Vulpe Nicolae
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Research interests
Qualitative theory of systems of differential equations, theory of algebraic invariants, development of algorithms and software for invariant polynomials utilizationImportant publications
- Characterization of the finite weak singularities of quadratic systems via invariant theory.
Nonlinear Analysis. Theory, Methods and Applications, 74 (2011), No. 4, p. 6553–-6582 (fară coautori) - Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral.
Rocky Mountain Journal of Mathematics, Vol. 41 (2011), No. 5, p. 1585–-1629 (coautori J. Llibre, A. Mahdi) - Global classification of the planar Lotka-Volterra differential systems according to the configurations of invariant straight lines
Journal of Fixed Point Theory and Applications, 8 (2010), p. 177–-245 (coautor D. Schlomiuk). - Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space $\mathbb{R}^{12}$.
Rendiconti del Circolo Matematico di Palermo 59 (2010), p. 419–-449 (coautori: J. Artes, J. Llibre). - Bifurcation diagrams and moduli spaces of planar quadratic vector fields with invariant lines of total multiplicity four and having exactly three real singularities at infinity.
Qualitative Theory of Dynamical Systems, 9 (2010), No. 1-2, p. 251-300 (coautor D. Schlomiuk). - Quadratic systems with a polynomial first integral: a complete classification in the coefficient space $\mathbb{R}^{12}$.
J. Differential Equations, 246 (2009), p. 3535-3558 (coautori: J. Artes, J. Llibre). - Integrals and phase portraits of planar quadratic differential systems with invariant lines of at least five total multiplicity.
Rocky Mountain Journal of Mathematics, Vol. 38 (2008), No. 6, p. 2015-2075 (coautor D. Schlomiuk). - When singular points determine quadratic systems.
Electronic Journal of Differential Equations, Vol. 2008 (2008), No. 82, p. 1-37. (coautori: J. Artes, J.Llibre). - The full study of planar quadratic differential systems possessing a line of singularities at infinity.
Journal of Dynamics and Diff. Equations, 20 (2008), No. 4, p. 737-775 (coautor D. Schlomiuk). - The types of the singular points for quadratic system: a complete solution of the problem in the coefficient space $\mathbb{R}^{12}$.
International Journal of Bifurcation Theory and Chaos, 18, No.2 (2008), 1301--1373 (coautori: J. Artes, J. Llibre). - Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four
Buletinul A.ş.M., Matematica, No. 1(56), 2008, 27--83 (coautor D. Schlomiuk). - Planar quadratic differential systems with invariant straight lines of total multiplicity four.
Nonlinear Anal., 68 (2008), No. 4, 681-715 (coautor D. Schlomiuk). - Quadratic systems with a rational first integral of degree 2: a complete classification in the coefficient space $\mathbb{R}^{12}$.
Rendiconti Circolo Matematico di Palermo, Serie II, T. LVI (2007), 417--444 (coautori: J. Artes, J.Llibre). - Planar cubic polynomial differential systems with the maximum number of invariant straight lines.
Rocky Mountain J. Math., 36, No.4, 2006, 1301--1373 (coautor: J.Llibre). - Geometry of quadratic differential systems in the neighbourhood of the line at infinity.
J. Differential Equations, 215 (2005) 357--400 (coautor D. Schlomiuk).
Membership in Societies and Editorial Boards
- Editor-in-Chief of the journal "Buletinul Academiei de Stiinte a Moldovei. Matematica" (since 1993).
- Member of the Mathematical Society of the Republic of Moldova.
Distinctions
- Laureate of "Academician C. Sibirsky" Award for cycle of publications "Application of invariant polynomials in qualitative study of systems of differential equations" (2000).
- Laureate of the Republican Award for Young Scientists for cycle of publications in the domain of algebraic invariants of differential systems (1978).
Activity
- Deputy Chief of the scientific seminar "Qualitative Theory of Differential Equations" at the Moldova State University.
- Member of the IMCS Scientific Council.
- Membru al Adunării Secţiei de Ştiinţe Exacte şi Economice.
Pregătirea cadrelor ştiinţifice:
1. Dr. V. Cebanu susţinut 1987, Центроаффинные комитанты дифференциальной системы с кубическими нелинейностями и их приложения, Kiev, Universitatea de Stat T. G. Şevcenko.
2. Dr. V. Daniliuc susţinut 1988, Комитанты квадратично-кубической системы и их приложения, Odessa, Universitatea de Stat I. I. Mecinikov.
3. Dr. I. Nikolaev susţinut 1990, Центроаффинные комитанты и особые точки системы с квадратическими нелинейностями, Odessa, Universitatea de Stat I. I. Mecinikov.
4. Dr. Iu. Calin susţinut 1997, Качественное исследование некоторых классов полных квадратичных систем, Chişinău, Universitatea de Stat din Moldova.
5. Dr. A. Voldman susţinut în 1997, Comitants and singular points of quadratic differential systems, Chişinău, Universitatea de Stat din Moldova.
6. Dr. L. Gheorghiu susţinut în 1998, Repartizarea multiplicităților punctelor singulare infinite ale sistemului diferențial cubic, Chişinău, Universitatea de Stat din Moldova.
7. Dr. M. Lupan susţinut în 2007, Clasificarea topologică a sistemului pătratic complet cu centru de simetrie, Chişinău, Universitatea de Stat din Moldova.
Vizite la alte universităţi şi centre Ştiinţifice:
- Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 26.04.2011-15.06.2011)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 19.10.2011-18.12.2011)
- Universitat Autònoma de Barcelona (Spain – prof. J. Artes, 6.04.2010-03.06.2010)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 20.10.2010-20.12.2010)
- Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 01.03.2009-30.04.2009)
- Institute for Advanced Study (Princeton, SUA – prof. Robert P. Langlands, 05.10.2009-05.12.2009)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 06.12.2009-16.12.2009)
- Universitat Autònoma de Barcelona (Spain – prof. J. Artes, 02.05.2008-30.06.2008)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 20.10.2008-20.12.2008)
- Banff International Research Station (Canada – Workshop, 23.11.2008-28.11.2008)
- Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 10.04.2007-10.07.2007)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 18.10.2007-16.12.2007)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 05.02.2006-07.04.2006)
- Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 24.04.2006-24.06.2006)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 17.10.2006-16.12.2006)
- Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 06.05.2005-04.06.2005)
- L’Université de Montréal (Canada – prof. D.Schlomiuk , 03.02.2005-04.05.2005)
- Universitat Autònoma de Barcelona (Spain – prof. J. Llibre, 20.09.2005-20.12.2005)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 01.01.2004-04.03.2004, 04.09.2004-16.10.2004)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 20.11.2003-25.12.2003)
- Universitat Autònoma de Barcelona (Spain, 01.05.2002-14.10.2002 – a câştigat concursul pentru a ţine un curs de lecţii studenţilor acestei universităţi)
- Centre de Recherches Mathématiques (CRM), L’Université de Montréal (Canada, 02.06.2000-04.07.2000 – subsidat de Proramul FICU (Ref/99/PAS/09) al AUPELF-UREF, Agenţia universitară Francofonă)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 01.11.2000-15.12.2000)
- The York University (Yoork, England, 15.02.1999-31.03.1999 – în cadrul programului susţinut financiar de Royal Society)
- L’Université de Montréal (Canada – prof. D. Schlomiuk, 19.06.1999-02.07.1999)
- Delft University of Technology (Delft, Netherlands – prof. J. Reyn, 01.02.1997-25.02.1997, a participat în calitate de referent oficial la susţinerea unei teze de doctor)
Publications in Computer Science Journal of Moldova, Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica and Quasigroups and Related Systems
- 2009 A complete classification of quadratic differential systems according to the dimensions of Aff(2, R)-orbits
- 2008 Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four.
- 2003 Classification of quadratic systems with a symmetry center and simple infinite singular points. (English)
- 1999 Real quadratic systems with two imaginary invariant straight lines. (English)
- 1998 The differential operators and multiplicity of singular points for polynomial differential system. (English)
- 1996 The repartition of multiplicity between three real isp of cubis differential system. (English)
- 1996 A complete algebraic basis of centro-affine invariants of a differential system with fourth-order homogeneous right-hand sides. (Russian)
- 1995 The repartition of multiplicity between four infinite singular points of cubic differential system. (English)
- 1995 Affine invariant conditions for topologically distinguishing quadratic systems without finite critical points. (English)
- 1995 Affine invariant conditions for topological classification of quadratic systems with $m_f=1$. (English)
- 1994 Quadratic systems with dicritical points. (Russian)
- 1993 Topological classification of quadratic systems with a unique finite second order singularity with two zero eigenvalues. (English)
- 1993 Affine-invariant conditions for determining the number and multiplicity of singular points of quadratic differential systems. (English)
- 1992 On the number, multiplicity and types of singular points of a differential system. (Russian)
- 1992 Topological classification of quadratic systems with a unique third-order singular point. (English)
- 1992 Coefficient conditions for the coexistence of two singular points of summed multiplicity 4 in a finite part of a phase plane of a quadratic system. (Russian)
