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Of course, this function does not satisfy the additivity equation everywhere.
The phase of the extremal function does not satisfy this requirement because of the logarithmic term.
Note that the solution is nontrivial since the zero function does not satisfy the ODE.
In fact we prove limit formulas which contain three terms, and the weight function does not satisfy condition (1.6).
In particular, under the first approach the value function does not satisfy the dynamic programming principle and thus does not provide a representation for the PPDE.
It is shown that the norm of the Morlet wavelet function does not satisfy the normalization condition and that the normalized Morlet wavelet function is identical to the Gabor wavelet function with the parameter σ=1.
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Unfortunately, the interesting case of OFDMA and log-throughput user utility functions does not satisfy the constraints.
But f, g, θ being nonzero functions do not satisfy ( G M f f g g ).
For more consistency, we next show how certain discrete Mittag-Leffler functions do not satisfy the above mentioned semigroup property.
Subsequently, we develop a Discontinuous Spectral Method (DSM) of Petrov Galerkin sense for the aforementioned FIVPs and FFVPs, where the basis functions do not satisfy the initial/final conditions.
We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com