Alternate Entropy Computations by Applying Recurrence Matrix Masking

In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.

The sub-supersolution method for a nonhomogeneous elliptic equation involving Lebesgue generalized spaces

In this paper, a nonhomogeneous elliptic equation of the form $$\begin{aligned}& - \mathcal{A}\bigl(x, \vert u \vert _{L^{r(x)}}\bigr) \operatorname{div}\bigl(a\bigl( \vert \nabla u \vert ^{p(x)}\bigr) \vert \nabla u \vert ^{p(x)-2} \nabla u\bigr) \\& \quad =f(x, u) \vert \nabla u \vert ^{\alpha (x)}_{L^{q(x)}}+g(x, u) \vert \nabla u \vert ^{ \gamma (x)}_{L^{s(x)}} \end{aligned}$$ − A ( x , | u | L r ( x ) ) div ( a ( | ∇ u | p ( x ) ) | ∇ u | p ( x ) − 2 ∇ u ) = f ( x , u ) | ∇ u | L q ( x ) α ( x ) + g ( x , u ) | ∇ u | L s ( x ) γ ( x ) on a bounded domain Ω in ${\mathbb{R}}^{N}$ R N ($N >1$ N > 1 ) with $C^{2}$ C 2 boundary, with a Dirichlet boundary condition is considered. Using the sub-supersolution method, the existence of at least one positive weak solution is proved. As an application, the existence of at least one solution of a generalized version of the logistic equation and a sublinear equation are shown.

A Kinetic model for submerged citric acid production by Aspergillus versicolor using oil palm empty fruit bunch

The fermentation kinetics of citric acid by Aspergillus versicolor was studied in a submerged batch system. The logistic equation for growth, the Luedeking–Piret equation for citric acid production and modified Luedeking–Piret-like equation for glucose consumption was proposed for this study. The model appeared to provide a reasonable description for each parameter during the growth phase. The production of citric acid was growth-associated.

Harvest Management Problem with a Fractional Logistic Equation

In this article, we study a fractional control problem that models the maximization of the profit obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this problem, we develop different resolution techniques, both for the classical case and for the fractional case. We perform several numerical simulations to make a comparison between both cases.

Investigation of Well Control Parameterization with Reduced Number of Variables Under Reservoir Uncertainties

Although several studies have shown that life-cycle well control strategies can significantly improve a field's economic return, the industry often relies on short-term strategies. One drawback of traditional parameterization, adopted for well control life-cycle numerical optimization, is that it often generates control strategies that yield impractical abrupt changes in production curves. Another issue, especially in cases with a large number of decision variables, is the local optima convergence related to the non-convex optimization problems. In this context, we proposed and compared four life-cycle well control parameterizations to maximize the net present value (NPV) of the field under uncertainties, which are able to mitigate both the above-mentioned problems. The first parameterization optimizes the apportionment of well rates at the beginning of the field management and well shut-in time. The other three are based on optimizing the coefficients of parametric equations (first-and second-order polynomials, and logistic equation) to guide the bottom-hole pressure (BHP) over time. We executed each parameterization five times in a deterministic reservoir scenario and compared them with well control short-term strategy that prioritizes production in wells with higher oil-water ratio and that aimed to replicate the general industry practice. In this strategy, the wells’ priority rank was updated at every 30-simulation days. Subsequently, the best parameterization was used to select the well control life-cycle strategy under reservoir uncertainties and this strategy was applied to the reference model representing a real reservoir. The results showed that all the proposed parametrizations significantly improved the NPV in comparison to the well control short-term strategy, while simultaneously ensuring a smooth well production curve. The logistic equation presented the best result among all parameterizations, as it delivered both the highest average of NPV and the smallest dispersion over the five experiment repetitions. This parameterization also produced similar results when applied under uncertainties and for the reference model. These results endorse the importance of not only relying on a short-term strategy, but also planning it for the life-cycle.