Optimization of heterogeneous Catalyst-assisted fatty acid methyl esters biodiesel production from Soybean oil with different Machine learning methods

There is a growing attention to the bio and renewable energies due to fast depletion of fossil fuels as well as the global warming problem. Here, we developed a modeling and simulation method by means of artificial intelligence (AI) for prediction of the bioenergy production from vegetable bean oil. AI methods are well known for prediction of complex and nonlinear process. Three distinct Adaptive Boosted models including Huber regression, LASSO, and Support Vector Regression (SVR) as well as artificial neural network (ANN) were applied in this study to predict actual yield of Fatty acid methyl esters (FAME) production. All boosted utilizing the Adaptive boosting algorithm. The important influencing parameters on the biodiesel production such as the catalyst loading (CAO/Ag, wt%) and methanol to oil (Soybean oil) molar ratio were selected as the input variables of models while the yield of FAME production was selected as output. Model hyper-parameters were tuned to maintain generality while improving prediction accuracy. The models were evaluated using three distinct metrics Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R². Error rates of 8.16780E-01, 4.43895E-01, 2.06692E + 00, and 3.92713 E-01 were obtained with the MAE metric for boosted Huber, SVR, LASSO and ANN models. On the other hand, the RMSE error of these models were about 1.092E-02, 1.015E-02, 2.669E-02, and 1.01174E-02, respectively. Finally, the R-square score were calculated for boosted Huber, boosted SVR, and boosted LASSO as 0.976, 0.990, 0.872, and 0.99702, respectively. Therefore, it can be concluded that although the boosted SVR and ANN models were better models for prediction of process efficiency in terms of error, but all algorithms had high accuracy. The optimum yield of 83.77% and 81.60% for biodiesel production were observed at optimum operating values from boosted SVR and ANN models, respectively.     

Diffusive search with spatially dependent resetting

We consider a stochastic search model with resetting for an unknown stationary target $a\in \mathbb{R}$ with known distribution $\mu$. The searcher begins at the origin and performs Brownian motion with diffusion constant $D$. The searcher is also armed with an exponential clock with spatially dependent rate $r=r\left(\cdot \right)$, so that if it has failed to locate the target by the time the clock rings, then its position is reset to the origin and it continues its search anew from there. Denote the position of the searcher at time $t$ by $X\left(t\right)$. Let $E_0^{\left(r\right)}$ denote expectations for the process $X\left(\cdot \right)$. The search ends at time $T_a=inf\{t\ge 0:X\left(t\right)=a\}$. The expected time of the search is then ${\int }_{\mathbb{R}}\left(E_0^{\left(r\right)}{T}_a\right)\mu \left(da\right)$. Ideally, one would like to minimize this over all resetting rates $r$. We obtain quantitative growth rates for $E_0^{\left(r\right)}{T}_a$ as a function of $a$ in terms of the asymptotic behavior of the rate function $r$, and also a rather precise dichotomy on the asymptotic behavior of the resetting function $r$ to determine whether $E_0^{\left(r\right)}{T}_a$ is finite or infinite. We show generically that if $r\left(x\right)$ is of the order ${\left|x\right|}^{2l}$, with $l>-1$, then $log{E}_0^{\left(r\right)}{T}_a$ is of the order ${\left|a\right|}^{l+1}$; in particular, the smaller the asymptotic size of $r$, the smaller the asymptotic growth rate of $E_0^{\left(r\right)}{T}_a$. The asymptotic growth rate of $E_0^{\left(r\right)}{T}_a$ continues to decrease when $r\left(x\right)\sim \frac{D\lambda }{x^2}$ with $\lambda >1$; now the growth rate of $E_0^{\left(r\right)}{T}_a$ is more or less of the order ${\left|a\right|}^{\frac{1+\sqrt{1+8\lambda }}{2}}$. Note that this exponent increases to $\infty$ when $\lambda$ increases to $\infty$ and decreases to 2 when $\lambda$ decreases to 1. However, if $\lambda =1$, then $E_0^{\left(r\right)}{T}_a=\infty$, for $a\ne 0$. Our results suggest that for many distributions $\mu$ supported on all of $\mathbb{R}$, a near optimal (or optimal) choice of resetting function $r$ in order to minimize ${\int }_{{\mathbb{R}}^d}\left(E_0^{\left(r\right)}{T}_a\right)\mu \left(da\right)$ will be one which decays quadratically as $\frac{D\lambda }{x^2}$ for some $\lambda >1$. We also give explicit, albeit rather complicated, variational formulas for ${inf}_{r\gneqq 0}{\int }_{{\mathbb{R}}^d}\left(E_0^{\left(r\right)}{T}_a\right)\mu \left(da\right)$. For distributions $\mu$ with compact support, one should set $r=\infty$ off of the support. We also discuss this case.     

On the Discrete Criteria and JØ rgensen Inequalities for SL(m,F((t)))

In this paper, the author gives the discrete criteria and J\o rgensen inequalities of subgroups for the special linear group on $\overline{\mathrm{F}}((t))$ in two and higher dimensions.     

Synergistic Effects of Pseudocolor Imaging,Differentiation, and Square and Logarithmic Conversion on Accuracy of Quantification of Chemical Characteristics Using Test Strips and Similar Products

Test strips and similar products are highly feasible tools for the rapid and approximate determination of chemical characteristics. Although the application of both the quantitative observation of coloration and regression modeling has recently enabled these products to become quantitative tools, their precision and accuracy may be further improved. In this study, the pseudocolor imaging of the coloration image, derivative spectrophotometry-like differentiation of the coloration values, and logarithmic conversion of the raw and derivative values were compared in terms of the precision and accuracy of the quantitative determination of corrosiveness, glucose, nitrate, and pH using the products. The best regression models for the determination were provided by the combination of pseudocolor imaging and differentiation (nitrate and pH); pseudocolor imaging, differentiation, and square-conversion (corrosiveness); or all of the techniques (glucose). When compared to the use of the original 10 raw coloration variables of red-green-blue, cyan-magenta-yellow-key black, and L*a*b* color models only, the above combinations improved the normalized mean absolute error from 14.8% to 3.09% (corrosiveness), 6.33% to 3.15% (glucose), 7.46% to 4.56% (nitrate), and 3.22% to 0.94% (pH). These achievements were largely attributed to the combination of multiple variables that have non-linear and nonmonotonic relationships with the chemical characteristics.