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On the existence of hyperplanes separating disjoint convex sets
In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space. There are several rather similar
Hyperplane_separation_theorem
Index of articles associated with the same name
Separation theorem may refer to several theorems in different fields. Fisher separation theorem (corporation theory) - asserts that the objective of a
Separation_theorem
Theorem on extension of bounded linear functionals
Hahn–Banach theorem is known as the Hahn–Banach separation theorem or the hyperplane separation theorem, and has numerous uses in convex geometry. The theorem is
Hahn–Banach_theorem
Firm"s investment decision is independent of its owners' consumption preferences
In Economics, the Fisher separation theorem asserts that the primary objective of a corporation will be the maximization of its present value, regardless
Fisher_separation_theorem
Theorem in portfolio theory
In portfolio theory, a mutual fund separation theorem, mutual fund theorem, or separation theorem is a theorem stating that, under certain conditions
Mutual fund separation theorem
Mutual_fund_separation_theorem
Theorem in topology
curve theorem was independently generalized to higher dimensions by H. Lebesgue and L. E. J. Brouwer in 1911, resulting in the Jordan–Brouwer separation theorem
Jordan_curve_theorem
Theorem on eigenvalues and eigenvectors of Hermitian matrices
In mathematics, the Poincaré separation theorem, also known as the Cauchy interlacing theorem, gives some upper and lower bounds of eigenvalues of a real
Poincaré_separation_theorem
Theorem in temporal logic
In mathematical logic and computer science, Gabbay's separation theorem states that any formula in linear temporal logic (LTL) with past operators can
Gabbay's_separation_theorem
Topics referred to by the same term
Mazur's theorem may refer to: Ascoli–Mazur theorem, or Mazur's theorem, a corollary of the Hahn–Banach separation theorem in functional analysis Mazur's
Mazur's_theorem
Mathematical theorem
mathematics, in the field of ordinary differential equations, Sturm separation theorem, named after Jacques Charles François Sturm, describes the location
Sturm_separation_theorem
For 2 disjoint analytic subsets of Polish space, there is a Borel set containing only one
In descriptive set theory and mathematical logic, Lusin's separation theorem states that if A and B are disjoint analytic subsets of Polish space, then
Lusin's_separation_theorem
Hyperplane in geometry
is the half-space that includes the points within the hyperplane. This theorem states that if S {\displaystyle S} is a convex set in the topological vector
Supporting_hyperplane
Topics referred to by the same term
Cauchy–Peano theorem in the study of ordinary differential equations Cauchy's limit theorem Cauchy's argument principle Poincaré separation theorem, also known
Cauchy_theorem
Topics referred to by the same term
Separation process, in chemistry Separation theorem (disambiguation): several different theorems related to separation, in different scientific disciplines
Separation
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
Polish mathematician (1910–1943)
the hyperplane separation theorem are also known (in German) as Trennungssatz von Eidelheit (Eidelheit separation theorem). A theorem on the solubility
Meier_Eidelheit
Manifold or algebraic variety of dimension n in a space of dimension n+1
into two connected components; this is related to the Jordan–Brouwer separation theorem. An algebraic hypersurface is an algebraic variety that may be defined
Hypersurface
Hyperplane separation theorem, the theorem that disjoint compact convex sets are linearly separable Watson, Donald (1973), "A refinement of theorems of Kirchberger
Kirchberger's_theorem
Concept in mathematical optimization
m\right\}} , the proof of the Karush–Kuhn–Tucker theorem makes use of the hyperplane separation theorem. The system of equations and inequalities corresponding
Karush–Kuhn–Tucker_conditions
Principle in quantum information theory
In physics, the no-communication theorem (also referred to as the no-signaling principle) is a no-go theorem in quantum information theory. It asserts
No-communication_theorem
American economist (1867–1947)
the Fisher hypothesis, the international Fisher effect, the Fisher separation theorem and Fisher market. Fisher was perhaps the first celebrity economist
Irving_Fisher
special case where both equations are identical one obtains the Sturm separation theorem. C. Sturm, Mémoire sur les équations différentielles linéaires du
Sturm–Picone comparison theorem
Sturm–Picone_comparison_theorem
Solvability theorem for finite systems of linear inequalities
possibilities. The closedness condition is necessary, see Separation theorem I in Hyperplane separation theorem. For original Farkas' lemma, S {\displaystyle \mathbf
Farkas'_lemma
Class of ordinary differential equations
we obtain that u ( x ) = 0 {\textstyle u(x)=0} everywhere. Sturm's Separation Theorem: If y 1 , y 2 {\textstyle y_{1},y_{2}} are linearly independent solutions
Sturm–Liouville_theory
of the above Mutual fund separation theorem - relating to the construction of optimal portfolios Fisher separation theorem - discussing an analogous
Separation_property_(finance)
Topics referred to by the same term
complement is also analytic is a Borel set, a special case of the Lusin separation theorem Any analytic set in Rn is the projection of a Borel set in Rn+1 Analytic
Suslin's_theorem
Topics referred to by the same term
end of jobs on a printer Separatrix (disambiguation) Separation (disambiguation) Separation theorem (disambiguation) Decimal separator Thousands separator
Separator
Poincaré–Miranda theorem Poincaré–Neumann operator Poincaré plot Poincaré polynomial Poincaré recurrence Poincaré residue Poincaré separation theorem Poincaré
List of things named after Henri Poincaré
List_of_things_named_after_Henri_Poincaré
Overview of finance and finance-related topics
theory – Mathematical framework for investment risk Mutual fund separation theorem – Theorem in portfolio theory Post-modern portfolio theory – Portfolio
Outline_of_finance
infinite-dimensional spaces, topological degree theory, Jordan separation theorem, Lefschetz fixed-point theorem) Morse theory and Lusternik–Schnirelmann category
Nonlinear_functional_analysis
Polygon that is the boundary of a convex set
corners of the polygon to recover the entire polygon shape. Hyperplane separation theorem: Any two convex polygons with no points in common have a separator
Convex_polygon
Technique for solving differential equations
applicability of separation of variables is a result of the spectral theorem. In some cases, separation of variables may not be possible. Separation of variables
Separation_of_variables
Academic discipline studying businesses and investments
investment under "certainty" (Fisher separation theorem, "theory of investment value", and Modigliani–Miller theorem). Here, theory and methods are developed
Finance
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Certain cohomology groups of coherent sheaves are separated
In mathematics, the Andreotti–Vesentini separation theorem, introduced by Aldo Andreotti and Edoardo Vesentini (1965, 1965b) states that certain cohomology
Andreotti–Vesentini_theorem
inequality Weyl's inequality in matrix theory Cauchy interlacing theorem Poincaré separation theorem Bonse's inequality Large sieve inequality Pólya–Vinogradov
List_of_inequalities
Method of determining minimum distance between two convex sets
if contains_origin: accept Minkowski Portal Refinement Hyperplane separation theorem Montanari, Mattia; Petrinic, Nik; Barbieri, Ettore (30 June 2017)
Gilbert–Johnson–Keerthi distance algorithm
Gilbert–Johnson–Keerthi_distance_algorithm
Sets with no element in common
the element and the index of the set that contains it. Hyperplane separation theorem for disjoint convex sets Mutually exclusive events Relatively prime
Disjoint_sets
Subspace of n-space whose dimension is (n-1)
space are separated by a hyperplane, a result called the hyperplane separation theorem. In machine learning, hyperplanes are a key tool to create support
Hyperplane
Square roots of the eigenvalues of the self-adjoint operator A* A
Kolmogorov width. Condition number Cauchy interlacing theorem or Poincaré separation theorem Schur–Horn theorem Singular value decomposition Tao, Terence (2012)
Singular_value
Dutch mathematician and logician
Brouwer proved a number of theorems in the emerging field of topology. The most important were his fixed point theorem, the topological invariance of
L._E._J._Brouwer
feedback loop. The proof of the following theorem can be found in Georgiou and Lindquist 2013. Separation theorem. Given the linear stochastic system d x
Separation principle in stochastic control
Separation_principle_in_stochastic_control
Surname list
Minkowski's theorem Minkowski's question mark function Abraham–Minkowski controversy Hasse–Minkowski theorem Minkowski separation theorem Smith–Minkowski–Siegel
Minkowski
Hypersurface used by a classification algorithm
decision boundary and data points. Discriminant function Hyperplane separation theorem Corso, Jason J. (Spring 2013). "Quiz 1 of 14 - Solutions" (PDF). Department
Decision_boundary
Concepts in convex analysis
smallest convex cone containing C (a consequence of the hyperplane separation theorem) A cone C in a vector space X is said to be self-dual if X can be
Dual_cone_and_polar_cone
Canadian physicist (1934–2023)
multivariable control with A. Stephen Morse. In 1968, Wonham proved a separation theorem for controls in a more general cost functional class with many technical
W._M._Wonham
Problem in financial theory
which underlies several other results in economics like the Fisher separation theorem. Feldstein and Horioka argued that if the assumption is true and there
Feldstein–Horioka_puzzle
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
Property for sets of functions
\mathbb {R} } or C , {\displaystyle \mathbb {C} ,} then the Hahn–Banach separation theorem implies that continuous linear functionals on X {\displaystyle X}
Separating_set
Branch of mathematical logic
are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast
Reverse_mathematics
Normed vector space that is complete
called a norming functional for x . {\displaystyle x.} The Hahn–Banach separation theorem states that two disjoint non-empty convex sets in a real Banach space
Banach_space
Italian computer scientist (1923–2017)
lambda calculus, he established an important separation theorem between normal forms, known as Böhm's theorem, which states that for every two closed λ-terms
Corrado_Böhm
Mathematical framework for investment risk
Marginal conditional stochastic dominance Markowitz model Mutual fund separation theorem Omega ratio Post-modern portfolio theory Sortino ratio Treynor ratio
Modern_portfolio_theory
Israeli logician (born 1945)
(age 80) Education Hebrew University (BSc, MSc, PhD) Known for Gabbay's separation theorem, foundations for non-monotonic reasoning in expert systems Awards
Dov_Gabbay
Theorem in functional analysis
This is a consequence of the hyperplane separation theorem, which is a consequence of the Hahn–Banach theorem. Now, define the dual vector e n ∈ V ∗ {\displaystyle
Auerbach's_lemma
Overview of corporate finance and corporate finance-related topics
securities Fisher separation theorem – Firm"s investment decision is independent of its owners' consumption preferences Modigliani–Miller theorem – Economic
Outline_of_corporate_finance
Pathological embedding of the sphere in 3D space
without passing through the surface. According to the Jordan-Brouwer separation theorem, any embedding of a 2-sphere into R 3 {\displaystyle \mathbb {R} ^{3}}
Alexander_horned_sphere
Complexity class used in circuit complexity
polynomial-size majority circuit of depth d + 1 {\displaystyle d+1} . As a separation theorem, it is known that the n {\displaystyle n} -input Boolean inner product
TC0
Process of selecting a portfolio
portfolio is not efficient Merton's portfolio problem Mutual fund separation theorem, giving a property of mean-variance efficient portfolios Portfolio
Portfolio_optimization
Geometric property of a pair of sets of points in Euclidean geometry
maximize their distance. Clustering (statistics) Hyperplane separation theorem Kirchberger's theorem Perceptron Vapnik–Chervonenkis dimension Boyd, Stephen;
Linear_separability
Scientific study of digital information
transmission is justified by the information transmission theorems, or source–channel separation theorems that justify the use of bits as the universal currency
Information_theory
Measure of covariance of components of a random vector
financial economics, especially in portfolio theory and its mutual fund separation theorem and in the capital asset pricing model. The matrix of covariances
Covariance_matrix
Matroid with no linear representation
1016/0095-8956(78)90080-1, MR 0485461. Bachem, Achim; Wanka, Alfred (1988), "Separation theorems for oriented matroids", Discrete Mathematics, 70 (3): 303–310, doi:10
Vámos_matroid
oscillation theory are: Kneser's theorem (differential equations) Sturm–Picone comparison theorem Sturm separation theorem Atkinson, F.V. (1964). Discrete
Oscillation_theory
Theorem in mathematical logic
It is evident from the proof how the theorem relies on the axiom of pairing as well as an axiom of separation, of which there are notable variations
Diaconescu's_theorem
French mathematician (1803–1855)
made a significant addition to equation theory with his work, Sturm's theorem. Sturm was born in Geneva, Switzerland in 1803. The family of his father
Jacques Charles François Sturm
Jacques_Charles_François_Sturm
Model particles in statistical mechanics
accurate integral equation theory for hard spheres: Role of the zero-separation theorems in the closure relation". The Journal of Chemical Physics. 103 (21):
Hard_spheres
Planar maps require at most four colors
to be meaningful, the intuitive statement of the four color theorem – "given any separation of a plane into contiguous regions, the regions can be colored
Four_color_theorem
American economist (born 1960)
among cash, bonds, and stocks is inconsistent with the mutual-fund separation theorem, which states that all investors should hold the same composition
David_N._Weil
spending. fiscal theory of the price level Fisher equation Fisher separation theorem fixed costs Costs that have to be paid even if a firm is not producing
Glossary_of_economics
French mathematician, physicist and engineer (1854–1912)
Poincaré–Lefschetz duality theorem: a version of Poincaré duality in geometric topology, applying to a manifold with boundary Poincaré separation theorem: gives the upper
Henri_Poincaré
– Financial instrument – Fiscal policy – Fisher equation – Fisher separation theorem – Forecasting – Fractional-reserve banking – Free good – Free-rider
Index_of_economics_articles
General principle for managing complexity through abstraction
The fundamental theorem of software engineering is a humorous observation, credited variously to Roger Needham or David Wheeler, to the effect that: Any
Fundamental theorem of software engineering
Fundamental_theorem_of_software_engineering
Process of producing small rectangular items of fixed dimensions
weight can be separated. See also: Geometric separator Hyperplane separation theorem Some recently studied variants of the problem include: Guillotine-cutting
Guillotine_cutting
Topics referred to by the same term
cemeteries and kevarim (gravesites) of Torah notables Math Gabbay's separation theorem, a term in mathematical logic and computer science, named after Dov
Gabbay
Nonlinear differential operator used to study conformal mappings
[ a i , a i + 1 ] {\displaystyle [a_{i},a_{i+1}]} . By the Sturm separation theorem, the non-vanishing of u 2 ( z ) {\displaystyle u_{2}(z)} forces λ
Schwarzian_derivative
Academic discipline concerned with the exchange of money
certainty", and usually framed in the context of a corporation. The Fisher separation theorem, asserts that the objective of the corporation will be the maximization
Financial_economics
Sums of sets of vectors are nearly convex
Shapley–Folkman theorem". Economic Theory. 3 (2): 371–372. doi:10.1007/bf01212924. ISSN 0938-2259. Starr, Ross M. (September 2009). "8 Convex sets, separation theorems
Shapley–Folkman_lemma
Both deterministic and nondeterministic machines can solve more problems given more space
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines
Space_hierarchy_theorem
Mathematical concept
to a given value of μ P {\displaystyle \mu _{P}} ; see Mutual fund separation theorem for details. Alternatively, the efficient set can be specified by
Multi-objective_optimization
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
Framework for corporate funding, capital structure, and investments
maximize or to continually increase shareholder value (see Fisher separation theorem). Here, the three main questions that financial managers addresses
Corporate_finance
American mathematician
from each of these domains. In his "A converse of the Jordan-Brouwer separation theorem in three dimensions" (1930), Wilder showed that a subset of Euclidean
Raymond_Louis_Wilder
Theorem regarding the existence of a solution to a differential equation
Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees
Peano_existence_theorem
"certainty" is initially considered (Fisher separation theorem, "theory of investment value", Modigliani–Miller theorem). Choice under uncertainty is then introduced
Master_of_Financial_Economics
Branch of ordinary differential equations
defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to Gaston Floquet (1883), gives a canonical form
Floquet_theory
Network or circuit of neurons
Modern development of concentration of measure theory (stochastic separation theorems) with applications to artificial neural networks give mathematical
Neural_circuit
consumption/saving decisions can be analyzed separately (see Fisher separation theorem). The main feature of financial markets that leads to imperfection
Capital_market_imperfections
Existence and uniqueness theorem for certain partial differential equations
the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential
Cauchy–Kovalevskaya_theorem
Brazilian mathematician (1929–2017)
(1987). "Orientability of smooth hypersurfaces and the Jordan-Brouwer separation theorem". Expositiones Mathematicae. vol. 5, pp. 283–286. Spectrum (topology)
Elon_Lages_Lima
exponent, then in the presence of a risk-free asset a two-fund monetary separation theorem results: every investor holds the available risky assets in the same
Hyperbolic absolute risk aversion
Hyperbolic_absolute_risk_aversion
Type of topological space
normal space equivalent?". Engelking, Theorem 2.1.6, p. 68 Munkres 2000, p. 213 Willard 1970, pp. 100–101. "separation axioms in nLab". ncatlab.org. Retrieved
Normal_space
Characterization of normal spaces by continuous functions
generalised by (and usually used in the proof of) the Tietze extension theorem. The lemma is named after the mathematician Pavel Samuilovich Urysohn.
Urysohn's_lemma
Statement on solutions to ordinary differential equations
existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows existence
Carathéodory's existence theorem
Carathéodory's_existence_theorem
seminorm. Geometrically, it is a generalization of the hyperplane separation theorem. Heine A topological vector space is said to have the Heine–Borel
Glossary of functional analysis
Glossary_of_functional_analysis
Theorem in quantum information science
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement
No-cloning_theorem
American mathematician (1926–2013)
functional analysis": "the main rule is the separation theorem (a.k.a. [also known as] the Hahn–Banach theorem): Like the standard advice given in mountaineering
Robert_Phelps
Theorem in quantum mechanics
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion)
Spin–statistics_theorem
Theorem in classical statistical mechanics
mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of
Equipartition_theorem
Theorem in set theory
In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there
Schröder–Bernstein_theorem
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