In mathematics, the bipolar theorem is a theorem in functional analysis that characterizes the bipolar (that is, the polar of the polar) of a set. In convex...

a star Bipolar coordinates, a two-dimensional orthogonal coordinate system Bipolar set, a derivative of a polar set Bipolar theorem, a theorem in convex...

Banach–Alaoglu theorem, setting τ {\displaystyle \tau } to the Weak-* topology. That 1. implies 2. is an application of the Bipolar theorem. Let M {\displaystyle...

{\displaystyle f^{**}\leq f} . This can be seen as a generalization of the bipolar theorem. It is used in duality theory to prove strong duality (via the perturbation...

and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of...

_{c\in C}\langle c,y\rangle .} Banach–Alaoglu theorem – Theorem in functional analysis Bipolar theorem – Theorem in convex analysis Polar cone – Concepts in...

-closure of the convex balanced hull of A . {\displaystyle A.} The bipolar theorem: The bipolar of A , {\displaystyle A,} denoted by A ∘ ∘ , {\displaystyle A^{\circ...

cone C in X, the polar cone is equivalent to the polar set for C. Bipolar theorem Polar set Schaefer & Wolff 1999, pp. 215–222. Boyd, Stephen P.; Vandenberghe...

Cone (disambiguation) Cone (geometry) Cone (topology) Farkas' lemma Bipolar theorem Ordered vector space Boyd, Stephen; Vandenberghe, Lieven (2004-03-08)...

that are compact (and thus complete) but not closed. The bipolar theorem states that the bipolar (that is, the polar of the polar) of a subset of a locally...

only if S is an orthonormal basis; i.e., maximal orthonormal set. bipolar bipolar theorem. bounded A bounded operator is a linear operator between Banach...

the setting of the DC operating point of an electronic component. For bipolar junction transistors (BJTs), the operating point is defined as the steady-state...

∘ = H ∘ ∘ = H {\displaystyle U^{\circ }=H^{\circ \circ }=H} by the bipolar theorem, it follows that a continuous linear functional f {\displaystyle f}...

more numerous than the natural numbers. Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal...

Burma Pharmaceutical Industry, a pharmaceutical brand name in Myanmar Bipolar I disorder Brachial plexus injury, an injury to the nerves that conduct...

Atlas, Homma, and Marks. "An Artificial Neural Network for Spatio-Temporal Bipolar Patterns: Application to Phoneme Classification" (PDF). Neural Information...

acyclic orientation with a single source and a single sink is called a bipolar orientation. A transitive orientation is an orientation such that the resulting...

family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. They were discovered by Apollonius of Perga, a renowned ancient...

orientations of complete graphs are called transitive tournaments. The bipolar orientations are a special case of the acyclic orientations in which there...

applied to the design of one-way road networks. According to Robbins' theorem, the graphs with strong orientations are exactly the bridgeless graphs...

vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy...

Khazanov was reported missing in June 2001. He suffered from depression or bipolar disorder at the time of his disappearance. Born to Anna and Leonid Khazanov...

sources are useful, for example, in modeling the behavior of amplifiers. A bipolar junction transistor can be modeled as a dependent current source whose...

load. Modern semiconductor switches such as MOSFETs or insulated-gate bipolar transistors (IGBTs) are well suited components for high-efficiency controllers...

No. 35 on the Top Independent Albums chart. Townsend was diagnosed with bipolar disorder around 1998, a condition that was unknowingly exacerbated by his...

or I2L) is a class of digital circuits built with multiple collector bipolar junction transistors (BJT). When introduced it had speed comparable to...

possible circles that pass through both foci. These circles form the basis of bipolar coordinates. The circles of Apollonius of a triangle are three circles...

communication, the field of information theory (in particular, the Shannon–Hartley theorem) motivates the need for studying the signal-to-noise ratio (SNR). In a...

diode Schottky diode Avalanche diode Laser diode DIAC Thyristor Transistor Bipolar transistor (BJT) Field effect transistor (FET) Darlington transistor IGBT...

non-concentric circles can be aligned with the circles of a system of bipolar coordinates. In that case, the radical axis is simply the y {\displaystyle...