Sentence examples for methods and elementary from inspiring English sources

By using variational methods and elementary analysis, the conditions for the existence of positive and negative solutions to a nonlinear system are given.

Impaired diastolic function can be detected using a simple method and elementary echocardiography equipment [ 35, 66, 67].

The target field of application of this method is DNS and LES but this paper focuses on the method development and elementary test cases.

Most of them, both in 2D and 3D, share a common approach, using numerical data to manage geometric knowledge and elementary methods to compute derived objects.

Remark 2 In this section, we prove Theorem 1 by using a simple and elementary method, which is slightly different from the proof method in [14].

Our methods are elementary and use only symmetry arguments via the representations of the symmetry group of the set.

The mode II initiation fracture toughness of wood measured from the three-point bend end notched flexure (3-ENF) test was analyzed by the eight conventional analysis methods: the elementary and Timoshenko's beam theory methods, three of the Williams end correction methods, two compliance calibration methods, and the crack shear displacement (CSD) measurement method.

We shall show how to motivate affine coordinates and affine transformations, fractal curves and iterated function systems, relaxation methods and subdivision schemes from elementary notions in turtle geometry and turtle programming.

By applying some elementary methods and techniques, we establish some combinatorial identities for the ( p, q ) -Fibonacci and Lucas polynomials.

By applying elementary methods and techniques, we establish some symmetric identities for these numbers and polynomials, by virtue of which, various known results are derived as special cases.

In this paper, we shall use the elementary methods and estimate for character sums to study this problem, and prove the following conclusion.