Sentence examples for expressions of the first from inspiring English sources

For a class of fifth degree nilpotent system, the shortened expressions of the first eight quasi-Lyapunov constants are presented.

Explicit expressions of the first and second order derivatives of natural frequencies and eigenvectors with respect to the configuration parameters are derived by differentiating the eigenvalue equation.

Two numerical examples have been selected to illustrate the application and the utility of the derived expressions of the first- and second-order eigensensitivities.

In the inverse eigenvalue problem, variations of natural frequencies caused by changes of multiple design variables are approximated using the first and second order Taylor series expansions, which are based on explicit expressions of the first and second order derivatives of natural frequencies and eigenvectors with respect to the configuration parameters.

Immunohistochemistry results indicated that the expressions of the first three proteins were upregulated in liver cancer tissues, but the expression of the last one was downregulated, compared with normal liver tissues.

In resting adult muscle, Wnt5a, Wnt5b, Wnt7a and Wnt4 are expressed, and the expression of the first three Wnts increases in the early phase of muscle injury.

On basis of an analytical phase expression with an explicit significance, the expressions of the second-, third- and approximate fourth-order phases at the central wavelength are presented with only independent variables.

The highest expression of the first category is the "mysticism of infinity" that is characteristic of the higher aspects of Hindu and Buddhist religious experience.

The same pattern again and again: everything out of nothing, from halting ignorance to a mode of expression of the first order.

The expression of the first two mechanisms, taking into account the blockage due to adsorption of an organic vapour on membrane pore wall, was developed before.

In the expression of the first conditional probability in terms of the second conditional probability, however, there occur certain quantities, known as the "Bayesian prior probabilities".