Sentence examples for by utilizing the equations from inspiring English sources
This is illustrated by utilizing the equations to derive expressions for the electromagnetic fields generated by systems in which current pulses injected by lightning flashes are propagating.
Formation of potential tetrahedral blocks has been algebraically discerned by utilizing the plane equations of discontinuities.
The investigations are made by utilizing the exact equations of linear viscoelasto-dynamics.
The investigations are carried out within the framework of the piecewise homogeneous body model by utilizing the exact equations of motion and relations of the linear theory of electro-elasticity.
By utilizing the above equation, MTBF can be expressed as a function based on fuzzy numbers.
We found that the density, hardness, and secondary dendrite arm spacing responses could be obtained by utilizing the nonlinear regression equations and the same set of process variables.
In both cases, stabilizing controllers are explicitly constructed by utilizing the parametric Lyapunov equation based low gain design approach we recently developed.
To grasp the in-depth dynamics of the system damping, an analytical modeling of the SFD of both rocking and bending modes is performed by utilizing the modified Reynolds equation.
Under the assumption that each agent is asymptotically null controllable with bounded controls and there exists at least one leader that has directed path to each followers, both state feedback and output feedback control protocols are designed by utilizing the algebraic Riccati equation.
By utilizing the designed auxiliary dynamic equations for state estimation, the proposed sliding mode controller is able to drive the state's trajectory towards a designated sliding surface in finite time and achieve asymptotic stability.
RQs were calculated with SDS software supplied by the manufacturer (Applied Biosystems), utilizing the equation RQ = 2-ΔCt [ 43], where Ct is the number of cycles at which the sample reaches a software-determined threshold within the exponential amplification phase.
