Third-degree Polynomial Equation Research Articles

Cole type Pitot tube, discharge factor survey and calibration

This article proposes that the Pitot Cole tube used for measuring water flow in the distribution does not require calibration, as it is an intrinsically self-calibrated equipment. Its function is to transform flow speed (kinetic energy) into manometric pressure, where the measurement is made by manometers or Pitometry Cases. The article also cites a third-degree polynomial equation that automatically corrects the Pitot Cole tube discharge factor rangeability from 3:1 up to 35:1. As a fundamental highlight, added to other article contributions, the credibility achieved today during a flow measurement is cited, reaching an accuracy from 3:1 or better, in the entire measurement range, of 35:1. In the water industry, the Pitot Cole tube interconnected in the Pitometry Case measure and record electronically the flow of treated and distributed water in the consumer sectors and, through specific software, it executes and issues a report comparing the Pitometric measurements against installed and fixed measurement equipment on the same network.

Stability analysis of spherical viscous fluid-Oldroyd B viscoelastic fluid interface: A viscous potential flow approach

The present study investigates the stability of a spherical interface formed by a combination of a viscous fluid and an Oldroyd B viscoelastic fluid using the linear stability analysis. The spherical geometry consists of a viscous fluid occupying the inner sphere, while the outer sphere is filled with the viscoelastic fluid. The governing equations are derived based on the viscous-viscoelastic irrotational theory, and their solutions are obtained using mathematical methods. The analysis results in a third-degree polynomial equation that describes the growth of perturbations, which is then evaluated numerically. It is found that the perturbations grow more rapidly at the interface between the viscoelastic and viscous fluids than at the interface between the viscous fluid and the surrounding medium. The instability of the interface increases with an increase in the Weissenberg number, which is a dimensionless parameter that characterizes the viscoelasticity of the fluid.

Simple adsorptive removal of crystal violet, a triarylmethane dye, from synthetic wastewater using Fe (III)-treated pine needle biochar.

Untreated and Fe (III)-treated pine needle biochar (PNB) were evaluated at different pH for the removal of toxic crystal violet (CV) dye from synthetic wastewaters. Adsorption kinetics followed the pseudo-first-order kinetics involving intra-particle diffusion process. The adsorption rate constant increased with Fe treatment of PNB especially at pH 7.0. Adsorption data of CV conformed well to Freundlich adsorption isotherms and both adsorption capacity (ln K) and order of adsorption (1/n) of CV were nearly doubled with Fe (III) treatment of PNB at pH 7.0. Desorption of adsorbed CV from both untreated and Fe (III)-treated PNB could be accounted satisfactorily by third-degree polynomial equations. An increase in ionic strength and temperature enhanced dye adsorption onto untreated and Fe (III)-treated PNB. Adsorption of CV was an endothermic and spontaneous reaction with an increase in entropy of the system. FTIR spectra revealed that C = O of carboxylic acid aryls and C = O and C-O-C in lignin residues of PNB reacted with Fe (III) besides the formation of some iron oxyhydroxide minerals. The changes in FTIR confirmed the possible bonding of positively charged moiety of CV with the untreated and Fe-treated PNB. Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) revealed the porous surfaces of PNB with clear accumulation of Fe (III) after treatment and deposition of CV dye on surfaces and pores of PNB. Iron (III)-treated PNB at pH 7.0 can serve as an ecofriendly and cost-effective adsorbent for the efficient removal of CV dye from wastewaters.

Characterization of a Novel Approach for Neonatal Hematocrit Screening Based on Penetration Velocity in Lateral Flow Test Strip.

Hematocrit (HCT) is a crucial parameter for both adult and pediatric patients, indicating potentially severe pathological conditions. Most common methods for HCT assessment are microhematocrit and automated analyzers; however, developing countries present specific needs often not addressed by these technologies. Paper-based devices can be suitable for those environments being inexpensive, rapid, easy to use, and portable. The aim of this study is to describe and validate against a reference method, a novel HCT estimation method based on penetration velocity in lateral flow test strips complying with the requirements in low- or middle-income country (LMIC) scenarios. To calibrate and test the proposed method, 145 blood samples of 105 healthy neonates with gestational age greater than 37 weeks were collected (29 calibration set, 116 test set) in the range of HCT values (31.6-72.5%). The time difference (Δt) from the whole blood sample loading into the test strip instant till the nitrocellulose membrane saturation instant was measured by a reflectance meter. A nonlinear relation was observed between HCT and Δt and was estimated by a third-degree polynomial equation (R2 = 0.91) valid in 30% to 70% HCT interval. The proposed model was subsequently used to estimate HCT values on the test set showing a good agreement between the estimated HCT and the HCT measured by the reference method (r = 0.87, p < 0.001), with a low mean difference of 0.53 ± 5.04% and a slight trend of overestimation for higher hematocrit values. The mean absolute error was 4.29%, while the maximum absolute error was 10.69%. Although the proposed method did not present a sufficient accuracy to be used for diagnostic purposes, it could be suitable as a fast, low-cost, easy-to-use screening tool especially in LMIC scenarios.

Evaluation of low-cost electronic sensors for monitoring soil moisture in an experimental area in the Brazilian semiarid

PurposeThis paper aims to determine and evaluate the calibration curve for low-cost electronic sensors in soils from a reclaimed and degraded area in the Brazilian semiarid region.Design/methodology/approachThe probes were made, programmed and inserted in soil previously conditioned in polyethylene cylinders. The sets “cylinder + probe + soil” were subjected to saturation for a period of 24 h and, subsequently, gravitational drainage at room temperature and daily weighings were performed. When the set reached constant weight, the samples were taken to dry in an oven at 105°C to determine the dry mass and later, determine the gravimetric moisture and convert it into volumetric. The volumetric moistures obtained were related to measured frequency variations and the adjustments were analyzed by regression, which was subjected to analysis of variance (p = 0.05), and related by a third-degree polynomial equation whose quality of the fit was verified with coefficient of determination (R2).FindingsThe obtained moistures were related to the estimated moistures and evaluated by the root-mean-square error and straight 1:1. The results demonstrate that the sensors are not accurate for moistures in saturation, but representative and statistically acceptable results for moistures up to field capacity.Originality/valueThis paper has not been published before in its current, or similar form.

Fat And Carbohydrate Oxidation During Cardiopulmonary Exercise Test In Childhood Acute Lymphoblastic Leukemia Survivors

PURPOSE: Analyses of indirect calorimetry during cardiopulmonary exercise tests (CPET) have the potential to bring new evidence about the metabolic health of childhood acute lymphoblastic leukemia (ALL) survivors. To propose a better knowledge of survivors’ metabolic health, we aimed to compare their carbohydrate and fat oxidation during a CPET. Moreover, we explored the long-term effects of doxorubicin and dexrazoxane on survivors’ metabolic health. METHODS: A total of 250 childhood ALL survivors were categorized into three groups depending on their prognostic risk (i.e., standard risk (SR), high risk with and without cardio-protective agent dexrazoxane (HR + DEX and HR)). They underwent a CPET on ergocycle to assess their oxygen consumption and their carbon dioxide production. Carbohydrate and fat oxidation rates were determined using the Peronnet and Massicotte’s equation. For each childhood ALL survivor, we produced a third-degree polynomial equation in order to obtain the best-fit curve for fat and carbohydrate oxidation rate (mg/min) against exercise intensity (%VO2peak). We also used them to compare carbohydrate and fat oxidation over a range of exercise intensities and to determine the maximal fat oxidation (MFO) rate and the peak fat oxidation (Fatmax) rate. MFO and Fatmax comparisons were made using one-way ANOVA. Multiple linear regression analysis was used to quantify each variable’s influence on the MFO and the Fatmax. RESULTS: We observed that MFO parameter was not different between the groups (p = 0.078) (SR = 273.7 ± 99.5 mg·min-1; HR + DEX = 247.3 ± 93.2 mg·min-1; and HR = 239.2 ± 86.0 mg·min-1). There was no difference between the groups for the Fatmax parameter (p = 0.865) (SR = 35.1 ± 7.4%; HR + DEX = 34.6 ± 7.5%; and HR = 35.7 ± 8.1%) and 14% of the variability was explained by the maximum oxygen uptake, sex and obesity. CONCLUSIONS: This study shows that although childhood ALL survivors have a reduced fat oxidation rates, that does not depend on the prognostic risk group. However, we observed a trend that suggests that the reduction of fat oxidation is doxorubicin dose-dependent and that the dexrazoxane treatment has the potential to limit these effects. Our study highlights that survivors’ metabolic health and substrate oxidation are compromised during a maximal cardiopulmonary exercise test.

Improved extraction of carrageenan from red seaweed (Chondracantus canaliculatus) using ultrasound-assisted methods and evaluation of the yield, physicochemical properties and functional groups

Red seaweed Chondracanthus canaliculatus, an underexploited algae species, was used as a potential source for the obtaining of carrageenan. Seaweed was treated under alkaline conditions using ultrasound alone or combined with conventional procedures, to improve the yield extraction. Color, syneresis behavior, water retention capacity, and functional groups of the gelling and non-gelling fractions of carrageenan were determined; these properties were compared with those of commercial carrageenans named A and B. Ultrasound alone or with heat significantly (p < 0.05) increased the yield extraction up to 41-45% and influenced color parameters, in comparison with conventional treatments. Functional groups kappa and iota, and alginates, were confirmed in both carrageenan fractions. Syneresis behavior was well fitted to a third-degree polynomial equation within days 1 to 6, after which, it reached a plateau. While, the use of ultrasound at room temperature gave carrageenan properties more similar to those of the commercial carrageenan type A.

Experimental Research on the Hysteretic Behaviour of Pressurized Artificial Muscles Made from Elastomers with Aramid Fibre Insertions

Inherent hysteresis behaviour of pressurized artificial muscles is complicated to understand and handle, calling for experimental research that allows the modelling of this phenomenon. The paper presents the results of the experimental study of the hysteretic behaviour of a small-size pneumatic muscle. The specific hysteresis loops were revealed by isotonic and isometric tests. Starting from hypothesis according to that the tube used for the pneumatic muscle is made entirely of aramid fibres enveloped by an elastomer material that merely ensures their airtightness, the paper presents the hysteresis curves that describe the radial and axial dimensional modifications as well as the variation of the developed forces for different feed pressures. The obtained third-degree polynomial equations underlie the configuration of high-performance positioning systems.

Generating roots of cubic polynomials by Cardano's approach on correspondence analysis

Cardano's formula is among the most popular cubic formula to solve any third-degree polynomial equation. In this paper, we propose the Cardano's approach as the alternative solution to generate the roots of the cubic characteristic polynomial analytically. In the context of correspondence analysis, these roots referred to eigenvalues, which play an important role in assessing the quality of the correspondence plot. Considering the correspondence analysis on the I×J contingency table for I=4 and J=4,5,⋯, we obtained a cubic characteristic polynomial (since zero is one of its eigenvalues). Therefore, Cardano's formula allows us to obtain the eigenvalues directly without involving numerical processes, e.g., using singular value decomposition. We note several advantages of using Cardano's approach, such as (1) it produces the roots with the same result as singular value decomposition, as well more precise because without errors involving, (2) the algorithm is simpler and does not depend on initial guess, hence the computation time becomes shorter than numerical process, and (3) the manual calculation is easy because it uses a formula. The results show that the matrix operations on correspondence analysis can be replaced by a formula for determining eigenvalues and eigenvectors of the standard residual matrix directly. Some mathematical results are also presented.

Permeation characterization and modelling of polyethylene/clay nanocomposites for packaging

The approach of upgrading barrier properties of polymer with nanofillers is effectual and well established now-a-days to manufacture films and quality packaging. This research deals with enhancement of barrier attributes of clay-based high density polyethylene nanocomposites against oxygen and water permeability. Na-Montmorillonite and two grades of kaolin clays were used for HDPE/clay nanocomposites preparation in twin-screw extruder with temperature profile of 160, 170, 180, 190 and 200 °C along the extruder at 110 rpm with clay loading up to 10 wt%. The extent of maximum reduction in water and oxygen vapors permeation was more prominent at 5 wt% sample of each clay. XRD analysis revealed no exfoliation in kaolin clay samples but indicated presence of exfoliation in Na-MMT samples. SEM and TEM micrographs revealed nano-level dispersion for both kaolin clays and Na-MMT and agglomerate formation at high wt% of clays. Experimental data for oxygen and water vapors permeation through nanocomposites were fitted on Nielsen, Cussler and Gusev–Lutsi models. Modelling of barrier performance was utilized for acquiring aspect ratio of filler for nanocomposites. Maximum and average aspect ratio of fillers and third-degree polynomial equation for nanocomposite, through curve fitting, were determined to predict improved barrier properties of nanocomposites.

A Geometric Model to Determine Patient-Specific Cup Anteversion Based on Pelvic Motion in Total Hip Arthroplasty.

Introduction Cup position is critical to stability in total hip arthroplasty and is affected by pelvis motion during positions of daily life. The purpose of this study was to explicitly define the relationship between sagittal pelvic motion and resultant cup functional anteversion and create a tool to guide the surgeon to a patient-specific intra-operative anteversion. Materials and Methods 10,560 combinations of inclination, anteversion, and pelvic tilt were generated using a geometric model. Resultant functional anteversion was calculated for each iteration and variables were correlated. An electronic mobile tool was created that compares inputted patient-specific values to population-based averages to determine pelvic positions and dynamics that may lead to instability. Results A third-degree polynomial equation was used to describe the relationship between variables. The freely downloadable mobile tool uses input from pre-operative plain radiographic measurements to provide the surgeon a quantitative correction to intra-operative cup anteversion based on differences in functional anteversion compared to population-based averages. Conclusion This study provides a geometric relationship between planned cup position, pelvic position and motion, and the resultant functional anteversion. This mathematical model was applied to an electronic tool that seeks to determine an individualized intra-operative cup anteversion based on measured patient-specific pelvic dynamics.

A methodological approach of predicting threshold channel bank profile by multi-objective evolutionary optimization of ANFIS

More accurate stable channel design methods are necessary for analyzing the complex bank profile cross sections of alluvial channels that achieve equilibrium state. This study introduces a new hybrid method that combines an adaptive neuro-fuzzy inference system (ANFIS), Differential Evolution (DE) algorithm and Singular Value Decomposition (SVD) to predict the bank profile of a threshold channel. SVD and DE serve to optimally determine the consequent linear parameters and antecedent nonlinear parameters of the TSK-type fuzzy rules in ANFIS. Moreover, by defining two objective functions and using the Pareto curve, the tradeoff of function is selected as the optimal modeling point. The authors carried out laboratory experiments at four discharge rates of 1.16, 2.18, 2.57 and 6.20 l/s to measure the coordinates of the points in a stable channel boundary profile. The ANFIS-DE/SVD results are compared with the results of a simple ANFIS model and 7 previous research works (based on numerical and experimental models and mathematical principles). The RMSE error index (0.019) of the ANFIS-DE/SVD model is lower than the ANFIS model (0.027), but both models outperform the best available model (CKM, Cao and Knight, 1998) (RMSE = 0.120). The ANFIS-DE/SVE model is more accurate for larger y (water surface level) values than the simple ANFIS model. Moreover, the superior performance of the hybrid ANFIS-DE/SVD over the simple ANFIS model is more pronounced at greater discharge rates. ANFIS-DE/SVD estimates the bank profile shape of a stable channel as a third-degree polynomial equation, which can be used to design and implement stable alluvial channels.

195 - The Role RHCD40L in Triggering Secretion of TNFa and VEGF on Bone Marrow Mononuclear Cells in MDS

Cardano's formula is among the most popular cubic formula to solve any third-degree polynomial equation. In this paper, we propose the Cardano's approach as the alternative solution to generate the roots of the cubic characteristic polynomial analytically. In the context of correspondence analysis, these roots referred to eigenvalues, which play an important role in assessing the quality of the correspondence plot. Considering the correspondence analysis on the I×J contingency table for I=4 and J=4,5,⋯, we obtained a cubic characteristic polynomial (since zero is one of its eigenvalues). Therefore, Cardano's formula allows us to obtain the eigenvalues directly without involving numerical processes, e.g., using singular value decomposition. We note several advantages of using Cardano's approach, such as (1) it produces the roots with the same result as singular value decomposition, as well more precise because without errors involving, (2) the algorithm is simpler and does not depend on initial guess, hence the computation time becomes shorter than numerical process, and (3) the manual calculation is easy because it uses a formula. The results show that the matrix operations on correspondence analysis can be replaced by a formula for determining eigenvalues and eigenvectors of the standard residual matrix directly. Some mathematical results are also presented.

Mathematical Modeling of Surface Roughness of Castings Produced Using ZCast Direct Metal Casting

Aim of this investigation is to develop a mathematical model for predicting surface roughness of castings produced using ZCast process by employing Buckingham’s π-theorem. A relationship has been proposed between surface roughness of castings and shell wall thickness of the shell moulds fabricated using 3D printer. Based on model, experiments were performed to obtain the surface roughness of aluminium, brass and copper castings produced using ZCast process based on 3D printing technique. Based on experimental data, three best fitted third-degree polynomial equations have been established for predicting the surface roughness of castings. The predicted surface roughness values were then calculated using established best fitted equations. An error analysis was performed to compare the experimental and predicted data. The average prediction errors obtained for aluminium, brass and copper castings are 10.6, 2.43 and 3.12 % respectively. The obtained average surface roughness (experimental and predicted) values of castings produced are acceptable with the sand cast surface roughness values range (6.25–25 µm).

Frequency, Moisture, Temperature, and Density-Dependent Dielectric Properties of Wheat Straw

<abstract><title><italic>Abstract.</italic></title> The dielectric constant (ε′) and dielectric loss factor (ε″), components of the complex permittivity relative to free space, of wheat straw samples at moisture content of 10.4% to 20.3% wet basis (w.b.) were determined with a parallel-plate electrode assembly over the frequency range from 1 to 1000 kHz, bulk density range from 47.2 to 108.1 kg m^-3, and temperature range from 5°C to 40°C. Obvious negative and linear relationships between logarithmic permittivities (ε′ and ε″) and logarithmic frequency were found below about 500 kHz. Over the investigated ranges of the variables, both ε′ and ε″ increased almost linearly with increasing temperature and increased obviously with an increase in moisture content and bulk density at higher levels. The relationship between the dielectric properties and moisture content, temperature, and bulk density at some selected frequencies could be described by third-degree polynomial equations. Analysis of variance showed that moisture content, temperature, and bulk density were all significant factors of these equations at a significance level of 0.0001. The equations were verified to be accurate in calculating the dielectric properties of wheat straw from a given moisture content, temperature, and bulk density at the selected frequency. This study offers useful information for developing moisture sensors of wheat straw from dielectric properties.

Prediction of ice content in biological model solutions when frozen under high pressure

High pressure is, at least, as effective as cryoprotective agents (CPAs) and are used for decreasing both homogenous nucleation and freezing temperatures. This fact gives rise to a great variety of possible cryopreservation processes under high pressure. They have not been optimized yet, since they are relatively recent and are mainly based on the pressure-temperature phase diagram of pure water. Very few phase diagrams of biological material are available under pressure. This is owing to the lack of suitable equipment and to the difficulties encountered in carrying out the measurements. Different aqueous solutions of salt and CPAs as biological models are studied in the range of 0 degrees C down to -35 degrees C, 0.1 up to 250 MPa, and 0-20% w/w total solute concentration. The phase transition curves of glycerol and of sodium chloride with either glycerol or sucrose in aqueous solutions are determined in a high hydrostatic pressure vessel. The experimental phase diagrams of binary solutions were well described by a third-degree polynomial equation. It was also shown that Robinson and Stokes' equation at high pressure succeeds in predicting the phase diagrams of both binary and ternary solutions. The solute cryoconcentration and the ice content were calculated as a function of temperature and pressure conditions during the freezing of a binary solution. This information should provide a basis upon which high-pressure cryopreservation processes may be performed and the damages derived from ice formation evaluated.

Kinetic study on colour changes in wheat germ due to heat

Colour change during infrared heating of wheat germ was studied at 100–150°C for 5–40 min. An increase in L values and a decrease in a values were observed at increased time and temperature of heating. Scattered data were obtained for the b values. Results showed that the L and a values can be successfully modelled using a third-degree polynomial equation, which can be used to estimate the colour changes during heating. The activation energy for the colour changes in wheat germ, based on the L values, was found as 36.6 kJ/mol.

FORESHORE DEPOSITIONAL PATTERNS ALONG THE RHODE ISLAND SOUTHSHORE

An application of polynomial curve fitting to sediment cumulative frequency distributions is presented to delineate the foreshore depositional patterns along the barrier beaches of the Rhode Island southshore. The analysis is based on 92 sampled stations where data for beach geometry, tidal stage, and sediment size were collected. Using the size-frequency classes obtained from sieving the foreshore sediment samples at 0.25 O intervals and fitting third-degree polynomial equations to these data, over 94% of the variation within the sediment cumulative frequency distributions is explained. The four curve coefficients (a, b, c, d) derived from the predicted third-degree equation are used in a discriminant function analysis to test the relationship between the curve shape and sediment source. Comparison of the discriminant scores with the respective station locations suggests that a series of Pleistocene headlands which occur as discrete points along the beach are serving as independent sources of sediment fo...

Embryonic trunk circumference: A new biometric parameter for estimation of gestational age

One hundred thirty-one uncomplicated, singleton pregnancies between 7 and 12 weeks of gestation were ultrasonically examined. Evaluation included confirmation of cardiac activity and measurements of fetal crown-rump length and trunk circumference. Both crown-rump length and trunk circumference were curvilinearly correlated with gestational age. A second- and third-degree polynomial equation best described this curvilinear relationship between trunk circumference and gestational age and between crown-rump length and gestational age. The crown-rump length and trunk circumference were similar in their prediction of gestational age, but the combination of the two parameters did not improve the prediction of gestational age. A nomogram of gestational age as predicted by trunk circumference was generated. These data provide an additional measurement for the estimation of gestational age in the first trimester of pregnancy.

A quantitative study of cochlear potentials along the scala media of the guinea pig.

The relationship between the parameters of pure-tone acoustic stimuli and those of the cochlear microphonics (CM) and summating potentials (SP) was studied for measurements from scala media in each of the four turns of the guinea-pig cochlea. For each turn similarities in the shapes of the input-output functions over a wide range of frequencies permitted adequate quantitative description of these functions by a single third-degree polynomial equation. Therefore, the properties of both cochlear potentials (CM and SP) can be described by a nonlinear transfer curve over the specified frequency range. These results imply the SP should not be regarded as being generated by a process different from the CM but as an expression of the nonlinear characteristics of the generator of cochlear potentials. At frequencies where the measuring electrode is near the peak of the mechanical traveling wave envelope, the transfer curve no longer described the cochlear potentials. Calculations based upon phase measurements and upon theoretical considerations indicate that this is due to interference effects from the out-of-phase generators in the vicinity of the electrode.