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The finite cardinalities of level sets of the Takagi function
Takagi function Nowhere-differentiable function Level set Self-similarity Takagi expansion
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2011/8/25
Abstract: Let T be Takagi's continuous but nowhere-differentiable function. It is known that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. We show that the mos...
Parent formulation at the Lagrangian level
Parent formulation Lagrangian level
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2011/3/2
The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the pare...