The Single First Order Equation

1975 ◽  
pp. 6-47
Author(s):  
F. John
Keyword(s):  
Order Equation ◽  
First Order

scholarly journals ON SUPERLUMINAL FERMIONS WITHIN THE SECOND DERIVATIVE EQUATION

2012 ◽  
Vol 27 (14) ◽  
pp. 1250081 ◽  
Author(s):  
S. I. KRUGLOV
Keyword(s):  
Energy Momentum Tensor ◽  
Canonical Quantization ◽  
Vacuum Expectation ◽  
Momentum Tensor ◽  
Order Equation ◽  
Quantum Mechanical ◽  
Projection Operators ◽  
The Novel ◽  
First Order ◽  
Electromagnetic Interactions

We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy–momentum tensor are found. The minimal and nonminimal electromagnetic interactions of fermions are considered and Schrödinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators.

On the Vibration of a Rotating Disk

1972 ◽  
Vol 39 (4) ◽  
pp. 1143-1144 ◽  
Author(s):  
S. Barasch ◽  
Y. Chen
Keyword(s):  
Approximate Calculation ◽  
Initial Conditions ◽  
Rotating Disk ◽  
Equation Of Motion ◽  
Outer Radius ◽  
Order Equation ◽  
System Of Differential Equations ◽  
Fourth Order Equation ◽  
First Order ◽  
Inner Radius

The equation of motion of a rotating disk, clamped at the inner radius and free at the outer radius, is solved by reducing the fourth-order equation of motion to a set of four first-order equations subject to arbitrary initial conditions. A modified Adams’ method is used to numerically integrate the system of differential equations. Results show that Lamb-Southwell’s approximate calculation of the frequency is justified.

scholarly journals Electrochemical Removal of Chromium (VI) from Wastewater

2019 ◽  
Author(s):  
Hao Peng ◽  
Yumeng Leng ◽  
Jing Guo
Keyword(s):  
Reaction Temperature ◽  
Current Density ◽  
Reduction Rate ◽  
Reduction Process ◽  
Order Equation ◽  
First Order ◽  
Chromium Vi ◽  
Reduction Efficiency ◽  
Pseudo First Order ◽  
Electrochemical Removal

Removal of hexavalent chromium had attracted much more attention as it was a hazardous contaminant. Electrochemical reduction technology was applied to removal chromium (VI) from wastewater. The mechanism and parameters affect the reduction process were investigated. The results showed that the reduction efficiency was significantly affected by the concentration of H2SO4, current density and reaction temperature. And the reduction efficiency was up to 86.45% at concentration of H2SO4 of 100g/L, reaction temperature of 70 ℃, current density at 50 A/m2, reaction time at 180 min and stirring rate of 500 rpm. The reduction process of chromium (VI) was followed pseudo-first-order equation, and the reduction rate could be expressed as Kobs = k [H2SO4]1• [j] 4•exp-4170/RT.

The Characteristics and Kinetic Equation of 4-CP Biodegradation by Fusarium sp. HJ01

2012 ◽  
Vol 554-556 ◽  
pp. 1925-1928 ◽  
Author(s):  
Ji Wu Li ◽  
Xiao Hong Zhu ◽  
Jun Ya Pan
Keyword(s):  
Carbon Source ◽  
Sole Carbon Source ◽  
Degradation Rate ◽  
Order Equation ◽  
First Order ◽  
Haldane Model ◽  
Effects Of Ph ◽  
Fusarium Sp ◽  
Ph Range ◽  
Kinetics Of

The stain of Fusarium sp. HJ01 used in 4-chlorophenol (4-CP) degradation was isolated in our laboratory. The effects of pH, temperature, 4-CP concentration, carbon source on 4-CP degradation rate were studied. It was concluded that Fusarium sp. HJ01 could grow with 4-CP as the sole carbon and energy source. 4-CP concentration of 100mg/L in the pH range of 4~10 and temperature range of 25°C~35°C could be degraded completely. The capacity of 4-CP degradation was effectively enhanced by the addiction of sucrose. The kinetics of 4-CP degradation could well accord with the Haldane model for 4-CP as the sole carbon source and with first order equation for added other sucrose.

scholarly journals A Partial Lagrangian Approach to Mathematical Models of Epidemiology

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naz ◽  
I. Naeem ◽  
F. M. Mahomed
Keyword(s):  
Mathematical Models ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
First Integrals ◽  
Order Equation ◽  
Second Order ◽  
Lagrangian Approach ◽  
Hiv Model ◽  
First Order ◽  
Partial Lagrangian

This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second-order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system. We investigate the SIR and HIV models. We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.

Modeling Diclofop Activity on ThreeBromusSpecies

Weed Science ◽  
1985 ◽  
Vol 33 (2) ◽  
pp. 250-252
Author(s):  
Phillip W. Stahlman
Keyword(s):  
Methyl Ester ◽  
Bromus Tectorum ◽  
Polynomial Equation ◽  
Order Equation ◽  
Propanoic Acid ◽  
Downy Brome ◽  
First Order ◽  
Bromus Secalinus ◽  
Cubic Polynomial ◽  
Over Time

The methyl ester of diclofop {2-[4-(2,4-dichlorophenoxy)phenoxy] propanoic acid} mixed with soil at 1, 2, and 3 ppmw reduced the growth ofBromusspecies in the greenhouse as follows: downy brome (Bromus tectorumL. ♯ BROTE) more than Japanese brome (Bromus japonicusThunb. ex Murr. ♯ BROJA) more than cheat (Bromus secalinusL. ♯ BROSE). The decrease in herbicide effect (decay) over time was described better using a second-order equation than a first-order equation. Plant response-herbicide dose relationships were described best with a cubic polynomial equation.

Kinetics of Glyphosate Adsorption on Composite Resin from Aqueous Solution

2013 ◽  
Vol 803 ◽  
pp. 157-160
Author(s):  
Zhen Zhen Kong ◽  
Dong Mei Jia ◽  
Su Wen Cui
Keyword(s):  
Experimental Data ◽  
Aqueous Solution ◽  
Composite Resin ◽  
Order Equation ◽  
Second Order ◽  
First Order ◽  
Basic Resin ◽  
Pseudo Second Order ◽  
Kinetics Of ◽  
Best Fit

The composite weakly basic resin (D301Fe) was prepared and examined using scanning electron microscopy and Fourier transform infrared spectroscopy. The adsorption kinetics of glyphosate from aqueous solution onto composite weakly basic resin (D301Fe) were investigated under different conditions. The experimental data was analyzed using various adsorption kinetic models like pseudo-first order, the pseudo-second order, the Elovich and the parabolic diffusion models to determine the best-fit equation for the adsorption of glyphosate onto D301Fe. The results show that the pseudo-second order equation fitted the experimental data well and its adsorption was chemisorption-controlled.

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