Development of blends of vegetable oils for a healthy diet

The analysis of vegetable oils was carried out in accordance with the recommendations of physiological needs for different groups of the population and FAO / WHO to meet the need for the consumption of vegetable oils. The aim of the work is to create blends of vegetable oils with an optimized composition of polyunsaturated fatty acids ?3, ?6, ?9 for healthy human nutrition. The objects of research are vegetable oils obtained by cold pressing from milk thistle, sunflower, rapeseed and camelina. The analysis of the fatty acid composition of the oils was carried out using gas chromatography. It was found that the greatest amount of ?6 is contained in sunflower oil – 66%, in milk thistle oil – 53%, in rapeseed oil 20%, in camelina oil 17%. Camelina oil is rich in ?3 – 37%, rapeseed oil ?9 – 59%, which corresponds to the standards for these types of oils. Using the method of linear programming, the calculation of four-component blends of various types of oils, balanced by ?3, ?6, ?9, in accordance with the norms recommended for satisfying the daily nutritional needs of a person is presented. Blends of vegetable oils were designed. The ratio in fatty acid blends ?3: ?6: ?9 - 1: 1.5: 1.3 has been established. By means of modeling, 5 blends of vegetable oils with different compositions were obtained. Based on the data obtained, the partial desirability functions for each blend and the general Harrington index were calculated. The values of the desirability functions that exceed 0.9 and the generalized Harrington criterion of 0.97 were obtained, which corresponds to the standard level of the desirability scale "excellent". In this regard, it can be argued that the resulting blends have a balanced composition. It should be noted that the next step is a tasting studies in order to obtain satisfactory organoleptic characteristics.

Integration of Response Surface Methodology (RSM) and Principal Component Analysis (PCA) as an Optimization Tool for Polymer Inclusion Membrane Based-Optodes Designed for Hg(II), Cd(II), and Pb(II)

An optimization of the composition of polymer inclusion membrane (PIM)-based optodes, and their exposure times to metal ion solutions (Hg(II), Cd(II), and Pb(II)) was performed using two different chromophores, diphenylthiocarbazone (dithizone) and 1-(2-pyridylazo)-2-naphthol (PAN). Four factors were evaluated (chromophore (0.06–1 mg), cellulose triacetate (25–100 mg) and plasticizer amounts (25–100 mg), and exposure time (20–80 min)). Derringer’s desirability functions values were employed as response variables to perform the optimization obtained from the results of three different processes of spectral data treatment: two full-spectrum methods (M1 and M3) and one band-based method (M2). The three different methods were compared using a heatmap of the coefficients and dendrograms of the Principal Component Analysis (PCA)reductions of their desirability functions. The final recommended M3 processing method, i.e., using the scores values of the first two principal components in PCA after subtraction of the normalized spectra of the membranes before and after complexation, gave more discernable differences between the PIMs in the Design of Experiments (DoE), as the nodes among samples appeared at longer distances and varyingly distributed in the dendrogram analysis. The optimal values were time of 35–65 min, 0.53 mg–1.0 mg of chromophores, plasticizers 34.4–71.9 of chromophores, and 62.5–100 mg of CTA, depending on the metal ion. In addition, the method yielded the best outcomes in terms of interpretability and an easily discernable color change so that it is recommended as a novel optimization method for this kind of PIM optode.

Some applications of a novel desirability function in simultaneous optimization of multiple responses

In the framework of multi-response optimization techniques, the optimization methodology based on the desirability function is one of the most popular and most frequently used methodologies by researchers and practitioners in engineering, chemistry, technology and many other fields of science and technique. Numerous desirability functions have been introduced to improve the performance of this optimization methodology. Recently, a novel desirability function for multi-response optimization is proposed, which is smooth, nonlinear, and differentiable, and thus more suitable for applying some of the more efficient gradient-based optimization methods. This paper evaluates the performance of the proposed method through six real examples. After a comparative analysis of the results, it is shown that the proposed method in a certain measure outperforms the other competitive optimization methods.

APPLICATION OF THE HARRINGTON DESIRE FUNCTION IN DESIGNING COMPLEX MULTI-COMPONENT FOOD

The article discusses the issue of design automation and optimization of complex multicomponent food products using mathematical programming methods. Food design methods based on generalized modeling criteria with one vector of mixture quality indicators lead to the formulation of a quadratic programming problem. Determination of the universal quality indicator can be carried out using the asymmetric Harrington desirability functions. The application of the criterion with the specified lower and upper permissible levels of consumption for each of the quality indicators allows one to take into account deviations in the direction of insufficiency or overdose of nutrients. One of the possible expressions for desirability functions of this kind is the use of the product of Gompertz curves to express particular criteria of balance. The use of this methodology on the example of the development of a marshmallow formulation with the addition of apple and sea buckthorn to achieve an optimal balance of nutrients has significantly improved the percentage of balance of the mixture.

Optimization of Osmotic Dehydration of Tomatoes in Solutions of Non-Conventional Sweeteners by Response Surface Methodology and Desirability Approach

The osmotic dehydration (OD) of tomatoes in solutions of alternative sweeteners was investigated using Response Surface Methodology (RSM), while selected desirability functions were implemented in order to define the optimum process parameters (temperature/duration of osmotic treatment, osmotic solution composition and concentration). Mass exchange, color and texture were measured during the process. Changes in color occurred rapidly at the beginning of the process, while firmness was significantly increased, indicating that OD processing led to tomato texture improvement. Color and firmness changes were adequately modeled using a polynomial model. RSM coupled with desirability functions was applied to optimize OD procedure in terms of color retention and maximum solid gain, a requirement for candied products. A maximum desirability was obtained by incorporating oligofructose into the osmotic solution, at relatively short treatment times. Results were validated and sensory analysis was conducted at the optimized conditions to assess samples’ organoleptic acceptance.

Using desirability functions when making managerial decisions in the mineral resource complex

Relevance. The ever-growing flows of information, tight deadlines for decision-making, the need to maintain competitive positions require ranking calculations to identify leaders and promote leadership factors, ranking units of business entities according to selected criteria, etc. Reliability, visualization, and often acceleration of obtaining results predetermine the appeal to mathematical techniques. Purpose of the study: substantiation of choice of the most acceptable option of the desirability function for use in the process of making managerial decisions related to the development of subsoil resources. Research method: comparative analysis of options for calculating the desirability function, comparison method, methods of mathematical statistics. Results. Two options for calculating the desirability function are considered. The first one developed by E. Harrington, who proposed a special verbal-numerical scale, which made it possible to formalize the system of preferences of different experts. The partial function of desirability, in this case, is constructed so that it is close to "satisfactory" linear one. According to recommendations, the lower and upper boundaries of “satisfactorily” correspond to the minimum and maximum values of indicators for the available data array. There is a slightly different approach to the determination of the partial function of desirability described in a number of works. The generalized desirability function is a convolution of particular functions and is defined as the geometric mean or logarithmic mean. It is possible to use weighting factors with different significance of particular desirability functions. Comparison of various approaches is made for the conditions of management of logistics and equipment of OOO Gazpromtransgaz-Yekaterinburg. An analysis of the results shows that despite discreteness of the particular desirability functions, which in the first case lie in the range from 0.37 to 0.69, and give the entire range of values from 0 to 1 in the second one, the ratings for the generalized desirability function completely coincide with regard to determining a rating of quarterly values of industrial and economic activity. It follows that both methods of calculating partial functions are legitimate, however, the first option seems more convenient technically due to the absence of values of partial desirability functions close to zero, which complicate calculations using computer technology. A third version of the rating was also tested using calculated percentage estimates of the indicators under consideration with respect to the maximum desired value (taking into account their conversion into the relative indices). As in previous cases, the rating of countries according to the generalized function of desirability turned out to be comparable with previously calculated. Conclusions. Comparative calculations confirmed the validity of both options for finding particular desirability functions, since the ratings for the generalized desirability function coincide. The first version of the calculation is more convenient due to the lack of values of particular desirability functions close to zero, which simplifies the use of computer technology

Adsorptive of Nickel in Wastewater by Olive Stone Waste: Optimization through Multi-Response Surface Methodology Using Desirability Functions

Pollution from industrial wastewater has the greatest impact on the environment due to the wide variety of wastes and materials that water can contain. These include heavy metals. Some of the technologies that are used to remove heavy metals from industrial effluents are inadequate, because they cannot reduce their concentration of the former to below the discharge limits. Biosorption technology has demonstrated its potential in recent years as an alternative for this type of application. This paper examines the biosorption process for the removal of nickel ions that are present in wastewater using olive stone waste as the biosorbent. Kinetic studies were conducted to investigate the biosorbent dosage, pH of the solution, and stirring speed. These are input variables that are frequently used to determine the efficiency of the adsorption process. This paper describes an effort to identify regression models, in which the biosorption process variables are related to the process output (i.e., the removal efficiency). It uses the Response Surface Method (RSM) and it is based on Box Benken Design experiments (BBD), in which olive stones serves as the biosorbent. Several scenarios of biosorption were proposed and demonstrated by use of the Multi-Response Surface (MRS) and desirability functions. The optimum conditions that were necessary to remove nickel when the dosage of biosorbent was the minimum (0.553 g/L) were determined to be a stirring speed of 199.234 rpm and a pH of 6.369. The maximum removal of nickel under optimized conditions was 61.73%. Therefore, the olive stone waste that was investigated has the potential to provide an inexpensive biosorbent material for use in recovering the water that the nickel has contaminated. The experimental results agree closely with what the regression models have provided. This confirms the use of MRS since this technique and enables satisfactory predictions with use of the least possible amount of experimental data.