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To determine the leak location, the mathematical formulation has been solved by the method of characteristics.
The mathematical formulation has revealed the relation between the distribution of energy in their spectra and their immunity to noise.
The proposed mathematical formulation has been developed based on a membrane superstructure, which mainly consists of SWRO, NF, and SPP as its primary synthesis units.
To achieve this goal, a mathematical formulation has been derived for change in a mode shape due to damage with damage parameters.
The mathematical formulation has been given and four simulation scenarios were proposed: two WiFi configurations with a different throughput requirement, one UMTS voice call scenario, and one LTE high-throughput scenario.
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Several methods have been proposed and corresponding mathematical formulations have been introduced in the literature during the last decades.
New sets of mathematical formulations have been derived to account for the impedance mismatch between the incidence and transmitter bars.
These mathematical formulations have been implemented in finite element code to predict the bone behaviour when an artificial fixation or prosthesis is implanted.
The different flamelet mathematical formulations have been tested and compared using well verified reference calculations obtained solving the set of the Full Transport Equations (FTE) in the physical space.
Starting with the general theory established in Kanatani (1984) of describing the directional distributions of orientations, mathematical formulations have been extended to address the directional distributions of vector-valued directional data, which is the most common data type being dealt with in micromechanical investigations.
Thus, the mathematical consistency of the inverse problem formulation has been guaranteed.
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