The phrase "a sequence of dual" is not correct and does not convey a clear meaning in written English.
It may be intended to describe a series or pattern involving two elements, but the phrasing is awkward and unclear.
Example: "The study revealed a sequence of dual responses from the participants, indicating a complex interaction."
Alternatives: "a series of pairs" or "a pattern of two".
We firstly formulate a robust max-min SINR beamforming problem and show that the optimal solution can be obtained by solving a sequence of its "dual" min-max power problems.
Yet those travelling through Dundee can see nothing of this, kept instead to a grim sequence of dual carriageway and roundabouts that skirt the city's north-western corner.
The stochastic approach is based on the representation of a sequence of alarms under the dual form of a homogeneous Markov chain and its corresponding superposition of Poisson processes.
Moreover, for a special nonlinearity (f x,u =lambda |u|^{q-2}u+|u|^{r-2}u) ((1< q< p< r< p^)), we prove that problem (P) has at least two nonnegative solutions via the Nehari manifold method and a sequence of solutions with negative energy by the dual fountain theorem.
If for each k = 1, 2, …, there exists ρ k > r k > 0 such that(A2) = inf u ∈ Z k, ∥ u ∥ = r k E ( u ) → + ∞ as k → ∞.; (A3) = max u ∈ Y k, ∥ u ∥ = ρ k E ( u ) ≤ 0.; (A4) = E satisfies the ( P S ) c condition for every c > 0. Then E has a sequence of critical values tending to +∞.. Proposition 5.2 (Dual Fountain Theorem, see [11]).
In addition, we also find out the standard dual of a direct limit of a sequence of operator bimodules.
A novel cDNA sequence of a dual-specificity phosphatase was identified in both sexual and asexual stages of P. falciparum, and named PfYVH1, since the predicted primary structure of the 278-amino acid polypeptide showed significant similarity to the human and yeast YVH1 phosphatases.
MAPKKK gene models were only accepted if they displayed the consensus sequences of dual-specificity protein kinases.
