On the unit circle, we derive a sufficient condition for weighted-norm inequalities for the Hilbert transform for two weights.
The contribution by Araujo and Linhares Sales is on graph theory, specifically on the problem of determining the minimum weight of a proper coloring of a vertex-weighted graph (G. ) The authors show a necessary and sufficient condition for the weighted chromatic number of (G) to be at least (k), for any positive real (k).
Sufficient conditions for a weighted L2-gain and the stabilization are derived.
We will obtain some sufficient conditions for the weighted exponential stability of nonlinear generalized delay functional differential equations.
In the extraction phase, it is sufficient to compute the weighted sum of the pixel group which is illustrated in (2) (2).
In addition, Čižmešija et al. [11] obtained a class of new sufficient conditions for a weighted modular inequality involving the above operator (A_{k}), so that they refined the classical Godunova inequality.
The above procedure allows us to determine whether there is sufficient signal in the weighted LD curve to reject the null hypothesis (under which a ^ (d ) is random "colored" noise in the sense that it contains autocorrelation).
The relative gain-to-loss weight is set prior to reconstruction; the pattern of losses and gains with the minimum weighted score, sufficient to produce the observed presence-absence pattern, is selected 88, 89.
In [6], Muckenhoupt derives a necessary and sufficient condition on two-weighted norm inequalities for the Poisson integral operator.
As mentioned above, in [7], Muckenhoupt derives a necessary and sufficient condition on two-weighted norm inequalities for the Poisson integral operator, and then in [8], Muckenhoupt and Wheeden provided two-weighted norm inequalities for the Hardy-Littlewood maximal operator and the Hilbert transform.
