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Exact(11)
That works out to a ratio of 0.9125 processing-rate dollars to each valuation dollar.
One may note that | n | ≤ 1 in each valuation field, every triangle is isosceles and there may be no unit vector in a non-Archimedean normed space; cf. [12].
Each valuation is translated into a bid (b_{1}) and (b_{2}) based upon an optimal bidding strategy that is determined from a Bayesian-Nash equilibrium for the resulting game (transaction between gas marketer and GFGs).
Table 2 Representing Boolean valuations by predicates V r has each valuation v such that V t has each valuation v such that Related Predicates w v) ⊕ z v) = 1 w v) ⊕ z v) = 0 B: B v) is True iff w v) ≠ z v) ~B: B v) is True iff w v) = z v) w v) ∨ z v) = 1 ~w v) ∧ ~ z v) = 0 B: B v) is True iff w v) ∨ z v) = 1 ~B: B v) is True iff ~ w((v) ∨ z v)) ≠ 1.
We would like to associate with each valuation \ v\) a mapping \(T_v\) from formulas of LPCR to truth values but since things like the liar sentence are formulable, \(T_v\) must be a partial function, and so we must be careful even about familiar things like propositional connectives.
That is, each valuation (omega _{j_{1},dots},j_{s,j_{N}}in Omega ') can be seen as the aggregation of partial valuations (omega _{j_{1}},dots,omega _{j_{N}}) over the disjunct sets of atomic propositions, A 1,…,A n, A n+1,…,A 2n, until A (N−1)n+1,…,A Nn.
Similar(48)
Subsequently, each particular valuation problem can be addressed by solving a suitable BSDE.
A formula such as πr² for the area of a circle of radius r describes infinitely many possible computations, one for each possible valuation of its variables.
Each partial valuation (omega _{j_{k}}) is a "translation" of (omega _{j_{k}}in Omega ) to the kth set of atomic propositions A (k−1)n+1,…,A (k−1)n+n.
When comparing each two valuation methods across groups, the laypersons give the most inconsistent valuations between methods.
The correlation between each two valuation methods per respondent group was plotted to visualize group clustering in valuations and to expose valuation tendencies per group-method combination.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com