Jet Riemann-Lagrange Geometry and Some Applications in Theoretical Biology

Nicola, Ileana Rodica; Neagu, Mircea

doi:10.1080/1726037X.2008.10698541

Open Access Original Articles

Jet Riemann-Lagrange Geometry and Some Applications in Theoretical Biology

Ileana Rodica Nicolanicola_rodica@yahoo.comDepartment of Mathematics IFaculty of Applied SciencesUniversity Politehnica of BucharestSplaiul Independenţei 313, Bucharest, 060042, RomaniaView full profile → , Mircea Neagumirceaneagu73@yahoo.comFaculty of Mathematics and InformaticsUniversity Transilvania of BraşovStr. Lămâiţei, Nr. 66, Bl. 93, Sc. G, Ap. 10, Braşov Bv 500371, RomaniaView full profile →

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pp. 13–25Vol. 6Issue 1June 2013DOI: 10.1080/1726037X.2008.10698541XML

Published Online:: 03 Jun 2013
Article type:: Original Articles
Language:: EN
Article no.:: 1726037X.2008.10698541
Pages:: 13–25

Abstract

The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet electromagnetic Yang-Mills energies, starting from some given nonlinear evolution ODEs systems modelling biologic phenomena like the cancer cell population model or the infection by human immunodeficiency virus-type 1 (HIV-1) model.

Keywords

1-jet spaces jet least squares Lagrangian functions jet Riemann-Lagrange geometry cancer cell population evolution model infection by HIV-1 evolution model

References

Asanov, G.S.1990 . Jet extension of Finslerian gauge approach . , 38 ( 8 ) : 571 – 610 .
Garner, A.L., Lau, Y.Y., Jordan, D.W., Uhler, M.D. and Gilgenbach, R.M.2006 . Implication of a simple mathematical model to cancer cell population dynamics . , 39 : 15 – 28 .
Luciani, A.M., Rosi, A., Matarrese, P., Arancia, G., Guidoni, L. and Viti, V.2001 . Changes in cell volume and internal sodium concentration in HrLa cells during exponential growth and following ionidamine treatment . , 80 : 187 – 195 .
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Neagu, M.2005 . , Bucharest: Matrix Rom .
Neagu, M. and Nicola, I.R.2004 . Geometric dynamics of calcium oscillations ODEs systems . , 9 ( 2 ) : 36 – 67 .
Neagu, M. and Udrişte, C.2001 . From PDEs systems and metrics to geometric multi-time field theories . , 79 : 1 – 33 .
Nelson, P.W. and Perelson, A.S.2002 . Mathematical analysis of delay differential equation models of HIV-1 infection . , 179 : 73 – 94 .
Nicola, I.R.2007 . , Bucharest: Bren . (in Romanian).
Obădeanu, V.2006 . , Timişoara: Editura Universităţii de Vest . (in Romanian).
Olver, P.J.1986 . , Springer-Verlag .
Perelson, A.S. and Nelson, P.W.1999 . Mathematical analysis of HIV-1 dynamics in vivo . , 41 ( 1 ) : 3 – 44 .
Poincaré, H.1880 . Sur les courbes definies par les equations différentielle . , 90 : 673 – 675 .
Reya, T., Morrison, S.J., Clarke, M.F. and Weissman, I.L.2001 . Stem cells, cancer, and cancer stem cells . , 414 : 105 – 111 .
Saunders, D.1989 . , New York, London: Cambridge University Press .
Solyanik, G.I., Berezetskaya, N.M., Bulkiewicz, R.I. and Kulik, G.I.1995 . Different growth patterns of a cancer cell population as a function of its starting growth characteristichs: Analysis by mathematical modelling . , 28 : 263
Udrişte, C.2000 . , Kluwer Academic Publishers .
Udrişte, C., Ferrara, M. and Opriş, D.2004 . , Bucharest: Geometry Balkan Press .
Vondra, A.1994 . Symmetries of connections on fibered manifolds . , 30 : 97 – 115 .

Views: 58Downloads: 57Citations: 1

[1] Asanov, G.S.1990 . Jet extension of Finslerian gauge approach . , 38 ( 8 ) : 571 – 610 .

[2] Garner, A.L., Lau, Y.Y., Jordan, D.W., Uhler, M.D. and Gilgenbach, R.M.2006 . Implication of a simple mathematical model to cancer cell population dynamics . , 39 : 15 – 28 .

[3] Luciani, A.M., Rosi, A., Matarrese, P., Arancia, G., Guidoni, L. and Viti, V.2001 . Changes in cell volume and internal sodium concentration in HrLa cells during exponential growth and following ionidamine treatment . , 80 : 187 – 195 .

[4] Miron, R. and Anastasiei, M.1994 . , Kluwer Academic Publishers .

[5] Neagu, M.2005 . , Bucharest: Matrix Rom .

[6] Neagu, M. and Nicola, I.R.2004 . Geometric dynamics of calcium oscillations ODEs systems . , 9 ( 2 ) : 36 – 67 .

[7] Neagu, M. and Udrişte, C.2001 . From PDEs systems and metrics to geometric multi-time field theories . , 79 : 1 – 33 .

[8] Nelson, P.W. and Perelson, A.S.2002 . Mathematical analysis of delay differential equation models of HIV-1 infection . , 179 : 73 – 94 .

[9] Nicola, I.R.2007 . , Bucharest: Bren . (in Romanian).

[10] Obădeanu, V.2006 . , Timişoara: Editura Universităţii de Vest . (in Romanian).

[11] Olver, P.J.1986 . , Springer-Verlag .

[12] Perelson, A.S. and Nelson, P.W.1999 . Mathematical analysis of HIV-1 dynamics in vivo . , 41 ( 1 ) : 3 – 44 .

[13] Poincaré, H.1880 . Sur les courbes definies par les equations différentielle . , 90 : 673 – 675 .

[14] Reya, T., Morrison, S.J., Clarke, M.F. and Weissman, I.L.2001 . Stem cells, cancer, and cancer stem cells . , 414 : 105 – 111 .

[15] Saunders, D.1989 . , New York, London: Cambridge University Press .

[16] Solyanik, G.I., Berezetskaya, N.M., Bulkiewicz, R.I. and Kulik, G.I.1995 . Different growth patterns of a cancer cell population as a function of its starting growth characteristichs: Analysis by mathematical modelling . , 28 : 263

[17] Udrişte, C.2000 . , Kluwer Academic Publishers .

[18] Udrişte, C., Ferrara, M. and Opriş, D.2004 . , Bucharest: Geometry Balkan Press .

[19] Vondra, A.1994 . Symmetries of connections on fibered manifolds . , 30 : 97 – 115 .

Journal of Dynamical Systems and Geometric Theories

WoS JIF 2026 : 0.5 (Q3)

Jet Riemann-Lagrange Geometry and Some Applications in Theoretical Biology

Abstract

Keywords

References