Separation theorem may refer to several theorems in different scientific fields.
Economics
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Fisher separation theorem
In economics, the Fisher separation theorem asserts that the primary objective of a corporation will be the maximization of its present value, regardless of the preferences of its shareholders. The theorem therefore separates management's "product ...
(corporation theory) - asserts that the objective of a corporation will be the maximization of its present value, regardless of the preferences of its shareholders.
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Mutual fund separation theorem (portfolio theory) states that, under certain conditions, any investor's optimal portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the number of mutual funds is smaller than the number of individual assets in the portfolio.
Mathematics
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Gabbay's separation theorem (mathematical logic and computer science) states that any arbitrary temporal logic formula can be rewritten in a logically equivalent "past → future" form.
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Planar separator theorem
In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into smaller pieces by removing a small number of vertices. Specifically, the removal of verti ...
(graph theory) states that any planar graph can be split into smaller pieces by removing a small number of vertices.
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Lusin's separation theorem (descriptive set theory) states that for any two disjoint analytic subsets of a Polish space there is a Borel subset containing one but disjoint from the other.
Geometry
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Hyperplane separation theorem
In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in ''n''-dimensional Euclidean space. There are several rather similar versions. In one version of the theorem, if both these sets are closed and at least one ...
- either of two theorems about disjoint convex sets in n-dimensional Euclidean space. Also known as: Separating axis theorem.
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Geometric separator A geometric separator is a line (or another shape) that partitions a collection of geometric shapes into two subsets, such that proportion of shapes in each subset is bounded, and the number of shapes that do not belong to any subset (i.e. the shape ...
theorems - theorems regarding the existence of lines separating objects in the plane without harming too many of them.
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Guillotine separation theorems - theorems regarding the possibility of separating objects in the plane using guillotine-cuts.
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