The state equation-based method is useful, in general, with relatively small number of equations making it easier to generalize the solutions.
If you unnaturally extend or generalize cloud solutions to me, or if you pontificate cloud idealisms without providing tangible platforms that can service what I am, then you waste my time.
Since this article can be considered as an attempt to generalize this solution methodology to general wireless communication and networking problems it is instructive to close this introduction by reviewing the derivation of the waterfilling solution.
Lions's publications include Generalized Solutions of Hamilton-Jacobi Equations (1982), Stochastic Differential Systems, Stochastic Control Theory, and Applications (1988; coedited with Wendell Fleming), and Mathematical Topics in Fluid Mechanics (2 vols., 1996 98).
They might then extend that understanding to mathematics more generally (by increasing the level of abstraction of their mental models) and consequently, see how these solutions also connect to everyday math-related situations (generalize their solution strategies and/or models in order to transfer them to other situations; e.g., math classes, science classes, or even everyday life).
Inverse ductility and hardening/softening indexes have been introduced as dimensionless parameters to generalize the solution to all elastic-plastic-hardening and softening systems.
Furthermore, we generalize our solution for the case of multiple production sections on the wellbore for both well testing and Wireline formation tester packer modules.
The current solutions extend and generalize the recent solutions of two-dimensional equilibrium dispersive transport model (EDM).
and they established the general solution and generalized Hyers-Ulam-Rassias stability problem for this functional equation.
In this paper, we investigate the general solution and generalized Hyers-Ulam stability for a new two-variable Jensen functional equation of the following form: 2 F ( x + u 2, y + v 2 ) = F ( x, y ) + F ( u, v ) x, y, u, v ∈ X, Open image in new window (2).
