In particular, transmission electron microscopy and diffraction measurements from tensile tests show that the nitrogen addition decreases the calculated matrix stacking fault energy and enhances both deformation-induced martensite transformation at room temperature and deformation twinning at elevated temperature.
Due to fine channels between the γ′ particles, coupled with a low γ matrix stacking fault energy, the a/2〈1 1 0〉 matrix dislocations dissociate into a/6〈1 1 2〉 Shockley partials, which were commonly observed to be decorrelated from one another, creating extended intrinsic stacking faults in the γ matrix.
In this case, we will denote the stacked N g ×1 outcome vector as y g and the N g ×K matrix stacking node-level vectors of covariates for graph g as X g.
w y (G, Y) is an (left (sum _{g=1}^{M}{N_{g}}times Rright)) matrix stacking the (1×R) node-level vector of network statistics that vary at the node or network level and that may be interacted with Y22.
(tilde {boldsymbol {X}}=left (tilde {boldsymbol {X}}_{1}^{prime },tilde {boldsymbol {X}}_{2}^{prime },ldots,tilde {boldsymbol {X}}_{M}^{prime }right)^{prime }), where (tilde {boldsymbol {X}}_{g}=(boldsymbol {X}_{g},boldsymbol {omega }_{g})) is a matrix stacking together the network-level matrices of exogenous explanatory variables and (own) network statistics of interest.
where vec are the columns of a matrix stacked into a column vector and the L 2×L matrix (mathbf {C} = left [operatorname {vec}left {mathbf {a}_{1} mathbf {a}_{1}^{mathrm {H}}right }, hdots, operatorname {vec}left {mathbf {a}_{L} mathbf {a}_{L}^{mathrm {H}}right }right ]).
Finally, we introduce notation for vectors and matrices stacking together the network-level outcome vectors, covariate matrices and adjacency matrices for all networks in the data.
The algorithm supports additional types of potentials, such as position-specific scoring matrices, stacked residue-pairs (Waldispühl et al., 2008a), and chemical propensities (Miyazawa and Jernigan, 1985), although these are not used here.
Performance matrices including stack electrical efficiency, system electrical efficiency, thermal efficiency, and CHP efficiency are presented.
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