Second-degree Polynomial Equation Research Articles

Influence of porosity on the Umov effect in silicate and organic refractory aggregates

This study investigates the influence of porosity on the Umov effect, a phenomenon observed in the scattering of light from celestial objects. The Umov effect describes an inverse relationship between the degree of linear polarization and the object’s reflectance (geometric albedo). To study the dependence of porosity on the Umov effect, a wide range of porosity (i.e., from 0.64 to 0.99) is considered. Four types of aggregates, ballistic cluster–cluster aggregate (BCCA), ballistic particle cluster aggregate (BPCA) or ballistic agglomeration (BA), ballistic agglomeration with one migration (BAM1), and ballistic agglomeration with two migrations (BAM2) each having porosity 0.99, 0.87, 0.74, and 0.64 are considered in this study. The multi-sphere T-matrix code is utilized to calculate the linear polarization and geometric albedo (A) considering silicate and organic refractory compositions for monodisperse aggregates. The results are reported for six different wavelengths, ranging from near-ultraviolet to the visible spectrum. When the polarization maximum (Pmax) is plotted against the geometric albedo (A) on a logarithmic scale, an inverse relation is observed. This relation exhibits non-linear changes, fitted by a second-degree polynomial equation, as the porosity changes from 0.64 to 0.99. This finding constitutes one of the interesting results of our study. In addition, the study explores the effect of porosity (P) on the ratio between log(Pmax) and log(A), showing a non-linear relationship. A comparison is drawn between the results obtained from organic refractory compositions and amorphous silicate compositions, emphasizing the importance of porosity and wavelength in regulating the Umov effect. In addition, the research investigates how mixing affects the results at different wavelengths, assuming the aggregates are blends of organic refractory and amorphous silicate compositions. The computations have also been performed for polydisperse aggregates (considering BCCA, BA, BAM1, and BAM2 structures) at a wavelength of 0.45 μm for silicate compositions, which also showed a non-linear dependence as observed in the case of monodisperse aggregates.

Efficient and Low-Cost Water Remediation for Chitosan Derived from Shrimp Waste, an Ecofriendly Material: Kinetics Modeling, Response Surface Methodology Optimization, and Mechanism

The hydrothermal production of chitosan from the carapaces of gray shrimp was carried out, and the obtained material was characterized via X-ray diffraction analysis, infrared spectroscopy, and pH zero-charge point, giving the expected results. Orange G dye adsorption onto synthetized chitosan was investigated in a batch system, the kinetic study was well-described by a nonlinearized pseudo-second-order model, and the equilibrium data indicated that the nonlinear Langmuir form was appropriate to describe the adsorption system with a maximum adsorption capacity of 34.63 mg/g compared with that found experimentally of 31.9 mg/g. The influences of most of the operating parameters, such as pH, adsorbent concentration, temperature, initial dye concentration, and contact time, were studied. These five independent variables acting on the adsorption performance of Orange G were selected for optimization and modeling processes through a central rotating composite design using response surface methodology (RSM). The percentage of removal of Orange G by chitosan prepared from shrimp shells was predicted with a second-degree polynomial equation, and the postulated model was valid and represented well the phenomenon studied in the experimental domain, with an R2 = 0.98 and an RAdj = 0.95. An initial Orange G concentration of 10 mg/L, a pH of 6.5, a chitosan amount of 0.3 g/L, a temperature of 25 °C, and an adsorption time of 450 min were found to be the optimum conditions in batch mode for the maximum uptake of Orange G (removal of 97.43%).

A study of the correlation between polarization maximum to minimum ratio and scattering parameters in a spheroid dust model

This paper investigates the correlation between the ratio of polarization maximum to polarization minimum (Pz) and different scattering parameters such as complex refractive indices (m=n+ik), effective radius (reff), effective variance (veff), and axial ratio (E) for spheroidal particles. The simulations are executed using the double-precision T-matrix code for randomly oriented spheroidal particles, considering different sets of scattering parameters. For a specific range of n, k, E, reff, and veff, a strong correlation between Pz and other scattering parameters is observed in all cases, which can be fitted by a second-degree polynomial equation. The simulations are conducted at two wavelengths (λ=0.50 µm and 0.65 µm). Additionally, we compare our results obtained from numerical simulation with the experimental data for a few forsterite samples conducted by Muñoz et al. (2021). A set of conclusions is presented based on our work.

Optimization of the Extraction of Antioxidant Compounds from Roselle Hibiscus Calyxes (Hibiscus sabdariffa), as a Source of Nutraceutical Beverages

Secondary metabolites from Hibiscus sabdariffa have been used to prevent different diseases. Roselle Hibiscus is known for being rich in phenolic bioactive compounds. The extraction conditions are directly related to the chemical composition and then to the overall bioactivity of the extract. In this study, a Box-Behnken experimental design has been used to optimize the antioxidant activity, considering four variables: ethanol:water ratio, temperature, extraction time, and solvent:solid ratio. The experiment comprises 27 experiments and 3 repetitions at the central point. The results are described by surface response analysis and a second-degree polynomial equation. The model explains 87% of the variation in the response. The maximum antioxidant activity is yielded when 1% solids are extracted in 35.5% ethanol at 60 °C for 33 min. Finally, a nutritional functional supplement of 495 µmol Trolox Equivalent (TE) antioxidant capacity was prepared with the optimized extract.

PREPARATION OF ACTIVATED CARBON FROM TIRE DERIVED PYROLYTIC CHAR FOR ADSORPTION OF TETRACYCLINE HYDROCHLORIDE

Effects of activation variables on performance of the obtained activated carbon (AC) were investigated for removal of tetracycline hydrochloride (TCH). Pyrolytic char derived from waste tire was chemically activated via two-step of KOH impregnation following by thermal treatment. According to regression analysis and fitting with second-degree polynomial equation, empirical models were developed to correlate performance of AC in TCH adsorption (percentage removal and adsorption capacity at equilibrium) with three activation variables: impregnation ratio (IR), activation temperature (T) and holding time of thermal treatment (t). The analysis of variance indicated that only T, T2 and IR2 were significant to the prediction of both percentage removal and adsorption capacity. According to the developed models, it is suggested that the pyrolytic char should be activated at IR = 6, T = 750 °C and t = 2 h to obtain the highest efficiency of TCH removal in the tested range of activation condition.

Drawbar performance of a power tiller on a sandy loam soil of the Nadia district of West Bengal

A 9.69 kW power tiller's drawbar performance was tested by using a drawbar loading vehicle consisting of a power tiller with a mould board (MB) plough. A spring-loaded dynamometer was attached between the tested power tiller and the loading vehicle to measure the drawbar pull. The drawbar pull was changed from 0.905 kN to 2.232 kN by varying the operating depth of the MB plough. Empirical equations were developed to correlate the drawbar pull to the wheel slip, drawbar power, fuel consumption, and drawbar specific fuel consumption (DBSFC), and one was developed to correlate the drawbar power to the wheel slip. The wheel slip increased exponentially with an increase in the drawbar pull and drawbar power. A maximum wheel slippage of 48.94% was observed at a 2.232 kN drawbar pull and 0.763 kW drawbar power. A second-degree polynomial equation was found to correlate the drawbar pull to the drawbar power, fuel consumption, and DBSFC. The maximum drawbar power was found as 0.763 kW at a 2.02 kN drawbar pull, which was 7.87% of the rated engine power. The fuel consumption increased by 66.93%, and the DBSFC reduced by 10.56% due to the increase of the drawbar pull from 0.905 kN to 2.232 kN. The lowest DBSFC of 2.01 kg·kWh<sup>–1</sup> was found at a 2.232 kN drawbar pull.

Comparison of Erythrocyte and Reticulocyte Indices for Evaluation of Iron Deficiency by Two Automated Hematologic Analyzers.

The reticulocyte hemoglobin content and hypochromic erythrocyte percentage offer advantages in evaluation of iron deficiency, especially in inflammatory conditions. The aim of this study was to evaluate the correlation of reticulocyte hemoglobin content (CHr, Ret-He) and hypochromic erythrocyte percentage (%HYPO, Hypo-He) between two automated hematologic analyzers. The CHr and %HYPO values were determined using the Advia 2021i (Siemens), while the Ret-He and Hypo-He levels were assessed using the XN-3000 (Sysmex). Data from a total of 971 cases and 834 patients were collected. For reticulocyte hemoglobin content, there was a good linear correlation between CHr and Ret-He (r = 0.857, p < 0.001). For percentage of hypochromic erythrocytes, there was a better correlation between the two measures when using a second-degree polynomial equation (Hypo-He* = 0.4818 - 0.0218 x %HYPO + 0.0069 x %HYPO2) (r = 0.786, p < 0.001).

Conics in Place

A method is presented for creating a problem, solving it, and confirming that the solution is correct. The problem is to analyze a second-degree polynomial equation in two variables, in order to identify and draw the defined conic section, with its axes, without changing coordinates. One creates the problemby choosing conjugate diameters that are not axes.

Numerical Analysis of Additional Stresses in Railway Track Elements Due to Subgrade Settlement Using FEM Simulation

The prediction of additional stresses in ballasted track due to subgrade deformation is the main objective of the present paper. In this context, a 2D finite element model of ballasted railway track was built using the ANSYS Workbench program. Based on this model, an investigation of stresses and deformation values of track elements was conducted in three cases with different contact types. It was found that the case introducing the status of a new track, which has frictional contacts between sleepers and ballast with bonded contacts between other elements, has lower stresses in most of the track elements. Moreover, this case was applied for studying the effect of the settlement on track elements. It was found that stresses increased with increasing the settlement value. The average percentages of increased stresses are 4.18%, 5.85%, and 7.21% in railhead, tie plate, and sleeper, respectively, due to a 1 mm increase in the settlement. Finally, a second-degree polynomial equation was derived to predict the additional stresses in each element due to track settlement. It is expected that this study would help to decrease the maintenance costs and extend the service life of the track elements by predicting the additional stresses in them.

Analysis of Vehicle Specific Acceleration and Deceleration Characteristics at Toll Plazas in India

Acceleration and deceleration are amongst the vehicular characteristics, which are both time dependent and location dependent. The present study aims to quantify the variation in acceleration and deceleration characteristics at manually operated toll plaza under mixed traffic conditions. The field data collected for seven different vehicle categories observed at Ghoti toll plaza using global position system based P-box survey. The discretization of speed profile technique was developed and used for evaluation of acceleration and deceleration values in Zone of Influence (ZOI) precisely. The results of descriptive statistics showed that the ZOI for toll plaza was about 500 m totally with 250 m in upstream and 250 m in downstream. The speed versus distance and acceleration/deceleration versus distance plots were plotted and regression analysis was carried out for finding out relation. One-way analysis of variance test was also performed to check whether the significant difference exist between the acceleration/deceleration values for each section and within the section for all seven categories. It was found that the second-degree polynomial equation was best fit for both acceleration and deceleration with respect to distance. Accuracy of the developed model was checked using the t statistics.

Influence of high and subsequent low-temperature artificial ageing on exfoliation corrosion of AA2024

The present study aims at assessing the mechanical behavior of aluminum alloy (AA2024) subjected to exfoliation corrosion. The material was exposed to high temperature and subsequent low temperature (HLA) treatment and further the heat-treated samples were subjected to exfoliation corrosion for the duration of 48 and 96 h at room temperature. The HLA treatment increases the retention property of material in the corrosive environment. Further, hardness and impact strength was also increased under the corrosive environment with HLA treatment. In addition to the experimental investigation, a series of simple second-degree polynomial equations were developed to predict the various mechanical properties at different intervals of corrosion durations of AA2024 specimens subjected to HLA exfoliation corrosion.

Effect of Cooking Methods on Canned Chontaduro (Bactris gasipaes Kunth)

Background:: The aim of the work was to determine the effects of the stage of peeling and different thermal processes on the physicochemical and sensory properties of canned peach palm or Chontaduro (Bactris gasipaes). Methods:: The thermal processes involved two cooking temperatures (107 and 92ºC) and three types of cooking and peeling process (unpeeled, peeled after cooking process and peeled before cooking process). Results:: The thermal process resulted in a decrease of soluble solids and an increase in the pH, following a second-degree polynomial equation; also, a decrease in protein content, total carotenoids and hardness. Conclusion:: Canned chontaduro, previously peeled and cooked at 107ºC, had significantly better physicochemical, nutritional, microbiological and sensory properties.

Enzyme-Assisted Extraction of Anthocyanin from Kokum (Garcinia indica Choisy) Rinds

Background: The kokum rind consists of high amount of anthocyanin. The traditional methods are not capable to extract anthocyanin completely.&#x0D; Aims: The present study was focused on the optimization of enzyme pretreatment for extraction of anthocyanin from Kokum rind.&#x0D; Methodology: A central composite design was used to optimize the enzyme-assisted extraction of anthocyanin from the Kokum rinds. Kokum rinds was pretreated with food-grade pectinase and cellulase enzymes separately and then subjected to acidified ethanol extraction. The factors investigated included enzyme concentration (0 – 2%), Incubation time (1-5 h) and pretreatment temperature (15–55ºC).&#x0D; Results: Overall, 107.17- to 63.71 - fold increase in anthocyanin recovery when treated with pectinase and cellulase, respectively was observed compared to the untreated rinds. From a response surface analysis of the data, a second-degree polynomial equation was developed which provided the following optimal extraction conditions i.e. enzyme concentration 0.5%, Incubation time 2.0h and temperature 35ºC for pectinase pretreatment. Whereas, in case of cellulase the optimum conditions was enzyme concentration 1.42%, Incubation time 4.0h and temperature 32ºC. The obtained results strongly support the idea of using cell-wall degrading enzymes as an effective means for recovering anthocyanin from Kokum rinds.

Supplies of suspended matter by surface water of the Mazafran drainage basin (western Algiers, Algeria)

The Mazafran wadi is characterized by a strong connection of the solids flow in kilograms per second to the liquid flow in cubic meters per second. However, high solids flow can also be associated to low liquid flow after severe summer storms. We also note that high water flows generate low solids transport; this is probably because of the groundwater draining after major floods. The relation between the daily solids flow and the average daily liquid flow varies from 50 to 600 m3 s−1. It is represented as follows: Qs = 2.03 Qmj2.626. The correlation of suspended matter and liquid flow concentrations follows the Serrat model which is presented as a second-degree logarithmic-based polynomial equation. Both equations show that the Total Suspended Solid (TSS) increases with the downstream and upstream flow. The suspended solids transport occurs mainly in the winter and to a less extent in the spring and autumn.

An Iterative Approach to Stratification: Poverty at Regional Level in Italy

We develop an iterative procedure to generate stratification in non-overlapping classes of a population based on a one-dimensional variable, namely, the Italian income. The procedure works under the assumption that the income distribution is generated by a log-normal mixture of homogeneous income groups. The number of income groups is not determined a priori but rather endogenously by the iterative procedure that stops when the solution to a specific second-degree polynomial equation does not exist. We apply the approach to study the heterogeneity of Italian incomes and the poor population at regional level in the years 2005, 2010, and 2015. The cross-regional comparisons show differences in inequality and stratification dynamics while comparisons over time show the evolution of the classes.

Subcooled critical heat flux on laser-textured stainless-steel ribbon heaters in pool boiling of FC-72

This study investigates critical heat flux (CHF) enhancement in pool boiling of FC-72 under saturated and subcooled conditions using laser-textured stainless-steel surfaces in combination with a hydrophobic coating. Multiple types of surfaces with capillary-length-spaced circular spots of different diameters are prepared with the spots being either untreated, hydrophobized or laser pretreated and hydrophobized. Pool boiling measurements are performed at atmospheric pressure on electrically heated ribbons. The CHF versus subcooling behavior is modeled using an established linear equation, while a modification into a second-degree polynomial is also tested to better account for nonlinear behavior of some surfaces. All developed surfaces are found to increase the CHF with enhancements ranging from 36 to 73% at saturation and 34–65% at 12 K of subcooling. Surfaces with mixed regions of low and high wettability generally exhibited the highest CHF enhancement at a 31% coverage with low wettability areas. Samples with laser-pretreated and hydrophobized spots exhibited the highest overall performance at saturation but a less steep trend of CHF versus liquid subcooling increase and CHF increase with increased superhydrophobic area ratio, indicating a different enhancement mechanism with hydrophobized microcavities presumably serving as preferential nucleation sites. Modeling of the CHF versus subcooling trend showed that (i) a second-degree polynomial equation is more appropriate for some surface types and (ii) the obtained constants differ significantly from surface to surface. Evaluation of a universal model based on all datapoints obtained within this study showed inadequate performance with error margins of ±13.5%. Consequently, the use of individual models for each type of enhanced surfaces with an overall accuracy of ±5.9% is recommended.

Optimization of Technological Modes of Extraction of Tea Raw Material Used in Emulsion Beverages Technology

The article observes the technological modes optimization of tea raw materials extraction (black tea and hibiscus tea beverage) used in the technology of emulsion drinks as natural food additives (dyes, flavorings, surfactants) and sources of valuable biologically active substances. The researchers studied the mass fraction dependence of soluble solids and vitamin C in tea extracts on the determining factors (hydromodule, duration and temperature) that affect the extraction kinetics of the biologically active substances using mathematical modeling. Based on the experiment results processing, a man obtained second-degree polynomial equations that adequately described the mathematical dependence of the mass fraction of soluble dry extract substances on the hydromodule and the extraction time. The researchers experimentally determined the optimal extraction parameters: time – 15 and 20 minutes; temperature – 70 and 60 °C for black tea and hibiscus drink, respectively; hydromodule – 1:5. The mass fraction of the functional ingredient (vitamin C) under the specified modes was from 84.6 to 189.2 mg/%. The researchers run the commodity quality evaluation of tea extracts obtained according to the developed parameters. On organoleptic and safety indicators tea extracts met the requirements of the current normative documentation.

Прогнозування діаметра без кори на різній висоті стовбурів дерев ялиці білої в Українських карпатах

Дослідження особливостей взаємозв'язку між діаметрами в корі та без кори на різних висотах стовбурів ялиці білої здійснено за результатами замірів 60 модельних дерев (27 для умов С3 та 33 для умов D3) у модальних ялицевих деревостанах Українських Карпат. Встановлено, що досліджувані типи лісорослинних умов (ТЛРУ) С3 та D3 не мають істотного впливу на значення товщини кори дерев ялиці. Регресійні залежності між діаметрами в корі та без кори встановлено способом порівняння біометричних показників восьми рівнянь, які запропонували різні автори. Розраховані на основі дев'яти біометричних показників середні ранги досліджуваних рівнянь показали, що найкраще взаємозв'язок між діаметрами в корі та без кори для стовбурів дерев ялиці описує рівняння, яке запропонував Crous (2009) (№ 4), а найгірші результати – рівняння № 6 (Meyer, 1946). Рівняння, що враховують висоту заміру діаметрів, загалом дали точніші результати, порівняно з іншими. Найбільші значення відхилень між фактичними та модельними значеннями діаметрів без кори спостережено у верхівковій частині стовбура (відносна висота – понад 0,8). Здійснено вирівнювання отриманих коефіцієнтів регресії для рівняння Crous (2009) за способом найменших квадратів з використанням квадратичної функції. Середнє відхилення між фактичними та змодельованими діаметрами без кори становить 0,13 %, що свідчить про адекватність підібраного рівняння.

Controlled Design of Phase- and Size-Tunable Monodisperse Ni2P Nanoparticles in a Phosphonium-Based Ionic Liquid through Response Surface Methodology

Nanoparticles of nickel phosphide are finding wide ranging utility as catalysts for hydrodesulfurization, hydrogen evolution reaction, and hydrodeoxygenation of bio-oils. Herein, we present a methodology to tailor monodisperse nickel phosphide nanoparticles in terms of size and phase through the use of a statistical response surface methodology. Colloidal nickel phosphide nanoparticles were synthesized by replacing octadecene (ODE), a commonly used organic solvent, by a more sustainable phosphonium-based ionic liquid (IL). The replacement of ODE with the phosphonium-based IL resulted in faster crystallization at lower temperatures to yield phase-pure, monodisperse Ni2P nanoparticles. Using a first-order design, the PPh3/Ni precursor ratio was identified as the most critical factor influencing the resulting size and phase of the nanoparticles. Optimization using a Doehlert matrix for second-order design yielded a second-degree polynomial equation used to predict the mean diameter of the nanoparticles (over...

Age- and Sex-Specific Reference Values for Media/Lumen Ratio in Small Arteries and Relationship With Risk Factors.

Small-artery remodeling is an early feature of target organ damage in hypertension and retains a negative prognostic value. The aim of the study is to establish age- and sex-specific reference values for media/lumen in small arteries obtained in humans by biopsy. Data from 91 healthy individuals and 200 individuals with cardiovascular risk factors in primary prevention from 4 Italian centers were pooled. Sex-specific equations for media/lumen in the healthy subpopulation, with age as dependent variable, were calculated. These equations were used to calculate predicted media/lumen values in individuals with risk factors and Z scores. The association between classical risk factors and Z scores was then explored by multiple regression analysis. A second-degree polynomial equation model was chosen to obtain sex-specific equations for media/lumen, with age as dependent variable. In the population with risk factors (111 men, age 50.5±14.0 years, hypertension 80.5%), media/lumen Z scores were independently associated with body mass index (standardized β=0.293, P=0.0001), total cholesterol (β=0.191, P=0.031), current smoking (β=0.238, P=0.0005), fasting blood glucose (β=0.204, P=0.003), systolic blood pressure (β=0.233, P=0.023), and female sex (β=0.799, P=0.038). A significant interaction between female sex and total cholesterol was found (β=-0.979, P=0.014). Results were substantially similar in the hypertensive subgroup. A method to calculate individual values of remodeling and growth index based on reference values was also presented. Age- and sex-specific percentiles of media/lumen in a healthy population were estimated. In a predominantly hypertensive population, media/lumen Z scores were associated with major cardiovascular risk factors, including body mass index, cholesterol, smoking, glucose, and systolic blood pressure. Significant sex differences were observed.