Multivariate optimization and comparison between conventional extraction (CE) and ultrasonic-assisted extraction (UAE) of carotenoid extraction from cashew apple

Carotenoids are an essential component of cashew and can be used in pharmaceuticals, cosmetics, natural pigment, food additives, among other applications. The present work focuses on optimizing and comparing conventional and ultrasound-assisted extraction methods. Every optimization step took place with a 1:1 (w:w) mixture of yellow and red cashew apples lyophilized and ground in a cryogenic mill. A Simplex-centroid design was applied for both methods, and the solvents acetone, methanol, ethanol, and petroleum ether were evaluated. After choosing the extractor solvent, a central composite design was applied to optimize the sample mass (59–201 mg) and extraction time (6–34 min). The optimum conditions for the extractor solvent were 38% acetone, 30% ethanol, and 32% petroleum ether for CE and a mixture of 44% acetone and 56% methanol for UAE. The best experimental conditions for UAE were a sonication time of 19 min and a sample mass of 153 mg, while the CE was 23 min and 136 mg. Comparing red and yellow cashews, red cashews showed a higher carotenoid content in both methodologies. The UAE methodology was ca. 21% faster, presented a more straightforward composition of extracting solution, showed an average yield of superior carotenoid content in all samples compared to CE. Therefore, UAE has demonstrated a simple, efficient, fast, low-cost adjustment methodology and a reliable alternative for other applications involving these bioactive compounds in the studied or similar matrix.     

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ${?}_1$-norm of q.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Non parametric estimation of the diffusion coefficients of a diffusion with jumps

In this article, we consider a jump diffusion process ${\left(X_t\right)}_{t\ge 0}$, with drift function $b$, diffusion coefficient $\sigma$ and jump coefficient ${\xi }^2$. This process is observed at discrete times $t=0,\Delta ,\dots ,n\Delta$. The sampling interval $\Delta$ tends to 0 and the time interval $n\Delta$ tends to infinity. We assume that ${\left(X_t\right)}_{t\ge 0}$ is ergodic, strictly stationary and exponentially $\beta$-mixing. We use a penalized least-square approach to compute adaptive estimators of the functions ${\sigma }^2+{\xi }^2$ and ${\sigma }^2$. We provide bounds for the risks of the two estimators.     

New lower bounds on 2-spontaneous emission error designs

The combinatorial object named $t$-spontaneous emission error design ($t$-SEED) was proposed by Beth et al. in 2003 in order to correct errors caused by quantum jumps. The newly rising category of $t$-SEEDs has been studied extensively in recent years. Especially, the maximal possible dimensions for 2-SEEDs with block size 3 were determined completely; lower bounds on 2-SEEDs were established by applying affine groups. In this paper we utilize the action of twisted affine groups on finite fields and obtain new lower bounds on the dimensions of 2-$(q^2,k;m)$ SEEDs, some of which outperform the known ones.     

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.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Residual stress in polyethylene pipes

This paper deals with residual stress in polyethylene (PE) pipes as an important factor that influences their lifetime. Residual hoop stress distribution in a PE pipe was determined using a methodology previously carried out by the authors on polypropylene pipes. Axial residual stress magnitude was determined by comparison of experimental data and finite element modelling. Based on the obtained results, a new simplified methodology for determining the residual hoop stress is proposed. The method needs only one circular specimen made of pipe, but, unlike older methods, provides a more precise estimation of residual hoop stress distribution taking into account its exponential shape. Some older results from literature are recalculated using this method and residual hoop stress of various PE pipe grades and dimensions are then compared. To provide an idea of residual hoop stress influence on lifetime of a pipe, a lifetime estimation is carried out for the examined pipe.