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Abu-Saleem, M.
- Homology Group on the Dynamical Trefoil Knot
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Authors
Affiliations
1 Department of Mathematics, Allaith University College (Girls Branch), Umm AL-Qura University, SA
1 Department of Mathematics, Allaith University College (Girls Branch), Umm AL-Qura University, SA
Source
Indian Journal of Science and Technology, Vol 6, No 5 (2013), Pagination: 4514-4518Abstract
In this article, we introduce the homology group of the dynamical trefoil knot. Also the homology group of the limit dynamical trefoil knot will be achieved. The knot group of the limit dynamical sheeted trefoil knot is presented. The dynamical trefoil knots of variation curvature and torsion of manifolds on their homology groups are deduced. Theorems governing these relations are obtained.Keywords
Dynamical Trefoil Knot, Homolog Group, KnotsFull Text
References
- Abu-Saleem M (2008). Folding on the chaotic Cartesian product of manifolds and their fundamental group, Tamkang Journal of Mathematics, vol 39, No.4, 353-361.
- Abu-Saleem M (2010). Folding on the wedge sum of graphs and their fundamental group, Applied Sciences, vol 12, 14-19.
- Abu-Saleem M (2010). Homology group on manifolds and their foldings, Tamkang Journal of Mathematics, vol 41, No. 1, 31-38.
- Abu-Saleem M (2010). Dynamical manifolds and their fundamental group, Advanced Studies in Contemporary Mathematics, vol 20, No.1, 125-131.
- Abu-Saleem M (2010). Conditional fractional folding of a manifold and their fundamental group, Advanced Studies in Contemporary Mathematics, vol 20, No. 2, 271-277.
- Abu-Saleem M (2011). Dynamical chaotic homotopy group and its applications, International Journal of Nonlinear Science, vol 11, No. 2, 206-212.
- Abu-Saleem M (2011). On dynamical chaotic de sitter spaces and their deformation retracts, Proceedings of the Jangjeon Mathematical society, vol 14 , 231-238.
- Abu-Saleem M (2012). On the dynamical hyperbolic 3-spaces and their deformation retracts. Proceedings of the Jangjeon Mathematical society 15, No. 2, 189-193.
- Birkhoof G D (2000). Dynamical systems, Bulletin of the American Mathematics Society, vol 37, No.1, 88-121.
- Burde G, and Zieschang H (2003). Knots,Walter de Gruyter GmbH & Co. KG.
- Damiond G, Peltier S (2008). Computing homology generators for volumes using minimal generralized maps, Proceeding of 12 th IWCIA, volume 4959 of LNCS, USA, 63-74.
- Giblin P J (1977). Graphs surfaces and homology:An introduction to Algebraic topology, Canada, Jon Wiley & Sons, New York.
- Hatcher A (2002). Algebraic topology, Cambridge University Press.
- Massey W S (1967). Algebraic topology: An introduction, Harcourt Brace and world, New York.
- Saveliev N (2002). Invariants for homology 3-spheres, Springer -Verlage, New York.
- Sibirsky K S (1975). Introduction to topological dynamics, Noordhoff International Pub., Leyden, The Netherlands.
- Retractions of Chaotic Buchdahi Space and their Chaotic Fundamental Groups
Abstract Views :377 |
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Authors
Affiliations
1 Faculty of Science, Taibah University, Madinah, SA
2 Department of Mathematics, Allaith University College (Girls Branch), Umm Al-Qura University, Allaith, SA
1 Faculty of Science, Taibah University, Madinah, SA
2 Department of Mathematics, Allaith University College (Girls Branch), Umm Al-Qura University, Allaith, SA
Source
Indian Journal of Science and Technology, Vol 6, No 8 (2013), Pagination: 5155-5162Abstract
The purpose of this paper is to give a combinatorial characterization and also construct representations of the chaotic fundamental groups of the chaotic submanifolds of chaotic Buchdahi space by using some geometrical transformations. The chaotic homotopy groups of the limit for chaotic Buchdahi space are presented. The chaotic fundamental groups of some types of chaotic geodesics in chaotic Buchdahi space are discussed. New types of homotopy maps are deduced.Keywords
Chaotic Buchdahi Space, Chaotic Homotopy Groups, Chaotic Folding, Chaotic Retractions, Chaotic Deformation RetractsFull Text
References
- El-Ahmady A E (2007). The variation of the density on chaotic spheres in chaotic space-like Minkowski space time, Chaos, Solitons and Fractals, vol 31(5), 1272–1278.
- El-Ahmady A E (2007). Folding of fuzzy hypertori and their retractions, Proceedings of the Physico-Mathematical Society., vol 85, No.1 , 1–10.
- El-Ahmady A E (2006). Limits of fuzzy retractions of fuzzy hyperspheres and their foldings, Tamkang Journal of Mathematics, vol 37, No. 1, 47–55.
- El-Ahmady A E (2004). Fuzzy folding of fuzzy horocycle, Circolo Matematico di Palermo Serie II, Tomo L III, 443–450.
- El-Ahmady A E (2004). Fuzzy Lobachevskian space and its folding, The Journal of Fuzzy Mathematics, vol 12, No. 2, 609–614.
- El-Ahmady A E (1994). The deformation retract and topological folding of Buchdahi space, Periodica Mathematica Hungarica, vol 28(1), 19–30.
- El-Ahmady A E (2011). The geodesic deformation retract of Klein bottle and its folding, The International Journal of Nonlinear Science, vol 9, No. 3, 1–8.
- El-Ahmady A E (2013). Folding and fundamental groups of Buchdahi space, Indian Journal of Science and Technology, vol 6, No. 1, 3940–3945.
- El-Ahmady A E(2012). Retraction of null helix in Minkowski 3-space, The Scientific Journal of Applied Research, vol 1(2), 28–33.
- El-Ahmady (2013). On elastic Klein bottle and fundamental groups, Applied Mathematics, vol 4, No. 3, 499–504.
- El-Ahmady A E (2011). Retraction of chaotic black hole, The Journal of Fuzzy Mathematics, vol 19, No. 4, 833–838.
- El-Ahmady A E ( 2013). On the fundamental group and folding of Klein bottle, International Journal of Applied Mathematics and Statistics, vol 37, No. 6, 56–64.
- El-Ahmady A E (2013). Fuzzy elastic Klein bottle and its retractions, International Journal of Applied Mathematics and Statistics, vol 42, No. 12, 94–102.
- El-Ahmady A E (2013). Folding and fundamental groups of flat Robertson-Walker Space, Indian Journal of Science and Technology, vol 6, No. 4, 4235–4242.
- El-Ahmady A E (2013). Fundamental groups and folding of Minkowski space, European Journal of Scientific Research, vol 104, No. 2, 284–293.
- El-Ahmady A E (2013). Retraction of chaotic Schwarzchild space, European Journal of Scientific Research, vol 104, No. 3, 333–339.
- El-Ahmady A E (2013). The isonormal folding of fuzzy manifolds and its retractions , European Journal of Scientific Research, vol. 104, No. 3, 340–347.
- El-Ahmady A E, and Al-Rdade A (2013). Deformation retracts of the Reissner-Nordström spacetime and its foldings, American Journal of Applied Sciences, vol 10, No. 7, 740–745.
- El-Ahmady A E, and Al-Rdade A (2013). On the geometry of fuzzy Reissner-Nordström spacetime and its foldings, Euro-pean Journal of Scientific Research, vol 104, No. 2, 294–303.
- El-Ahmady A E, and Al-Rdade A (2013). Fuzzy retraction of fuzzy spacetime, Indian Journal of Science and Technology, vol 6, No. 6, 4687–4696.
- El-Ahmady A E, and Al-Hazmi N (2013). On the folding of Buchdahi space, European Journal of Scientific Research, vol 100, No. 2, 315–322.
- El-Ahmady A E, and Al-Hazmi N (2013). The exponential deformation retract of the hypertori and its foldings, European Journal of Scientific Research, vol 104, No. 4, 561–568.
- El-Ahmady A E, and Al-Onema K (2013). The deformation retractions of fuzzy sphere in fuzzy Lobachevsky space and its folding, European Journal of Scientific Research, vol 104, No. 4, 549–560.
- El-Ahmady A E (2012). Folding and unfolding of chaotic spheres in chaotic space-like Minkowski space-time, The Scientific Journal of Applied Research, vol 1(2), 34–43.
- Abu-Saleem M (2013). Homology group on the dynamical trefoil knot, Indian Journal of Science and Technology, vol 6(5), 4514–4518.
- Abu-Saleem M (2013). On chaotic cartesian product of graphs and their retractions, International Journal of Nonlinear Science, vol 15, No. 1, 86–90.
- Abu-Saleem M (2013). On chaotic homotopy group, Advanced Studies in Contemporary Mathematics, vol 23, No. 1, 69–75.
- Abu-Saleem M (2012). On the dynamical hyperbolic 3-spaces and their deformation retracts. Proceedings of the Jangjeon Mathematical society, vol 15, No. 2, 189–193.
- Abu-Saleem M (2011). Dynamical chaotic homotopy group and its applications, International Journal of Nonlinear Science, vol 11, No. 2, 206–212.
- Abu-Saleem M (2011). On dynamical chaotic de sitter spaces and their deformation retracts, Proceedings of the Jangjeon Mathematical Society, vol 14, 231–238.
- Abu-Saleem M (2011). On dynamical chaotic Weyle representations of the vacuum C metric and their retractions, International Journal of Mathematical Combinatorics, vol 3, 47–54.
- Abu-Saleem M (2010). Folding on the wedge sum of graphs and their fundamental group, Applied Sciences, vol 12, 14–19.
- Abu-Saleem M (2010) Homology group on manifolds and their foldings, Tamkang Journal of Mathematics, vol 41, No. 1, 31–38.
- Abu-Saleem M (2010). Folding and unfolding of manifolds and their fundamental groups, International Journal of Contemporary Mathematical Sciences, vol 5, No. 1, 1–19.
- Abu-Saleem M (2010). Dynamical Knot and their fundamental group, International Journal of Mathematical Combinatorics, vol 1, 80–86.
- Abu-Saleem M (2010). Dynamical manifolds and their fundamental group, Advanced Studies in Contemporary Mathematics, vol 20, No. 1, 125–131.
- Abu-Saleem M (2010). Conditional fractional folding of a manifold and their fundamental group, Advanced Studies in Contemporary Mathematics, vol 20, No. 2, 271–277.
- Abu-Saleem M (2008). Folding on the chaotic Cartesian product of manifolds and their fundamental group, Tamkang Journal of Mathematics, vol 39, No. 4, 353–361.
- Lefeschets S (1942). Algebraic Topology, American Mathematical Society.
- Naber G L (2011). Topology, Geometry and Gauge Fields, Foundations, Chapter 1, Springer-Verlage New York, Berlin.
- Arkowitz M (2011). Introduction to Homotopy Theory, Chapter 1, Springer-Verlage.
- Strom J (2011). Modern Classical Homotopy Theory, Chapter 1 and 13, American Mathematical Society.
- Homology Groups and Foldings on Buchdahi Space
Abstract Views :380 |
PDF Views:0
Authors
Affiliations
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
2 Department of Mathematics, Allaith University College (Girls Branch), Umm Al-Qura University, SA
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
2 Department of Mathematics, Allaith University College (Girls Branch), Umm Al-Qura University, SA
Source
Indian Journal of Science and Technology, Vol 6, No 9 (2013), Pagination: 5249-5256Abstract
The purpose of this paper is to give a combinatorial characterization and also construct representations of the homology group of the submanifolds of Buchdahi space by using some geometrical transformations. The homology groups of the limit Buchdahi space are presented. The homology groups of some types of geodesics in Buchdahi space are discussed. Theorems governing this connection are achieved.Keywords
Buchdahi Space, Homology Group, Folding, Retractions, Deformation RetractFull Text
References
- El-Ahmady A E (2007). The variation of the density on chaotic spheres in chaotic space-like Minkowski space time, Chaos, Solitons and Fractals, vol 31(5), 1272–1278.
- El-Ahmady A E (2007). Folding of fuzzy hypertori and their retractions, Proc. Math. Phys. Soc., vol 85, No. 1, 1–10.
- El-Ahmady A E (2006). Limits of fuzzy retractions of fuzzy hyperspheres and their foldings, Tamkang Journal of Mathematics, vol 37, No. 1, 47–55.
- El-Ahmady A E (2004). Fuzzy folding of fuzzy horocycle, Circolo Matematico di Palermo Serie II, Tomo L III, 443–450.
- El-Ahmady A E (2004). Fuzzy Lobachevskian space and its folding, The Journal of Fuzzy Mathematics, vol 12, No. 2, 609–614.
- El-Ahmady A E (1994). The deformation retract and topological folding of Buchdahi space, Periodica Mathematica Hungarica, vol 28, 19–30.
- El-Ahmady A E (2011). The geodesic deformation retract of Klein bottle and its folding, The International Journal of Nonlinear Science, vol 9, No. 3, 1–8.
- El-Ahmady A E (2013). Folding and fundamental groups of Buchdahi space, Indian Journal of Science and Technology, vol 6, No. 1, 3940–3945.
- El-Ahmady A E (2012). Retraction of null helix in Minkowski 3-space, The Scientific Journal of Applied Research, vol 1(2), 28–33.
- El-Ahmady A E (2013). On elastic Klein bottle and fundamental groups, Applied Mathematics, vol 4, No. 3, 499–504.
- El-Ahmady A E (2011). Retraction of chaotic black hole, The Journal of Fuzzy Mathematics, vol 19, No. 4, 833–838.
- El-Ahmady A E (2013). On the fundamental group and folding of Klein bottle, International Journal of Applied Mathematics and Statistics, vol 37, No. 6, 56–64.
- El-Ahmady A E (2013). Fuzzy elastic Klein bottle and its retractions, International Journal of Applied Mathematics and Statistics, vol 42, No. 12, 94–102.
- El-Ahmady A E (2013). Folding and fundamental groups of flat Robertson-Walker Space, Indian Journal of Science and Technology, vol 6, No. 4, 4235–4242.
- El-Ahmady A E (2013). Fundamental groups and folding of Minkowski space, European Journal of Scientific Research, vol 104, No. 2, 284–293.
- El-Ahmady A E (2013). Retraction of chaotic Schwarzchild space, European Journal of Scientific Research, vol 104, No. 3, 333–339.
- El-Ahmady A E (2013). The isonormal folding of fuzzy manifolds and its retractions, European Journal of Scientific Research, vol 104, No. 3, 340–347.
- El-Ahmady A E, and Al-Rdade A (2013). Deformation retracts of the Reissner-Nordström spacetime and its foldings, American Journal of Applied Sciences, vol 10, No. 7, 740–745.
- El-Ahmady A E, and Al-Rdade A (2013). On the geometry of fuzzy Reissner-Nordström spacetime and its foldings, European Journal of Scientific Research, vol 104, No. 2, 294–303.
- El-Ahmady A E, and Al-Rdade A (2013). Fuzzy retraction of fuzzy spacetime, Indian Journal of Science and Technology, vol 6, No. 6, 4687–4696.
- El-Ahmady A E, and Al-Hazmi N (2013). On the folding of Buchdahi space, European Journal of Scientific Research, vol 100, No. 2, 315–322.
- El-Ahmady A E, and Al-Hazmi N (2013). The exponential deformation retract of the hypertori and its foldings, European Journal of Scientific Research, vol 104, No. 4, 561–568.
- El-Ahmady A E, and Al-Onema K (2013). The deformation retractions of fuzzy sphere in fuzzy Lobachevsky space and its folding, European Journal of Scientific Research, vol 104, No. 4, 549–560.
- El-Ahmady A E (2012). Folding and unfolding of chaotic spheres in chaotic space-like Minkowski space-time, The Scientific Journal of Applied Research, vol 1(2), 34–43.
- Abu-Saleem M (2013). Homology group on the dynamical trefoil knot, Indian Journal of Science and Technology, vol 6 (5), 4514–4518.
- Abu-Saleem M (2013). On chaotic Cartesian product of graphs and their retractions, International Journal of Nonlinear Science, vol 15, No. 1, 86–90.
- Abu-Saleem M (2013). On chaotic homotopy group, Advanced Studies in Contemporary Mathematics, vol 23, No. 1, 69–75.
- Abu-Saleem M (2012). On the dynamical hyperbolic 3-spaces and their deformation retracts, Proceedings of the Jangjeon Mathematical Society, vol 15, No. 2, 189–193.
- Abu-Saleem M (2011). Dynamical chaotic homotopy group and its applications, International Journal of Nonlinear Science, vol 11, No. 2, 206–212.
- Abu-Saleem M (2011). On dynamical chaotic de sitter spaces and their deformation retracts, Proceedings of the Jangjeon Mathematical Society, vol 14, 231–238.
- Abu-Saleem M (2011). On dynamical chaotic Weyle representations of the vacuum C metric and their retractions, International Journal of Mathematical Combinatorics, vol 3, 47–54.
- M. Abu-Saleem (2010). Folding on the wedge sum of graphs and their fundamental group, Applied Sciences, vol 12, (14–19), 14–19.
- Abu-Saleem M (2010). Homology group on manifolds and their foldings, Tamkang Journal of Mathematics, vol 41, No. 1, 31–38.
- Abu-Saleem M (2010). Folding and unfolding of manifolds and their fundamental groups, International Journal of Contemporary Mathematical Sciences, vol 5, No.1, 1–19.
- Abu-Saleem M (2010). Dynamical knot and their fundamental group, International Journal of Mathematical Combinatorics, vol 1, 80–86.
- Abu-Saleem M (2010). Dynamical manifolds and their fundamental group, Advanced Studies in Contemporary Mathematics, vol 20, No.1, 125–131.
- Abu-Saleem M (2010). Conditional fractional folding of a manifold and their fundamental group, Advanced Studies in Contemporary Mathematics, vol 20, No. 2, 271–277.
- Abu-Saleem M (2008). Folding on the chaotic Cartesian product of manifolds and their fundamental group, Tamkang Journal of Mathematics, vol 39, No. 4, 353–361.
- Lefeschets S (1942). Algebraic Topology, American Mathematical Society.
- Naber G L (2011). Topology, Geometry and Gauge Fields, Foundations, Chapter 1, Springer-Verlage New York, Berlin.
- Arkowitz M (2011). Introduction to Homotopy Theory, Chapter 1, Springer- Verlage.
- Strom J (2011). Modern classical homotopy theory, Chapter 1 and 13, American Mathematical Society.