Vulpe Nicolae
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Domeniul de cercetare
Teoria calitativă a sistemelor de ecuaţii differenţiale; teoria invarianţilor algebrici; elaborarea de algoritme şi programe pentru utilizarea polinoamelor invarianteLucrări importante
- 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), 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), 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, 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), 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, 2015--2075 (coautor D. Schlomiuk). - When singular points determine quadratic systems.
Electronic Journal of Differential Equations, Vol. 2008 (2008), No. 82, 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, 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).
Apartenenţa la societăţi, redacţii
- Redactor responsabil al revistei periodice de matematică „Buletinul Academiei de ştiinţe a Moldovei. Matematica” (începând cu anul 1993).
- Societatea Matematică din Republica Moldova (SMRM).
Distincţii
- Laureat al Premiului „Academician C.Sibirschi” pe anul 2000 pentru ciclul de lucrări „Aplicarea polinoamelor invariante în studiul calitativ al sistemelor de ecuaţii diferenţiale”.
- Laureat al Premiului Republican pentru tineri cercetători pentru ciclul de lucrări în domeniul invarianţilor algebrici ai sistemelor diferenţiale (1978).
Activitate
- Conducător adjunct al seminarului ştiinţific „Teoria calitativă a ecuaţiilor diferenţiale” de la Universitatea de Stat din Moldova.
- Membru al Consiliului ştiinţific al IMI.
Publicaţii în Computer Science Journal of Moldova, Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica şi 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)
