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So, we give an example of a hydrodynamic system having, generally, a large number degrees of freedom, which behaves like a small-sized stochastic system heavily dependent on fluctuations, even far from the point of bifurcation.
Noticing that inequality (1) is a homogeneous kernel of degree −1, in 2009, a survey of the study of Hilbert-type inequalities with the homogeneous kernels of negative number degrees was given by [4].
The plateau-patella angle was designed [ 26] to yield an absolute number (degrees) rather than a ratio, and for consistency, was the only method used here.
Significance of model fit and random factors was assessed with likelihood ratio tests (LRT), testing the difference in the −2 log likelihood between hierarchal models against a chi-square distribution with number degrees of freedom equal to the difference in number of estimated terms [ 67].
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This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency.
The role of the contact angle of the droplet is investigated as a function of Reynolds number, degree of subcooling and characteristic of used cooled surface (substrate).
The effects of the number, degree and location of the openings on the maximum distortion and recovering rate of the plate are analysed.
The fundamental spectral properties such as the diameter, girth, maximum and minimum degree, chromatic number, clique number, degree sequence, irregularity index and dominating number for this new graph are presented in [1].
In this paper, we mainly obtain some certain values for the diameter, girth, maximum and minimum degree, chromatic number, clique number, degree sequence, irregularity index and domination number of the graph Γ ( S M ).
In this paper, the diameter, girth, maximum and minimum degrees, domination number, chromatic number, clique number, degree sequence, irregularity index and also perfectness of Γ ( S M ) have been established.
The main purpose of this article is to establish a half-discrete inequality with the mixed homogeneous kernel of real number degree.
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