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The proposed friction coupling formulation produces an asymmetric system stiffness matrix that yields a set of complex conjugate eigenvalues.

The computed similarity scores for each conformer pair were stored with the translation/rotation matrix that yields the corresponding alignment.

Thus, by choosing λ appropriately, we construct either an admissible matrix that yields a higher secondary rate or a matrix yielding the same secondary rate, and such that (40c) is satisfied with equality.

The paper proposes a novel factorization technique for static condensation of a spectral-element discretization matrix that yields a linear operation count of just 13N multiplications for the residual evaluation, where N is the total number of unknowns.

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The weighted G matrices that yielded the overall best accuracies were those informed with realized marker effects from Ridge Regression and Bayesian LASSO, while discriminating markers based on their P-value led to average or null improvement of predictive performance.

To simulate enrichment over a repetitive element, we specified a transition state probability matrix that yielded more frequent occupancy of the high emission state for their coordinates.

Linearization about ((0,0,0)) yields a matrix that has double zero eigenvalue and a negative eigenvalue, (-1/tau).

Estimation is conducted by employing a continuous-time finite-state Markov chain approximation that yields probability elements on matrix exponentiation of the transition rate matrix.

A mathematical argument in favor of the hexahedral element is that the volume defined by one element must be represented by at least five tetrahedral elements, which in turn yields a system matrix that is computationally more expensive.

Inserting the weights to the matrix in Fig. 2a yields the distance matrix that makes it easier to calculate many analysis functions that are important such as clustering coefficient, degree distribution, the distance matrix created in Fig. 3 is an appropriate way to represent the dataset and make it much more uncomplicated and simpler to analyze the dataset and to visualize it.

The data matrix thus obtained was then normalized by using the DPFT and subsequently factorized using the SISAL algorithm to yield a mixing matrix that contains the end-member signatures and an abundance matrix, rows of which were reshaped to yield relative abundance maps for the end-members as shown in Fig. 4. The relative abundance maps for the end-members constitute the NMF FLIM features.

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