Refine your search
Collections
Co-Authors
Year
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
El-Ahmady, A. E.
- Folding and Fundamental Groups of Buchdahi Space
Abstract Views :388 |
PDF Views:124
Authors
Affiliations
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
Source
Indian Journal of Science and Technology, Vol 6, No 1 (2013), Pagination: 3940-3945Abstract
The purpose of this paper is to give a combinatorial characterization and also construct representations of the fundamental group of the submanifolds of Buchdahi space by using some geometrical transformations. The homotopy groups of the limit Buchdahi space are presented. The fundamental groups of some types of geodesics in Buchdahi space are discussed. New types of homotopy maps are deduced. Theorems governing this connection are achieved.Keywords
Buchdahi Space, Homotopy Groups, Folding, Deformation RetractsFull Text
References
- A.E. El-Ahmady, The variation of the density on chaotic spheres in chaotic space-like Minkowski space time, Chaos, Solitons and Fractals, 31 (1272-1278) (2007).
- A.E. El-Ahmady, Folding of fuzzy hypertori and their retractions, Proc. Math. Phys. Soc. Egypt, Vol.85, No.1 (1-10) (2007).
- A.E. El-Ahmady, Limits of fuzzy retractions of fuzzy hyperspheres and their foldings, Tamkang Journal of Mathematics, Volume37, No. 1 (47-55) Spring, (2006).
- A.E. El-Ahmady, Fuzzy folding of fuzzy horocycle, Circolo Matematico di Palermo Serie II ,Tomo L III (443-450) (2004).
- A.E. El-Ahmady, Fuzzy Lobachevskian space and its folding, The Journal of Fuzzy Mathematics, Vol. 12 No. 2, (609-614) (2004).
- A.E. El-Ahmady, The deformation retract and topological folding of Buchdahi space, Periodica Mathematica Hungarica Vol. 28 (19-30) (1994).
- A.E. El-Ahmady, Foldings of some types of Einstein spaces, The International Journal of Nonlinear Science, (Accepted).
- A.E. El-Ahmady , The geodesic deformation retract of Klein bottle and its folding, The International Journal of Nonlinear Science, Vol. 12, No. 3, (323-330), (2011).
- A.E. El-Ahmady and H.M. Shamara, Fuzzy deformation retract of fuzzy horospheres, Indian J. Pure Appl. Math. 32 (10), 1501-1506, October (2001).
- A.E. El-Ahmady and A. El-Araby, On fuzzy spheres in fuzzy Minkowski space, Nuovo Cimento Vol.125B (2010).
- A.E. El-Ahmady, Retraction of chaotic black hole, The Journal of Fuzzy Mthematics, 19(4): 833-838. (2011).
- A.E. El-Ahmady, On the fundamental group and folding of Klein bottle, International Journal of Applied Mathematics and Statistics, Vol.37, No. 6,(56-64), (2013).
- A. Z. Petrov, Einstein spaces, London, New York (1969).
- D. Erik, Demainel, Folding and unfolding, Ph. D. Thesis, Waterloo University, Canada (2001).
- G. L. Naber, Topology, Geometry and Gauge fields, Foundations, Springer-Verlage, New York, Berlin,,(2011).
- G. L. Naber, Topology, Geometry and gauge fields, Interactions, Springer-Verlage New York, Berlin, (2011).
- M.El-Ghoul, A.E. El-Ahmady and M. Abu-saleem, The fundamental group of the connected sum of manifolds and their foldings , Chungcheong Mathematical Society, Vol. 18, (161-172)2005.
- M.El-Ghoul, A.E. El-Ahmady and M. Abu-saleem, Folding on the Cartesian product of manifolds and their fundamental group, Applied Sciences ,Vol.9 (86 -91 ) 2007 .
- M.El-Ghoul, A.E. El-Ahmady and M. Abu-saleem, On Chaotic fundamental group and their foldings, The Journal of Fuzzy Mathematics Vol. 17,No. 2, (311-322 ), (2009).
- M. Abu-saleem, Some geometric transformations on manifolds and their algebraic structures, Ph. D. Thesis, Tanta University, Egypt, (2007).
- M. Reid and Balazs Szendroi, Topology and geometry, Cambridge, New York, (2005). 22. M. Arkowitz, Introduction to homotopy theory, Springer- Verlage, New York,( 2011).
- Shick Pl., Topology: Point-Set and geometry, New York, Wiley, (2007).
- Strom, J., Modern classical homotopy theory, American Mathematical Society.
- Foldings and Deformation Retractions of Hypercylinder
Abstract Views :584 |
PDF Views:154
Authors
Affiliations
1 Mathematics Department, Faculty of Science, Tanta University, Tanta, EG
2 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
1 Mathematics Department, Faculty of Science, Tanta University, Tanta, EG
2 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
Source
Indian Journal of Science and Technology, Vol 6, No 2 (2013), Pagination: 4084-4093Abstract
Our aim in the present work is to introduce and study new types of retractions of hypercylinder. Types of the deformation retracts of hypercylinder are presented. The relations between the folding and the deformation retract of hypercylinder are deduced. Types of minimal retractions of hypercylinder are introduced. Also, the isometric and topological folding in each case and the relation between the deformation retracts after and before folding are obtained. New types of homotopy maps are deduced. Theorems governing this connection are achieved.Keywords
Hypercylinder, Retraction, FoldingFull Text
References
- A. E. El-Ahmady, The variation of the density on chaotic spheres in chaotic space-like Minkowski space time, Chaos, Solitons and Fractals, 31 (1272-1278) (2007).
- A. E. El-Ahmady, Folding of fuzzy hypertori and their retractions, Proc. Math. Phys. Soc. Egypt, Vol.85, No.1 (1-10) (2007).
- A. E. El-Ahmady, Limits of fuzzy retractions of fuzzy hyperspheres and their foldings, Tamkang Journal of Mathematics, Volume37, No. 1 (47-55) Spring, (2006).
- A. E. El-Ahmady, Fuzzy folding of fuzzy horocycle, CircoloMatematico di Palermo Serie II ,Tomo L III (443-450) (2004).
- A. E. El-Ahmady, Fuzzy Lobachevskian space and its folding, The Journal of Fuzzy Mathematics, Vol. 12 No. 2, (609-614) (2004).
- A. E. El-Ahmadyand H. Rafat, Retraction of chaotic Ricci space, Chaos, Solutions and Fractals, 41 (394-400) (2009).
- A. E. El-Ahmadyand H. Rafat, A calculation of geodesics in chaotic flat space and its folding, Chaos, Solutions and Fractals, 30 (836-844) (2006).
- A. E. El-Ahmadyand A. El-Araby, On fuzzy spheres in fuzzy Minkowski space, NuovoCimentoVol.125B(2010) .
- A. E. El-Ahmady, Retraction of chaotic black hole, The Journal of Fuzzy Mathematics Vol.19, No. 3, (2011).
- A. E. El-Ahmady, The geodesic deformation retract of Klein Bottle and its folding, The International Journal of Nonlinear Science, Vol. 12, No. 3, (2011).
- E. Michael, Closed retract and perfect retracts, Topology and its Applications 12(451-468) (2003).
- G. L. Naber, Topology, Geometry and Gauge fields: Foundations, Texts in Applied Mathematics 25, Edition, Springer-Verlage New York, Berlin, (2011).
- M. Baronti, E. Casini, C. Franchetti, The retraction constant in some Banach spaces, Journal of Approximation Theory, 120 (296-308) (2003).
- M. Reid and BalazsSzendroi.Topology and Geometry, Cambridge University Press, Cambridge, New York, (2005).
- P. DI-Francesco, Folding and coloring problem in Mathematics and Physics, Bulliten of the American Mathematics Society, Vol. 37, No. 3, (251-307) (2000).
- P. Pellicer-Covarrubias, Retractions in hyperspaces, Topology and its Applications 135 (277-291) (2004).
- Shick Pl. Topology: Point-Set and Geometry, New York, Wiley, (2007).
- Folding and Fundamental Groups of Flat Robertson-walker Space
Abstract Views :558 |
PDF Views:326
Authors
Affiliations
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
Source
Indian Journal of Science and Technology, Vol 6, No 4 (2013), Pagination: 4235-4242Abstract
This paper aims to give a combinatorial characterization and also construct representations of the fundamental groups of the submanifolds on flat Robertson-Walker space by using some geometrical transformations. The homotopy groups of the limit folding on flat Robertson-Walker space are presented. The homotopy groups of the retractions and deformation retract on flat Robertson-Walker space are obtained. The fundamental groups of some types of geodesics in the flat Robertson-Walker space are discussed. New types of homotopy maps are deduced. Theorems governing this connection are achieved.Keywords
Flat Robertson-Walker Space W4, Homotopy Groups, Foldings, Retractions, 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 & Fractals, vol 31(5), 1272-1278.
- El-Ahmady A E (2007). Folding of fuzzy hypertori and their retractions, Proc. Math. Phys. Soc. Egypt, vol 85(1), 1-10.
- El-Ahmady A E (2006). Limits of fuzzy retractions of fuzzy hyperspheres and their foldings, Tamkang Journal of Mathematics, vol 37(1), 47-55.
- El-Ahmady A E (2004). Fuzzy folding of fuzzy horocycle, Rendiconti del Circolo Matematico di Palermo Serie II, Tomo L III, vol 53(3), 443-450.
- El-Ahmady A E (2004). Fuzzy Lobachevskian space and its folding, Journal of Fuzzy Mathematics, vol 12(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, International Journal of Nonlinear Science, vol 12(3), 323-330.
- El-Ahmady A E (2013). Folding and fundamental groups of Buchdahi space, Indian Journal of Science and Technology, vol 6(1), 3940-3945.
- El-Ahmady A E (In press). Folding of some types of Einstein spaces, The International Journal of Nonlinear Science.
- El-Ahmady A E. On elastic Klein bottle and fundamental groups, Applied Mathematics, (Accepted).
- El-Ahmady A E (2011). Retraction of chaotic black hole, The Journal of Fuzzy Mathematics, vol 19(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( 6), 56-64.
- El-Ahmady A E. Fuzzy elastic Klein bottle and its retractions International Journal of Applied Mathematics and Statistics, (Accepted).
- El-Ahmady A E, and Al-Luhaybi A S (2013). A Calculation of geodesics in flat Robertson-Walker space and its folding, International Journal of Applied Mathematics and Statistics, vol 33(3), 83-91.
- El-Ahmady A E, and A S Al-Luhaybi (2013). Fuzzy retractions of fuzzy open flat Robertson-Walker space, Advances in Fuzzy Systems, vol 2013, 1-7.
- El-Ahmady A E, and Al-Luhaybi A S (2012). Ageometrical characterization of spatially curved Robertson-Walker space and its retractions, Applied Mathematics, vol 12(3), 1153-1160.
- El-Ahmady A E, and Al-Luhaybi A S (2012). Retractions of spatially curved Robertson-Walker space, The Journal of American Sciences, vol 8(5), 548-553.
- El-Ahmady A E, and Al-Luhaybi A S. On fuzzy retracts of fuzzy closed flat Roberstion-Walker spaces, Advances in fuzzy sets and systems,(Accepted).
- El-Ahmady A E, and Al-Luhaybi A S. Retractions of fuzzy flat Robertson-Walker space , International Journal of Applied Mathematics and Statistics,(Accepted).
- Naber G L (2011). Topology, Geometry and Gauge fields, Foundations, New York, Berlin.
- Hartle J B (2003). Gravity, An introduction to Einstein’s general relativity, Addison-Wesley, New York.
- 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.
- 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, and Al-Hazmi N (2013). Foldings and deformation retractions of hypercylinder, Indian Journal of Science and Technology, vol 6(2), 4084-4093.
- Abu-Saleem M (2007). Some geometric transformations on manifolds and their algebraic structures, Ph. D. Thesis, Tanta University, Egypt.
- Reid M, and Szendroi B (2005). Topology and geometry, Cambridge, New York.
- Arkowitz M (2011). Introduction to homotopy theory, Springer-Verlage, New York.
- Shick P L (2007). Topology: Point-Set and geometry, New York, Wiley.
- Strom, J (2011). Modern classical homotopy theory, American Mathematical Society.
- On Fuzzy Spheres in Fuzzy Lobachevsky Space and its Retractions
Abstract Views :495 |
PDF Views:140
Authors
Affiliations
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
2 Mathematics Department, Faculty of Science, Tanta University, Tanta, EG
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
2 Mathematics Department, Faculty of Science, Tanta University, Tanta, EG
Source
Indian Journal of Science and Technology, Vol 6, No 4 (2013), Pagination: 4243-4248Abstract
This paper attempts to introduce and study new connection between fuzzy retractions, fuzzy foldings and fuzzy deformation retracts of open fuzzy spheres in fuzzy Lobachevsky space and fuzzy open ball in fuzzy Euclidean space. Types of fuzzy foldings and fuzzy deformation retracts of fuzzy open sphere are discussed. Types of minimal fuzzy retractions of fuzzy open sphere are presented. The fuzzy foldings of fuzzy open sphere is deduced, also the limit of this folding is obtained. The connection between fuzzy foldings and fuzzy central projection map is achieved; also the connection between fuzzy retractions and fuzzy exponential map is discussed. Some applications are presented.Keywords
Fuzzy Retractions, Fuzzy Foldings, Fuzzy Deformation Retracts, Central Projection Map, Fuzzy Open Sphere in Fuzzy Lobachevsky SpaceFull Text
References
- El-Ahmady A E (2007). The variation of the density on chaotic spheres in chaotic space-like Minkowski space time, Chaos, Solitons & Fractals, vol 31(5), 1272-1278.
- El-Ahmady A E (2007). Folding of fuzzy hypertori and their retractions, Proceedings of the Mathematical and Physical Society of Egypt, vol 85(1), 1-10.
- El-Ahmady A E (2006). Limits of fuzzy retractions of fuzzy hyperspheres and their foldings, Tamkang Journal of Mathematics, vol 37(1), 47-55.
- El-Ahmady A E (Accepted). Fuzzy elastic Klein bottle and its retractions, International Journal of Applied Mathematics and Statistics.
- 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.
- El-Ahmady A E, and El-Araby A (2010). On fuzzy spheres in fuzzy Minkowski space, Nuovo Cimento, vol 125B(10), 1153-1160.
- El-Ahmady A E (2011). Retraction of chaotic black hole, The Journal of Fuzzy Mathematics, vol 19(4), 833-838.
- 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 (2004). Fuzzy Lobachevskian space and its folding, The Journal of Fuzzy Mathematics, vol 12(2), 609-614.
- 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, and Shamara H M (2001). Fuzzy deformation retracts of fuzzy horospheres, Indian Journal of Pure and Applied Mathematics, vol 32(10), 1501-1506.
- El-Ahmady A E, and Al-Luhaybi A S (2013). Fuzzy retractions of fuzzy open flat Robertson-Walker space, Advances in Fuzzy Systems, vol 2013.
- El-Ahmady A E, and Al-Onemi K (2013). On the folding of Lobachevsky space, International Journal of Applied Mathematics and Statistics, vol 4(10), 13-23.
- El-Ahmady A E (2011). The geodesic deformation retract of Klein bottle and its folding, The International Journal of Nonlinear Science, vol 9(3), 1-8.
- El-Ahmady A E (2013). On the fundamental group and folding of Klein bottle, International Journal of Applied Mathematics and Statistics, vol 37(6), 56-64.
- El-Ahmady A E (2013). Folding and fundamental groups of Buchdahi space, Indian Journal of Science and Technology, vol 6(1), 3940-3945.
- El-Ahmady A E, and Al-Hazmi N (2013). Foldings and deformation retractions of hypercylinder, Indian Journal of Science and Technology, vol 6(2), 4084-4093.
- El-Ahmady A E, and Al-Luhaybi A S (Accepted). On fuzzy retracts of fuzzy closed flat Roberstion-Walker spaces, Advances in fuzzy sets and systems.
- El-Ahmady A E, and Al-Luhaybi A S (2013). Retractions of fuzzy flat Robertson-Walker space , International Journal of Applied Mathematics and Statistics, vol 41(11), 116-129.
- Schmeikal B (2010). Primordial Space -The Metric Case, Chapter 1, New York.
- Naber G L (2011). Topology, Geometry and Gauge fields, Chapter 1, Springer-Verlage New York, Berlin.
- Hartle J B (2003). Gravity, An introduction to Einstein’s general relativity, Chapter 3, Addison-Wesley, New York .
- Griffiths J B, and Podolsky J I (2009). Exact Space-Times in Einstein’s General Relativity ,Cambridge University Press, Cambridge, New York.
- Zadeh L A (1975). Fuzzy sets and their application to congnitive and decision, Chapter 1, New York, Academic Press.
- Reid M, and Szendroi B (2005). Topology and Geometry, Chapter 1, Cambridge University Press, Cambridge, New York.
- Arkowitz M (2011). Introduction to homotopy theory, Chapter 1, Springer- Verlage, New York.
- Palaniappan N (2002). Fuzzy Topology, Chapter 1, London, New York.
- Straumann N (2004). General relativity with application to astrophysics, Chapter 4, Springer-Verlage, New York, Heidelberg, Berlin.
- Strom J (2011). Modern classical homotopy theory, Chapter 1, American Mathematical Society.
- Kudryashov V V, Kurochkin Y A (2010). Motion caused by magnetic field in Lobachevsky space, arXiv :1006. 5202vI [math-ph], vol 1205, 108-111.
- Fuzzy Retraction of Fuzzy Space Time
Abstract Views :331 |
PDF Views:0
Authors
Affiliations
1 Mathematics Department, Faculty of Science, Tanta University, Tanta, EG
2 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
1 Mathematics Department, Faculty of Science, Tanta University, Tanta, EG
2 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
Source
Indian Journal of Science and Technology, Vol 6, No 6 (2013), Pagination: 4687-4696Abstract
Our aim in the present article is to introduce and study a new type of metric, namely fuzzy space time metric. The geodesics of fuzzy space time metric will be obtained from the view point of Lagrangian equations. Types of the fuzzy retraction of fuzzy space time metric are presented. Types of the fuzzy folding of fuzzy space time metric are defined and discussed. The deformation retraction is also discussed. Some applications concerning these relations are presented.Keywords
Fuzzy Space Time Metric, Fuzzy Retraction, Fuzzy Deformation Retraction, Fuzzy Geodesics, Fuzzy FoldingFull Text
References
- El-Ahmady A E (2007). The variation of the density functions on chaotic spheres in chaotic space-like Minkowski space time, Chaos, Solitons and Fractals, vol 31(2007), 1272-1278.
- El-Ahmady A E. Folding of fuzzy hypertori and their retractions, Proceedings of the Mathematical and Physical Society of Egypt, 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(1), 3940-3945.
- El-Ahmady A E ( In press). Folding of some types of Einstein spaces, The International Journal of Nonlinear Science.
- 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 (Accepted). Fuzzy elastic Klein bottle and its retractions, International Journal of Applied Mathematics and Statistics.
- El-Ahmady A E, and Al-Luhaybi A S (2013). A calculation of geodesics in flat Robertson-Walker space and its folding, International Journal of Applied Mathematics and Statistics, vol 33, No. 3, 83-91.
- El-Ahmady A E, and Al-Luhaybi A S (2013). Fuzzy retractions of fuzzy open flat Robertson-Walker space, Advances in Fuzzy Systems, vol 2013, 1-7.
- El-Ahmady A E, and Al-Luhaybi A S (2012). A geometrical characterization of spatially curved Robertson-Walker space and its retractions, Applied Mathematics, vol 12, No. 3, 1153-1160.
- El-Ahmady A E, and Al-Luhaybi A S (2012). Retractions of spatially curved Robertson-Walker space, The Journal of American Sciences, vol 8, No. 5, 548-553.
- El-Ahmady A E, and Al-Luhaybi A S (Accepted). On fuzzy retracts of fuzzy closed flat Roberstion-Walker spaces, Advances in Fuzzy Sets and Systems, (Accepted).
- El-Ahmady A E, and Al-Luhaybi A S (2013). Retractions of fuzzy flat Robertson-Walker space, International Journal of Applied Mathematics and Statistics, vol 41(11), 116-129.
- 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.
- 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, and Al-Hazmi N (2013). Foldings and deformation retractions of hypercylinder, Indian Journal of Science and Technology, vol 6(2), 4084-4093.
- El-Ahmady A E, and El-Araby A (2010). On fuzzy spheres in fuzzy Minkowski space, Nuovo Cimento, vol 125B, No. 10, 1153-1160.
- El-Ahmady A E, and Shamara H M (2001). Fuzzy deformation retracts of fuzzy horospheres, Indian Journal Pure Applied Mathematics, vol 32(10), 1501-1506.
- El-Ahmady A E, and Al-Rdade A (2013). A geometrical characterizations of Reissner - Nordström spacetime and its retractions, International Journal of Applied Mathematics and Statistics, vol 36(6), 83-91.
- El-Ahmady A E, and Al-Hesiny E (2012). Folding and deformation retract of hyperhelix, Journal of Mathematics and Statistics, vol 8(2), 241-247.
- El-Ghoul M, El-Ahmady A E et al. (2011). The most general fuzzy topological space and its graph, The Journal of Fuzzy Mathematics, vol 19, No. 1, 79-86.
- Naber G L (2011). Topology, Geometry and Gauge fields, Foundations, 2nd Edn., Chapters 2 and 3, New York, Berlin, 129-133.
- Hartle J B (2003). Gravity, An introduction to Einstein’s general relativity, Chapter 7, Addison-Wesley, New York, 136.
- Reid M, and Szendroi B (2005). Topology and geometry, Cambridge, New York.
- Arkowitz M (2011). Introduction to homotopy theory, Springer-Verlage, New York
- Shick P L (2007). Topology: Point-Set and geometry, New York, Wiley.
- Strom J (2011). Modern classical homotopy theory, American Mathematical Society, Chapter 1, 13.
- Folding of Fuzzy Hyperboloid
Abstract Views :456 |
PDF Views:0
Authors
Affiliations
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
2 Mathematics Department, Faculty of Science, Tanta University, Tanta, SA
1 Mathematics Department, Faculty of Science, Taibah University, Madinah, SA
2 Mathematics Department, Faculty of Science, Tanta University, Tanta, SA
Source
Indian Journal of Science and Technology, Vol 6, No 8 (2013), Pagination: 5013-5018Abstract
Our aim in the present paper is to introduce and study new connection between fuzzy retractions, fuzzy foldings and fuzzy deformation retracts of fuzzy open hyperboloid in fuzzy Minkowski space and fuzzy open ball in fuzzy Euclidean space. Types of fuzzy foldings and fuzzy deformation retracts of fuzzy open hyperboloid are discussed. Types of minimal fuzzy retractions of fuzzy open hyperboloid are presented. The fuzzy foldings of fuzzy open hyperboloid will be deduced. Some applications are presented.Keywords
Fuzzy Retractions, Fuzzy Foldings, Fuzzy Deformation Retracts, Fuzzy Open Hyperboloid in Fuzzy Minkowski SpaceFull Text
References
- El-Ahmady A E (2007). The variation of the density functions 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 Mathematical and Physical Society of Egypt, 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 (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.
- El-Ahmady A E, and El-Araby A (2010). On fuzzy spheres in fuzzy Minkowski space, Nuovo Cimento, vol 125B, No. 10, 1153–1160.
- 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 (2004). Fuzzy lobachevskian space and its folding, The Journal of Fuzzy Mathematics, vol 12, No. 2, 609–614.
- El-Ahmady A E (2004). Fuzzy folding of fuzzy horocycle, Rendiconti del Circolo Matematico di Palermo, vol 53(3), 443–450.
- El-Ahmady A E, and Shamara H M (2001). Fuzzy deformation retracts of fuzzy horospheres, Indian Journal Pure Applied Mathematics, vol 32(10), 1501–1506.
- El-Ahmady A E, and Al-Onema K (2013). On fuzzy spheres in fuzzy Lobachevsky space and its retractions, Indian Journal of Science and Technology, vol 6, No. 4, 4242–4248.
- El-Ahmady A E, and Al-Luhaybi A S (2013). Fuzzy retractions of fuzzy open flat Robertson-Walker space, Advances in Fuzzy Systems, vol 2013(2013), 1–7.
- El-Ahmady A E, and Al-Luhaybi A S (2013). On fuzzy retracts of fuzzy closed flat Roberstion-Walker spaces, Advances in Fuzzy Sets and Systems, vol 14(1), 53–69.
- El-Ahmady A E, and Al-Rdade A (2013). A geometrical characterizations of Reissner – Nordstrom spacetime and its retractions, International Journal of Applied Mathematics and Statistics, vol 36(6), 83–91.
- 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 (2013). Fuzzy elastic Klein bottle and its retractions, International Journal of Applied Mathematics and Statistics, vol 42( 12), 94–102.
- 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). 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). Folding and fundamental groups of Buchdahi space, Indian Journal of Science and Technology, vol 6(1), 3940–3945.
- El-Ahmady A E (2013). On elastic Klein bottle and fundamental groups, Applied Mathematics, vol 4, No. 3, 499–504.
- 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). Folding and fundamental groups of flat Robertson-Walker Space, Indian Journal of Science and Technology, vol 6(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-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.
- Arkowitz M (2011). Introduction to homotopy theory, Chapter 1, Springer-Verlage, New York.
- Strom J (2011). Modern classical homotopy theory, Chapters 1 and 13, American Mathematical Society.
- Sean Carroll (2004). Space time and geometry, Chapter 8, San Francisco, Boston, New York.
- Retractions of Chaotic Buchdahi Space and their Chaotic Fundamental Groups
Abstract Views :377 |
PDF Views:0
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.