Thus in by the (generalized) Lebesgue Theorem, and (2.12) follows.
Thus, in this paper, the generalized sidelobe canceler (GSC) structure is used, which can be thought as an updating rule of the equivalent problem without constraints.
Thus, in many realizations of a generalized 2-state system (generalized spin (hat {sigma }_{z})), there is a "natural" choice of such states [14].
We thus consider generalized solutions in Krasowskii and Filippov sense and guarantee that these solutions have a good behavior, i.e., when only s is acting (h = 0) the generalized solutions coincide with the optimal synthesis trajectories.
Thus, generalized reductions in stocking rates of cattle or elk populations were not warranted with respect to sustainability of meadows, and in fact increased numbers of both elk and cattle could be supported by current habitat conditions on LNF.
The normality was confirmed for the thickness difference; thus, a generalized linear model (GLM) procedure in R was used.
Thus in [3], a proof of the generalized Hyers-Ulam stability for the linear mapping between Banach spaces was obtained.
Thus in the theory of hypergeometric and generalized hypergeometric series, summation formulas and transformation formulas play an important role.
Thus in this work, we present a generalized design framework for IIR multiple notch filters whereby we aim to: a) deduce an improved design process of the all-pass filter-based method, b) maximize the availability of phase information of all-pass filter, and c) introduce selection mechanisms and weighting strategies to enable the unified representation of a family of all-pass filter-based methods.
Elevated blood pressure often results in generalized vascular disease (45), stroke (46) and dementia (47), and thus, it is a major risk factor for death.
