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References Anastasiei, M. - Geometry of Lagrangians and semisprays on Lie algebroids , Proceedings of the 5th Conference of Balkan Society of Geometers, 10-17, BSG Proc., 13, Geom. Balkan Press, Bucharest, 2006. Druţă, S. L. - The holomorphic sectional curvature of general natural Kähler structures on cotangent bundles , An. Ştiinţ. Univ. "Al. I. Cuza" Iaşi. Mat. (N. S.), 56 (2010), 113-130. Lang, S. - Fundamentals of Differential Geometry , Graduate Texts in Mathematics, 191, Springer-Verlag, New York, 1999. Higgins, P. J.; Mackenzie, K. - Algebraic

References [1] L. A. Bokut, Embedddings in prime associative algebras, Algebra i Logica, 15(2) (1976), 117- 142 (in Russ.) [2] G. P. Kukin, Primitive elements of free Lie algebras, Algebra i Logica, 9(4) (1970), 458-472 (in Russ.). [3] G. P. Kukin, On subalgebras of free Lie p-algebras, Algebra i Logica 11(5) (1972) 535-550 (in Russ.). [4] W. Magnus, Uber diskontinuierliche Gruppen mit einer definierden Relation (Der Frei- heitssatz), J. Reine Angew. Math. 163 (1930), 141-165. [5] A. I. Malcev, On algebras with identity relations, Mat. Sborn. 26/1 (1950), 19

References [1] M., Anastasiei, Banach Lie Algebroids. An. St. Univ. ”Al.I. Cuza” Iasi S.N. Matematica, T. LVII, 2011 f.2, 409-416. [2] M. Anastasiei, A. Sandovici, Banach Dirac bundles. Int. J. Geom. Methods Mod. Phys. 10(7), (2013), 1350033 (16 pages) DOI: 10.1142/S0219887813500333. [3] T. Courant, Dirac structures, Trans. A.M.S. 319 (1990), 631-661. [4] T. Courant, A. Weinstein, Beyond Poisson structures, Seminaire Sud-Rhodanien de Geometrie, Travaux en cours 27 (1988), 39-49, Hermann, Paris. [5] M. Crasmareanu, Dirac structures from Lie integrability, Int. J

References Anastasiei, M. - Metrizable linear connections in a Lie algebroid , J. Adv. Math. Stud., 3 (2010), 9-18. Bucataru, I. - Metric nonlinear connections , Differential Geom. Appl., 25 (2007), 335-343. Bucataru, I.; Dahl M.F. - Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations , J. Geom. Mech., 1 (2009), 159-180. Crâşmăreanu, M. - Metrizable systems of autonomous second order differential equations , Carpathian J. Math., 25 (2009), 163-176. Fernandes, R.L. - Lie algebroids, holonomy and characteristic

Interrupted Cries. Routledge, London. SEARLES, H.F. (1959). The Oedipal love in countertransference. In Collected Papers on Schizophrenia and Related Subjects . The Hogart Press, London, 1965. STEINER, J. (1993). Psychic Retreats: Pathological organizations in psychotic, neurotic and borderline patients. Routledge, London. TABAK DE BIANCHEDI, E. T. et al. (2000). The various faces of lies, in Bion Talamo, P., Borgogno, F., Merciai, S.A. (Eds.) W.R. Bion: Between Past and Future . Karnac, London. WINNICOTT, D.W. (1963). Communicating and Not Communicating Leading to a

References [1] Bade W.G., Dales H.G., Lykova Z.A., Algebraic and strong splittings of extensions of Banach algebras, Mem. Amer. Math. Soc. 137 (1999), no. 656. [2] Benkovic D., Lie triple derivations of unital algebras with idempotents, Linear Multilinear Algebra 65 (2015), 141-165. [3] Cheung W.-S., Mappings on triangular algebras, PhD Dissertation, University of Victoria, 2000. [4] Cheung W.-S., Lie derivations of triangular algebras, Linear Multilinear Algebra 51 (2003), 299-310. [5] Du Y., Wang Y., Lie derivations of generalized matrix algebras, Linear

References 1. Agrachev, A.A.; Sachkov, Y.L. - Control Theory From the Geometric Viewpoint , Encyclopaedia of Mathematical Sciences, 87, Control Theory and Optimization, II. Springer-Verlag, Berlin, 2004. 2. Biggs, R.; Remsing, C.C. - A category of control systems , An. S¸tiint¸. Univ. ”Ovidius” Constant¸a Ser. Mat., 20 (2012), 355-367. 3. Biggs, R.; Remsing, C.C. - On the equivalence of control systems on Lie groups (submitted). 4. Biggs, R.; Remsing, C.C. - A note on the affine subspaces of three-dimensional Lie algebras (submitted). 5. Biggs, R.; Remsing

1 Introduction Parafree groups arose from G. Baumslag’s works [ 2 , 3 ]. G. Baumslag has obtained some interesting results about parafree groups [ 4 , 5 ]. In 1978, H. Baur has translated the notion of parafree groups to parafree Lie algebras [ 6 ]. He has defined parafree Lie algebras as in the group case and he proved the existence of a non-free parafree Lie algebra [ 5 ]. Further, N. Ekici and Z. Velioğlu have worked on unions [ 9 ] and direct limit [ 10 ] of parafree Lie algebras. In [ 12 ], Z. Velioğlu has investigated a residual property of metabelian

REFERENCES 1. Azad H., Mustafa M. T., Arif A. F. M. (2010), Analytic Solutions of Initial-Boundary-Value Problems of Transient Conduction Using Symmetries, Applied Mathematics and Computation, Vol. 215, 41324140. 2. Bluman G. W., Cole J. D. (1974), Similarity Methods for Differential Equations, Springer-Verlag, New York, 1974. 3. Champagne B., Hereman W. , Winternitz P. (1991), The Computer Calculation of Lie Point Symmetries of Large Systems of Differential Equations, Computer Physics Communications, Vol. 66, 319-340. 4. Drew M. S., Kloster S. (1989

References 1. Anastasiei, M. - Mechanical systems on Lie algebroids , Algebras Groups Geom., 23 (2006), 235-245. 2. Bucataru, I. - Metric nonlinear connection , Differential Geom. Appl., 25 (2007), 335-343. 3. Bucataru, I.; Dahl, M.F. - Semi-basic 1-forms and Helmholtz conditions for the inverse problem of the calculus of variations , J. Geom. Mech., 1 (2009), 159-180. 4. Crampin, M. - Tangent bundle geometry for Lagrangian dynamics , J. Phys. A, 16 (1983), 3755-3772. 5. Crâşmăreanu, M. - Metrizable systems of autonomous second order differential equations