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Much ado about 248 [article]

M.C. Nucci, P.G.L. Leach
2007 arXiv   pre-print
In this note we present three representations of a 248-dimensional Lie algebra, namely the algebra of Lie point symmetries admitted by a system of five trivial ordinary differential equations each of order  ...  forty-four, that admitted by a system of seven trivial ordinary differential equations each of order twenty-eight and that admitted by one trivial ordinary differential equation of order two hundred and  ...  Acknowledgements PGLL thanks the University of Kwazulu-Natal for its continued support.  ... 
arXiv:0704.0096v1 fatcat:bbzk2t5abrb65bmo4wjkthv2yu

Applications of symmetry groups and the Wahlquist-Estabrook procedure in general relativity

Phillip Charles Harmsworth
1988 Bulletin of the Australian Mathematical Society  
A new method is described identifying the resulting (prolongation) structures with finite dimensional Lie algebras, which augments that of Dodd and Fordy [4] .  ...  The final section outlines the formulation of a system of partial differential equations with an associated set of nontrivial pseudopotentials as a zero-curvature condition on a principal bundle [8].  ...  A new method is described identifying the resulting (prolongation) structures with finite dimensional Lie algebras, which augments that of Dodd and Fordy [4] .  ... 
doi:10.1017/s0004972700027106 fatcat:xyd7jfivovfahajmlojkj4m4cq

Differential equations associated to Families of Algebraic Cycles [article]

Pedro Luis del Angel, Stefan Müller-Stach
2008 arXiv   pre-print
We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups).  ...  This formalism is related to inhomogeneous Picard--Fuchs type differential equations. For families of K3 surfaces the corresponding non-linear ODE turns out to be symilar to Chazy's equation.  ...  For varying t, E t defines a local system E over B which is an extension of H by a trivial local system of rank one.  ... 
arXiv:math/0305288v7 fatcat:xzk2363zerfshctfqsummda7gu

Page 822 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
, Mohamed (MRC-CADSS; Marrakech) Triviality and dimension of a system of algebraic differential equations.  ...  A fundamental problem of the algorithmic theory of a differ- ential polynomial ideal is the triviality of the system ¥ (that is, whether = has a solution in some differential extension field of K ) and  ... 

Page 8738 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
Algorithms of power geometry are applicable to equations of various types: algebraic, ordinary differential and partial differ- ential, and also to systems of such equations.  ...  Summary: “We introduce concepts of Lyapunov exponents and of Lyapunov spectra of a linear differential algebraic equation (DAE) and derive Lyapunov’s inequality for a DAE of index 1.  ... 

Differential Equations associated to Families of Algebraic Cycles

Pedro Luis del Angel, Stefan Müller-Stach
2008 Annales de l'Institut Fourier  
For varying t, E t defines a local system E over B which is an extension of H by a trivial local system of rank one.  ...  Differential Equations associated to families of algebraic cycles In this section we study differential equations arising from families of algebraic cycles.  ... 
doi:10.5802/aif.2406 fatcat:bmwjkep62fa6jgc5z5ibhgel4e

Page 7395 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
The paper is concerned with the existence of non-trivial global solutions for a class of ordinary differential equations including u"+u=|u'|\?-'u’, t>0, p> 1.  ...  Summary: “We give a new set of local characterizing quantities for the treatment of linear differential-algebraic equations with variable coefficients.  ... 

Hilbert and Hilbert—Samuel polynomials and partial differential equations

A. G. Khovanskii, S. P. Chulkov
2005 Mathematical Notes  
Systems of linear partial differential equations with constant coefficients are considered. The spaces of formal and analytic solutions of such systems are described by algebraic methods.  ...  The Hilbert and Hilbert-Samuel polynomials for systems of partial differential equations are defined.  ...  We study the relation between the algebraic variety M and the spaces of formal and analytic solutions of the initial system of differential equations.  ... 
doi:10.1007/s11006-005-0013-3 fatcat:qr65hnyiprggln7dm3axe5xojq

On solvable Lie algebras and integration method of ordinary differential equations [article]

T. Pailas, P. A. Terzis, T. Christodoulakis
2020 arXiv   pre-print
" has been applied upon some Abelian sub-algebra of generators {Z_i} for the system of equations to be reduced.  ...  Some more general "inheritance conditions" have been found for a given set of symmetry generators {Z_l̅} acting on some set of coupled ordinary differential equations, once the "first integration method  ...  Acknowledgements The research work was supported by the Hellenic Foundation for Research and Innovation (HFRI) and the General Secretariat for Research and Technology (GSRT), under the HFRI PhD Fellowship  ... 
arXiv:2002.01195v1 fatcat:2n5k4qeat5darbkeen4ujy4uby

Global Lie–Tresse theorem

Boris Kruglikov, Valentin Lychagin
2016 Selecta Mathematica, New Series  
Remark The whole symmetry algebra of the 2nd Plebaǹski equations is by 3 dimensions bigger (the symmetry algebra of I -by 2 dimensions).  ...  Restriction to E yields non-trivial algebra of differential invariants A = u y , u yy , u yyy , . . . , generated by u y and the invariant derivation D y mod D x .  ...  Trying to extend this to the algebra H 1 = P 0 ⊕ P 1 violates the Jacobi identity because of the cut tails, and we shall allow more gradings.  ... 
doi:10.1007/s00029-015-0220-z fatcat:oqiyl4mia5a2tkj5aw5srxouja

Ax-Schanuel type theorems and geometry of strongly minimal sets in differentially closed fields [article]

Vahagn Aslanyan
2020 arXiv   pre-print
the differential equation of j defines a strongly minimal set with trivial geometry (which is not ℵ_0-categorical though).  ...  In this paper we explore the connection between Ax-Schanuel type theorems (predimension inequalities) for a differential equation E(x,y) and the geometry of the set U:={ y:E(t,y) ∧ y' ≠ 0 } where t is  ...  I would like to thank Boris Zilber and Jonathan Pila for valuable suggestions and comments. This work was supported by the University of Oxford Dulverton Scholarship.  ... 
arXiv:1606.01778v4 fatcat:hzsmlyhyanadhcjdirm62ckdvm

Consistent Interactions Between Gauge Fields: The Cohomological Approach [article]

Marc Henneaux
1997 arXiv   pre-print
The cohomological approach to the problem of consistent interactions between fields with a gauge freedom is reviewed. The role played by the BRST symmetry is explained.  ...  Applications to massless vector fields and 2-form gauge fields are surveyed.  ...  Acknowledgements The author is grateful to Glenn Barnich, Friedemann Brandt, Stanley Deser, Michel Dubois-Violette, Bernard Knaepen, Jim Stasheff, Michel Talon and Claude Viallet for useful discussions  ... 
arXiv:hep-th/9712226v1 fatcat:2yovbutstzazbjbacg23lgwz24

Local and global solutions of a differential equation on a curve

M. van der Put
1986 Indagationes Mathematicae (Proceedings)  
Let equation (d/k) -A of type (0.1) be locally trivial and let Q : r+Gl(n,K) denote the corresponding representation. The DGal((d/dz) -A) is the smallest algebraic subgroup of Gl(n,K) containing em.  ...  The differential equation above can be translated into a connection (0.2) v : w&(,),~ @ v in which I/ is an n-dimensional vectorspace over K(C) and where !  ... 
doi:10.1016/1385-7258(86)90010-7 fatcat:enjtob7fubdofgvzocijvtcdcm

Page 490 of Mathematical Reviews Vol. 49, Issue 2 [page]

1975 Mathematical Reviews  
Grothendieck: Let A(z) be an nxn matrix of rational functions of z with coefficients in an algebraic number field K; consider the system of n homogeneous linear differential equations d Y /dz = A(z)Y with  ...  Katz, Nicholas M. 2728 Algebraic solutions of differential equations (p-curvature and the Hodge filtration). Invent. Math. 18 (1972), 1-118.  ... 

Differential flatness and defect: an overview

Michel Fliess, Jean Lévine, Philippe Martin, Pierre Rouchon
1995 Banach Center Publications  
We utilize differential algebra which suits well to the fact that, in accordance with Willems' standpoint, flatness and defect are best defined without distinguishing between input, state, output and other  ...  We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous.  ...  Hilbert [31] and E. Cartan [4] on under-determined systems of differential equations, where the number of equations is strictly less than the number of unknowns.  ... 
doi:10.4064/-32-1-209-225 fatcat:t6miq54rtrhhpcltoekuyp7rsi
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