Sentence examples for presented analytically from inspiring English sources

The results are presented analytically in Table 3.

The expressions for the Rayleigh number for both stationary and oscillatory convection have been presented analytically in equations (28) and (29) respectively.

New properties of intersections and coincidences of transient concentration curves were discovered and are presented analytically using the classical consecutive mechanism A→B→C as an example.

In this paper, active control and dynamic analysis of shallow doubly curved functionally graded material (FGM) panels integrated with sensor/actuator piezoelectric layers are presented, analytically.

The conservation equations in light of lubrication approximation theory (LAT) are non-dimensionalized and solutions for the velocity, volumetric flow rate and pressure gradient are presented analytically using Adomian decomposition method.

Based on the PM-PM-HS/ID model, the dynamic response of an isothermal three-phase catalytic reactor with a first order reaction in uniform spherical catalyst particles was presented analytically.

The article carefully presents analytically solvable cases, such as the Ornstein Uhlenbeck process, as a foundation for perturbative approaches to nonlinear dynamics.

Table S1 in Additional file 1 presents the photovoltaic parameters obtained from the J-V characteristic curves (Figure S1 in Additional file 1) of the PMII-I2-PC electrolytes, while Figure 1 presents analytically the dependence of the cell parameters (V oc, ff, J sc and η) on the iodine concentration.

The advantage of mode selectivity of IDT over PZT patch is presented both analytically and experimentally.

A new method has been presented for analytically solving the Duffing-harmonic oscillator.

Estimates of the variance of the solution is presented both analytically and numerically.