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ACAT 2007}, YEAR = {2007}, volume = {PoS(ACAT)083}, note = {[arXiv:hep-ph/0709.1769]} } @article{Schneider:08e, author = {I. Bierenbaum and J. Bl{\"u}mlein and S. Klein and C. Schneider}, title = {Two--Loop Massive Operator Matrix Elements for~Unpolarized~Heavy~Flavor~Production~to~$O(\epsilon)$}, journal = {Nucl.Phys. B}, volume = {803}, number = {1-2}, pages = {1--41}, year = {2008}, note = {[arXiv:hep-ph/0803.0273]} } @MASTERSTHESIS{Wegschaider:97, author = {K. Wegschaider}, title = {Computer generated proofs of binomial multi-sum identities}, school = {RISC Linz, Johannes Kepler University}, year = {1997}, type = {Di\-plo\-ma Thesis} } @Article{PauleSchorn:95, author = {P. Paule and M. Schorn}, title = {{A Mathematica version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities}}, journal = {J.~Symbolic Comput.}, year = {1995}, volume = {20}, number = {5-6}, pages = {673-698} } @InCollection{PauleRiese:97, author = {P. Paule and A. 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ACAT 2008}, AUTHOR = {J.~Bl{\"u}mlein and M.~Kauers and S.~Klein and C.~Schneider}, TITLE = {From Moments to Functions in Quantum Chromodynamics}, YEAR = {2009}, volume = {PoS(ACAT08)106}, note = {[arXiv:hep-ph/0902.4095]} } @Book{AAR, author = {G.E.~Andrews and R.~Askey and R.~Roy}, title = {Special Functions}, publisher = {Cambridge UP}, year = {2000}, series = {Encyclopedia of Mathematics and its applications}, number = {71} } @InProceedings{Abramov:94, author = {S.A. Abramov and M. Petkov{\v s}ek}, title = {D'{A}lembertian solutions of linear differential and difference equations}, booktitle = {Proc. ISSAC'94}, pages = {169-174}, publisher = {ACM Press}, year = {1994}, editor = {J.~von zur Gathen} } @ARTICLE{Vermaseren:99, AUTHOR = {J.A.M. Vermaseren}, TITLE = {Harmonic sums, {M}ellin transforms and integrals}, JOURNAL = {Int. J. Mod. Phys. A}, YEAR = {1999}, volume = {14}, pages = {2037--2076} } @misc{bostan08a, author = "Alin Bostan and Manuel Kauers", title = "Automatic Classification of Restricted Lattice Walks", howpublished = "arXiv:0811.2899", year = "2008" } @misc{bostan08, author = "Alin Bostan and Manuel Kauers", title = "The full counting function for {G}essel walks is algebraic", note = "(in preparation)", year = "2009" } @techreport{kauers08g, author = "Manuel Kauers and Christoph Koutschan and Doron Zeilberger", title = "Proof of {I}ra {G}essel's Lattice Path Conjecture", note = "(submitted)", institution = "SFB F013, Johannes Kepler Universit{\"a}t", number = "2008-08", year = "2008" } @article{kauers07v, author = "Manuel Kauers and Doron Zeilberger", title = "The Quasi-Holonomic Ansatz and Restricted Lattice Walks", journal = "Journal of Difference Equations and Applications", volume = "14", number = "10", pages = "1119--1126", year = "2008" } @article{bousquet05, author = "Mireille Bousquet-Melou", title = "Walks in the quarter plane: {K}reweras' algebraic model", journal = "The Annals of Applied Probability", volume = "15", number = "2", pages = "1451--1491", year = "2005" } @inproceedings{bousquet02, author = "Mireille Bousquet-Melou", title = "Counting Walks in the Quarter Plane", booktitle = "Trends Math.", year = "2002", publisher = "Birkh{\"a}user", pages = "49--67" } @misc{bousquet08, author = "Mireille Bousquet-M{\'e}lou and Marni Mishna", title = "Walks with small steps in the quarter plane", howpublished = "ArXiv 0810.4387", year = "2008" } @inproceedings{mishna06, author = "Marni Mishna", title = "Classifying Lattice Walks Restricted to the Quarter Plane", booktitle = "Proceedings of FPSAC'07", year = "2007" } @mastersthesis{mallinger96, author = "Christian Mallinger", title = {{Algorithmic Manipulations and Transformations of Univariate Holonomic Functions and Sequences}}, school = "RISC-Linz", month = "August", year = "1996" } @article{gh3, author = {M. Ghil and D. Kondrashov and F. Lott and A.W. Robertson}, title = {{ Intraseasonal oscillations in the mid-latitudes: observations, theory, and GCM results.}}, language = {english}, journal = {Proc. ECMWF/CLIVAR Workshop on Simulations and prediction of Intra-Seasonal Variability with Emphasis on the MJO. November 3-6, 2003.}, pages = {35-53}, publisher = {ECMWF, Reading, UK}, isbn_issn = {0587-4254}, year = {2004}, refereed = {yes}, length = {18} } @article{LynchHoughton04, author = {P. Lynch and C. Houghton}, title = {{Pulsation and precession of the resonant swinging spring}}, language = {english}, journal = {Physica D}, volume = {190}, issue = {1-2}, pages = {38-62}, publisher = {Elsevier}, isbn_issn = {ISSN: 0167-2789}, year = {2004}, refereed = {yes}, length = {24} } @BOOK{book-triad, author = "E.T. Whittaker", year = "1990", title = "A Course in Modern Analysis", publisher = "Cambridge University Press" } @BOOK{ped, author = "J. Pedlosky ", year = "1987", title = "Geophysical Fluid Dynamics", publisher = "New York Heidelberg Berlin: Springer-Verlag", isbn_issn = "3540903682" } @article{longuet_higgens, author = {M.S. Longuet-Higgins and A.E. Gill}, title = {{ Resonant Interactions between Planetary Waves}}, language = {english}, journal = {Proc. R. Soc. London, Ser. A}, volume = {299}, issue = {1456}, pages = {120-140}, publisher = {Royal Society London}, isbn_issn = {0587-4254}, year = {1967}, refereed = {yes}, length = {20} } @article{Astr, author = {W. Kluzniak}, title = {{Quasi periodic oscillations and the possibility of an abservational distinction between neutron and quark stars}}, language = {english}, journal = {Acta Physica Polonica B}, volume = {37}, issue = {4}, pages = {1361-1366}, publisher = {THE POLISH PHYSICAL SOCIETY}, isbn_issn = {0587-4254}, year = {2006}, refereed = {yes}, length = {6} } @BOOK{Arn3, author = "V.I. Arnold", year = "1983", title = "Geometrical methods in the theory of ordinary differential equations", series = "A Series of Comprehensive Studies in Mathematics", publisher = "New York Heidelberg Berlin: Springer-Verlag", isbn_issn = "3540906819" } @article{cancer, author = {C. Vedruccio and E. Mascia and V. Martines}, title = {{Ultra High Frequency and Microwave Non-linear Interaction Device for Cancer Detection and Tissue Characterization, a Military Research approach to prevent Health Diseases}}, language = {english}, journal = {International Review of the Armed Forces Medical Services (IRAFMS)}, volume = {78}, issue = {2}, pages = {120-132}, publisher = {Elsevier}, isbn_issn = {ISSN: 0167-2789}, year = {2005}, refereed = {yes}, length = {12}, url = {http://www.trimprobe.com/ita/pubblicazioni/_abstracts/CNR_International_Summer_School_Lecce_2005.pdf} } @article{Large, author = {F. Almonte and V.K. Jirsa and E.W. Large and B. Tuller}, title = {{Integration and segregation in auditory streaming}}, language = {english}, journal = {Physica D}, volume = {212}, issue = {1-2}, pages = {137-159}, publisher = {Elsevier}, isbn_issn = {ISSN: 0167-2789}, year = {2005}, refereed = {yes}, length = {23} } @article{Helium, author = {A.L. Karuzskii and A.N. Lykov and A.V. Perestoronin and A.I. Golovashkin}, title = {{Microwave nonlinear resonance incorporating the helium heating effect in superconducting microstrip resonators}}, journal = {Physica C: Superconductivity}, volume = {408-410}, pages = {739-740}, publisher = {Elsevier}, isbn_issn = {ISSN: 0921-4534}, year = {2004}, refereed = {yes}, length = {2} } @article{Mech, author = {D.A. Kovriguine and G.A. Maugin}, title = {{Multiwave nonlinear couplings in elastic structures}}, journal = {Mathematical Problems in Engineering}, volume = {2006}, pages = {76041}, isbn_issn = {1024123X}, year = {2006}, refereed = {yes}, length = {11} } @article{Turbine, author = {K. Horvat and M. Miskovic and O. Kuljaca}, title = {{Avoidance of nonlinear resonance jump in turbine governor positioning system using fuzzy controller}}, journal = {Industrial Technology}, volume = {2}, pages = {881-886}, isbn_issn = {0780378520}, year = {2003}, refereed = {yes}, length = {4} } @BOOK{Tesla, author = "M. Cheney", year = "1993", title = "Tesla Man Out Of Time", publisher = "Barnes \& Noble", isbn_issn = "0880294191" } @BOOK{zakh92, author = "V.E. Zakharov and V.S. L'vov and G. Falkovich", year = "1992", title = "Kolmogorov Spectra of Turbulence", publisher = "Springer", isbn_issn = "0 387 54533 6", url = "http://www.amazon.com/Kolmogorov-Spectra-Turbulence-Springer-Nonlinear/dp/0387545336" } @article{Laser, author = {M. Kundu and D. Bauer}, title = {{Nonlinear Resonance Absorption in the Laser-Cluster Interaction}}, journal = {Physical Review Letters}, volume = {96}, pages = {123401}, publisher = {American Physical Society}, year = {2005}, refereed = {yes}, length = {4} } @incollection{Kuk04, author = {B. Kuksin}, title = {{Fifteen years of KAM for PDE}}, booktitle = {{AMS Translations 2}}, language = {english}, volume = {212}, pages = {237-258}, year = {2004}, publisher = {American Mathematical Society}, isbn_issn = {0821841130}, refereed = {yes}, length = {21} } @article{RISC3788, author = {M.D. Bustamante and E. Kartashova}, title = {{Effect of the dynamical phases on the nonlinear amplitudes' evolution}}, language = {english}, journal = {Europhysics Letters}, volume = {85}, pages = {34002--5}, publisher = {IOP }, isbn_issn = {ISSN (print edition): 0295-5075 ISSN (online): 1286-4854}, year = {2009}, refereed = {yes}, length = {5}, url = {http://www.iop.org/EJ/abstract/0295-5075/85/3/34002} } @article{RISC3438, author = {M.D. Bustamante and E. Kartashova}, title = {{Dynamics of nonlinear resonances in Hamiltonian systems}}, language = {english}, abstract = {It is well known that the dynamics of a Hamiltonian system depends crucially on whether or not it possesses nonlinear resonances. In the generic case, the set of nonlinear resonances consists of independent clusters of resonantly interacting modes, described by a few low-dimensional dynamical systems. We formulate and prove a new theorem on integrability which allows us to show that most frequently met clusters are described by integrable dynamical systems. We argue that construction of clusters can be used as the base for the Clipping method, substantially more effective for these systems than the Galerkin method. The results can be used directly for systems with cubic Hamiltonian.}, journal = {Europhysics Letters }, volume = {85}, pages = {14004--6}, publisher = {IOP }, isbn_issn = {0295-5075 (print) , 1286-4854 (online)}, year = {2009}, refereed = {yes}, length = {6}, url = {http://www.iop.org/EJ/abstract/0295-5075/85/1/14004/} } @article{RISC3393, author = {E. Kartashova and V. L'vov}, title = {{Cluster Dynamics of Planetary Waves}}, language = {english}, abstract = {Dynamics of nonlinear atmospheric planetary waves is determined by a small number of independent wave clusters consisting of a few connected resonant triads. We classified different types of connections between neighbor triads that determines general dynamics of a cluster. Each connection type corresponds to substantially different scenarios of energy flux among the modes. The general approach can be applied directly to various mesoscopic systems with 3-mode interactions, encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.}, journal = {Europhys. Letters}, volume = {83}, pages = {50012-1--50012-6}, isbn_issn = {ISSN: 0295-5075 (Print) 1286-4854 (Online)}, year = {2008}, refereed = {yes}, length = {6}, url = {http://arxiv.org/abs/0801.3374} } @article{RISC2930, author = {E. Kartashova and V. L'vov}, title = {{A model of intra-seasonal oscillations in the Earth atmosphere}}, journal = {Physical Review Letters}, volume = { 98}, number = {19}, pages = {198501}, publisher = {American Physical Society}, year = {2007}, month = {May}, url = {http://link.aps.org/abstract/PRL/v98/e198501} } @article{RISC2984, author = {E. Kartashova and A. Kartashov}, title = {{Laminated wave turbulence: generic algorithms II}}, journal = {CiCP (Communications in Computational Physics)}, volume = {2}, number = {4}, pages = {783--794}, isbn_issn = {ISSN 1815-2406 (print), 1991-7120 (electronic)}, year = {2007}, url = {http://global-sci.com/} } @article{RISC3021, author = {E. Kartashova and A. Kartashov}, title = {{Laminated wave turbulence: generic algorithms III}}, journal = {Physica A: Statistical Mechanics and Its Applications}, volume = {380}, pages = {66--74}, publisher = {Elsevier}, year = {2007}, url = {http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4N6NJXF-5&_user=10&_coverDate=03%2F07%2F2007&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=9180e0bcb1f36c878e413ec1b5936797} } @article{RISC3037, author = {E. Kartashova}, title = {{Exact and quasi-resonances in discrete water-wave turbulence}}, journal = {Physical Review Letters}, volume = {98}, number = {21}, pages = {214502}, publisher = {American Physical Society}, year = {2007}, url = {http://link.aps.org/abstract/PRL/v98/e214502} } @article{RISC3082, author = {E. Kartashova and G. Mayrhofer}, title = {{Cluster formation in mesoscopic systems}}, journal = {Physica A: Statistical Mechanics and Its Applications}, volume = {385}, pages = {527--542}, publisher = {Elsevier}, year = {2007} } @incollection{RISC3344, author = {E. Kartashova and C. Raab and Ch. Feurer and G. Mayrhofer and W. Schreiner}, title = {{Symbolic Computations for Nonlinear Wave Resonances}}, booktitle = {{``Extreme Ocean Waves''}}, abstract = {Tralala}, publisher = {Springer}, year = {2007}, note = {(submitted)}, editor = {Ch. Harif and E. Pelinovsky} } @article{RISC2861, author = {E. Kartashova}, title = {{A model of laminated turbulence}}, journal = {Letters JETP (Letters to Journal of Experimental and Theoretical Physics)}, volume = {83}, number = {7}, pages = {341--345}, publisher = {Springer}, year = {2006}, month = {April}, url = {http://dx.doi.org/10.1134/S0021364006070058} } @article{RISC2887, author = {E. Kartashova}, title = {{Fast Computation Algorithm for Discrete Resonances among Gravity Waves}}, journal = {JLTP (Journal of Low Temperature Physics)}, volume = {145}, number = {1}, pages = {287--295}, publisher = {Springer}, year = {2006}, url = {http://www.springerlink.com/content/212w68177r81745k/} } @article{RISC2955, author = {E. Kartashova and A. Kartashov}, title = {{Laminated wave turbulence: generic algorithms I}}, journal = {IJMPC (International Journal of Modern Physics C)}, volume = {17}, number = {11}, pages = {1579--1596}, publisher = {World Scientific}, year = {2006}, url = {http://www.worldscinet.com/ijmpc/17/1711/S0129183106010042.html} } @incollection{RISC3345, author = {Elena Kartashova}, title = {{Wave resonances in systems with discrete spectra}}, booktitle = {{Nonlinear Waves and Weak Turbulence}}, language = {english}, series = {AMS Translations 2}, volume = {182}, pages = {95--130}, publisher = {American Mathematical Society}, isbn_issn = {0821841130}, year = {1998}, editor = {V.E. Zakharov}, refereed = {yes}, length = {36}, url = {http://books.google.at/books?id=jEDzcOHMcGUC&dq=zakharov+nonlinear+waves+and+weak+turbulence} } @article{RISC3410, author = {E. Kartashova and S. Nazarenko and O. Rudenko}, title = {{Resonant interactions of nonlinear water waves in a finite basin}}, language = {english}, abstract = {We study exact four-wave resonances among gravity water waves in a square box with periodic boundary conditions. We show that these resonant quartets are linked with each other by shared Fourier modes in such a way that they form independent clusters. These clusters can be formed by two types of quartets: (1) {\it angle-resonances} which cannot directly cascade energy but which can redistribute it among the initially excited modes and (2) {\it scale-resonances} which are much more rare but which are the only ones that can transfer energy between different scales. We find such resonant quartets and their clusters numerically on the set of 1000 x 1000 modes, classify and quantify them and discuss consequences of the obtained cluster structure for the wavefield evolution. Finite box effects and associated resonant interaction among discrete wave modes appear to be important in most numerical and laboratory experiments on the deep water gravity waves, and our work is aimed at aiding the interpretation of the experimental and numerical data.}, journal = {Physical Review E}, volume = {78 }, number = {016304}, pages = {1--9}, publisher = {American Physical Society}, isbn_issn = {1539-3755 (print) , 1550-2376 (online)}, year = {2008}, refereed = {yes}, length = {9}, url = {http://link.aps.org/abstract/PRE/v78/e016304} } @article{RISC3350, author = {Elena Kartashova}, title = {{Weakly nonlinear theory in resonators}}, language = {english}, journal = {Physical Review Letters}, volume = {72}, pages = {2013--2016}, publisher = {American Physical Society}, isbn_issn = {ISSN 1079-7114 (online), 0031-9007 (print)}, year = {1994}, refereed = {yes}, length = {4}, url = {http://prola.aps.org/abstract/PRL/v72/i13/p2013_1} } @InProceedings{FG2004, author = {R. Feng and X.-S. Gao}, title = {{Rational General Solutions of Algebraic Ordinary Differential Equations}}, booktitle = {{Proc. ISSAC 2004 (Internat. Symp. on Symbolic and Algebraic Computation)}}, pages = {155--162}, year = {2004}, editor = {J. Gutierrez}, publisher = {ACM Press, New York} } @Article{FG2006, author = {R. Feng and X.-S Gao}, title = {{A Polynomial Time Algorithm to Find Rational General Solutions for First Order Autonomous ODEs}}, journal = {J. Symbolic Computation}, year = {2006}, volume = {41}, pages = {735--762} } @Article{PV2000, author = {D. Poulakis and E. Voskos}, title = {{On the Practical Solutions of Genus Zero Diopantine Equations}}, journal = {J. Symbolic Computation}, year = {2000}, volume = {30}, pages = {573--582} } @Article{PV2002, author = {D. Poulakis and E. Voskos}, title = {{Solving Genus Zero Diopantine Equations with at Most Two Infinity Valuations}}, journal = {J. Symbolic Computation}, year = {2002}, volume = {33}, pages = {479--491} } @Book{SWP2008, author = {Sendra, J.R. and Winkler, F. and P\'erez-D\'iaz, S.}, title = {{Rational Algebraic Curves --- A Computer Algebra Approach}}, publisher = {Springer-Verlag Heidelberg}, year = {2008}, volume = {22}, series = {Algorithms and Computation in Mathematics} } @Book{BeckerWeispfenning1993, author = {T. Becker and V. Weispfenning}, title = {{Gr{\"o}bner Bases: A Computational Approach to Commutative Algebra}}, publisher = {Springer, New York}, year = {1993} } @InBook{Buchberger1998, author = {B. Buchberger}, editor = {B. Buchberger and F. Winkler}, title = {{Groebner Bases and Applications}}, chapter = {{Introduction to Groebner Bases}}, publisher = {Cambridge University Press}, year = {1998}, volume = {251}, series = {London Mathematical Society Lecture Note Series}, pages = {3-31} } @Proceedings{BuchbergerWinkler1998, title = {{Gr{\" o}bner Bases and Applications. Proc. of the International Conference ``33 Years of Groebner Bases''}}, year = {1998}, editor = {Bruno Buchberger and Franz Winkler}, volume = {251}, series = {London Mathematical Society Lecture Note Series}, publisher = {Cambridge University Press}, note = {560 pages} } @Article{HeldtKreuzerPokuttaPoulisse2006, author = {D. Heldt and M. Kreuzer and S. Pokutta and H. Poulisse}, title = {{Algebraische Modellierung mit Methoden der approximativen Computeralgebra und Anwendungen in der {\" O}lindustrie}}, journal = {OR-News}, year = {2006}, volume = {28}, note = {issn 1437-2045} } @InProceedings{FaugereJoux2003, author = {J.C. Faugere and A. Joux}, title = {{Algebraic Cryptoanalysis of Hidden Field Equation (HFE) Cryptosystems Using Groebner Bases}}, booktitle = {CRYPTO 2003}, pages = {44-60}, year = {2003}, editor = {D. Boneh}, volume = {2729}, series = {Lecture Notes in Computer Science} } @inproceedings{IdaTepeneuBuchberger2004, author = {T. Ida and D. Tepeneu and B. Buchberger and J. Robu}, title = {{Proving and Constraint Solving in Computational Origami}}, booktitle = {{Proceedings of AISC 2004 (7 th International Conference on Artificial Intelligence and Symbolic Computation)}}, language = {english}, series = {Springer Lecture Notes in Artificial Intelligence}, volume = {3249}, pages = {132--142}, publisher = {Copyright: Springer-Berlin}, isbn_issn = {ISSN 0302-9743, ISBN 3-540-232}, year = {2004}, month = {22-24 September}, annote = {2004-09-22-B}, editor = {B. Buchberger and John Campbell}, refereed = {yes}, institution = {RISC, Johannes Kepler University, Austria}, length = {10} } @Book{KreuzerRobbiano2000, author = {M. Kreuzer and L. Robbiano}, title = {{Computational Commutative Algebra I}}, publisher = {Springer New York--Heidelberg}, year = {2000} } @InProceedings{ChifmanPetrovic2007, author = {J. Chifman and S. 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