We start with two basic results that will prove useful when proving more complex theorems.
However, the numerical simulations show that the dynamic behavior of model (4.1) will become more complex if the conditions of Theorem 3.2 are unsatisfied (see Figure 3).
The techniques of the proof of our theorems are more complex then in the corresponding previously published articles, since a new technique was necessary for the considered class of mappings.
Although the condition ( H 1 ′ ) in Theorem A (Theorem 3.1 is[9]) isatisfieded, it is more complex to check the condition |Γ t)| > θ, ∀t ∈ [0, ω] in Theorem A than to test Γ t) > 0, ∀t ∈ [0, ω].
For more complex statements, such as van der Waerden's theorem or Kruskal's theorem, intuitionistic validity is not so straightforward.
The model is chosen to provide an intermediary description between perfect plasticity, for which general minimum theorems are already known, and more complex and realistic creep constitutive relationships involving internal state variable.
To enhance the efficiency of the proposed scheme when treating more complex nonlinear systems, we then derive an iterative algorithm based on Girsanov's theorem on the change of measure, which features importance sampling.
Additionally, our degenerated assumptions for the existence theorem equal to (A 1 -(A 4) in [2], the more complex assumption (A 5) [2] is not necessary.
Some relatively recent approaches include more complex Bayesian networks (Quang et al [ 24]) where conditional and joint probabilities of responses using Bayes theorem may compute posterior probabilities of each EQ-5D-5L response and consequently the expected utilities [ 24].
Putting this into Bayes's theorem, the probability that a person testing positive is actually infected, PrE(H), is PrE(H) = (0.25 × 0.95)/[ 0.25 × 0.95) + (0.75 × 0.004)] = 0.988 Applications of Bayes's theorem used to be limited mostly to such straightforward problems, even though the original version was more complex.
