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Random walks obeying this transition probability matrix are shown to guarantee the following: For any graph, (b) the hitting time is O(n2), and (c) the cover time is O(n2logn).
The remarkable thermal stability of the ordered-mesoporous alumina structure (along 40 h of run) along with the stabilization of well-dispersed Ni0 within the alumina matrix are shown to be key factors accounting for the excellent long term catalytic performances in spite of the harsh conditions (temperature and steam) imposed by the reaction.
In the case of Laplace's equation in a two-dimensional disk-like domain with linear boundary elements and associated three-node linear finite elements, the eigenvalues of this matrix are shown to cluster around zero as the discretization level is raised, which means that the corresponding eigenvectors representing boundary waves are rapidly removed up to the working spatial resolution.
The average overall sparsity and column sparsity of the eigenphone matrix are shown in parentheses.
The eigenvalues obtained by performing SVD on the three covariance matrix are shown in Fig. 4.
where the source matrix and the direction matrix are shown as follows (4).
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An approximate payoff matrix is shown below.
The glassy matrix is shown to form viscoelastic ligaments.
The interactor matrix is shown to be a useful tool for multivariable controller design.
Pull-out behaviour from concrete matrix is shown to be slip softening and sensitive to loading rate and embedment length.
3 6, the resulting matrix is shown in Table 9.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com