Sentence examples for matrices and analytical from inspiring English sources

A 'scalar random phase' ensemble is defined in terms of random eigenvalues of the product ST of the scattering matrices, and analytical expressions are derived for the average and variance of the energy responses over this ensemble.

There are considerations for using each of these matrices and analytical techniques have been published in peer reviewed analytical journals, and successfully used in a number of studies investigating environmental and occupational exposure to benzene.

The weighted decision matrix and analytical hierarchy process was used to compare these concepts.

In Section 4, the sensitivity of these equalization techniques to RIR perturbations is evaluated by means of the condition number of the (weighted) convolution matrix and analytical insights on increasing the robustness by decreasing the reshaping filter length are provided.

Biological matrices, timing, and analytical methods of the measurements varied between cohorts.

The construction of higher order mass matrices and the analytical results for vibration frequencies are systematically demonstrated by a set of numerical examples.

The kinematics and dynamic modeling of the mechanical system of the stage are conducted by resorting to compliance matrix method, and analytical models for electromagnetic forces are also established, both mechanical structure and electromagnetic model are validated by finite element analysis FEA) performed with ANSYS.

Endogenous factors include ethnicity, gender, age and genetic polymorphisms whereas exogenous factors comprise medications, diet, matrix composition and analytical tools used for the quantification.

We investigate the uniqueness of the solution to the inverse problem through the use of the Hessian matrix and an analytical approach.

The correlation matrix, Σ K, is modeled according to the normalization of Lemma 1; thus, σ 1=1+K ρ and σ 2=σ 3=1. Figure 2 shows the impact of varying the number of received samples (N) while the SNR variation is considered in Fig. 3. Results show a perfect match between the empirical SCN distribution of the central semi-correlated Wishart matrix and the analytical form in Section 5.

Constraining the G-matrix has computational and analytical advantages: fewer parameters results in more robust estimates and lower computational requirements (Kirkpatrick and Meyer 2004).