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Similar to [22], by rearranging the terms in the instantaneous problem, it can be divided into three instantaneous Subproblems (SPs) which will be presented in the next subsections.
Therefore, there is an O(1/V) gap between the optimal utility of the stochastic problem and the utility obtained from solving the instantaneous problem, which can be arbitrarily reduced by choosing a large V.
In addition to those constraints, the contributions of our current paper can be classified into two categories: one category is the identification of important factors that should be taken into account in the instantaneous problem formulation.
In this section, we first describe the instantaneous problem to be addressed in each time slot and propose some parameters that need to be included in it to make it suitable for relay-assisted cellular networks.
Using the well-known Lyapunov drift-plus-penalty policy, we extract the instantaneous problem that needs to be solved in each slot to control the data admission and allocate the time slots, power, and subchannels.
If the solution algorithm for instantaneous problem (7) also leads to an approximate value of the objective function (7a) within distance C from its optimal value (e.g., due to a suboptimal solution), then the aforementioned gap will be (frac {D+C}{V}).
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So for each frequency bin, an individual instantaneous ICA problem arises [2].
Explicit analytical expressions were developed for the instantaneous pulse problem formulated from the generalized Dirac delta function for situations with first-type or third-type inlet boundary conditions of both finite and semi-infinite domains.
Transforming Equation (1) into the frequency domain reduces the convolutions to multiplications with the corresponding transfer functions, so that for each frequency bin an individual instantaneous ICA problem X ≈ A S + N (4).
The instantaneous forward problem (IFP) singularities of a parallel manipulator (PM) must be determined during the manipulator design and avoided during the manipulator operation, because they are configurations where the end-effector pose (position and orientation) cannot be controlled by acting on the actuators any longer, and the internal loads of some links become infinite.
DOA involves optimization over the entire time period to obtain flux profiles over time, while SOA involves dividing the batch time into several time intervals and solving the instantaneous optimization problem at the beginning of each time interval.
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