditive set functions (more general than supermodular), a ( log m ) 1 + ϵ
Welfare_maximization
Generalization of a measure
_{i=1}^{n}A_{i}\right)\leq \sum _{i=1}^{n}\mu (A_{i}).} σ {\displaystyle \sigma } -Superadditivity: For any we A i ∈ A ( i = 1 , 2 , … ) {\displaystyle A_{i}\in {\mathcal
Content_(measure_theory)
Property of some mathematical functions
vs. an ideal solution Choquet integral – Subadditive or superadditive integral Superadditivity – Property of a function Triangle inequality – Property
Subadditivity
Operation in mathematical calculus
fractional Brownian motion. The Choquet integral, a subadditive or superadditive integral created by Gustave Choquet in 1953. The Bochner integral, a
Integral
American mathematician (born 1932)
California, Los Angeles (1959) on the dissertation Minimal Superadditive Extensions of Superadditive Functions advised by John Green (mathematician). He joined
Andrew_M._Bruckner
Reducing aromatic compound used as developing agent in black and white photography
greater than the sum of rates of development by each agent used alone (superadditivity). This combination is very versatile; by varying the quantities of
Metol
Product of numbers from 1 to n
Centre National de la Recherche Scientifiques. Alzer, Horst (2009). "A superadditive property of Hadamard's gamma function". Abhandlungen aus dem Mathematischen
Factorial
American businessman
Stevenson & Sloman (1999). Opening Pandora's Box: Selective Unpacking and Superadditivity, ECCS, 265–270. Stibel (1995). The Effects of Associativity, Interconnectivity
Jeff_Stibel
Bounds of a sequence
\limsup _{n\to \infty }b_{n}.} Analogously, the limit inferior satisfies superadditivity: lim inf n → ∞ ( a n + b n ) ≥ lim inf n → ∞ a n + lim inf n → ∞
Limit inferior and limit superior
Limit_inferior_and_limit_superior
Real function with secant line between points above the graph itself
( 0 ) ≤ 0 {\displaystyle f(0)\leq 0} , then f {\displaystyle f} is superadditive on the positive reals, that is f ( a + b ) ≥ f ( a ) + f ( b ) {\displaystyle
Convex_function
Extension of the factorial function
for positive integer values of x. The Hadamard's gamma function has a superadditive property: H ( x ) + H ( y ) ≤ H ( x + y ) , {\displaystyle H(x)+H(y)\leq
Hadamard's_gamma_function
Model for quantum noise in quantum systems
doi:10.1109/TIT.2002.806153 Hastings, M. B. (15 March 2009), "Superadditivity of communication capacity using entangled inputs", Nature Physics,
Quantum_depolarizing_channel
Cognitive bias
Hu (2020) shows the endowment effect when the utility function is superadditive, i.e., the value of the whole is greater than the sum of its parts.
Endowment_effect
Cognitive tendency where lack of information affects decision making
explanations. This is due to people either exhibiting optimism, leading to superadditivity, or pessimism, lead to subadditivity. This mechanism involves individuals
Ambiguity_effect
subadditivity condition above is instead replaced by the condition: Superadditivity: for X , Y ∈ H {\displaystyle X,Y\in {\mathcal {H}}} then E [ X ] +
Nonlinear_expectation
Concept in game theory
\varphi _{i}(v)\leq v(\{i\})} . Similarly, if v {\displaystyle v} is a superadditive set function, i.e., if v ( S ∪ T ) ≥ v ( S ) + v ( T ) {\displaystyle
Shapley_value
share is worth even more. On the contrary, when the valuations are only superadditive, PR still implies EF with two partners, but EF no longer implies PR
Proportional_division
American marketing academic (born 1961)
Lwin, May, Maureen Morrin, & Aradhna Krishna (2010), "Exploring the Superadditive Effects of Scent and Pictures on Verbal Recall: An Extension of Dual
Aradhna_Krishna
Criterion for fair division
share is worth even more. On the contrary, when the valuations are only superadditive, PR still implies EF with two partners, but EF no longer implies PR
Envy-freeness
Group theory function
functions of finitely presented groups. In particular, if f(n) ≥ n4 is a superadditive function whose binary representation is computable in time O ( f ( n
Dehn_function
Chemical(s) which convert a latent image on photographic film to a visible image
developer, and D-96 motion picture negative developer. Hydroquinone is superadditive with metol, meaning that it acts to "recharge" the metol after it has
Photographic_developer
that the entropy power of suitably well-behaved random variables is a superadditive function. The entropy power inequality was proved in 1948 by Claude
Entropy_power_inequality
Function from sets to numbers
(\varnothing )=0} then μ {\displaystyle \mu } is finitely subadditive. superadditive if μ ( E ) + μ ( F ) ≤ μ ( E ∪ F ) {\displaystyle \mu (E)+\mu (F)\leq
Set_function
Probability theory for low quality data
(previsions), aim to fill this gap. A lower probability function is superadditive but not necessarily additive, whereas an upper probability is subadditive
Imprecise_probability
Concept in geometric group theory
case, a subgroup that is not locally finite has superadditive distortion; conversely every superadditive function (up to asymptotic equivalence) can be
Subgroup_distortion
Class of mathematical functions
supermodular function. A non-negative supermodular function is also a superadditive function. There are specialized techniques for optimizing submodular
Supermodular_function
which the value of f (x + y) is less than or equal to f (x) + f (y). Superadditive function: for which the value of f (x + y) is greater than or equal
List_of_types_of_functions
In additive number theory, a way to measure how dense a sequence of numbers is
its conclusion stops short of showing σ {\displaystyle \sigma } being superadditive. Yet, Schnirelmann provided us with the following results, which sufficed
Schnirelmann_density
Greek mathematician (1908–1974)
Funktionentheorie, Springer 1961 Minkowskische Summen und Integrale. Superadditive Mengenfunktionale. Isoperimetrische Ungleichungen (1961) Einführung
Alexander_Dinghas
Mathematics concept
[ λ n , k ] {\displaystyle \operatorname {E} [\lambda _{n,k}]} is superadditive: for all m and n, E [ λ m + n , k ] ≥ E [ λ m , k ] + E [ λ n
Chvátal–Sankoff_constants
Israeli mathematician (1927-2008)
Peleg and L.S. Shapley, 1979, Mathematics of Operations Research "Superadditive Solution for the Nash bargaining Game", with M. Perles, 1981, IJGT "Game
Michael_Maschler
Ecological mechanism enabling species to coexist
competition on fitness does not change with the environment. If γ > 0 (superadditivity), it means that the adverse effects of competition during a bad year
Storage_effect
Term in quantum information theory
1007/s00220-010-1172-y. ISSN 0010-3616. Hastings, M. B. (2009-03-15). "Superadditivity of communication capacity using entangled inputs". Nature Physics.
Classical_capacity
Theory of generalized measures in mathematics
E ) + g ( F ) {\displaystyle g(E\cup F)+g(E\cap F)\leq g(E)+g(F)} ; superadditive if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} such that
Fuzzy_measure_theory
American psychologist (1954–2020)
memories so that strong memories get even stronger, a principle called "superadditive". Hierarchical relational binding theory explains both neuroimaging
Arthur_P._Shimamura
zero); that is, φ ( ∅ ) = 0 {\displaystyle \varphi (\varnothing )=0} Superadditive: For any disjoint sets A {\displaystyle A} and B , {\displaystyle B
Inner_measure
additive positive utilities, but also for any superadditive utilities, whether positive or negative: For superadditive utilities, there is a polynomial-time algorithm
Fair allocation of items and money
Fair_allocation_of_items_and_money
functions is subadditive (dually, the minimum of additive functions is superadditive). Formally, for each i ∈ { 1 , … , m } {\displaystyle i\in \{1,\dotsc
Subadditive_set_function
Russian mathematician
particular p. 112. Holme, Audun; Roberts, Joel (1994), "Zak's theorem on superadditivity", Arkiv för Matematik, 32 (1): 99–120, Bibcode:1994ArM....32...99H
Fyodor_Zak
Fair division problem for discrete items
Hence, every mFS-fair allocation is proportional. For every agent with superadditive utility, the MMSis worth at most 1 / n {\displaystyle 1/n} . Hence,
Fair_item_allocation
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Girl/Female
Tamil
Flowering, Blooming, Flower
Girl/Female
Arabic, Muslim
Nature
Girl/Female
Indian
Paradise, Heaven, Garden
Girl/Female
American, British, English
Island of Linden Trees; From the Linden Tree Island
Girl/Female
Indian
Peaceful
Boy/Male
Hindu, Indian, Tamil
Wellness; Victory
Girl/Female
Muslim
Brook, Rivulet, Small stream
Surname or Lastname
English
English : variant spelling of London.
Surname or Lastname
English
English : variant spelling of Joslin.The Josselyn name appears in Black Point (now Scarborough, ME) before 1638, when the author John Josselyn came to visit his brother Henry, who was for many years a principal representative in eastern New England of the interests of the Mason and Gorges heirs, which were endangered by the Massachusetts Bay colony’s expansion into Maine. Their father was Sir Thomas Josselyn, of Torrell’s Hall in Willingale, Essex, England.
Boy/Male
Hindu
Lord Vishnu
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