An investigation of basic assumption in enzyme kinetics using results of the geometric theory of differential equations

1967 ◽  
Vol 29 (2) ◽  
pp. 335-341 ◽  
Author(s):  
I. G. Darvey ◽  
R. F. Matlak
Keyword(s):  
Differential Equations ◽  
Enzyme Kinetics ◽  
Basic Assumption ◽  
Geometric Theory

Smooth conjugacy of centre manifolds

1992 ◽  
Vol 120 (1-2) ◽  
pp. 61-77 ◽  
Author(s):  
Almut Burchard ◽  
Bo Deng ◽  
Kening Lu
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Ordinary Differential Equations ◽  
Parabolic Equations ◽  
Geometric Theory ◽  
Unstable Manifolds ◽  
Centre Manifolds ◽  
Smooth Conjugacy

SynopsisIn this paper, we prove that for a system of ordinary differential equations of class Cr+1,1, r≧0 and two arbitrary Cr+1, 1 local centre manifolds of a given equilibrium point, the equations when restricted to the centre manifolds are Cr conjugate. The same result is proved for similinear parabolic equations. The method is based on the geometric theory of invariant foliations for centre-stable and centre-unstable manifolds.

scholarly journals QUANTUM LIE SYSTEMS AND INTEGRABILITY CONDITIONS

2009 ◽  
Vol 06 (08) ◽  
pp. 1235-1252 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
JAVIER DE LUCAS
Keyword(s):  
Quantum Mechanics ◽  
Differential Equations ◽  
Geometric Theory ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Integrable Quantum ◽  
Systems Of Differential Equations ◽  
Integrability Conditions ◽  
Mechanical Models ◽  
Lie Systems

The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analyzed from a geometric perspective. In this paper we use both developments to obtain a geometric theory of integrability in Quantum Mechanics and we use it to provide a series of non-trivial integrable quantum mechanical models and to recover some known results from our unifying point of view.

scholarly journals Multi-symplectic magnetohydrodynamics: II, addendum and erratum

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
G. M. Webb ◽  
J. F. McKenzie ◽  
G. P. Zank
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Differential Form ◽  
Compatibility Condition ◽  
Conservation Law ◽  
Differential Forms ◽  
Geometric Theory ◽  
Momentum Equation ◽  
Plasma Phys

A recent paper by Webb et al. (J. Plasma Phys., vol. 80, 2014, pp. 707–743) on multi-symplectic magnetohydrodynamics (MHD) using Clebsch variables in an Eulerian action principle with constraints is further extended. We relate a class of symplecticity conservation laws to a vorticity conservation law, and provide a corrected form of the Cartan–Poincaré differential form formulation of the system. We also correct some typographical errors (omissions) in Webb et al. (J. Plasma Phys., vol. 80, 2014, pp. 707–743). We show that the vorticity–symplecticity conservation law, that arises as a compatibility condition on the system, expressed in terms of the Clebsch variables is equivalent to taking the curl of the conservation form of the MHD momentum equation. We use the Cartan–Poincaré form to obtain a class of differential forms that represent the system using Cartan’s geometric theory of partial differential equations

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