About Solutions of Nonlinear Algebraic System with Two Variables

Rakhshanda Dzhabarzadeh

doi:doi:10.11648/j.pamj.20130201.15

| Peer-Reviewed

About Solutions of Nonlinear Algebraic System with Two Variables

Rakhshanda Dzhabarzadeh

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 1)

Published: 20 February 2013

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced. At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 1)
DOI	10.11648/j.pamj.20130201.15
Page(s)	32-37
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Algebraic, Spectral, Resultant, Nonlinear

References

[1]	Atkinson F.V. Multiparameter spectral theory. Bull.Amer.Math.Soc.1968, 74, 1-27
[2]	Balinskii A.I Generation of notions of Bezutiant and Re-sultant DAN of Ukr SSR, ser.ph.-math and tech. of sciences,1980, 2, pp.3-6( in Russian).
[3]	Browne P.J. Multiparameter spectral theory. Indiana Univ. Math. J,24, 3, 1974.
[4]	Dzhabarzadeh R.M. On existence of common eigen value of some operator-bundles, that depends polynomial on parameter. International conference of topology, 3-9 oct., 1987, Baku. Tez., part 2,page 99
[5]	Dzhabarzadeh R.M. Spectral theory of two parameter system in finite dimensional space. Transactions of Azerbaijan Na-tional Academy of Sciences, v.XVIII,3-4,pp.12-18
[6]	Dzhabarzadeh R.M. Multiparameter spectral theory. Lambert Academic Publishing , 2 mart 2012, pp.182
[7]	Prugoveĉku E. Quantum mechanics in Hilbert space. Aca-demic Press, New York, London, 1971
[8]	Sleeman B.D. Multiparameter spectral theory in Hilbert space. Pitnam Press, London, 1978, pp.118.
[9]	Hargrave B.A., Sleeman B.D. The numerical solution of two-parameter eigenvalue to the problem of diffraction by a plane angular sector. J. Inst.Math. Applic.14, 1974, 9-22.
[10]	Voytovich N.N., Katsenelenbaum B.Z., Sivov A.N.Generaliz a method of characteristic oscillations in the theory of a dif-fraction - М.: publishing "Science", 1977. - pp. 416.
[11]	Genchev Т.Q. (Генчев) About the ultraparabolic equations. DAS of USSR, 1963, т.151, №2, p.265-268 (in Russian)
[12]	Keldysh М.V. About completeness of eigenfunctions of some classes of self-conjugate linear operators. UMN, 1971, т.27, issue 4, p.15-41.(in Russian)
[13]	Levi P. (Леви). Stochastic processes and a Brownian motion. М.: publishing "Science", 1979, pp 375 (in Russian).
[14]	MarchukG.I. (Марчук) . Metody of calculation of nuclear reactors. М.: , "State Atom Publishing",1961 (in Russian).
[15]	Richmakher R (Рихмахер). Printsipy of modern mathematical physics., M. publishing "Mir", 1982,p. 486 (in Russian). Fok V.A. (Фок). The beqinnings of a quantum mechanics. М.: Publishing "Science", 1976, pp,376.
[16]	Khayniq Q (Хайниг). Abstract analog of an eliminant of two polynomial bundles. The Functional analysis and its appli-cations, 1977, 2, issue 3, pp.94-95. (in Russsian)

Cite This Article

Plain Text BibTeX RIS

APA Style

Rakhshanda Dzhabarzadeh. (2013). About Solutions of Nonlinear Algebraic System with Two Variables. Pure and Applied Mathematics Journal, 2(1), 32-37. https://doi.org/10.11648/j.pamj.20130201.15

Copy | Download

ACS Style

Rakhshanda Dzhabarzadeh. About Solutions of Nonlinear Algebraic System with Two Variables. Pure Appl. Math. J. 2013, 2(1), 32-37. doi: 10.11648/j.pamj.20130201.15

Copy | Download

AMA Style

Rakhshanda Dzhabarzadeh. About Solutions of Nonlinear Algebraic System with Two Variables. Pure Appl Math J. 2013;2(1):32-37. doi: 10.11648/j.pamj.20130201.15

Copy | Download

@article{10.11648/j.pamj.20130201.15,
  author = {Rakhshanda Dzhabarzadeh},
  title = {About Solutions of Nonlinear Algebraic System with Two Variables},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {1},
  pages = {32-37},
  doi = {10.11648/j.pamj.20130201.15},
  url = {https://doi.org/10.11648/j.pamj.20130201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130201.15},
  abstract = {For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced.  At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - About Solutions of Nonlinear Algebraic System with Two Variables
AU  - Rakhshanda Dzhabarzadeh
Y1  - 2013/02/20
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130201.15
DO  - 10.11648/j.pamj.20130201.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 32
EP  - 37
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130201.15
AB  - For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced.  At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.
VL  - 2
IS  - 1
ER  -

Copy | Download

Author Information

Rakhshanda Dzhabarzadeh

?nstitute Mathematics and Mechanics of NAN of Azerbaijan, Baku

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Rakhshanda Dzhabarzadeh. (2013). About Solutions of Nonlinear Algebraic System with Two Variables. Pure and Applied Mathematics Journal, 2(1), 32-37. https://doi.org/10.11648/j.pamj.20130201.15

Copy | Download

ACS Style

Rakhshanda Dzhabarzadeh. About Solutions of Nonlinear Algebraic System with Two Variables. Pure Appl. Math. J. 2013, 2(1), 32-37. doi: 10.11648/j.pamj.20130201.15

Copy | Download

AMA Style

Rakhshanda Dzhabarzadeh. About Solutions of Nonlinear Algebraic System with Two Variables. Pure Appl Math J. 2013;2(1):32-37. doi: 10.11648/j.pamj.20130201.15

Copy | Download

@article{10.11648/j.pamj.20130201.15,
  author = {Rakhshanda Dzhabarzadeh},
  title = {About Solutions of Nonlinear Algebraic System with Two Variables},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {1},
  pages = {32-37},
  doi = {10.11648/j.pamj.20130201.15},
  url = {https://doi.org/10.11648/j.pamj.20130201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130201.15},
  abstract = {For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced.  At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - About Solutions of Nonlinear Algebraic System with Two Variables
AU  - Rakhshanda Dzhabarzadeh
Y1  - 2013/02/20
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130201.15
DO  - 10.11648/j.pamj.20130201.15
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 32
EP  - 37
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130201.15
AB  - For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced.  At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.
VL  - 2
IS  - 1
ER  -

Copy | Download