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In addition, we obtain some stochastic properties for consecutive 2-within-m-out-of-n systems consisting of components satisfying the proportional hazard rate model.
Microbes in industrial bioreactors generally encounter nutrient media that contain a spectrum of components satisfying various nutritional requirements with individual substrates playing roles that may be viewed as substitutable, complementary or combinations of the two to varying extents.
This process can be also applied to other components satisfying (x_{i}^{ k^{prime prime }+1)}+1).
In this case, a group sparse vector can be divided into groups of components satisfying (a) only a few of groups contain nonzero values and (b) these groups are not needed to be sparse.
By means of the corresponding auxiliary equations, we obtain a sequence of unbounded components via Rabinowitz's global bifurcation theorem [8], and this enables us to find unbounded components satisfying (1.11).
In other words, the basis functions are built by summing up components which are multiples of the same periodicity q, and only components satisfying (p, q) = 1 contribute to the sum.
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Thus the Gaussian mixture model can be estimated in the feature space with each component satisfying multivariate Gaussianity.
Indeed, it suffices to show the existence of such a component satisfying { ( μ, 0 ) } ∈ K μ ν ¯.
Additionally, we show that our approach corresponds to a micro-macro decomposition of the model, where the macro field corresponds to the incompressible component satisfying a perturbed low Mach number limit equation and the micro field is the potential component of the velocity.
By means of the corresponding auxiliary equations, we obtain a sequence of unbounded components via Rabinnowitz's global bifurcation theorem [10], and this enables us to find an unbounded component satisfying (1.10).
In a computer procedure, α k in (6) is obtained by searching in the set { β, β ρ, β ρ 2 …, } such that α k is the largest component satisfying (6), where ρ ∈ ( 0, 1 ) and β > 0 are given constant scalars.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com