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・ Bipolar Disorders (journal)
・ Bipolar electric motor
・ Bipolar electrochemistry
・ Bipolar encoding
・ Bipolar I disorder
・ Bipolar II disorder
・ Bipolar Integrated Technology
・ Bipolar junction transistor
・ Bipolar nebula
・ Bipolar neuron
・ Bipolar orientation
・ Bipolar outflow
・ Bipolar signal
・ Bipolar spectrum diagnostic scale
・ Bipolar Sunshine
Bipolar theorem
・ Bipolar transistor biasing
・ Bipolar violation
・ Bipolaris
・ Bipolaris cactivora
・ Bipolaris cookei
・ Bipolaris incurvata
・ Bipolaris sacchari
・ Bipolarity
・ Bipolaron
・ Bipont Editions
・ Bipop Carire
・ Biporispora
・ BIPP
・ Bippen


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Bipolar theorem : ウィキペディア英語版
Bipolar theorem
In mathematics, the bipolar theorem is a theorem in convex analysis which provides necessary and sufficient conditions for a cone to be equal to its bipolar. The bipolar theorem can be seen as a special case of the Fenchel–Moreau theorem.
== Statement of theorem ==
For any nonempty set C \subset X in some linear space X, then the bipolar cone C^ = (C^o)^o is given by
:C^ = \operatorname(\operatorname \)
where \operatorname denotes the convex hull.〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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