scholarly journals Formal solutions of a class of Pfaffian systems in two variables

2014 ◽  
Author(s):  
Suzy S. Maddah ◽  
Moulay A. Barkatou ◽  
Hassan Abbas
Keyword(s):  
Pfaffian Systems ◽  
Formal Solutions

scholarly journals Formal solutions of completely integrable Pfaffian systems with normal crossings

2017 ◽  
Vol 81 ◽  
pp. 41-68
Author(s):  
Moulay A. Barkatou ◽  
Maximilian Jaroschek ◽  
Suzy S. Maddah
Keyword(s):  
Pfaffian Systems ◽  
Completely Integrable ◽  
Formal Solutions

Normal approximations for distributions arising in the stochastic approach to chemical reaction kinetics

1981 ◽  
Vol 18 (01) ◽  
pp. 263-267 ◽  
Author(s):  
F. D. J. Dunstan ◽  
J. F. Reynolds
Keyword(s):  
Reaction Kinetics ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Stochastic Approach ◽  
Algebraic Functions ◽  
Chemical Reaction Kinetics ◽  
Normal Approximations ◽  
Formal Solutions

Earlier stochastic analyses of chemical reactions have provided formal solutions which are unsuitable for most purposes in that they are expressed in terms of complex algebraic functions. Normal approximations are derived here for solutions to a variety of reactions. Using these, it is possible to investigate the level at which the classical deterministic solutions become inadequate. This is important in fields such as radioimmunoassay.

scholarly journals Limit Theorems and Fluctuations for Point Vortices of Generalized Euler Equations

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Carina Geldhauser ◽  
Marco Romito
Keyword(s):  
Euler Equations ◽  
Mean Field ◽  
Point Vortices ◽  
Positive Temperature ◽  
Field Limit ◽  
Mean Field Limit ◽  
Large Numbers ◽  
The Mean ◽  
Formal Solutions ◽  
2D Torus

AbstractWe prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean-field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.

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