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Proof From the proof of Observation 2 we know that (h, l | h ) ≽ (h, h | h ) requires E β a (π c ) > V − P h and γ ⩾ (P h − P l ) / [ E β a (π c ) − V + P h ] ⩾ 1, where the last inequality follows from E β a (π c ) ⩽ V − P l ∀ β a.
Beliefs and theories are possibly true depending on how rational they are whereas knowledge and facts are definitely true based on the proof of observation and experience.
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Based on the observations from the proof-of-concept implementation, we extend WirelessHART services in this section to support deterministic and periodic downlink transmissions to allow actuators and safety protocols more efficiently.
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