Sentence examples for solution of random from inspiring English sources

This paper addresses the numerical solution of random crack propagation problems via response surface and direct coupling methods.

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms.

By employing the generalized harmonic transformation and equivalent nonlinearization technique, established here is a semi-analytical solution of random response for nonlinear vibration energy harvesters subjected to Gaussian white noise excitation.

G(x│y can be approximated using the solution of random walk model below.

Herein, we combine the differential co-expression study with stochastic process model by using the solution of random walk model to approximate the condition probability of correlations.

The first strand cDNA was synthesized from 2.7  μg of total RNA in a 30  μl reaction mixture containing 5  μl 5 × RT reaction buffer (BRL, Gaithersburg, MD, USA), 200  μ M dNTP, 100  μ M solution of random hexadeoxynucleotide mixture, 50 units of Rnasin (Promega, Madison, WI, USA), 2  μl of 0.1  M dithiothreitol, and 100 U of Molony leukaemia virus RT (BRL).

Section 4 contains existence results for solutions of random quasi-variational inequalities with random fuzzy mappings.

Sections 3 and 4 are devoted to proving the existence and uniqueness of solutions of random equations defined on fixed domains which are transformed from time-varying domains.

Further, by using the generalized regularized gap function we obtain global error bounds of solutions of random generalized variational inequalities with and without a Lipschitz continuity assumption.

Remark 1 The above theorem can be compared with Theorem 5 in [34] which states an existence result for the solutions of random quasi-variational inequalities in case that A i : ∏ i ∈ I X i → 2 X i is upper semicontinuous for each ω ∈ Ω and i ∈ I.

By using a generalized regularized gap function we calculated global error bounds, i.e., upper estimates on the distance to the solution set of random generalized variational inequality problems, which is one of the useful applications of gap functions.