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Provides conditions for a parametric optimization problem to have continuous solutions
The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The
Maximum_theorem
Theorem in electrical engineering
In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a power source with internal resistance
Maximum power transfer theorem
Maximum_power_transfer_theorem
Equivalence of optimization problems
science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink
Max-flow_min-cut_theorem
On bipartite matching and vertex cover
mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem and the minimum
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Theorem that tells the maximum rate at which information can be transmitted
In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified
Shannon–Hartley_theorem
On graph coloring and neighborhood size
theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected
Brooks'_theorem
Mathematical theorem in complex analysis
mapping theorem, which states that a nonconstant holomorphic function maps open sets to open sets: If | f | {\displaystyle |f|} attains a local maximum at
Maximum_modulus_principle
Theorem in convex analysis
In convex analysis, Danskin's theorem is a theorem which provides information about the derivatives of a function of the form f ( x ) = max z ∈ Z ϕ ( x
Danskin's_theorem
Largest and smallest value taken by a function at a given point
the extreme value theorem, global maxima and minima exist. Furthermore, a global maximum (or minimum) either must be a local maximum (or minimum) in the
Maximum_and_minimum
respects with those given in a discussion of the maximum-flow minimum-cut theorem. Cederbaum's theorem applies to a particular type of directed graph:
Cederbaum's maximum flow theorem
Cederbaum's_maximum_flow_theorem
Continuous real function on a closed interval has a maximum and a minimum
the maximum and minimum values of f {\displaystyle f} on the interval [ a , b ] , {\displaystyle [a,b],} which is what the extreme value theorem stipulates
Extreme_value_theorem
Extremal graph theory bound on clique-free graph edges
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given
Turán's_theorem
corresponding eigenvalue λ. The Courant minimax principle is a result of the maximum theorem, which says that for q ( x ) = ⟨ A x , x ⟩ {\displaystyle q(x)=\langle
Courant_minimax_principle
Method of estimating the parameters of a statistical model, given observations
Indeed, the maximum a posteriori estimate is the parameter θ that maximizes the probability of θ given the data, given by Bayes' theorem: P ( θ ∣ x
Maximum_likelihood_estimation
Solution concept of a non-cooperative game
have strategies. Condition 2. and 3. are satisfied by way of Berge's maximum theorem. Because u i {\displaystyle u_{i}} is continuous and compact, r ( σ
Nash_equilibrium
Mathematical method
selection theorem Zero-dimensional Michael selection theorem Robert Aumann measurable selection theorem Blaschke selection theorem Maximum theorem Border
Selection_theorem
On the existence of hyperplanes separating disjoint convex sets
the supporting hyperplane theorem. In the context of support-vector machines, the optimally separating hyperplane or maximum-margin hyperplane is a hyperplane
Hyperplane_separation_theorem
Theorem in statistics
variance, while the Fisher–Tippet–Gnedenko theorem only states that if the distribution of a normalized maximum converges, then the limit has to be one of
Fisher–Tippett–Gnedenko theorem
Fisher–Tippett–Gnedenko_theorem
Study of mathematical algorithms for optimization problems
The extreme value theorem of Karl Weierstrass states that a continuous real-valued function on a compact set attains its maximum and minimum value. More
Mathematical_optimization
About maxima and minima of functions
titled Maxima et minima a method to find maximum or minimum, similar to the modern interior extremum theorem using an approach he called adequality. After
Interior_extremum_theorem
All derivatives have the intermediate value property
theorem. Because φ ′ ( a ) = f ′ ( a ) − y > 0 {\displaystyle \varphi '(a)=f'(a)-y>0} , we know φ {\displaystyle \varphi } cannot attain its maximum value
Darboux's_theorem_(analysis)
Theorem in mathematics and economics
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization
Envelope_theorem
Theorem in graph theory
discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that
Menger's_theorem
Computational problem in graph theory
severing s from t) in the network, as stated in the max-flow min-cut theorem. The maximum flow problem was first formulated in 1954 by T. E. Harris and F.
Maximum_flow_problem
Mathematical rule for inverting probabilities
Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting conditional probabilities
Bayes'_theorem
On coloring the edges of graphs
Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree
Vizing's_theorem
Limit on data transfer rate
of information theory. Stated by Claude Shannon in 1948, the theorem describes the maximum possible efficiency of error-correcting methods versus levels
Noisy-channel_coding_theorem
Theorem in real analysis
derivative is zero. The theorem is named after Michel Rolle. The theorem is a special case of, and is used to prove, the mean value theorem. If a real function
Rolle's_theorem
Results about asymptotic posterior normality
In Bayesian inference, the Bernstein–von Mises theorem provides the basis for using Bayesian credible sets for confidence statements in parametric models
Bernstein–von_Mises_theorem
On chains and antichains in partial orders
order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an antichain of incomparable elements
Dilworth's_theorem
Theorem in complex analysis
In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Concept of complex analysis
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions
Residue_theorem
Planar maps require at most four colors
In mathematics, the four color theorem, or the four-color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
Uniqueness theorem in complex analysis
The theorem may be obtained from the Phragmén–Lindelöf theorem, which is itself an extension of the maximum-modulus theorem. Carlson's theorem is typically
Carlson's_theorem
Mathematical propositions in network flow theory
In graph theory, approximate max-flow min-cut theorems concern the relationship between the maximum flow rate (max-flow) and the minimum cut (min-cut)
Approximate max-flow min-cut theorem
Approximate_max-flow_min-cut_theorem
Complete, full information, perfectly competitive markets are Pareto efficient
obtain the maximum satisfaction subject to buying and selling at a uniform price'. Edgeworth took a step towards the first fundamental theorem in his 'Mathematical
Fundamental theorems of welfare economics
Fundamental_theorems_of_welfare_economics
Theorem in extremal set theory
Ahlswede–Khachatrian theorem generalizes the Erdős–Ko–Rado theorem to t-intersecting families. Given parameters n, k and t, it describes the maximum size of a t-intersecting
Ahlswede–Khachatrian_theorem
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Upper bound on intersecting set families
In mathematics, the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common.
Erdős–Ko–Rado_theorem
Concept in mathematical optimization
global maximum or minimum over the domain of the choice variables and a global minimum (maximum) over the multipliers. The Karush–Kuhn–Tucker theorem is sometimes
Karush–Kuhn–Tucker_conditions
On the existence of a continuous selection of a multivalued map from a paracompact space
selection theorem is a selection theorem named after Ernest Michael. In its most popular form, it states the following: Michael Selection Theorem—Let X be
Michael_selection_theorem
Complements of perfect graphs are perfect
perfect graph theorem states: The complement of a perfect graph is perfect. Equivalently, in a perfect graph, the size of the maximum independent set
Perfect_graph_theorem
Second theorem in extreme value theory
Unlike the first theorem (the Fisher–Tippett–Gnedenko theorem), which concerns the maximum of a sample, the Pickands–Balkema–de Haan theorem describes the
Pickands–Balkema–De Haan theorem
Pickands–Balkema–De_Haan_theorem
Theorem in complex analysis
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard
Cauchy's_integral_theorem
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
Existence and uniqueness of solutions to initial value problems
known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard,
Picard–Lindelöf_theorem
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Impossibility result for ranked-choice voting systems
The Gibbard–Satterthwaite theorem is a theorem in social choice theory. It was first conjectured by the philosopher Michael Dummett and the mathematician
Gibbard–Satterthwaite_theorem
Statement in mathematical combinatorics
In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)
Ramsey's_theorem
Mathematical inequality
mathematics, Bernstein's theorem is an inequality relating the maximum modulus of a complex polynomial function on the unit disk with the maximum modulus of its
Bernstein's theorem (polynomials)
Bernstein's_theorem_(polynomials)
Theorem in computational complexity theory
In computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity
PCP_theorem
Characterizes the height of any finite partially ordered set
and to the Erdős–Szekeres theorem on monotonic subsequences. The height of a partially ordered set is defined to be the maximum cardinality of a chain,
Mirsky's_theorem
Description of degree sequences of graphs
The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph
Erdős–Gallai_theorem
Microeconomic function
contradicts the optimality of x 1 , x 2 {\displaystyle x_{1},x_{2}} . The maximum theorem implies that if: The utility function u ( x ) {\displaystyle u(x)}
Marshallian_demand_function
Theory and paradigm of statistics
Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem describes the conditional probability
Bayesian_statistics
Theorem
equioscillation theorem concerns the approximation of continuous functions using polynomials when the merit function is the maximum difference (uniform
Equioscillation_theorem
French mathematician (1926–2002)
among the first to emphasize min-max theorems and LP-duality in combinatorics. He is also known for his maximum theorem in optimization and for Berge's lemma
Claude_Berge
Theorem in complex analysis
circles. The theorem follows by choosing the constant a so that this harmonic function has the same maximum value on both circles. The theorem can also be
Hadamard_three-circle_theorem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Statement in complex analysis
z_{1}} . The Schwarz–Ahlfors–Pick theorem provides an analogous theorem for hyperbolic manifolds. De Branges' theorem, formerly known as the Bieberbach
Schwarz_lemma
Mathematical theorem
groups were considered. Wedderburn's theorem is stated as an exchange property between direct decompositions of maximum length. However, Wedderburn's proof
Krull–Schmidt_theorem
Provides integral formulas for all derivatives of a holomorphic function
{f(z)}{z-a}}\,dz.} The proof of this statement uses the Cauchy integral theorem and like that theorem, it only requires f {\displaystyle f} to be complex differentiable
Cauchy's_integral_formula
Characterization of the size of a maximum matching in a graph
is a characterization of the size of a maximum matching in a graph. It is a generalization of Tutte's theorem on perfect matchings, and is named after
Tutte–Berge_formula
Perfect graphs have neither odd holes nor odd antiholes
bipartite graphs, are both equivalent to Kőnig's theorem relating the sizes of maximum matchings, maximum independent sets, and minimum vertex covers in
Strong_perfect_graph_theorem
Calculation of complex statistical distributions
(Ergodic Theorem). And we need aperiodicity, irreducibility and extra conditions such as reversibility to ensure the Central Limit Theorem holds in MCMC
Markov_chain_Monte_Carlo
Graph with tight clique-coloring relation
important minimax theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem on partially ordered sets, Kőnig's theorem on matchings, and
Perfect_graph
Theorem in complex analysis
Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle
Borel–Carathéodory_theorem
Topics referred to by the same term
Jacobi's theorem can refer to: Maximum power theorem, in electrical engineering The result that the determinant of skew-symmetric matrices with odd size
Jacobi's_theorem
Mathematical function that preserves angles
complex analytic functions. In three and higher dimensions, Liouville's theorem sharply limits the conformal mappings to a few types. The notion of conformality
Conformal_map
Theorem in linear algebra
In matrix theory, the Perron–Frobenius theorem, proved in its first part by Oskar Perron (1907) and extended by Georg Frobenius (1912), asserts that a
Perron–Frobenius_theorem
Theorem on holomorphic functions
function f {\displaystyle f} is open. Maximum modulus principle Rouché's theorem Schwarz lemma Open mapping theorem (functional analysis) Rudin, Walter
Open mapping theorem (complex analysis)
Open_mapping_theorem_(complex_analysis)
In graph theory, Berge's theorem states that a matching M in a graph G is maximum (contains the largest possible number of edges) if and only if there
Berge's_theorem
Principle in Bayesian statistics
that Bayes' theorem and the principle of maximum entropy are completely compatible and can be seen as special cases of the "method of maximum relative entropy"
Principle_of_maximum_entropy
Study of rates of change
calculus is to find maxima and minima of functions. Fermat's theorem implies that an interior maximum or minimum of a differentiable function can occur only
Differential_calculus
Zeta-like functions approximate arbitrary holomorphic functions
a theorem that generalizes the Riemann series theorem to a Hilbert space setting. Because of a relationship between the norm in H and the maximum absolute
Zeta_function_universality
Sequences of convex sets in a bounded set have convergent subsequences
The Blaschke selection theorem is a result in topology and convex geometry about sequences of convex sets. Specifically, given a sequence { K n } {\displaystyle
Blaschke_selection_theorem
Physics theorem
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete
Virial_theorem
Theorem about the range of an analytic function
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after
Picard_theorem
American applied mathematician
analysis by developing generalizations of Fatou's lemma and Berge's maximum theorem. Feinberg has also worked on applications including electric grid forecasting
Eugene_A._Feinberg
Theorem in economics
Coase theorem (/ˈkoʊs/) postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant
Coase_theorem
Chinese-American economist
Journal on Optimization, 2(3), 360–375. Tian, G., & Zhou, J. (1992). The maximum theorem and the existence of Nash equilibrium of (generalized) games without
Guoqiang_Tian
Functions in mathematics
analytic; they have a maximum principle and a mean-value principle; a theorem of removal of singularities as well as a Liouville theorem holds for them in
Harmonic_function
Mathematical result or axiom on order relations
A proof of equivalence of Zorn's lemma, the well-ordering theorem, and Hausdorff's maximum principle Halmos, Paul (1960). Naive set theory. Princeton
Hausdorff_maximal_principle
Theorem of thermodynamics of non-equilibrium processes
Prigogine's theorem is a theorem of non-equilibrium thermodynamics, originally formulated by Ilya Prigogine. The formulation of Prigogine's theorem is: In
Prigogine's_theorem
On coloring infinite graphs
extend from finite to infinite graphs the theorem that, whenever a graph has an orientation with finite maximum out-degree k {\displaystyle k} , it also
De Bruijn–Erdős theorem (graph theory)
De_Bruijn–Erdős_theorem_(graph_theory)
Number of connected components an algebraic curve can have
In real algebraic geometry, Harnack's curve theorem, named after Axel Harnack, gives the possible numbers of connected components that an algebraic curve
Harnack's_curve_theorem
Second-order partial differential equation
{\displaystyle u} is harmonic in D {\displaystyle D} , then the divergence theorem implies the compatibility condition ∫ ∂ D ∂ u ∂ ν d S = 0. {\displaystyle
Laplace's_equation
Mathematical theorem in complex analysis
theorem is a mathematical theorem in complex analysis, discovered by the British mathematician Mary Cartwright. It gives an estimate of the maximum modulus
Cartwright's_theorem
Mathematical theorem
In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number
Riemann_mapping_theorem
Theorem in combinatorics
}(G)=\chi '(G).} By Kőnig's edge-coloring theorem the chromatic index of a bipartite multigraph equals its maximum degree, so χ ℓ ′ ( G ) = Δ ( G ) {\displaystyle
Dinitz_theorem
American mathematician (1943–2024)
implicit function theorem, and many authors have attempted to put the logic of the proof into the setting of a general theorem. Such theorems are now known
Richard_S._Hamilton
Topics referred to by the same term
perpendiculars on triangle sides In physics: Carnot's theorem (thermodynamics), setting a maximum efficiency obtainable from a heat engine Carnot cycle
Carnot's_theorem
Statistical theorem
Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used to produce confidence intervals for maximum-likelihood
Wilks'_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Graph coloring with equal color classes
Hajnal–Szemerédi theorem, posed as a conjecture by Paul Erdős (1964) and proven by András Hajnal and Endre Szemerédi (1970), states that any graph with maximum degree
Equitable_coloring
Interpretation of probability
sequential use of Bayes' theorem: as more data become available, calculate the posterior distribution using Bayes' theorem; subsequently, the posterior
Bayesian_probability
DC circuit analysis technique
law Millman's theorem Source transformation Superposition theorem Thévenin's theorem Maximum power transfer theorem Extra element theorem Mayer, Hans Ferdinand
Norton's_theorem
Derivation of the laws of probability theory
Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. This
Cox's_theorem
Theorem in physics
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with
Bell's_theorem
Theorem about zeros of holomorphic functions
Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region K {\displaystyle
Rouché's_theorem
MAXIMUM THEOREM
MAXIMUM THEOREM
Boy/Male
Latin
Greatest.
Boy/Male
Italian American
The greatest.
Boy/Male
Arabic, French, Muslim
Lucky
Boy/Male
Latin
Greatest.
Male
Spanish
Spanish form of Latin Maximus, MÃXIMO means "the greatest."
Boy/Male
American, Australian, Chinese, Danish, French, German, Latin, Swedish
The Greatest; Form of Maximilian; Great; The Greatest Rival
Boy/Male
Indian
Auspicious, Prosperous
Boy/Male
Arabic
Trusting
Boy/Male
Russian American
The greatest.
Boy/Male
American, Australian, Chinese, French, German, Greek, Latin, Swedish
Greatest
Girl/Female
Arabic, Muslim
Increase; Excess; High Degree; Maximum; Feminine of Mazid
Girl/Female
Latin
The best.
Boy/Male
African, Arabic
Far
Male
French
French form of Latin Maximus, MAXIME means "the greatest."Â
Boy/Male
Muslim
Auspicious, Prosperous
Boy/Male
Latin French
Greatest.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sanskrit
Plenty; Maximum; Intelligent; Young and Dynamic; Earth
Male
Italian
Italian form of Latin Maximus, MASSIMO means "the greatest."
Boy/Male
American, Australian, French, Latin
Greatest
Male
Russian
(МакÑим) Variant spelling of Russian Maksim, MAXIM means "the greatest." Compare with another form of Maxim.
MAXIMUM THEOREM
MAXIMUM THEOREM
Girl/Female
Muslim
Premature daughter. First wife of Prophet Muhammad.
Female
Croatian
, strawberry.
Boy/Male
Indian, Malayalam
Rays of Sun
Girl/Female
Hindu
The meaning of Kiranila means the Love stands forever in the world
Boy/Male
Celtic Scottish
Rock.
Boy/Male
Indian
One who prays times and fasts, Forever, Immortal
Boy/Male
Afghan, Arabic, Celebrity, Indian, Kashmiri, Muslim, Parsi
Power of Discrimination; Happy; Fortunate
Girl/Female
Hindu, Indian
Way of Life
Girl/Female
Hindu, Indian, Tamil
Half of Siva; Money
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Luminous
MAXIMUM THEOREM
MAXIMUM THEOREM
MAXIMUM THEOREM
MAXIMUM THEOREM
MAXIMUM THEOREM
a.
Sententious; uttering or containing maxims, or striking detached thoughts; aphoristic.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.
n.
A brief reflection or maxim.
n.
A self-registering thermometer, especially one that registers the maximum and minimum during long periods.
n.
The greatest quantity or value attainable in a given case; or, the greatest value attained by a quantity which first increases and then begins to decrease; the highest point or degree; -- opposed to minimum.
pl.
of Maximum
pl.
of Minimum
n.
The longest note formerly used, equal to two longs, or four breves; a large.
n.
An established principle or proposition; a condensed proposition of important practical truth; an axiom of practical wisdom; an adage; a proverb; an aphorism.
n.
Minimum.
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
v. t.
A saying; a proverb; a maxim.
n.
A sewer; as, the Cloaca Maxima of Rome.
n.
An elementary principle or maximum; a short, proverbial rule, in law, ethics, or metaphysics.
n.
A popular maxim, adage, or proverb.
n.
The opinions and maxims of the Stoics.
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
n.
Fundamental principle; axiom; maxim.
n.
A coarse umbelliferous plant of Europe (Tordylium maximum).
n.
A proposition; a maxim.