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Artigo de periodico
Families of spherical surfaces and harmonic maps (2019)
Brander, David ; Tari, Farid
In: Geometriae Dedicata. Unidade: ICMC
Subjects: Geometria Diferencial Clássica, Geometria Global, Singularidades, Problema De Cauchy
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ABNT
BRANDER, David; TARI, Farid. Families of spherical surfaces and harmonic maps. Geometriae Dedicata, Dordrecht, Springer, v. 201, n. 1, p. 203-225, 2019. Disponível em: < http://dx.doi.org/10.1007/s10711-018-0389-3 > DOI: 10.1007/s10711-018-0389-3.
APA
Brander, D., & Tari, F. (2019). Families of spherical surfaces and harmonic maps. Geometriae Dedicata, 201( 1), 203-225. doi:10.1007/s10711-018-0389-3
NLM
Brander D, Tari F. Families of spherical surfaces and harmonic maps [Internet]. Geometriae Dedicata. 2019 ; 201( 1): 203-225.Available from: http://dx.doi.org/10.1007/s10711-018-0389-3
Vancouver
Brander D, Tari F. Families of spherical surfaces and harmonic maps [Internet]. Geometriae Dedicata. 2019 ; 201( 1): 203-225.Available from: http://dx.doi.org/10.1007/s10711-018-0389-3
Artigo de periodico
Frame and direction mappings for surfaces in 'R POT. 3' (2019)
Bruce, J W; Tari, Farid
In: Proceedings of the Royal Society of Edinburgh. Unidade: ICMC
Subjects: Geometria Diferencial Clássica, Teoria Das Singularidades, Teoria Das Catástrofes, Equações Algébricas Diferenciais
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ABNT
BRUCE, J W; TARI, Farid. Frame and direction mappings for surfaces in 'R POT. 3'. Proceedings of the Royal Society of Edinburgh, Cambridge, Cambridge University Press, v. 149, n. 3, p. 795-830, 2019. Disponível em: < http://dx.doi.org/10.1017/prm.2018.42 > DOI: 10.1017/prm.2018.42.
APA
Bruce, J. W., & Tari, F. (2019). Frame and direction mappings for surfaces in 'R POT. 3'. Proceedings of the Royal Society of Edinburgh, 149( 3), 795-830. doi:10.1017/prm.2018.42
NLM
Bruce JW, Tari F. Frame and direction mappings for surfaces in 'R POT. 3' [Internet]. Proceedings of the Royal Society of Edinburgh. 2019 ; 149( 3): 795-830.Available from: http://dx.doi.org/10.1017/prm.2018.42
Vancouver
Bruce JW, Tari F. Frame and direction mappings for surfaces in 'R POT. 3' [Internet]. Proceedings of the Royal Society of Edinburgh. 2019 ; 149( 3): 795-830.Available from: http://dx.doi.org/10.1017/prm.2018.42
Artigo de periodico
On vertices and inflections of plane curves (2018)
Dias, Fábio Scalco; Tari, Farid
In: Journal of Singularities. Unidade: ICMC
Subjects: Geometria Diferencial Clássica, Teoria Das Singularidades, Teoria Das Catástrofes, Deformações De Singularidades
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ABNT
DIAS, Fábio Scalco; TARI, Farid. On vertices and inflections of plane curves. Journal of Singularities, Cambridge, Worldwide Center of Mathematics, v. 17, p. 70-80, 2018. Disponível em: < http://dx.doi.org/10.5427/jsing.2018.17d > DOI: 10.5427/jsing.2018.17d.
APA
Dias, F. S., & Tari, F. (2018). On vertices and inflections of plane curves. Journal of Singularities, 17, 70-80. doi:10.5427/jsing.2018.17d
NLM
Dias FS, Tari F. On vertices and inflections of plane curves [Internet]. Journal of Singularities. 2018 ; 17 70-80.Available from: http://dx.doi.org/10.5427/jsing.2018.17d
Vancouver
Dias FS, Tari F. On vertices and inflections of plane curves [Internet]. Journal of Singularities. 2018 ; 17 70-80.Available from: http://dx.doi.org/10.5427/jsing.2018.17d
Artigo de periodico
On the flat geometry of the cuspidal edge (2018)
Sinha, Raúl Oset; Tari, Farid
In: Osaka Journal of Mathematics. Unidade: ICMC
Subjects: Singularidades, Topologia Diferencial, Geometria Diferencial Clássica
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ABNT
SINHA, Raúl Oset; TARI, Farid. On the flat geometry of the cuspidal edge. Osaka Journal of Mathematics, Osaka, University of Osaka, v. 55, n. 3, p. 393-421, 2018. Disponível em: < https://projecteuclid.org/euclid.ojm/1530691235 >.
APA
Sinha, R. O., & Tari, F. (2018). On the flat geometry of the cuspidal edge. Osaka Journal of Mathematics, 55( 3), 393-421. Recuperado de https://projecteuclid.org/euclid.ojm/1530691235
NLM
Sinha RO, Tari F. On the flat geometry of the cuspidal edge [Internet]. Osaka Journal of Mathematics. 2018 ; 55( 3): 393-421.Available from: https://projecteuclid.org/euclid.ojm/1530691235
Vancouver
Sinha RO, Tari F. On the flat geometry of the cuspidal edge [Internet]. Osaka Journal of Mathematics. 2018 ; 55( 3): 393-421.Available from: https://projecteuclid.org/euclid.ojm/1530691235
Artigo de periodico
Minkowski symmetry sets of plane curves (2017)
Reeve, Graham Mark; Tari, Farid
In: Proceedings of the Edinburgh Mathematical Society. Unidade: ICMC
Subjects: Geometria Diferencial, Geometria Diferencial Não Euclidiana, Singularidades
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ABNT
REEVE, Graham Mark; TARI, Farid. Minkowski symmetry sets of plane curves. Proceedings of the Edinburgh Mathematical Society, Cambridge, Cambridge University Press, v. 60, n. 2, p. 461-480, 2017. Disponível em: < http://dx.doi.org/10.1017/S0013091516000055 > DOI: 10.1017/S0013091516000055.
APA
Reeve, G. M., & Tari, F. (2017). Minkowski symmetry sets of plane curves. Proceedings of the Edinburgh Mathematical Society, 60( 2), 461-480. doi:10.1017/S0013091516000055
NLM
Reeve GM, Tari F. Minkowski symmetry sets of plane curves [Internet]. Proceedings of the Edinburgh Mathematical Society. 2017 ; 60( 2): 461-480.Available from: http://dx.doi.org/10.1017/S0013091516000055
Vancouver
Reeve GM, Tari F. Minkowski symmetry sets of plane curves [Internet]. Proceedings of the Edinburgh Mathematical Society. 2017 ; 60( 2): 461-480.Available from: http://dx.doi.org/10.1017/S0013091516000055
Artigo de periodico
On umbilic points on newly born surfaces (2017)
Hasegawa, Masaru; Tari, Farid
In: Bulletin of the Brazilian Mathematical Society, New Series. Unidade: ICMC
Subjects: Singularidades, Superfícies
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ABNT
HASEGAWA, Masaru; TARI, Farid. On umbilic points on newly born surfaces. Bulletin of the Brazilian Mathematical Society, New Series, Heidelberg, Springer, v. 48, n. 4, p. 679-696, 2017. Disponível em: < http://dx.doi.org/10.1007/s00574-017-0037-9 > DOI: 10.1007/s00574-017-0037-9.
APA
Hasegawa, M., & Tari, F. (2017). On umbilic points on newly born surfaces. Bulletin of the Brazilian Mathematical Society, New Series, 48( 4), 679-696. doi:10.1007/s00574-017-0037-9
NLM
Hasegawa M, Tari F. On umbilic points on newly born surfaces [Internet]. Bulletin of the Brazilian Mathematical Society, New Series. 2017 ; 48( 4): 679-696.Available from: http://dx.doi.org/10.1007/s00574-017-0037-9
Vancouver
Hasegawa M, Tari F. On umbilic points on newly born surfaces [Internet]. Bulletin of the Brazilian Mathematical Society, New Series. 2017 ; 48( 4): 679-696.Available from: http://dx.doi.org/10.1007/s00574-017-0037-9
Artigo de periodico
Flat and round singularity theory of plane curves (2017)
Salarinoghabi, Mostafa; Tari, Farid
In: The Quarterly Journal of Mathematics. Unidade: ICMC
Subjects: Singularidades, Teoria Das Singularidades, Curvas Planas
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ABNT
SALARINOGHABI, Mostafa; TARI, Farid. Flat and round singularity theory of plane curves. The Quarterly Journal of Mathematics, Oxford, Oxford University Press, v. 68, n. 4, p. 1289-1312, 2017. Disponível em: < http://dx.doi.org/10.1093/qmath/hax022 > DOI: 10.1093/qmath/hax022.
APA
Salarinoghabi, M., & Tari, F. (2017). Flat and round singularity theory of plane curves. The Quarterly Journal of Mathematics, 68( 4), 1289-1312. doi:10.1093/qmath/hax022
NLM
Salarinoghabi M, Tari F. Flat and round singularity theory of plane curves [Internet]. The Quarterly Journal of Mathematics. 2017 ; 68( 4): 1289-1312.Available from: http://dx.doi.org/10.1093/qmath/hax022
Vancouver
Salarinoghabi M, Tari F. Flat and round singularity theory of plane curves [Internet]. The Quarterly Journal of Mathematics. 2017 ; 68( 4): 1289-1312.Available from: http://dx.doi.org/10.1093/qmath/hax022
Artigo de periodico
Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics (2016)
Remizov, A. O; Tari, Farid
In: Geometriae Dedicata. Unidade: ICMC
Subjects: Geometria Diferencial, Geometria De Geodésicas, Equações Diferenciais Ordinárias
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ABNT
REMIZOV, A. O; TARI, Farid. Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics. Geometriae Dedicata, Dordrecht, Springer, v. 185, n. 1, p. 131-153, 2016. Disponível em: < http://dx.doi.org/10.1007/s10711-016-0172-2 > DOI: 10.1007/s10711-016-0172-2.
APA
Remizov, A. O., & Tari, F. (2016). Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics. Geometriae Dedicata, 185( 1), 131-153. doi:10.1007/s10711-016-0172-2
NLM
Remizov AO, Tari F. Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics [Internet]. Geometriae Dedicata. 2016 ; 185( 1): 131-153.Available from: http://dx.doi.org/10.1007/s10711-016-0172-2
Vancouver
Remizov AO, Tari F. Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics [Internet]. Geometriae Dedicata. 2016 ; 185( 1): 131-153.Available from: http://dx.doi.org/10.1007/s10711-016-0172-2
Artigo de periodico
On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations (2016)
Dias, Fábio Scalco; Tari, Farid
In: Tohoku Mathematical Journal. Unidade: ICMC
Subjects: Geometria, Equações Diferenciais Ordinárias, Teoria Das Singularidades
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ABNT
DIAS, Fábio Scalco; TARI, Farid. On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations. Tohoku Mathematical Journal, Sendai, Tohoku University, v. 68, n. 2, p. 293-328, 2016. Disponível em: < http://projecteuclid.org/euclid.tmj/1466172774 > DOI: 10.2748/tmj/1466172774.
APA
Dias, F. S., & Tari, F. (2016). On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations. Tohoku Mathematical Journal, 68( 2), 293-328. doi:10.2748/tmj/1466172774
NLM
Dias FS, Tari F. On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations [Internet]. Tohoku Mathematical Journal. 2016 ; 68( 2): 293-328.Available from: http://projecteuclid.org/euclid.tmj/1466172774
Vancouver
Dias FS, Tari F. On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations [Internet]. Tohoku Mathematical Journal. 2016 ; 68( 2): 293-328.Available from: http://projecteuclid.org/euclid.tmj/1466172774
Trabalho de evento-anais periodico
Minkowski medial axes and shocks of plane curves (2016)
Reeve, Graham Mark; Tari, Farid
In: Contemporary Mathematics. Conference title: International Workshop on Real and Complex Singularities. Unidade: ICMC
Subjects: Geometria Diferencial Não Euclidiana, Teoria Das Singularidades, Teoria Das Catástrofes, Geometria Simplética
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ABNT
REEVE, Graham Mark; TARI, Farid. Minkowski medial axes and shocks of plane curves. Contemporary Mathematics[S.l: s.n.], 2016.Disponível em: DOI: 10.1090/conm/675/13596.
APA
Reeve, G. M., & Tari, F. (2016). Minkowski medial axes and shocks of plane curves. Contemporary Mathematics. Providence: AMS. doi:10.1090/conm/675/13596
NLM
Reeve GM, Tari F. Minkowski medial axes and shocks of plane curves [Internet]. Contemporary Mathematics. 2016 ; 675 263-278.Available from: http://dx.doi.org/10.1090/conm/675/13596
Vancouver
Reeve GM, Tari F. Minkowski medial axes and shocks of plane curves [Internet]. Contemporary Mathematics. 2016 ; 675 263-278.Available from: http://dx.doi.org/10.1090/conm/675/13596
Artigo de periodico
Projections of surfaces in 'R POT.4' to 'R POT.3' and the geometry of their singular images (2015)
Sinha, Raúl Oset; Tari, Farid
In: Revista Matemática Iberoamericana. Unidade: ICMC
Subjects: Singularidades, Topologia Diferencial, Geometria Diferencial
A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas
ABNT
SINHA, Raúl Oset; TARI, Farid. Projections of surfaces in 'R POT.4' to 'R POT.3' and the geometry of their singular images. Revista Matemática Iberoamericana, Zurich, European Mathematical Society, v. 31, n. 1, p. 33-50, 2015. Disponível em: < http://dx.doi.org/10.4171/RMI/825 > DOI: 10.4171/RMI/825.
APA
Sinha, R. O., & Tari, F. (2015). Projections of surfaces in 'R POT.4' to 'R POT.3' and the geometry of their singular images. Revista Matemática Iberoamericana, 31( 1), 33-50. doi:10.4171/RMI/825
NLM
Sinha RO, Tari F. Projections of surfaces in 'R POT.4' to 'R POT.3' and the geometry of their singular images [Internet]. Revista Matemática Iberoamericana. 2015 ; 31( 1): 33-50.Available from: http://dx.doi.org/10.4171/RMI/825
Vancouver
Sinha RO, Tari F. Projections of surfaces in 'R POT.4' to 'R POT.3' and the geometry of their singular images [Internet]. Revista Matemática Iberoamericana. 2015 ; 31( 1): 33-50.Available from: http://dx.doi.org/10.4171/RMI/825
Monografia/livro
Differential geometry from a singularity theory viewpoint (2015)
Izumiya, Shyuichi; Fuster, Maria Del Carmen Romero; Ruas, Maria Aparecida Soares; Tari, Farid
Unidade: ICMC
Subjects: Singularidades, Geometria Diferencial, Teoria Das Singularidades
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ABNT
IZUMIYA, Shyuichi; FUSTER, Maria Del Carmen Romero; RUAS, Maria Aparecida Soares; TARI, Farid. Differential geometry from a singularity theory viewpoint. [S.l: s.n.], 2015.
APA
Izumiya, S., Fuster, M. D. C. R., Ruas, M. A. S., & Tari, F. (2015). Differential geometry from a singularity theory viewpoint. Hackensack: World Scientific.
NLM
Izumiya S, Fuster MDCR, Ruas MAS, Tari F. Differential geometry from a singularity theory viewpoint. 2015 ;
Vancouver
Izumiya S, Fuster MDCR, Ruas MAS, Tari F. Differential geometry from a singularity theory viewpoint. 2015 ;
Artigo de periodico
Projections of space curves and duality (2013)
Sinha, Raúl Oset; Tari, Farid
In: Quarterly Journal of Mathematics. Unidade: ICMC
Subjects: Geometria Diferencial, Teoria Das Singularidades
A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas
ABNT
SINHA, Raúl Oset; TARI, Farid. Projections of space curves and duality. Quarterly Journal of Mathematics, Oxford, Oxford University Press, v. 64, n. 1, p. 281-302, 2013. Disponível em: < http://dx.doi.org/10.1093/qmath/har035 > DOI: 10.1093/qmath/har035.
APA
Sinha, R. O., & Tari, F. (2013). Projections of space curves and duality. Quarterly Journal of Mathematics, 64( 1), 281-302. doi:10.1093/qmath/har035
NLM
Sinha RO, Tari F. Projections of space curves and duality [Internet]. Quarterly Journal of Mathematics. 2013 ; 64( 1): 281-302.Available from: http://dx.doi.org/10.1093/qmath/har035
Vancouver
Sinha RO, Tari F. Projections of space curves and duality [Internet]. Quarterly Journal of Mathematics. 2013 ; 64( 1): 281-302.Available from: http://dx.doi.org/10.1093/qmath/har035
Artigo de periodico
Umbilics of surfaces in the Minkowski 3-space (2013)
Tari, Farid
In: Journal of the Mathematical Society of Japan. Unidade: ICMC
Subjects: Singularidades
A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas
ABNT
TARI, Farid. Umbilics of surfaces in the Minkowski 3-space. Journal of the Mathematical Society of Japan, Tokyo, Mathematical Society of Japan, v. 65, n. 3, p. 723-731, 2013. DOI: 10.2969/jmsj/06530723.
APA
Tari, F. (2013). Umbilics of surfaces in the Minkowski 3-space. Journal of the Mathematical Society of Japan, 65( 3), 723-731. doi:10.2969/jmsj/06530723
NLM
Tari F. Umbilics of surfaces in the Minkowski 3-space. Journal of the Mathematical Society of Japan. 2013 ; 65( 3): 723-731.
Vancouver
Tari F. Umbilics of surfaces in the Minkowski 3-space. Journal of the Mathematical Society of Japan. 2013 ; 65( 3): 723-731.
Artigo de periodico
Apparent contours in Minkowski 3-space and first order ordinary differential equations (2013)
Izumiya, Shyuichi; Tari, Farid
In: Nonlinearity. Unidade: ICMC
Subjects: Singularidades
A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas
ABNT
IZUMIYA, Shyuichi; TARI, Farid. Apparent contours in Minkowski 3-space and first order ordinary differential equations. Nonlinearity, Bristol, IOP Publishing, v. 26, n. 4, p. 911-932, 2013. Disponível em: < http://dx.doi.org/10.1088/0951-7715/26/4/911 > DOI: 10.1088/0951-7715/26/4/911.
APA
Izumiya, S., & Tari, F. (2013). Apparent contours in Minkowski 3-space and first order ordinary differential equations. Nonlinearity, 26( 4), 911-932. doi:10.1088/0951-7715/26/4/911
NLM
Izumiya S, Tari F. Apparent contours in Minkowski 3-space and first order ordinary differential equations [Internet]. Nonlinearity. 2013 ; 26( 4): 911-932.Available from: http://dx.doi.org/10.1088/0951-7715/26/4/911
Vancouver
Izumiya S, Tari F. Apparent contours in Minkowski 3-space and first order ordinary differential equations [Internet]. Nonlinearity. 2013 ; 26( 4): 911-932.Available from: http://dx.doi.org/10.1088/0951-7715/26/4/911
Artigo de periodico
Curves in the Minkowski plane and their contact with pseudo-circles (2012)
Saloom, Amani; Tari, Farid
In: Geometriae Dedicata. Unidade: ICMC
Subjects: Singularidades
A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas
ABNT
SALOOM, Amani; TARI, Farid. Curves in the Minkowski plane and their contact with pseudo-circles. Geometriae Dedicata, Dordrecht, Springer, v. 159, n. 1, p. 109-124, 2012. Disponível em: < http://dx.doi.org/10.1007/s10711-011-9649-1 > DOI: 10.1007/s10711-011-9649-1.
APA
Saloom, A., & Tari, F. (2012). Curves in the Minkowski plane and their contact with pseudo-circles. Geometriae Dedicata, 159( 1), 109-124. doi:10.1007/s10711-011-9649-1
NLM
Saloom A, Tari F. Curves in the Minkowski plane and their contact with pseudo-circles [Internet]. Geometriae Dedicata. 2012 ; 159( 1): 109-124.Available from: http://dx.doi.org/10.1007/s10711-011-9649-1
Vancouver
Saloom A, Tari F. Curves in the Minkowski plane and their contact with pseudo-circles [Internet]. Geometriae Dedicata. 2012 ; 159( 1): 109-124.Available from: http://dx.doi.org/10.1007/s10711-011-9649-1
Artigo de periodico
A note on binary quintic forms and lines of principal curvature on surfaces in 'R POT. 5' (2012)
Ruas, Maria Aparecida Soares; Tari, Farid
In: Topology and its Applications. Unidade: ICMC
Subjects: Singularidades
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ABNT
RUAS, Maria Aparecida Soares; TARI, Farid. A note on binary quintic forms and lines of principal curvature on surfaces in 'R POT. 5'. Topology and its Applications, Amsterdam, Elsevier, v. fe 2012, n. 2, p. 562-567, 2012. Disponível em: < http://dx.doi.org/10.1016/j.topol.2011.09.032 > DOI: 10.1016/j.topol.2011.09.032.
APA
Ruas, M. A. S., & Tari, F. (2012). A note on binary quintic forms and lines of principal curvature on surfaces in 'R POT. 5'. Topology and its Applications, fe 2012( 2), 562-567. doi:10.1016/j.topol.2011.09.032
NLM
Ruas MAS, Tari F. A note on binary quintic forms and lines of principal curvature on surfaces in 'R POT. 5' [Internet]. Topology and its Applications. 2012 ; fe 2012( 2): 562-567.Available from: http://dx.doi.org/10.1016/j.topol.2011.09.032
Vancouver
Ruas MAS, Tari F. A note on binary quintic forms and lines of principal curvature on surfaces in 'R POT. 5' [Internet]. Topology and its Applications. 2012 ; fe 2012( 2): 562-567.Available from: http://dx.doi.org/10.1016/j.topol.2011.09.032
Relatorio tecnico
Codimension 2 singularities and their bifurcations in order 2 implicit differential equations (2003)
Tari, Farid
Unidade: ICMC
Subjects: Singularidades
A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas
ABNT
TARI, Farid. Codimension 2 singularities and their bifurcations in order 2 implicit differential equations. [S.l: s.n.], 2003.
APA
Tari, F. (2003). Codimension 2 singularities and their bifurcations in order 2 implicit differential equations. São Carlos: ICMC-USP.
NLM
Tari F. Codimension 2 singularities and their bifurcations in order 2 implicit differential equations. 2003 ;
Vancouver
Tari F. Codimension 2 singularities and their bifurcations in order 2 implicit differential equations. 2003 ;
Relatorio tecnico
On families of square matrices (2002)
Bruce, James William; Tari, Farid
Unidade: ICMC
Subjects: Singularidades
A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas
ABNT
BRUCE, James William; TARI, Farid. On families of square matrices. [S.l: s.n.], 2002.
APA
Bruce, J. W., & Tari, F. (2002). On families of square matrices. São Carlos: ICMC-USP.
NLM
Bruce JW, Tari F. On families of square matrices. 2002 ;
Vancouver
Bruce JW, Tari F. On families of square matrices. 2002 ;
Relatorio tecnico
Dupin indicatrices, families of curve congruences and the zero curves (2002)
Bruce, James William; Tari, Farid
Unidade: ICMC
Subjects: Singularidades
A citação é gerada automaticamente e pode não estar totalmente de acordo com as normas
ABNT
BRUCE, James William; TARI, Farid. Dupin indicatrices, families of curve congruences and the zero curves. [S.l: s.n.], 2002.
APA
Bruce, J. W., & Tari, F. (2002). Dupin indicatrices, families of curve congruences and the zero curves. São Carlos: ICMC-USP.
NLM
Bruce JW, Tari F. Dupin indicatrices, families of curve congruences and the zero curves. 2002 ;
Vancouver
Bruce JW, Tari F. Dupin indicatrices, families of curve congruences and the zero curves. 2002 ;