This property is a weakening of the property (1.6) ⇒ (1.7) and, as we will obtain below, leads to essentially less hard limitations on the given system.
This property is a weakening of the property (1.4) (1.5) and, as we will obtain below, leads to essentially less hard limitations on the given system.
Both these methods are used in this paper and the analytical approximations obtained below are compared to them.
and we obtain (23) below in a similar way in which we obtain (21) above, i.e., BER lognormal, QPSK, MRC = 1 π ∑ n = 1 N p w n BER AWGN, QPSK γ ^ X a n, (23).
When the ∞-Bakry Émery Ricci curvature is bounded from below, we obtain a global gradient estimate which is not dependent on (|nabla f|).
Using formulas (34), (40), (42), (43) and (45) on the right-hand side of Eq. (23), and with the parameter choices specified below, we obtain an expression for the expected profit Π(p 0,p 1) whose maximum with respect to p 0 and p 1 we want to find.
Therefore, we obtain the theorem below.
Combining Theorems 3.1 and 3.2 we obtain the corollary below.
Therefore, by (2.5), we obtain the theorem below.
Therefore, by (2.14) and Theorem 8, we obtain the theorem below.
Invoking Lemmas 4.1 and 4.2, we obtain the theorem below from Corollary 3.4 by putting S = I and T = P C ( I − γ A ∗ ( I − P Q ) A ) for all n ∈ N. Theorem 4.3 Let C and Q be nonempty closed convex subsets of two Hilbert spaces H 1 and H 2 respectively, and let A : H 1 → H 2 be a bounded linear mapping.
