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Much ado about 248
[article]

2007
*
arXiv
*
pre-print

In this note we present three representations

arXiv:0704.0096v1
fatcat:bbzk2t5abrb65bmo4wjkthv2yu
*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. ...##
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Applications of symmetry groups and the Wahlquist-Estabrook procedure in general relativity

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] . ...

##
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Differential equations associated to Families of Algebraic Cycles
[article]

2008
*
arXiv
*
pre-print

We develop

arXiv:math/0305288v7
fatcat:xzk2363zerfshctfqsummda7gu
*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. ...##
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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*...##
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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

2008
*
Annales de l'Institut Fourier
*

For varying t, E t defines

doi:10.5802/aif.2406
fatcat:bmwjkep62fa6jgc5z5ibhgel4e
*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. ...##
###
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. ...##
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Hilbert and Hilbert—Samuel polynomials and partial differential equations

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*. ...

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

2020
*
arXiv
*
pre-print

" has been applied upon some Abelian sub-

arXiv:2002.01195v1
fatcat:2n5k4qeat5darbkeen4ujy4uby
*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 ...##
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Global Lie–Tresse theorem

2016
*
Selecta Mathematica, New Series
*

Remark The whole symmetry

doi:10.1007/s00029-015-0220-z
fatcat:oqiyl4mia5a2tkj5aw5srxouja
*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. ...##
###
Ax-Schanuel type theorems and geometry of strongly minimal sets in differentially closed fields
[article]

2020
*
arXiv
*
pre-print

the

arXiv:1606.01778v4
fatcat:hzsmlyhyanadhcjdirm62ckdvm
*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. ...##
###
Consistent Interactions Between Gauge Fields: The Cohomological Approach
[article]

1997
*
arXiv
*
pre-print

The cohomological approach to the problem

arXiv:hep-th/9712226v1
fatcat:2yovbutstzazbjbacg23lgwz24
*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 ...##
###
Local and global solutions of a differential equation on a curve

1986
*
Indagationes Mathematicae (Proceedings)
*

Let

doi:10.1016/1385-7258(86)90010-7
fatcat:enjtob7fubdofgvzocijvtcdcm
*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 ! ...##
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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. ...##
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Differential flatness and defect: an overview

1995
*
Banach Center Publications
*

We utilize

doi:10.4064/-32-1-209-225
fatcat:t6miq54rtrhhpcltoekuyp7rsi
*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. ...
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