Observations on the Ternary Quadratic Equation X2=24α2+Y2

2022 ◽

Vol 10 (1) ◽

pp. 62-65

Author(s):

C. Saranya

Keyword(s):

Infinite Number ◽

Diophantine Equation ◽

Cubic Equation ◽

Zero Integral ◽

Integral Solutions

Abstract: The Ternary cubic Diophantine Equation represented by૟(࢞ ࢟ + ૛ ࢠૡૡ = ૛࢟࢞૚૚ − (૛ ૜ is analyzed for its infinite number of non-zero integral solutions. A few interesting among the solutions are also discussed. Keywords: Diophantine equation, Integral solutions, cubic equation with three unknowns, Ternary equation.

Download Full-text

Empirical model approach for the evaluation of pH and conductivity on pollutant diffusion in soil environment

10.31221/osf.io/zndpg ◽

2019 ◽

Author(s):

Chem Int

Keyword(s):

Mathematical Model ◽

Quadratic Equation ◽

Diffusivity Coefficient ◽

Soil Environment ◽

Irreversible Reaction ◽

Chemical Pollutant ◽

The Mathematical Model ◽

Coefficient Of Diffusion ◽

Level Of Agreement ◽

Model Approach

This work is aimed at developing a mathematical model equation that can be used to predict the fate of contaminant in the soil environment. The mathematical model was developed based on the fundamental laws of conservation and the equation of continuity given asand was resolved to obtain a quadratic equation of the form C(X) = DX2+vX+f. The developed equation was then used to fit the experimental data that were obtained from the Physio-chemical analysis of the soil samples which were obtained at various depths; within the vicinity of the H & H Asphalt plant Company, located at Enito 3 in Ahoada West L.G.A, River State, Nigeria. The Experimental and Model results obtained from the Calculation and Simulation of the developed models were compared numerically and graphically as presented in this work. It was observed that there is reasonable level of agreement between the three results. The polynomial of the curve was established to ascertain the validity of the model; this was done for all the parameters that were analyzed. From the findings the model developed can be used to predict the concentration of a chemical pollutant at various depths. The reliability of the model developed was established giving the fact that through this quadratic equation the diffusivity (coefficient of diffusion), the water velocity and the irreversible reaction decay rate could be determined.

Download Full-text

Study on Optimization of Tungsten Ore Flotation Wastewater Treatment by Response Surface Method (RSM)

Minerals ◽

10.3390/min11020184 ◽

2021 ◽

Vol 11 (2) ◽

pp. 184

Author(s):

Liping Zhang ◽

Xiaofei Jiao ◽

Shengnian Wu ◽

Xuejing Song ◽

Ruihan Yao

Keyword(s):

Water Glass ◽

Suspended Solids ◽

Good Accuracy ◽

Ph Value ◽

Quadratic Equation ◽

Equation Model ◽

Residual Water ◽

Turbidity Removal ◽

Design Expert ◽

Surface Method

A large amount of collectors, inhibitors and modifiers such as oleic acid, water glass and sodium carbonate are added to the flotation processing of tungsten ore, resulting in the difficulty of the suspended solids (SS) with the residual water glass settling down in the flotation wastewater. The removal efficiency of the suspended solids is low with commonly used reagents like polyaluminium chloride (PAC) and polyacrylamide (PAM). This paper innovatively applied calcium chloride (CaCl2) to treat flotation wastewater and optimized the dosage of CaCl2, PAM and the pH value. The experimental results showed that when the dosage of 595 mg/L CaCl2 was combined with 21 mg/L PAM at pH 12, the turbidity removal ratio could reach 99.98%, and the residual turbidity of the supernatant was 0.23 NTU. The effluent could fully meet the requirements for reuse in industrial, urban miscellaneous and scenic environment water consumption (turbidity < 5 NTU). The quadratic equation model fitted with Design-Expert 8.0.6 software was constructed as Y = 91.52 + 8.68A + 1.11B − 1.02C − 1.7AB + 0.86AC + 0.06BC − 1.56A2 + 2.09B2 − 1.89C2, which had a good accuracy of the predicted responses versus the experimental data.

Download Full-text

Path-integral solutions of wave equations with dissipation

Physical Review Letters ◽

10.1103/physrevlett.62.2201 ◽

1989 ◽

Vol 62 (19) ◽

pp. 2201-2204 ◽

Cited By ~ 51

Author(s):

Cecile DeWitt-Morette ◽

See Kit Foong

Keyword(s):

Path Integral ◽

Wave Equations ◽

Solutions Of Wave Equations ◽

Integral Solutions

Download Full-text

Estimating Resting Core Temperature Using Heart Rate

Journal for the Measurement of Physical Behaviour ◽

10.1123/jmpb.2017-0003 ◽

2018 ◽

Vol 1 (2) ◽

pp. 79-86 ◽

Cited By ~ 7

Author(s):

David P. Looney ◽

Mark J. Buller ◽

Andrei V. Gribok ◽

Jayme L. Leger ◽

Adam W. Potter ◽

...

Keyword(s):

Heart Rate ◽

Core Temperature ◽

Estimation Algorithm ◽

Quadratic Equation ◽

Estimation Accuracy ◽

Future Research ◽

Accuracy And Precision ◽

Military Populations ◽

Thermal Work ◽

Ct Data

ECTemp™ is a heart rate (HR)-based core temperature (CT) estimation algorithm mainly used as a real-time thermal-work strain indicator in military populations. ECTemp™ may also be valuable for resting CT estimation, which is critical for circadian rhythm research. This investigation developed and incorporated a sigmoid equation into ECTemp™ to better estimate resting CT. HR and CT data were collected over two calorimeter test trials from 16 volunteers (age, 23 ± 3 yrs; height, 1.72 ± 0.07 m; body mass, 68.5 ± 8.1 kg) during periods of sleep and inactivity. Half of the test trials were combined with ECTemp™’s original development dataset to train the new sigmoid model while the other was used for model validation. Models were compared by their estimation accuracy and precision. While both models produced accurate CT estimates, the sigmoid model had a smaller bias (−0.04 ± 0.26°C vs. −0.19 ± 0.29°C) and root mean square error (RMSE; 0.26°C vs. 0.35°C). ECTemp™ is a validated HR-based resting CT estimation algorithm. The new sigmoid equation corrects lower CT estimates while producing nearly identical estimates to the original quadratic equation at higher CT. The demonstrated accuracy of ECTemp™ encourages future research to explore the algorithm’s potential as a non-invasive means of tracking CT circadian rhythms.

Download Full-text

New stellar models generated using a quadratic equation of state

Pramana ◽

10.1007/s12043-018-1650-x ◽

2018 ◽

Vol 91 (6) ◽

Cited By ~ 6

Author(s):

Jefta M Sunzu ◽

Mashiku Thomas

Keyword(s):

Equation Of State ◽

Quadratic Equation ◽

Quadratic Equation Of State ◽

Stellar Models

Download Full-text

A new derivation of the quadratic equation for the masses of the proton and electron

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1940.0002 ◽

1940 ◽

Vol 174 (956) ◽

pp. 16-41 ◽

Cited By ~ 2

Keyword(s):

Relativistic Theory ◽

Quadratic Equation ◽

Relativity Theory ◽

Physical Problems ◽

Considerable Simplification ◽

Physical Insight ◽

The Masses

1. In this paper I introduce some improvements of method which will, I think, bring about a considerable simplification of most of the physical problems treated in Part II of my book, Relativity theory of protons and electrons (hereinafter referred to as P. and E. ). They also facilitate the extension of the theory to other problems awaiting solution. Here I confine myself to one of the problems, namely, the derivation of the fundamental quadratic 10 m 2 - 136 mm 0 + m 2 0 = 0 for the mass m of a proton or electron. The derivation in P. and E. is, I believe, valid, though it now appears clumsy. But a proof giving more physical insight was greatly to be desired, since a thorough understanding of the underlying meaning of this relation is the first condition for a general advance. A general acquaintance with the relativistic theory in P. and E. must be presumed; but, as it happens, there is little occasion to refer to the more specialized parts of the theory.

Download Full-text