Sentence examples for by using the algebraic from inspiring English sources

The results are compared with those obtained by using the algebraic polynomials as trial functions and the 3-D finite element solutions, respectively.

As applications, we also present some new upper bounds on the Estrada index for general graphs, bipartite graphs, trees and planar graphs, some of which improve the known results obtained by using the algebraic techniques.

Remark In the past few years, a number of upper bounds on the Estrada index of graphs have been established by using the algebraic techniques (see, for example, [10, 11, 14, 16]).

As applications, in Section 3 we present some new upper bounds on the Estrada index for general graphs, bipartite graphs, trees, and planar graphs, which improve some known results obtained by using the algebraic techniques.

By using the algebraic state space representation of disturbed BN, some necessary and sufficient criteria are obtained to ensure the global robust stability with respect to (w.r.t). a fixed point or w.r.t. a limit cycle.

Firstly, by using the algebraic form of the master slave system, a new Boolean control network (BCN) is constructed and an algorithm is given to find core input-state cycles of the newly constructed BCN.

By using the differential-algebraic system theory and bifurcation theory, the dynamic behaviors of the proposed model system with and without discrete time delay are investigated.

By using the differential-algebraic system theory and bifurcation theory, dynamic behavior of the proposed model system with and without discrete time delay is investigated.

(Chou 1987) proves over 500 geometry theorems using the algebraic approach offered by Wu's method and the Gröbner basis method by representing hypotheses and conclusions as polynomial equations.

We show that by using the eigenvalue theorem in Algebraic Geometry, a numerical method can be developed to design a superconducting cable satisfying a predetermined current distribution.

By using the method, one obtains linear algebraic equations instead of nonlinear algebraic equations.