This extra g multiplier is not essential for any of the results we derive here.
We derive here a consistent approximation for the viscous Navier Stokes equations using variable size vortex particles.
Because there is only one instance of pipe damage, the set of fragility functions we derive here are for individual WTPs and not pipe networks.
Following the same theoretical frame, we derive here an Eulerian diffuse interface model for elastic solid-compressible fluid interactions in situations involving extreme deformations.
Optimal stimulus frequency for the A-optimality criterion has been derived by Liu et al. (2004) whereas we derive here the optimal stimulus frequency for the D-optimality criterion.
Now we derive here some our obvious results of the unique existence and smoothness with respect to time variable of the weak solution of the problem (2.1)–(2.3) as lemmas of main results.
Despite the case considered in Sections 2, 3 is more general, we derive here conditions of the solvability in detail since the corresponding transformations are based on the properties of operators and spaces as applied to the case under consideration.
As mentioned above, we encounter several times throughout the paper the random variables Z = V|(V < U) and Q = V - U|(V > U) for any two arbitrary random variables V and U. We derive here the statistics of these two random variables.
It has previously been shown how a HNN can be used to decoded one balanced code at a time, but the HNN MLSE decoder we derive here is able to simultaneously decode any number of concatenated codewords in order to provide the ML transmitted sequence of codewords.
Since the energy method can be applied only to star-shaped domains, we derive here some crucial estimates of solutions for the case of small diffusion equations and extend the adapted method of comparison to sign-changing solutions on any bounded domains.
