It's 1 - beta^(r+1 -- this is one more than the upper limit on the summation and in the denominator is 1 - beta.
In the summation and the principal resonances, the trivial responses may become unstable and bifurcate into nontrivial responses for certain excitation frequencies.
For the ISI ξ in (16), we can assume that there are N1 terms in the first summation and N2 terms in the second for each interferer.
The summation and the minimization in (6) can be swapped, leaving (7).
The first step in data analysis was casting the summation and bipolar models in the form of competing equations, which are presented later.
Number of hidden layers, number of nodes connected with bias in each of the hidden layers, summation and the transfer function in hidden and output layers are the important structural parameters of neural network (Yadav and Kothari 2004).
Besides, the word-length for fixed-point representations is estimated based on both the (sum |h_{k}|) summation and the input range, in order to obtain optimized filters, in terms of reduced number of bits.
This orderliness also prompted the third goal of the present research, that is, to express the summation and bipolar dimension models in the form of competing equations intended to predict all the points on a man's phallometric response profile solely from the magnitude of his highest response regardless of whether his highest response is to males or females, to children, pubescents, or adults.
Either is easily modeled via slight modification of the ILP given earlier (with variables corresponding to non-existent edges removed, and summations in the edge constraints taken only over existing edges), and the resulting ILP can be used in conjunction with the numerous graph pruning techniques previously developed for this problem (e.g. [ 17]).
Proof By writing the right-hand side of Eq. (2.1) in the original summation and applying (2.7) to the resulting summation, after a little simplification, we find that, when the last resulting summation is expressed in terms of F q p in (1.5), this completes the proof of Corollary 1.
