Sentence examples for derived with the aid from inspiring English sources

Governing equations are derived with the aid of Lagrange's equations.

The equations of motion are derived with the aid of Lagrange's equations.

The governing differential equations and related boundary conditions are derived with the aid of minimum total potential energy principle.

The coupling equation of elastic modulus, shear modulus and first-order torsional frequency of cantilever plate was derived with the aid of energy method.

Then, the integrated design schemes of L2 observer-based fault detection systems are derived with the aid of Hamilton Jacobi inequalities (HJIs), respectively.

In this section, the Newell-Whitehead equation, NLS equation, and Fisher equation with degree three are considered again and the exact solutions are derived with the aid of Eq. (2).

Thus, we derive with the aid of Lemma 5.4 by writing H λ in place of A that a = ( a n ) ∈ { c 0 λ ( B ˜ ) } α = { c λ ( B ˜ ) } α iff sup K ∈ F ∑ n | ∑ k ∈ K h n k λ | < ∞.

Furthermore, a kinetic model for pyrolysis and combustion of MTHF was developed, which contains a detailed description of the reactions of MTHF and its derived radicals with the aid of new high-level theoretical calculations.

The imaged exit airway flow rate fractions are derived from regional ventilation with the aid of a three-dimensional (3D) and one-dimensional (1D) coupled airway tree that connects the airways to the alveolar tissue.

Indeed, it would seem that we can derive (ID-EX) with the aid of (ID).

In the frame of IVDTRS, we then focus on deriving three-way decisions with the aid of two conventional methods, i.e., a certain ranking method and a degree of possibility ranking method, respectively.