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In the model, stochastic stress process is interpreted by the random distribution of stress amplitude and cycles at given amplitude, and randomness of fatigue resistance of material is described by introducing a random variable of single cycle fatigue damage.
By introducing a random normal error data sets with typical experimental variance were generated.
In this paper, the supercritical carbonation process of cement-based materials is modelled by introducing a random porosity field to simulate the heterogeneous geometry of the carbonation profile.
By introducing a random iteration process with weak contraction random operator, we obtain a convergence theorem of the random iteration process to a random fixed point for nonexpansive random self-mappings.
This was quite drastic for node degree 4. From this figure, we can observe that success rate in this modified slotted Aloha-based control channel is indirectly proportional to the latency that the nodes are allowed to carry, i.e., by introducing a random delay in selection of the next slot for transmission, packet delivery ratio is considerably high.
By introducing a random variable, f t, that represents the index of the most relevant stream at time t, we can rewrite b i (o t ) as: b i ( o t ) = ∑ j = 1 M Pr ( e t = j | q t = i ; λ ) ∑ k = 1 L Pr ( o t | q t = i, e t = j, f t = k ; λ ) Pr ( f t = k | q t = i, e t = j ; λ ).
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Similarly, one might improve the flow of information through the Internet by introducing a few random links between backbone computers on the Internet, he said.
Using these model networks as the basis, one may generate novel networks by introducing a few random links whereby the local properties are preserved while the desired global properties are approximated.
To take into account the correlation between the siblings, we used multilevel models for the analyses, introducing a random effect shared by the siblings into the regression models.
The model decouples the correlation between ĉ and e by introducing a new uncorrelated random variable (RV) z, c = a ĉ + z, (3).
In what follows, we prefer summarizing this testing problem by introducing a Bernoulli distributed random variable ϵ t,f), valued in {0,1}, independent of Θ t,f) and S n ( t, f ), but defined on the same probability space, so as to write that S x ( t, f ) = ϵ ( t, f ) Θ ( t, f ) + S n ( t, f ).
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