Multi-objective optimal control of small-size wastewater treatment plants

In this work, a multi-objective dynamic optimization of the operating strategy of a small-size wastewater treatment plant is carried out. In-situ incineration of the excess sludge produced for electricity production is investigated in order to reduce the operating costs. The trade-offs between the treatment quality and the operating costs are characterized. Compared to the literature, emphasis is put on a more rigorous formulation of the problem and an accurate modeling of the underlying phenomena so as to get physically relevant solutions. Thus, from a mathematical perspective, the problem is formulated so that the solution is less sensitive to the – arbitrarily chosen – plant initial conditions. Modeling of physical phenomena e.g. the detrimental effect of the concentration of suspended solids in the mixed liquor, on oxygen transfer rate, has been included in the model. Several constraints are added to the problem so as to maintain the optimal solutions within the limits of validity of the mathematical model. The results provided a clear picture about the trade-offs between the treatment quality and the exploitation costs. Sludge incineration was shown to be of a high energetic profit, but it does not allow the plant to be electrically autonomou

Plus and minus logarithms and Amice transform

We give a new description of Pollack's plus and minus $p$-adic logarithms $\log_p^\pm$ in terms of distributions. In particular, if $\mu_\pm$ denote the pre-images of $\log_p^\pm$ under the Amice transform, we give explicit formulae for the values $\mu_\pm(a+p^n\mathbb{Z}_p)$ for all $a\in \mathbb{Z}_p$ and all integers $n\ge1$. Our formulae imply that the distribution $\mu_-$ agrees with a distribution studied by Koblitz in 1977. Furthermore, we show that a similar description exists for Loeffler's two-variable analogues of these plus and minus logarithms.Comment: 9 page

Stepwise results for each sub-task and both conditions (Spont and Stand).

<p>Stepwise results for each sub-task and both conditions (Spont and Stand).</p

TUG performance, COM parameters and foot clearance in hemiparetic patients and healthy subjects during Go, Turn and Return sub-tasks.

<p>* significant difference between hemiparetic patients and healthy subjects for the corresponding sub-task of the TUG p<0,05</p><p>† significant difference between Go, Turn and Return p<0.05</p><p>TUG performance, COM parameters and foot clearance in hemiparetic patients and healthy subjects during Go, Turn and Return sub-tasks.</p

Subject characteristics.

<p>Subject characteristics.</p

Correlations between TUG performance time, and COM and MFC parameters for hemiparetic patients and healthy subjects.

<p>* significant correlation between TUG performance and the corresponding parameter at p<0,05</p><p>Correlations between TUG performance time, and COM and MFC parameters for hemiparetic patients and healthy subjects.</p

Participants characteristics.

<p>Spasticity: sum of quadriceps, rectus femoris, hamstring and triceps surae assessed with Modified Ashworth Scale (0–4). MRC (Medical Research Council scale): sum of hip, knee and ankle flexors and extensors strength. Foot sole pressure was assessed with the Nottingham Sensory Assessment (0 = absent, 1 = impaired, 2 = normal). Toe proprioception was assessed with the Nottingham Sensory Assessment (0 = absent, 1 = direction incorrect, 2 = direction ok, inaccurate position, 3 = direction ok, position accurate to 10°). BBS: Berg Balance Scale (0 to 56). ABC: Activities-specific Balance Confidence (0 to 100%). Fall frequency: number of falling within 3 last months. Fear of falling between 0 (no fear) and 10 (extreme fear of falling).</p><p>Participants characteristics.</p

Experimental set-up.

<p>The circles indicate the position of the cameras. One camera was positioned directly above the object (80 cm high) (C1), and the other 2 were placed at a height of 75 cm on the contralateral side of the hand being evaluated: one 30° to the sagittal plane (at a distance of 75 cm from the object in the horizontal plane) (C2) and the other 30° behind the frontal plane (at a distance of 70 cm from the object in the horizontal plane) (C3).</p

Correlation between Oriented gait and Turn performance explanatory spatiotemporal and kinematic parameters from the stepwise analysis and the clinical data.

<p>MRC: Medical Research Council scale. BBS: Berg Balance Scale. ABC: Activities-specific Balance Confidence.</p><p>* significant correlation at p<0.05.</p><p>Correlation between Oriented gait and Turn performance explanatory spatiotemporal and kinematic parameters from the stepwise analysis and the clinical data.</p

Medio-lateral COM velocity.

<p>Medio-lateral COM velocity.</p