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At its best, it achieves a rare synthesis of virtues that is a primal value of the cinema: it revels in the power of cinematic artifice to tell a story that confronts big questions about real life.
The optimal primal value under uniform power allocation (UPA) assumption (the horizontal line) is also displayed.
The reason is that with the dual-based subgradient update solving the approximation problem, the primal value x ̂ k ( τ − 1 ) ( T ) can be infeasible.
Although the projected subgradient method may exhibit some fluctuations in primal value (Figures 4 and 5), we conclude that our proposed algorithm taking power allocation into account outperforms some previous works in terms of spectrum efficiency and QoS satisfaction.
Therefore, assuming that the j th optimal primal value, i.e., ŷ j k, ∗, lies inside the interval ( min Y j, max Y j ), then β j = α j = 0 due to slackness and ŷ j k = y j k − μ (with μ ∈ R ).
From μ k, the primal value y j k is obtained after solving the following convex optimization problem in d j d j ( μ k ) = min x j, y j k f j ( x j ) + μ k y j k s.t.
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Even so, the primal values of right and wrong — the requirements of compassion, honesty and honorable action — still apply.
Let t l, x l, and p l denote the primal values of the l th user, and t l ′ and x l ′ denote the new values randomly chosen by the l th user.
Hormels refrigerated segment was the only one to record a slight decline in sales because of softer demand for hams, bacon and commodity pork, and a weak food-service-sales environment, but the divisions profits jumped more than 50% on favorable spreads between hog costs and primal values.
It is known that with the dual-based subgradient algorithm using constant step size, the primal function sequence calculated from the running average primal values { x ̂ ( t ) = 1 t ∑ k = 1 t x ( k ), t = 1, 2, … } converges to an optimal value (of P 3 τ ) within an error ([18], Sec. 1.2).
Let r l and p l denote the primal values of the l th user, and r l ′ denote the new value randomly chosen by the l th user, which is treated as a new target transmission rate for the l th user.
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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