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More generally, if sm ∼ tn is false, then sm+k ∼ tn+k is false for all k ≥ 0. Formulas in the language of the typed theory with ∈ and ∼ have a monotonicity property: if φ is a generalized positive formula and one of its typed versions is false, then any version of the same formula obtained by raising types and refining the values of free variables in the formula will continue to be false.
By refining the values of a star's motion, the mass and orbital boundaries for possible planets are tightened: in this way astronomers are often able to describe what types of planets cannot orbit a given star.
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This further refined the values of k d and t e but resulted in the marginally reduced value of E idx.
The Gradient Descent method was used to refine the values of the five significant parameters from the values quoted in the literature.
The recalibration of the Cepheid period-luminosity relationship also helped to refine the value of Hubble's constant, which measures the rate at which the universe is expanding.
Additional theoretical investigations are necessary to refine the value of C d, and this is an active research area within the CS community.
Section 7.3 shows that failure to refine the value of b can lead to an apparent breakdown in the valence sum rule if the parameters are used uncritically.
In 1911, he refined the value to 1/192.
Addition of MPTD may help to refine the prognostic value of the current staging system for NPC and assist with treatment strategy selection.
However, more efforts are required to refine the prognostic value of SALP by different age, especially among preadult patients.
In the refining method, the value of OV's threshold T is set as 0.6, while the average co-active rate in the known protein complexes is larger than 0.5.
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