general equation
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2021 ◽  
Author(s):  
◽  
Keith Raymond Millar

<p>A vast volume of literature exists on this subject, the major portion being concerned with nucleophilic aliphatic substitution reactions covered by the general equation:- Y + Alk - X --> Alk - Y + X (SN) where the new bond is formed by co-ordination, and the old one broken by heterolysis, as indicated by the dotted line. There is necessarily and electron transfer from the substituting species Y to the centre of substitution in Alk, and from this centre to the expelled group X; hence Y becomes formally one electronic unit more positive and X one unit more negative.</p>


2021 ◽  
Author(s):  
◽  
Keith Raymond Millar

<p>A vast volume of literature exists on this subject, the major portion being concerned with nucleophilic aliphatic substitution reactions covered by the general equation:- Y + Alk - X --> Alk - Y + X (SN) where the new bond is formed by co-ordination, and the old one broken by heterolysis, as indicated by the dotted line. There is necessarily and electron transfer from the substituting species Y to the centre of substitution in Alk, and from this centre to the expelled group X; hence Y becomes formally one electronic unit more positive and X one unit more negative.</p>


2021 ◽  
Vol 2052 (1) ◽  
pp. 012040
Author(s):  
A V Sochilin ◽  
S I Eminov

Abstract The problem of excitation of a rectilinear ribbon vibrator near a perfectly conducting infinite screen is considered. A general equation, a two-dimensional integral equation, and a one-dimensional integral equation with respect to the current density are obtained. The results of numerical calculations are presented.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mátyás Szücs ◽  
Michal Pavelka ◽  
Róbert Kovács ◽  
Tamás Fülöp ◽  
Péter Ván ◽  
...  

Abstract Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s law and its various extensions—the Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys type, Ginzburg–Landau (Allen–Cahn) type and ballistic–diffusive heat conduction equations—are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.


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