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Applications of the theory of weakly nondegenerate conditions to zero decomposition for polynomial systems

Yong-Bin Li
2004 Journal of symbolic computation  
This paper presents some applications of the theory of weakly nondegenerate conditions obtained by analytic methods to zero decomposition of polynomial systems and sets.  ...  Some examples are given to illustrate the performance and effectiveness of the applications.  ...  Acknowledgements The author thanks Dr. Dongming Wang and the referees for their helpful comments and suggestions on an earlier version of this paper.  ... 
doi:10.1016/j.jsc.2003.10.004 fatcat:ra3zknsqezegnf27h65o7vfdyi

Index to Volumes 37 and 38

2004 Journal of symbolic computation  
-I., Characterization of Pythagorean curves and Pythagoreanization using a rational transform, 377 An effective decision method for semidefinite polynomials, 83 An objective representation of the Gaussian  ...  , 641 A symbolic test for (i, j )-uniformity in reduced zero-dimensional schemes, 403 AHN, M.  ...  surface, 1551 Algorithmic proofs of two theorems of Stafford, 1535 Applications of the theory of weakly nondegenerate conditions to zero decomposition for polynomial systems, 815 Automatic solution of  ... 
doi:10.1016/s0747-7171(04)00109-9 fatcat:q3cckydpknhjhinygacsvlj52y

Morse theory on Banach manifolds

K. Uhlenbeck
1972 Journal of Functional Analysis  
In addition, sufficient conditions for the critical points of variational problems to be weakly nondegenerate are given.  ...  The question of the genericity of nondegenerate critical points for * An announcement of the results of this paper has appeared as Morse theory on  ...  THE HANDLE-BODY DECOMPOSITION In this section, we construct the usual handle-body decomposition for a C2 function satisfying condition (C) and having only weakly nondegenerate critical points.  ... 
doi:10.1016/0022-1236(72)90039-0 fatcat:gqh4uvito5bndgpqi3cllnypfe

Morse theory on Banach manifolds

K. Uhlenbeck
1970 Bulletin of the American Mathematical Society  
In addition, sufficient conditions for the critical points of variational problems to be weakly nondegenerate are given.  ...  The question of the genericity of nondegenerate critical points for * An announcement of the results of this paper has appeared as Morse theory on  ...  THE HANDLE-BODY DECOMPOSITION In this section, we construct the usual handle-body decomposition for a C2 function satisfying condition (C) and having only weakly nondegenerate critical points.  ... 
doi:10.1090/s0002-9904-1970-12384-9 fatcat:qfnianhtcbh4hhymyxc2molfnu

Contents of Volumes 37 and 38

2004 Journal of symbolic computation  
-B., Applications of the theory of weakly nondegenerate conditions to zero decomposition for polynomial systems . . . . . . . . . . . 815 Fieker, C., Minimizing representations over number fields .  ...  A., Certified dense linear system solving . . . 485 Perdry, H., Strongly Noetherian rings and constructive ideal theory . . . . 511 Shi, H., Computation of the finitistic dimension of monomial algebras  ... 
doi:10.1016/s0747-7171(04)00108-7 fatcat:tmvrkoolp5b4jkrpklob3tet5q

Linear recurrence sequences satisfying congruence conditions

Gregory T. Minton
2014 Proceedings of the American Mathematical Society  
Our classification for the first type is in terms of linear dependencies of the characteristic zeros; for the second, it involves recurrence sequences vanishing on arithmetic progressions; and for the  ...  In addition to computing the dimension, our forthcoming argument implicitly gives an algorithm for computing the space of Fermat sequences in terms of the space of vanishing Q-linear combinations of {r  ...  Proof of Corollary 2.13. Lemma 6.9 implies that a nondegenerate vanishing sequence is zero.  ... 
doi:10.1090/s0002-9939-2014-12168-x fatcat:mjb52syap5f2nnmyg3n4zogfom

Techniques in equivariant Ehrhart theory [article]

Sophia Elia, Donghyun Kim, Mariel Supina
2022 arXiv   pre-print
Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action.  ...  We present a catalogue of techniques with applications in this field, including zonotopal decompositions, symmetric triangulations, combinatorial interpretation of the h^∗-polynomial, and certificates  ...  m i=1 (1 − z ℓi ) has a zero at z = −1 of order equal to the number of even ℓ i , condition (c) is exactly what is needed for cancellation to occur. Corollary 3.16.  ... 
arXiv:2205.05900v1 fatcat:aizfrbxebjedphtmxfdoqfz7tu

Parabolic subalgebras, parabolic buildings and parabolic projection [article]

David M. J. Calderbank, Passawan Noppakaew
2017 arXiv   pre-print
Indeed we derive such structure theory, from root systems to the Bruhat decomposition, from the properties of parabolic subalgebras.  ...  We present herein an elementary approach to the geometry of parabolic subalgebras, over an arbitrary field of characteristic zero, which does not rely upon the structure theory of semisimple Lie algebras  ...  zero, without relying on the structure theory of semisimple Lie algebras.  ... 
arXiv:1607.00370v2 fatcat:ekinsz3ehbg57fsnyv5us7h5ci

Analyzing and visualizing sequence and distance data using SplitsTree

A. Dress, D. Huson, V. Moulton
1996 Discrete Applied Mathematics  
The construction of this graph is based upon the splitdecomposition technique which is a procedure to decompose a given metric defined on a finite set in a canonical way into a sum of simpler metrics.  ...  The splits-graph and the theory behind it have been developed mainly in Bielefeld over the last 5 years.  ...  Additionally, the program contains two other methods for computing splits from a set of given sequences, namely spectral analysis [ 16, 241 followed by a yree& selection of a weakly compatible system  ... 
doi:10.1016/s0166-218x(96)00059-5 fatcat:57owzgwjyrayzfpbcrsj2hj6va

Reaction Network Analysis of Metabolic Insulin Signaling [article]

Patrick Vincent N. Lubenia, Eduardo R. Mendoza, Angelyn R. Lao
2022 arXiv   pre-print
Our analysis has also shown that the system has ACR in 8 species all coming from a deficiency zero subnetwork.  ...  Utilizing the network's deficiency-oriented coarsening, we have developed a method to determine positive equilibria for the entire network.  ...  A special case of condition (ii) of the said proposition is any weakly reversible power law system with reactantdetermined kinetics, zero deficiency, and a linked SF-pair in X.  ... 
arXiv:2204.04614v2 fatcat:ih7tegp7vfa4rjpxubmo75p23u

Extremal problems for matrix-valued polynomials on the unit circle and applications to multivariate stationary sequences

L. Klotz, A. Lasarow
2003 Journal of Approximation Theory  
Under some additional assumptions on M and J; the value of D is computed and the results are applied to linear prediction problems of multivariate weakly stationary random sequences.  ...  the set of matrix-valued polynomials with prescribed values of some of their derivatives at a finite set J of complex numbers.  ...  For the most part, our applications to prediction theory are analogous to Pourahmadi's results [18] concerning univariate weakly stationary random sequences.  ... 
doi:10.1016/j.jat.2003.09.010 fatcat:k2nscgov5zbdxasbfjditdk5cq

Concordant Chemical Reaction Networks and the Species-Reaction Graph [article]

Guy Shinar, Martin Feinberg
2012 arXiv   pre-print
These conditions are weaker than earlier ones invoked to establish kinetic system injectivity, which, in turn, is just one ramification of network concordance.  ...  , so long as the kinetics lies within the very broad and natural weakly monotonic class.  ...  Acknowledgment We are grateful to Daniel Knight for helpful discussions and to Uri Alon for his support and encouragement of this work.  ... 
arXiv:1203.6560v3 fatcat:2cbb33tnhjhnhguv5vm7e7takm

Real Stability Testing [article]

Prasad Raghavendra, Nick Ryder, Nikhil Srivastava
2016 arXiv   pre-print
The proof exploits properties of hyperbolic polynomials to reduce real stability testing to testing nonnegativity of a finite number of polynomials on an interval.  ...  As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials preserves real-rootedness.  ...  We now combine the above facts to obtain a crisp condition for real-rootedness of a one-parameter family.  ... 
arXiv:1610.00209v1 fatcat:w65d4bksszabxgqnkccpbvdua4

Identifiability of an X-rank decomposition of polynomial maps [article]

Pierre Comon, Yang Qi, Konstantin Usevich
2017 arXiv   pre-print
In the paper, we try to make results and basic tools accessible for general audience (assuming no knowledge of algebraic geometry or its prerequisites).  ...  In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning.  ...  We truly appreciate the help of the editors and the referees, their careful proofreading, and many thoughtful comments.  ... 
arXiv:1603.01566v3 fatcat:kxtnhhrvpnhmth7hpt322v3t7e

Concordant chemical reaction networks and the Species-Reaction Graph

Guy Shinar, Martin Feinberg
2013 Mathematical Biosciences  
These conditions are weaker than earlier ones invoked to establish kinetic system injectivity, which, in turn, is just one ramification of network concordance.  ...  , so long as the kinetics lies within the very broad and natural weakly monotonic class.  ...  Acknowledgments We are grateful to Daniel Knight for helpful discussions and to Uri Alon for his support and encouragement of this work.  ... 
doi:10.1016/j.mbs.2012.08.002 pmid:22940368 pmcid:PMC4701587 fatcat:qx5e73ohs5bafasfr5hl3rg4cy
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