Exact(3)
"Opportunistic" here means the probability that there exists a user whose instantaneous channel gains are close to matching the current powers and phases allocated at the transmit antennas.
Note that as, in each of the logical groups there exists a user with short-term fading and scheduling such users from each of the logical groups at the rate simultaneously minimizes the sum energy required to achieve the desired rates.
We have to show that for utility functions u k, û k ∈ U, the expression u k ( f ( u k, u − k ) ) = u k ( f ( û k, u − k ) ) holds for all k ∈ K. Let us assume that there exists a user k0, where k 0 ∈ K ∖ k, such that u k 0 ( f ( u k, u − k ) ) ≠ u k 0 ( f ( û k, u − k ) ).
Similar(57)
Then, there exists a D2D user (iin mathcal {D}) whose strategy is x i ∈x fin.
In Section "The SNR threshold problem", it is assumed that there exists a given user serving vector ϑ.
We can now proceed to prove that when, there always exists a value for a user utility function parameter denoted as such that when then their maximum willingness to pay is calculated by the second part of (17), because in (18) does not exist and hence, condition (A.1) is fulfilled.
See Appendix F. Based on the two previous lemmas, we can see that there always exists a value for a user utility function parameter when, such that for smaller than values of, the inflection point of function is always smaller that its separation point (i.e.e ).e
There exists a general consensus among users (each user in the network is an equal stakeholder) in the way data is both recorded and stored, so the role of third-parties is rendered obsolete.
According to Definition 3, there must exist a CR user and the policy, such that the power constraint of this CR user holds and.
In the downlink, two metrics result in p values equal to zero, meaning that there exists a strong relation between the user throughput and such metrics.
The models also potentially apply to instances of witchcraft, shamanism and magic in which the 'treatment' is believed to combat perceived underlying 'supernatural' causes of disease (e.g. the curse of a jealous neighbour, or a haunting by the ghost of an ancestor), so long as there exists a physical ailment in the user, and the treatment propagates through cultural transmission.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com