메뉴 건너뛰기




Volumn 34, Issue 2, 2005, Pages 252-294

Bernstein's second theorem and Viro's method for sparse polynomial systems in chemistry

Author keywords

[No Author keywords available]

Indexed keywords

CHEMISTRY; GRAPH THEORY; MATHEMATICAL MODELS; MATRIX ALGEBRA; REACTION KINETICS; VECTORS;

EID: 11244271554     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aam.2004.04.003     Document Type: Article
Times cited : (39)

References (36)
  • 1
    • 34249842390 scopus 로고
    • A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
    • D. Avis K. Fukuda A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra Discrete Comput. Geom. 8 3 1992 295-313
    • (1992) Discrete Comput. Geom. , vol.8 , Issue.3 , pp. 295-313
    • Avis, D.1    Fukuda, K.2
  • 2
    • 34250406508 scopus 로고
    • The number of roots of a system of equations
    • D.N. Bernstein The number of roots of a system of equations Funct. Anal. Appl. 9 1975 1-4
    • (1975) Funct. Anal. Appl. , vol.9 , pp. 1-4
    • Bernstein, D.N.1
  • 3
    • 0002190702 scopus 로고
    • Constructions and complexity of secondary polytopes
    • L.J. Billera P. Filliman B. Sturmfels Constructions and complexity of secondary polytopes Adv. Math. 83 1990 155-179
    • (1990) Adv. Math. , vol.83 , pp. 155-179
    • Billera, L.J.1    Filliman, P.2    Sturmfels, B.3
  • 4
    • 0004242420 scopus 로고
    • second ed., Cambridge Mathematical Library. Cambridge: Cambridge University Press
    • N. Biggs Algebraic Graph Theory second ed. Cambridge Mathematical Library 1993 Cambridge University Press Cambridge
    • (1993) Algebraic Graph Theory
    • Biggs, N.1
  • 5
    • 11244307537 scopus 로고
    • Asymptotes and intercepts of real-power polynomial surfaces from the geometry of the exponent polytope
    • B.L. Clarke Asymptotes and intercepts of real-power polynomial surfaces from the geometry of the exponent polytope SIAM J. Appl. Math. 35 4 1978 755-786
    • (1978) SIAM J. Appl. Math. , vol.35 , Issue.4 , pp. 755-786
    • Clarke, B.L.1
  • 6
    • 0002013127 scopus 로고
    • Stability of complex reaction networks
    • B.L. Clarke Stability of complex reaction networks Adv. Chem. Phys. 43 1980 1-213
    • (1980) Adv. Chem. Phys. , vol.43 , pp. 1-213
    • Clarke, B.L.1
  • 8
    • 0002803885 scopus 로고
    • The homogeneous coordinate ring of a toric variety
    • D.A. Cox The homogeneous coordinate ring of a toric variety J. Algebraic Geom. 4 1 1995 17-50
    • (1995) J. Algebraic Geom. , vol.4 , Issue.1 , pp. 17-50
    • Cox, D.A.1
  • 11
    • 0001105645 scopus 로고
    • Mechanistic classification of chemical oscillators and the role of species
    • I. Prigorine A. Rice John Wiley & Sons
    • M. Eiswirth A. Freund J. Ross Mechanistic classification of chemical oscillators and the role of species I. Prigorine A. Rice Advances in Chemical Physics vol. 80 1991 John Wiley & Sons 127-199
    • (1991) Advances in Chemical Physics , vol.80 , pp. 127-199
    • Eiswirth, M.1    Freund, A.2    Ross, J.3
  • 12
    • 0008563195 scopus 로고
    • Instability and oscillations in chemistry
    • M. Eiswirth Instability and oscillations in chemistry Suuri Kagaku 372 1994 59-64
    • (1994) Suuri Kagaku , vol.372 , pp. 59-64
    • Eiswirth, M.1
  • 14
    • 0003253612 scopus 로고    scopus 로고
    • Combinatorial convexity and algebraic geometry
    • New York: Springer-Verlag
    • G. Ewald Combinatorial convexity and algebraic geometry Grad. Texts in Math. vol. 168 1996 Springer-Verlag New York
    • (1996) Grad. Texts in Math. , vol.168
    • Ewald, G.1
  • 15
    • 0001364051 scopus 로고
    • The existence and uniqueness of steady states for a class of chemical reaction networks
    • M. Feinberg The existence and uniqueness of steady states for a class of chemical reaction networks Arch. Ration. Mech. Anal. 132 4 1995 311-370
    • (1995) Arch. Ration. Mech. Anal. , vol.132 , Issue.4 , pp. 311-370
    • Feinberg, M.1
  • 16
    • 0000112210 scopus 로고
    • Multiple steady states for chemical reaction networks of deficiency one
    • M. Feinberg Multiple steady states for chemical reaction networks of deficiency one Arch. Ration. Mech. Anal. 132 4 1995 371-406
    • (1995) Arch. Ration. Mech. Anal. , vol.132 , Issue.4 , pp. 371-406
    • Feinberg, M.1
  • 17
    • 11244265325 scopus 로고    scopus 로고
    • Thermisch stabiles up-scaling einer exothermen Modellreaktion (in German)
    • K.-H. Hoffmann, et al. (Eds.) Verbundprojekte zwischen Universität und Industrie Springer
    • B. Fiedler M. Efendiev A. Schuppert Thermisch stabiles up-scaling einer exothermen Modellreaktion (in German) K.-H. Hoffmann, et al. (Eds.) Mathematik: Schlüsseltechnologie für die Zukunft. Verbundprojekte zwischen Universität und Industrie 1997 Springer 83-90
    • (1997) Mathematik: Schlüsseltechnologie Für Die Zukunft , pp. 83-90
    • Fiedler, B.1    Efendiev, M.2    Schuppert, A.3
  • 18
    • 0017731760 scopus 로고
    • Chemical mechanism structure and the coincidence of the stoichiometric and kinetic subspaces
    • M. Feinberg F. Horn Chemical mechanism structure and the coincidence of the stoichiometric and kinetic subspaces Arch. Ration. Mech. Anal. 66 1 1977 83-97
    • (1977) Arch. Ration. Mech. Anal. , vol.66 , Issue.1 , pp. 83-97
    • Feinberg, M.1    Horn, F.2
  • 19
    • 0002893741 scopus 로고
    • Introduction to Toric Varieties
    • Princeton, NJ: Princeton University Press
    • W. Fulton Introduction to Toric Varieties Ann. of Math. Stud. vol. 131 1993 Princeton University Press Princeton, NJ
    • (1993) Ann. of Math. Stud. , vol.131
    • Fulton, W.1
  • 20
    • 11244254407 scopus 로고    scopus 로고
    • Counting stable solutions of sparse polynomial systems in chemistry
    • South Hadley, MA, 2000 Contemp. Math. Amer. Math. Soc. Providence, RI
    • K. Gatermann Counting stable solutions of sparse polynomial systems in chemistry Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering South Hadley, MA, 2000 Contemp. Math. vol. 286 2001 Amer. Math. Soc. Providence, RI 53-69
    • (2001) Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering , vol.286 , pp. 53-69
    • Gatermann, K.1
  • 21
    • 0036183849 scopus 로고    scopus 로고
    • A family of sparse polynomial systems arising in chemical reaction systems
    • K. Gatermann B. Huber A family of sparse polynomial systems arising in chemical reaction systems J. Symbolic Comput. 33 3 2002 275-305
    • (2002) J. Symbolic Comput. , vol.33 , Issue.3 , pp. 275-305
    • Gatermann, K.1    Huber, B.2
  • 23
    • 0003547058 scopus 로고    scopus 로고
    • Singular 2.0. A Computer Algebra System for Polynomial Computations
    • University of Kaiserslautern: Centre for Computer Algebra
    • G.-M. Greuel G. Pfister H. Schönemann Singular 2.0. A Computer Algebra System for Polynomial Computations 2001 Centre for Computer Algebra University of Kaiserslautern http://www.singular.uni-kl.de
    • (2001)
    • Greuel, G.-M.1    Pfister, G.2    Schönemann, H.3
  • 25
    • 84968520678 scopus 로고
    • A polyhedral method for solving sparse polynomial systems
    • B. Huber B. Sturmfels A polyhedral method for solving sparse polynomial systems Math. Comp. 64 212 1995 1541-1555
    • (1995) Math. Comp. , vol.64 , Issue.212 , pp. 1541-1555
    • Huber, B.1    Sturmfels, B.2
  • 26
    • 0003820984 scopus 로고    scopus 로고
    • The Regulation of Cellular Systems
    • New York: Chapman & Hall
    • R. Heinrich S. Schuster The Regulation of Cellular Systems 1996 Chapman & Hall New York
    • (1996)
    • Heinrich, R.1    Schuster, S.2
  • 27
    • 0032355157 scopus 로고    scopus 로고
    • Polyhedral end games for polynomial continuation
    • B. Huber J. Verschelde Polyhedral end games for polynomial continuation Numer. Algorithms 18 1 1998 91-108
    • (1998) Numer. Algorithms , vol.18 , Issue.1 , pp. 91-108
    • Huber, B.1    Verschelde, J.2
  • 28
    • 11244347248 scopus 로고    scopus 로고
    • Torische Ideale und chemische Reaktionssysteme (in German)
    • Diploma Thesis, Universität Hamburg
    • S. Karrenberg, Torische Ideale und chemische Reaktionssysteme (in German), Diploma Thesis, Universität Hamburg, 2003
    • (2003)
    • Karrenberg, S.1
  • 29
    • 27744563174 scopus 로고    scopus 로고
    • An interactive program in Matlab
    • FluxAnalyzer, Max-Planck Institut Magdeburg, available on request
    • S. Klamt, FluxAnalyzer, Max-Planck Institut Magdeburg, 2002. An interactive program in Matlab, available on request
    • (2002)
    • Klamt, S.1
  • 30
    • 0034339065 scopus 로고    scopus 로고
    • Global stability of complex balanced mechanisms
    • D. Siegel D. MacLean Global stability of complex balanced mechanisms J. Math. Chem. 27 2000 89-110
    • (2000) J. Math. Chem. , vol.27 , pp. 89-110
    • Siegel, D.1    MacLean, D.2
  • 31
    • 84972574115 scopus 로고
    • Gröbner bases of toric varieties
    • (2)
    • B. Sturmfels Gröbner bases of toric varieties Tohoku Math. J. (2) 43 2 1991 249-261
    • (1991) Tohoku Math. J. , vol.43 , Issue.2 , pp. 249-261
    • Sturmfels, B.1
  • 32
    • 0008599709 scopus 로고
    • On the number of real roots of a sparse polynomial system
    • A. Bloch (Eds.) Inst. Commun. Fields Inst. Commun. Amer. Math. Soc. Providence, RI
    • B. Sturmfels On the number of real roots of a sparse polynomial system A. Bloch (Ed.) Hamiltonian and Gradient Flows: Algorithms and Control Fields Inst. Commun. vol. 3 1994 Amer. Math. Soc. Providence, RI 137-143
    • (1994) Hamiltonian and Gradient Flows: Algorithms and Control , vol.3 , pp. 137-143
    • Sturmfels, B.1
  • 33
    • 0000408825 scopus 로고
    • Viro's theorem for complete intersections
    • (4)
    • B. Sturmfels Viro's theorem for complete intersections Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 21 3 1994 377-386
    • (1994) Ann. Sc. Norm. Super. Pisa Cl. Sci. , vol.21 , Issue.3 , pp. 377-386
    • Sturmfels, B.1
  • 34
    • 0003306410 scopus 로고    scopus 로고
    • Gröbner Bases and Convex Polytopes
    • Univ. Lecture Ser. Providence, RI:
    • B. Sturmfels Gröbner Bases and Convex Polytopes Univ. Lecture Ser. vol. 8 1996 Amer. Math. Soc. Providence, RI
    • (1996) Amer. Math. Soc. , vol.8
    • Sturmfels, B.1
  • 35
    • 0032264839 scopus 로고    scopus 로고
    • Polynomial equations and convex polytopes
    • B. Sturmfels Polynomial equations and convex polytopes Amer. Math. Monthly 105 10 1998 907-922
    • (1998) Amer. Math. Monthly , vol.105 , Issue.10 , pp. 907-922
    • Sturmfels, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.