For a link a∈A¯ with a speed limit s¯a (s¯a≤La/ta#), the mean link travel time t˜a(va) is a piecewise function in terms of link flow, consisting of three pieces of functions in the domains of [0,vaL], (vaL,vaU), and [vaU,+∞): (5)t˜a(va)={La/s¯...
This extension has been designed in the spirit of symbolic manipulation sys- tems, i.e., we have tried to nd an algorithm which can easily be implemented in today's computer algebra systems. Although a very pragmatic approach is used for this extension, it turns out that many functions can...
where εi and εf are the electron initial and final energies before and after each dipolarization/injection, εmin is the low energy threshold above which acceleration dominates over losses, and g(ε) is a piecewise function in the following form: (2)where Bzi and Bzf are the initial ...
(x), we can derive many general laws of limits, that help us to calculate limits quickly and easily. The following rules apply to any functions f(x) and g(x) and also apply to left and right sided limits: Suppose that c is a constant and the limits lim x→a f(x) and lim x→...
The method of interpolation used was a “shape-preserving piecewise cubic interpolation”, provided by the MATLAB/GNU Octave function interp1 with method “pchip”. Computations were performed in MATLAB R2015b with the script plot_BV_BB_script.m from the .zip archive which supplements this work...