In the general case with three ionic species, an exact expression for the polarization curve is given in implicit form.
We address this issue by introducing a secondary elastic field to derive an exact expression that predicts linear reduction in thermo-elastic damping with respect to frequency.
For a system with damping but no disorder (i.e., identical oscillators), an exact expression for the rate of exponential spatial amplitude decay is retrieved.
We provide an exact expression for the magnetic field produced by cylindrical saddle-shaped coils and their ideal shield currents in the low-frequency limit.
Here, we derive an exact expression for the distribution of completion times for an arbitrary pathway with a finite number of states, using a recursive method to solve algebraically for the appropriate moment-generating function.
The problem of finding an exact expression for the perimeter of an ellipse led to the development of elliptic functions, an important topic in mathematics and physics.
The model allows an exact expression for the velocity field in the Stokes flow regime, apparently the first for a mixer with genuinely moving parts, which permits accurate numerical tracking of material interfaces.
Sufficient conditions which can guarantee the stability of the control system are obtained by applying Lyapunov stability theory, and the design method of the controller gain is presented in an exact expression.
In this article we provide an exact expression for computing the autocorrelation coefficient ξ and the autocorrelation length ℓ of any arbitrary instance of the Quadratic Assignment Problem (QAP) in polynomial time using its elementary landscape decomposition.
Given a set of predetermined expansion points, an exact expression for the error between the output moment of the original system and that of the reduced-order system, related to each expansion point, is derived first.
For a linear survey estimator, the estimation of its design-based standard error for a simple probability sample design is straightforward and involves obtaining an exact expression of the true design-based variance and then estimating the true design-based variance by a design-based unbiased estimator.
