The General Theory for One First-Order Equation

2004 ◽  
pp. 1-10
Author(s):  
Vladimir I. Arnold
Keyword(s):  
General Theory ◽  
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 General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions

2000 ◽  
Vol 84 (21) ◽  
pp. 4794-4797 ◽  
Author(s):  
M. Biskup ◽  
C. Borgs ◽  
J. T. Chayes ◽  
L. J. Kleinwaks ◽  
R. Kotecký
Keyword(s):  
Phase Transitions ◽  
General Theory ◽  
First Order ◽  
First Order Phase

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.

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