The remainder of this paper is organized as follows: Section 2 describes the classical approach for GFDM modulation and demodulation and introduce reformulated expressions for a less complex implementation.
In this paper, we firstly reformulate the expressions of concordance and discordance indices for use in the MCDM problems with dependent criteria, especially prioritized criteria, based on the concepts of fuzzy measures and digraphs respectively.
After QR decomposition, the reformulated mathematical expression of (1) can be presented as follows: mathbf{z}=mathbf{R}mathbf{s}+tilde{mathbf{v}}, (2).
To achieve this, we introduce group majority signals similar to group propagate and generate signals in parallel prefix computations, use them to reformulate the carry expressions of a previous radix-4 FA, and as such we could extend it to higher radix FAs.
When it is reformulated with the true expression for the slope replacing x/r, the solution (which involves quite heavy mathematics) shows a variation of period with amplitude that has been rigorously verified.
This result allowed us to reformulate the ergodic sum capacity expression as a concave function, and the corresponding optimal power policies were derived by using a probabilistic power allocation technique.
B. burgdorferi indeed takes advantage of this and vigorously modifies its surface lipoprotein expression to constantly reformulate its overall surface antigenic architecture during its enzootic life cycle traveling between the tick vector and a mammal, and during the course of mammalian infection.
The Kocks Mecking theory is reformulated by finding a new expression for the recovery rate term.
When the ultrasonic pulse propagates deep within material ( -axis), then, it was demonstrated in [4] that for an attenuation law of the form (with, or ), the previous expression can be reformulated as (2).
With further manipulations, expression (12) can be reformulated as.
The following lemma reformulates the maximum-delay reduction problem in a more tractable form: The on-line decoding delay reduction problem (2) can be reformulated by the following more tractable expression: (3).
