Sentence examples for by utilizing the continuity from inspiring English sources

Based on the solutions, linear algebraic equations about the state variables only at the inner and outer spherical surfaces are derived by utilizing the continuity conditions at each interface.

On utilizing the continuity property of the norm we also have (2.5).

Then by utilizing the boundary and continuity conditions of the pile soil system, the dynamic response of the pile is obtained in a closed form in the frequency domain.

However, Dan Flavin gave continuity to his precedents practices by utilizing the light emitting object itself.

Pursue further research by utilizing the Internet.

Meanwhile, existence results of solutions are established by utilizing boundedness, continuity, monotonicity, nonnegative of Mittag-Leffler function (A_{alpha,beta}(w)), (alpha,betain(1,2)), (win R), and fixed point methods.

By utilizing resources, including.

(However, the origin of metric fixed point theory for a single mapping without continuity requirement can be traced back to Kannan [36].) Recently, Pant et al. [37] and Pant and Bisht [38] generalized the notion of reciprocal continuity by introducing weak reciprocal continuity and conditionally reciprocal continuity and utilized the same to obtain some common fixed point theorems.

We have previously characterized the reliability of utilizing cortical continuity and fracture lines in the assessment of fracture healing [ 72].

We utilized the simple asymptotic method with continuity correction to calculate the 95%% confidence intervals for proportions.

Note that the function (3.16). is continuous on by the continuity of on and the continuity of.