For example, one can derive the length $s$ of the shadow cast by a flagpole from the height $h$ of the pole and the angle θ of the sun above the horizon and laws about the rectilinear propagation of light.
Our main contribution relative to their work is to derive the length scale from the data, to directly state and investigate conjecture (1), and to relate the predictability of the next location to psychological factors.
An analytical model based on the fracture process zone ahead of the crack tip was used to examine the size effect and to derive the length of fracture process zone cf and size-independent constant KIf.
Although we have derived the effective length for the noise only data, our results reveal that this effective window length gives accurate results for the signal plus noise case.
In more detail, denoted by W the actuator weight, we derived the maximum length beyond which the ratio falls below a desired threshold σ, so that actuation might cease to be effective.
By using the matrix geometric method, they derived the stationary queue length distribution and mean system size.
Since Murotani et al. (2008) did not consider the aspect ratio of the rupture area, we derived the relation between length L (m) and width W (m) of the fault as L=0.1650{W}^{1.239} (4).
Thus, by counting linker lengths appearances in the 5000 sampled configurations we derived the sampled linker lengths distribution, plotted in Figure 2. Next, we collected all mono-nucleosome reads out of the sampled configurations, generating the sampled mono-nucleosome positioning data of the cell population.
It is better to derive the code length from the stationary distribution of the random walker on the nodes and links rather than measuring the code length of a long walk and dividing by the number of steps.
The modified dynamic Elsasser number is given by solid, starred markers in Fig. 2; here, (Lambda _{d}^) has been modified compared to Eq. 11 to include the pre-factor derived from the length scale calculations (Eq. 17): Lambda_{d}^ = 0.77 Lambda_{i} Rm^{-1/2}.
