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In general, any measurable function can be pushed forward. The push-forward then becomes a linear operator, known as the transfer operator or Frobenius–Perron operator.In finite spaces this operator typically satisfies the requirements of the Frobenius–Perron theorem, and the maximal eigenvalue of the operator corresponds to the invariant measure.
Let : be a smooth map of smooth manifolds. Given , the differential of at is a linear map : from the tangent space of at to the tangent space of at (). The image of a tangent vector under is sometimes called the pushforward of by .
Similarly, if is a smooth function on an open set in , then the same formula defines a smooth function on the open set (). (In the language of sheaves , pullback defines a morphism from the sheaf of smooth functions on N {\displaystyle N} to the direct image by ϕ {\displaystyle \phi } of the sheaf of smooth functions on M {\displaystyle M} .)
Blackman's theorem is a general procedure for calculating the change in an impedance due to feedback in a circuit. It was published by Ralph Beebe Blackman in 1943, [1] was connected to signal-flow analysis by John Choma, and was made popular in the extra element theorem by R. D. Middlebrook and the asymptotic gain model of Solomon Rosenstark.
WASHINGTON (Reuters) -President-elect Donald Trump said on Saturday the U.S. should not be involved in the conflict in Syria, where rebel forces are threatening the government of President Bashar ...
is known as Campbell's formula [2] or Campbell's theorem, [1] [12] [13] which gives a method for calculating expectations of sums of measurable functions with ranges on the real line. More specifically, for a point process N {\displaystyle N} and a measurable function f : R d → R {\displaystyle f:{\textbf {R}}^{d}\rightarrow {\textbf {R ...
The builders of Tehaleh, a development that will include up to 9,700 homes south of Bonney Lake, chose to pay a $768,588 fee instead of building the 711 low-income units that Pierce County ...
Financial guru Dave Ramsey continues to stir controversy, advising that many think only the wealthy are equipped for it. This time, it's his 8% retirement rule. On an episode of "The Ramsey Show ...