Sentence examples for optimal systems of from inspiring English sources

For this reason the development of optimal systems of radiation safety ensuring (RSES) acquires especial importance.

In order to demonstrate the classification of the group invariant solutions, Ovsiannikov put forward the concept of optimal systems of subalgebras of a Lie algebra [2].

The optimal systems of these vector fields contain the following sub-algebras: ( i ) V 2 + a 3 V 1, where a 3 is an arbitrary constant.

In this paper we firstly perform symmetry reductions of (1) using Lie group analysis [19] [24], which are based on the optimal systems of one-dimensional subalgebras.

Then this method extended to many examples of optimal systems of subgroups for the Lie group of mathematical physics models by Winternitz et al. [31, 32].

Similarity reductions and exact solutions, with the aid of the simplest equation method, were obtained based on optimal systems of one-dimensional subalgebras for the underlying system.

The integrated automation system consisting of production process management system, optimal system of production indices and process control system is established for the optimization of production indices of minerals processing.

Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained.

Designing an optimal system of fans, filters, and chambers is a difficult task and requires some trade-offs.

Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions.

In this subsection we present an optimal system of one-dimensional subalgebras for the system (1.1a) and (1.1b) to obtain an optimal system of group-invariant solutions.