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The known proofs on the symmetric Fock space make essential use of the Nevanlinna Pick properties.
To overcome this difficulty, we make essential use of the concept of two-scale Young measures for algebras with mean value, associated with bounded sequences in L2.
Our proofs make essential use of techniques based on a logarithmic Sobolev inequality, Rosen's inequality (proved via a new Fenchel Young inequality), and a very precise asymptotic formula due to Hartman and Wintner.
Many traditional definitions of epistemic justification make essential use of other evaluative epistemic terms.
As the (sparse) mixing operation of network coding finds natural connection to low-density parity-check (LDPC) codes, both make essential use of the LDPC coding structure.
This criticism of the scientific and philosophical use of certain ordinary terms goes along with rejection of philosophical questions which make essential use of those terms.
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The core of Cohen's method of proof the celebrated method of forcing was vastly more general than any previous technique; nevertheless his independence proof also made essential use of permutation and symmetry in essentially the form in which Fraenkel had originally employed them.
Foucault is, then, right: psychiatric practice makes essential use of moral (and other evaluative) judgments.
The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor.
The new calculus is termed the λσβ0-calculus, since it makes essential use of an extension of β0-unification (described in another paper).
"Not only can this procedure be repeated any finite number of times, it can also be iterated into the transfinite". Feferman investigated how far into the transfinite such progressions could be carried, and established fundamental completeness and incompleteness results for them, depending on the way that they are generated; these results made essential use of his work on arithmetization.
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