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Wei–Norman equations for classical groups via cominuscule induction

Jan Gutt, Szymon Charzyński, Marek Kuś
2015 Differential geometry and its applications  
We show how to reduce the nonlinear Wei-Norman equations, expressing the solution of a linear system of non-autonomous equations on a Lie algebra, to a hierarchy of matrix Riccati equations using the cominuscule  ...  A corresponding hierarchy of nonlinear, albeit no longer Riccati equations, is given for these exceptional cases.  ...  Acknowledgements The presented results are obtained in frames of the the Polish National Science Center project MAESTRO DEC-2011/02/A/ST1/00208 support of which is gratefully acknowledged by all authors  ... 
doi:10.1016/j.difgeo.2015.07.001 fatcat:4opcnycoq5cnnh2efkfflmyzy4

On the map between homology of henselization and completion of some local rings

G. Banaszak, W. Gajda, P. Krasoń
1998 Journal of Pure and Applied Algebra  
The method of the proof is based on an application of the At-tin approximation theorem to the bar complex which calculates the homology.  ...  We define hens&an ad& ring and prove that the integral homology of its special linear group injects into the homology of Sl of the finite adele ring.  ...  O+ m and 1 in order to stay inside SI. The system of equations obtained in this way has solutions in R, because of Eq. (2.1).  ... 
doi:10.1016/s0022-4049(97)00045-5 fatcat:a5cr66r45vdi3kjjfen5nzqkdi

The Power Matrix, coadjoint action and quadratic differentials

Eric Schippers
2006 Journal d'Analyse Mathematique  
As an application, we derive a set of integral invariants of Hamilton's equations which is in a certain sense complete.  ...  By work of Roth, this differential system can be interpreted as Hamilton's equations.  ...  Application of control theory requires the construction of a dual system to Loewner's equation.  ... 
doi:10.1007/bf02790277 fatcat:dj2yzssw7vffpa74edskflym24

Attributive concept descriptions with complements

Manfred Schmidt-Schauß, Gert Smolka
1991 Artificial Intelligence  
It is shown that deciding coherence and subsumption of such descriptions are PSPACE-complete problems that can be decided with linear space.  ...  We investigate the consequences of adding unions and complements to attributive concept descriptions employed in terminological knowledge representation languages.  ...  Acknowledgement We are grateful to Bernhard Nebel for inspiring discussions. The research reported in this paper was done while Schmidt-Schaul3 was with the DFKI in  ... 
doi:10.1016/0004-3702(91)90078-x fatcat:jrxjz4iby5hsbjyx3kwprjsloa

A continuation algorithm for a class of linear complementarity problems using an extrapolation technique

Jiu Ding
1993 Linear Algebra and its Applications  
The linear extrapolation technique is combined with the Newton iteration in the predictor-corrector procedure of the algorithm to numerically follow the solution curve of the homotopy equations arising  ...  The convergence rate of the method is proved to be 1 -4/(7&j after each cycle consisting of one extrapolation between two Newton steps.  ...  In each such cycle, we need to solve two systems of linear equations coming from the Newton iteration, but the decrease of rry, which measures how nearly x and y are complementary, is at the approximate  ... 
doi:10.1016/0024-3795(93)90291-u fatcat:qxo4srn4g5edtbcicscngdw5za

A Perron-type theorem for fractional linear differential systems [article]

N.D. Cong, T.S. Doan, H.T. Tuan
2016 arXiv   pre-print
We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution.  ...  We also obtain an explicit description for the set of all bounded (or decay) solutions for these systems.  ...  Use arguments similar to that of the proof of Proposition 8 and with the application of Proposition 6. Remark 10.  ... 
arXiv:1602.04695v2 fatcat:hcqgzood55ch5l5ic7mahrxirq

The structure of the moduli spaces of toric dynamical systems [article]

Gheorghe Craciun, Miruna-Stefana Sorea
2020 arXiv   pre-print
In particular, we emphasize the product structure of the moduli space: it is homeomorphic to the product of the set of complex balanced flux vectors and the affine invariant polyhedron.  ...  We consider complex balanced mass-action systems, also called toric dynamical systems. They are polynomial dynamical systems arising from reaction networks and have remarkable dynamical properties.  ...  Acknowledgements The authors gratefully acknowledge the support of Bernd Sturmfels and of the Max Planck Institute for Mathematics in the Sciences in Leipzig.  ... 
arXiv:2008.11468v1 fatcat:wivzoteoy5e4rebnyfgkzfus3y

Remarks on two approaches to the horizontal cohomology: compatibility complex and the Koszul-Tate resolution [article]

Alexander Verbovetsky
2001 arXiv   pre-print
The Koszul-Tate resolution is described in the context of the geometry of jet spaces and differential equations.  ...  The application due to Barnich, Brandt, and Henneaux of this resolution to computing the horizontal cohomology is analyzed. Relations with the Vinogradov spectral sequence are discussed.  ...  Stasheff for his interest to the text and useful suggestions, which were incorporated in the second version of this eprint.  ... 
arXiv:math/0105207v2 fatcat:plhoczrckvhephjzj63dkltbnu

Book reports

2005 Computers and Mathematics with Applications  
The Linear Structure of an Ideal. 30.2. Inverse System. 30.3. Representing and Computing the Linear Structure of an Ideal. 30.4. Noetherian Equations. 30.5.  ...  Propositional Inference. 4.1. From Models to Proofs. 4.2. Propositional Tableaus. 4.3. Implementing Propositional Tableau. 4.4. Propositional Resolution. 4.5.  ... 
doi:10.1016/j.camwa.2005.10.001 fatcat:smjkjmzbkfdbvezerczxaktjfy

Integrability conditions for a certain class of nonlinear evolution equations and Kähler geometry

E.M. Isaenko
1991 Differential geometry and its applications  
Abstract: Multicomponent evolution equations associated with linear connections on complex manifolds are considered.  ...  ., Integrability conditions for a certain class of nonlinear evolution equations and Kahler geometry, Diff. Geom. Appl. 1 (1991) 327-344.  ...  Proof of Corollary 2. 3 . 3 It is sufficient to apply the results of Section 1. Cl Proof of Proposition 2.1.  ... 
doi:10.1016/0926-2245(91)90012-x fatcat:5nwczzr5szdldd4uruxq2hz7o4

The Model-Theoretic Expressiveness of Propositional Proof Systems

Erich Grädel, Benedikt Pago, Wied Pakusa
2017 Leibniz International Proceedings in Informatics  
in the area of descriptive complexity theory.  ...  We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory.  ...  Finally, we discuss applications of our model-theoretic characterisations of propositional C S L 2 0 1 7 27:4 The Model-Theoretic Expressiveness of Propositional Proof Systems proof systems.  ... 
doi:10.18154/rwth-2020-09507 fatcat:s4ojkqjawbf4pf5wmi2xbnq6em

Group law on the neutral component of the Jacobian of a real hyperelliptic curve having many real components

Goulwen Fichou
2003 Journal of Pure and Applied Algebra  
It allows us to describe geometrically the neutral real component Pic o (C) o of the Jacobian of C thanks to an isomorphism with the product B1 × · · · × Bg.  ...  This induces an explicit geometric description of Pic o (C) o in the projective plane, where the group law is given by intersection with curves of genus g.  ...  Acknowledgements The author wish to thank Johan Huisman for his help during this work, and also Pawel Goldstein for his careful rereading of the English version.  ... 
doi:10.1016/s0022-4049(02)00312-2 fatcat:f7nqn5gtufgcfba4jecxfgmria

Generating hard tautologies using predicate logic and the symmetric group

S Riis
2000 Logic Journal of the IGPL  
in any propositional proof system.  ...  Our translation method shows that most sequences of tautologies being studied in propositional proof complexity can be systematically generated from Second Order Existential sentences  ...  See [8] for a description of PC proofs.  ... 
doi:10.1093/jigpal/8.6.787 fatcat:hm3bldzb7ngwvly6ogmg56c7p4

Algebraic Description and Simultaneous Linear Approximations of Addition in Snow 2.0 [chapter]

Nicolas T. Courtois, Blandine Debraize
2008 Lecture Notes in Computer Science  
We look at implicit quadratic equations describing this operation, and at probabilistic conditional linear equations.  ...  We show that the addition modulo 2 n can be partly or totally linearized when the output is fixed, and this for a large family of outputs.  ...  Acknowledgments: It is clear that the addition modulo 2 n can be described by a system of quadratic equations with extra variables (carries), see [5] .  ... 
doi:10.1007/978-3-540-88625-9_22 fatcat:xidwkdttsjdttjbjkicue4tgku

A generalized Levinson algorithm for covariance extension with application to multiscale autoregressive modeling

A.B. Frakt, H. Lev-Ari, A.S. Willsky
2003 IEEE Transactions on Information Theory  
The computational complexity of MAR model identification is an order of magnitude below that of explicitly computing a full covariance extension and is comparable to that required to build a standard autoregressive  ...  One contribution of this paper is the introduction of a generalization of this algorithm that is applicable to a substantially broader class of extension problems.  ...  APPENDIX DESCRIPTION OF MAR ENDPOINT MODEL AND PROOF OF PROPOSITION 1 For convenience, 12 we assume that for positive integer .  ... 
doi:10.1109/tit.2002.807315 fatcat:lfv3zs5blzaabpd6e6hmh3nxdy
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