Two-order Polynomial Research Articles

Optimization of Glycerolysis of Free Fatty Acids from Cocoa Bean with MgO Catalyst Using Response Surface Methodology

Diacylglycerol (DAG) is one of the oil derivatives that have relatively high economic value. It has considerable prospects in the global market, which can be synthesized chemically by glycerolysis of oil/fat containing triacylglycerols. The process uses an alkaline catalyst such as sodium hydroxide (NaOH) at the temperature of 210-260 °C. The present study utilized a free fatty acid compound from cocoa bean processing waste as alternative raw material for producing DAG. The reaction system using a MgO catalyst and tert-butanol as solvent was known to be more favorable. The solvent can increase the solubility of oil in glycerol so that the reaction temperature can be lowered to 70-90 °C. This study aims to determine the effect of temperature and the ratio of glycerol/FFA on the glycerolysis process and to determine the optimized variables that result in a maximum conversion. The glycolysis reaction was optimized with two factors using a central composite design, i.e., reaction temperature and glycerol/FFA ratio. The selected fixed variables were catalyst loading (3.5 wt%), the mass of FFA (10 grams), stirring speed (400 rpm), reaction time (4 hours), and volume of solvent (20 mL). The optimization process was evaluated using the response surface method, which shows that the optimum condition was achieved at a glycerol/FFA ratio of 5 g/ml and a reaction temperature of 90 °C. The experiment carried out under these optimum conditions resulted in 97.5% conversion, while the two-order polynomial model developed using RSM was able to predict the conversion of 96.7% under the same condition.

A liquid chromatography coupled to tandem mass spectrometry method for the quantification of spiramycin and its active metabolite neospiramycin in milk of major and minor species: Validation using the accuracy profile

A liquid chromatography with tandem mass spectrometry (LC-MS/MS) method was developed for the simultaneous quantification of residues of spiramycin, a macrolide antibiotic, and its active metabolite neospiramycin in cow's milk as well as in minor species ‘milk, goat and ewe. Spiramycin-d3 was used as internal standard for quantification of both analytes. This analytical method was validated using a global accuracy profile as a graphical decision tool built according to the trueness and the precision of the method. A unique and optimal linear model with logarithm transformation (with a determination coefficient of 0.9991) allowed the measurement of both analytes in the milks of the three animal species, in a wide range from 0.2 to 10 times the Maximal Residue Limit (MRL) (40–2000 µg.kg−1). The limits of detection and quantification were 13 µg.kg−1 and 40 µg.kg−1, respectively. The accuracy profile was established to get 80% of future measurements in routine assays that will fall within the acceptance limits. Trueness of the method, expressed as relative bias, was comprised between –1.6% and 5.7% over the whole range of concentrations. The mean relative standard deviation for repeatability and intermediate precision were comprised between 1.1% and 2.7%; 2.5 and 4.2%, respectively, in all levels of concentration for the three milks. Moreover, a two-order polynomial function was used to model the relative expanded uncertainty with a determination coefficient of 0.834. This function aimed to determine the uncertainty of the future quantifications within the validated dosing range. Overall, the global accuracy profile highlighted the reliability of the method for the routine assays of spiramycin and neospiramycin even in milk from minor species (goat, ewe) by using the most accessible milk (often from cow), while guaranteeing a very high proportion of samples within the fixed acceptance limits. The applicability of this method was tested during a depletion study of spiramycin and neospiramycin in the milk of cow, goat and ewe. The developed analytical method will be useful to assess the distribution profile of the antibiotic and its metabolite in milk of minor species where few studies are available.

Evaluation on Excess Entropy Scaling Method Predicting Thermal Transport Properties of Liquid HFC/HFO Refrigerants

The application of the excess entropy scaling (EES) method to predict the viscosity, thermal conductivity and thermal diffusivity of HFC/HFO refrigerants is evaluated in this paper. The universal coefficients of the EES model were firstly obtained from the properties of HFC refrigerants, and the accuracy of the model was further investigated with HFO properties. It was suggested that the EES model correlated the viscosity very well with the average absolute deviations (AADs) of most HFC refrigerants lower than 6.55% except R32. The correlations also provided very good prediction on the viscosity for R1234yf and R1234ze(E), but not for R1336mzz(Z). The prediction of thermal conductivity for both HFC and HFO refrigerants was generally well with the maximum AAD of 11.44%. However, the paper also indicated that there were no universal thermal diffusivity coefficients for even HFC refrigerants, and the linear function could not fit the thermal diffusivity curve very well. Therefore, the exclusively two-order polynomial correlations based on the EES model were presented for each HFC/HFO refrigerant.

Two‐order graph convolutional networks for semi‐supervised classification

Currently, deep learning (DL) algorithms have achieved great success in many applications including computer vision and natural language processing. Many different kinds of DL models have been reported, such as DeepWalk, LINE, diffusionconvolutional neural networks, graph convolutional networks (GCN), and so on. The GCN algorithm is a variant of convolutional neural network and achieves significant superiority by using a one-order localised spectral graph filter. However, only a one-order polynomial in the Laplacian of GCN has been approximated and implemented, which ignores undirect neighbour structure information. The lack of rich structure information reduces the performance of the neural networks in the graph structure data. In this study, the authors deduce and simplify the formula of two-order spectral graph convolutions to preserve rich local information. Furthermore, they build a layerwise GCN based on this two-order approximation, i.e. two-order GCN (TGCN) for semi-supervised classification. With the two-order polynomial in the Laplacian, the proposed TGCN model can assimilate abundant localised structure information of graph data and then boosts the classification significantly. To evaluate the proposed solution, extensive experiments are conducted on several popular datasets including the Citeseer, Cora, and PubMed dataset. Experimental results demonstrate that the proposed TGCN outperforms the state-of-art methods.

Regression Analysis to Estimate Morphology Parameters of Pepper Plant in a Controlled Greenhouse System

Regression analysis to predict growth indices of plant is essential for understanding the relationship between the total leaf area, production of fresh weight and dry matter, and expansion of the plant growth. An experiment was conducted to develop regression models for estimating leaf area, fresh weight, and dry weight from measurements of plant height at the vegetative phase of hot pepper (Capsicum annuum Linnaeus) grown in biodegradable pots in a greenhouse. Five models were evaluated and compared: linear regression model, two-order polynomial regression model (P. order 2), three-order polynomial regression model (P. order 3), four-order polynomial regression model (P. order 4), and power regression model. The models were compared using the coefficient of determination (R2), Pearson’s correlation coefficient (r), root mean square error (RMSE), relative standard error (RSE), and mean absolute percentage error (MAPE). Power regression involving plant height demonstrated the highest R-square among the other models with minimum error estimate for the expected leaf area (R2 > 0.96, r > 0.98, RMSE 0.98, r > 0.99, RMSE 0.97, r > 0.98, RMSE < 0.03, RSE < 0.02, and MAPE < 11.7) of the plant considering both the fit and degree of adjustment, and the interpretation of the model. This study creates scope for further experimentation on various species of crops by changing management practices under different environmental conditions to enhance knowledge and understanding of the growing patterns of plants.

Hydraulic design of a low-specific speed Francis runner for a hydraulic cooling tower

The air blower in a cooling tower is normally driven by an electromotor, and the electric energy consumed by the electromotor is tremendous. The remaining energy at the outlet of the cooling cycle is considerable. This energy can be utilized to drive a hydraulic turbine and consequently to rotate the air blower. The purpose of this project is to recycle energy, lower energy consumption and reduce pollutant discharge. Firstly, a two-order polynomial is proposed to describe the blade setting angle distribution law along the meridional streamline in the streamline equation. The runner is designed by the point-to-point integration method with a specific blade setting angle distribution. Three different ultra-low-specificspeed Francis runners with different wrap angles are obtained in this method. Secondly, based on CFD numerical simulations, the effects of blade setting angle distribution on pressure coefficient distribution and relative efficiency have been analyzed. Finally, blade angles of inlet and outlet and control coefficients of blade setting angle distribution law are optimal variables, efficiency and minimum pressure are objective functions, adopting NSGA-II algorithm, a multi-objective optimization for ultra-low-specific speed Francis runner is carried out. The obtained results show that the optimal runner has higher efficiency and better cavitation performance.

Practical approach for dispersion compensation in spectral-domain optical coherence tomography

We proposed and demonstrated a digital method of dispersion compensation suitable for spectral-domain optical coherence tomography. The wavelength coordinate of the coherence spectrum was calibrated digitally using a two-order polynomial. A software-based scheme was introduced to determine the polynomial coefficients of the polynomial fitting spectrum wavelength. Therefore, the spectrum deformation introduced by dispersion can be compensated effectively. This method was experimentally validated by in vivo imaging an early-stage chick embryonic heart.

Performance Evaluation of an Infrared Thermocouple

The measurement of the leaf temperature of forests or agricultural plants is an important technique for the monitoring of the physiological state of crops. The infrared thermometer is a convenient device due to its fast response and nondestructive measurement technique. Nowadays, a novel infrared thermocouple, developed with the same measurement principle of the infrared thermometer but using a different detector, has been commercialized for non-contact temperature measurement. The performances of two-kinds of infrared thermocouples were evaluated in this study. The standard temperature was maintained by a temperature calibrator and a special black cavity device. The results indicated that both types of infrared thermocouples had good precision. The error distribution ranged from −1.8 °C to 18 °C as the reading values served as the true values. Within the range from 13 °C to 37 °C, the adequate calibration equations were the high-order polynomial equations. Within the narrower range from 20 °C to 35 °C, the adequate equation was a linear equation for one sensor and a two-order polynomial equation for the other sensor. The accuracy of the two kinds of infrared thermocouple was improved by nearly 0.4 °C with the calibration equations. These devices could serve as mobile monitoring tools for in situ and real time routine estimation of leaf temperatures.

Statistical properties of nucleotides in human chromosomes 21 and 22

In this paper the statistical properties of nucleotides in human chromosomes 21 and 22 are investigated. The n -tuple Zipf analysis with n = 3, 4, 5, 6, and 7 is used in our investigation. It is found that the most common n -tuples are those which consist only of adenine (A) and thymine (T), and the rarest n -tuples are those in which GC or CG pattern appears twice. With the n -tuples become more and more frequent, the double GC or CG pattern becomes a single GC or CG pattern. The percentage of four nucleotides in the rarest ten and the most common ten n -tuples are also considered in human chromosomes 21 and 22, and different behaviors are found in the percentage of four nucleotides. Frequency of appearance of n -tuple f ( r ) as a function of rank r is also examined. We find the n -tuple Zipf plot shows a power-law behavior for r < 4 n −1 and a rapid decrease for r > 4 n −1 . In order to explore the interior statistical properties of human chromosomes 21 and 22 in detail, we divide the chromosome sequence into some moving windows and we discuss the percentage of ξη ( ξ , η = A, C, G, T) pair in those moving windows. In some particular regions, there are some obvious changes in the percentage of ξη pair, and there maybe exist functional differences. The normalized number of repeats N 0 ( l ) can be described by a power law: N 0 ( l ) ∼ l − μ . The distance distributions P 0 ( S ) between two nucleotides in human chromosomes 21 and 22 are also discussed. A two-order polynomial fit exists in those distance distributions: log P 0 ( S ) = a + bS + cS 2 , and it is quite different from the random sequence.