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i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 12 Issue 1

Performance Analysis of Convolutional Neural Networks for Image Classification with Appropriate Optimizers
The Behavior of Jump Discontinuous Function in Timbre
Parabolic Form of Casson Fluid Flow based on Angle of Inclination in Conducting Field
Common Fixed-Point Theorems via Notion of Pairwise Semi-Compatible Mappings and Occasionally Weakly Compatible Mappings (OWC) for Six Self-Mappings in Fuzzy Metric Spaces
Study of Goal Programming Approach in Resource Allocation in Acute Care Hospitals

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Volume 2 Issue 4 October - December 2013

Research Paper

Remarks On Four-Dimensional PseudosymmetricKahlerian Manifolds

Beldjilali Gherici* , Mohamed Belkhelfa, Hasni Abdelbasset*

-- Laboratoire de Physique Quantique de la matière et de Modélisation Math_ematique, (LPQ3M), Université de Mascara, Mascara, Algeria.

Gherici, B., Mohamed, B., and Abdelbasset, H. (2013). Remarks on Four-Dimensional Pseudosymmetric Kahlerian Manifolds. i-manager’s Journal on Mathematics, 2(4), 1-6. https://doi.org/10.26634/jmat.2.4.2609

Abstract

In the present paper, we prove that for a 4-dimensional properly pseudosymmetric Kählerian manifold M, the Ricci tensor vanishes on the set p Î {M/ f(p) 6≠ 0} where f is the structure fonction (i.e R(X,Y ) = f(XÙY).R) and for f > 0 the manifold is not compact. Various examples are discussed.

References

[1]. Beldjilali, G. (january,2012). La pseudosym_etrie holomorphique, Mémoire de Magister, Université de Mascara, Algérie.

[2]. Belkhelfa, M. & Hasni, A. (2011). Symmetric propreties of Thurston geometry F4, Proceedings of the Conference RIGA 2011, Mihai, Adela (ed.) et al., Riemannian Geometry and Applications, Bucharest, Romania, 29{40.

[3]. Defever, F., Deszcz, R., & Verstraelen, L. (1997). On pseudo-symmetric para-Kahler manifolds, Colloq. Math, 74 ,253{260.

[4]. Eisenhart L.P. (1997). Riemannian geometry, Princeton University Press, Princeton, NJ.

[5]. Haesen, S., & Verstraelen, L. (2009). Natural Intrinsic Geometrical Symmetries, Symmetry, Integrability and Geometry: Methods and Applications, SIGMA 5 , 086,15 pages.

[6]. Jelonek, W. (2009). Compact holomorphically pseudosymmetric Kählerian manifolds, Colloq. Math.; 117, 243-249.

[7]. Olszak, Z. (1989). Bochner at Kählerian manifolds with certain condition on the Ricci tensor, Simon Stevin, 63 , 295-303.

[8]. Olszak, Z. (2003). On the existence of pseudo-symmetric Kählerian manifolds, Colloq. Math, 95 , 185-189.

[9]. Olszak, Z. (2009). On compact holomorphically pseudosymmetric Kähler manifolds, Cent. Eur. J. Math., 7 , No. 3, 442- 451.

[10]. Olszak, Z. (Priprint). Weyl-pseudosymmetric and Bochner-pseudosymmetric Kählerian manifolds of dimension 4, Preprint.

[11]. Tachibana, S. (1974). A theorem on Riemannian manifolds of positive curvature operator. Proc. Jpn. Acad. Ser. Math. Sci. 50, 301-302.

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Research Paper

Synchronization and Anti-Synchronization Of A Chaotic Satellite Under The Effect Of Magnetic Torque Via Active Control

Mohammad * , Mohammed Raziuddin**

* Department of General Requirements, College of Applied Sciences, Nizwa, Oman.

** Department of Information Technology, Nizwa College of Technology, Nizwa, Oman.

Mohammad Shahzad and Mohammad Raziuddin (2013). Synchronization and Anti-Synchronization of A Chaotic Satellite Under The Effect of Magnetic Torque via Active Control. i-manager’s Journal on Mathematics, 2(4), 7-13. https://doi.org/10.26634/jmat.2.4.2610

Abstract

The determination and prediction of the orbit of a satellite is influenced by the perturbing forces causing chaos. In this paper, we have discussed the synchronization and anti-synchronization (AS) behavior of two such identical planar oscillation of a satellite in elliptic orbit influenced by magnetic torque evolving from different initial conditions using the active control technique. The designed controllers, with our own choice of the coefficient matrix of the error dynamics are found to be effective to achieve synchronization and AS between the states variables of two chaotic identical dynamical systems under consideration. All the results are validated by numerical simulations using mathematica.

References

[1]. Pecora, L. M. & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical Review Letters: 64, 821–824.

[2]. Lakshmanan, M & Murali, K. (1996). Chaos in Nonlinear Oscillators: Controlling and Synchronizing, World Scientific, Singapore.

[3]. Pikovsky, A., Rosenblum, M. & Kurths, J. (2001). Synchronization: A Unified Approach to Nonlinear Science, Cambridge University Press, Cambridge.

[4]. Ticos, C. M., Rosa Jr. E., Pardo, W. B., Walkenstein J. A. & Monti, M. (2000). Experimental real-time phase synchronization of paced chaotic plasma discharge, Physical Review Letters 85, 2929–2932.

[5]. Nimeijer, H. & Mareels Ivan, M. Y. (1997). An observer looks at synchronization, IEEE Transactions on Circuits and Systems I 44, 882–890.

[6]. Kim, C. M., Rim, S. Kye, W. H., Ryu, J. W. & Park, Y. J. (2000). Anti-synchronization of chaotic oscillators, Physics Letters A 320, 39–49.

[7]. Zhang Y. & Sun, J. (2004). Chaotic synchronization and anti-synchronization based on suitable separation, Physics Letters A 330, 442–447.

[8]. Emadzadeh, A. A. & Mohammed, H. (2005). Anti-synchronization of two different chaotic systems via active control, Transactions on Engineering, Computing and Technology 6, 62–65.

[9]. Li, C. & Liao, X. (2006). Anti-synchronization of a class of coupled chaotic systems via linear feedback control, International Journal of Bifurcation and Chaos 16, 1041–1047.

[10]. Nakata, S., Miyata, T., Ojima, N. & Yoshikawa, K. (1998). Self-synchronization in coupled salt–water oscillators, Physica D: 115, 313–320.

[11]. Idowu, B. A., Vincent. U. E. & Njah, A. N. (2007). Anti-synchronization of chaos in nonlinear gyros via active control, Journal of Mathematical Control Science and Applications 1,191–200.

[12]. Idowu, B. A., Vincent, U. E. & Obawole, A. O. (2007). Anti-synchronization between two new different chaotic systems via active control, Journal of the Nigerian Association of Mathematical Physics: 11, 15–20.

[13]. Vincent, U. E. & Ucar, A. (2007). Synchronization and anti-synchronization of chaos in permanent magnet reluctance machine, Far East Journal of Dynamical Systems: 9, 211–221.

[14]. Vincent, U. E. & Laoye, J. A. (2007). Synchronization, anti-synchronization and current transport in non-identical chaotic ratchets, Physica A 384, 230–240.

[15]. Bai, E. W., Lonngren, K. E. & Sprott, J. C. (2002). On the synchronization of a class of electronic circuits that exhibit chaos, Chaos, Solitons and Fractals 13, 1515–1521.

[16]. Chen, H. K. (2005). Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lu, Chaos, Solitons and Fractals 25, 1049–1056.

[17]. Vincent, U. E. (2005). Synchronization of Rikitake chaotic attractor via active control, Physics Letters A: 343,133–138.

[18]. Vincent, U. E. (2008). Synchronization of identical and non-identical 4-D chaotic systems via active control, Chaos, Solitons and Fractals 37, 1065–1075.

[19]. Lei, Y., Xu, W. & Xie, W. (2007). Synchronization of two chaotic four-dimensional systems using active control, Chaos, Solitons and Fractals 32, 1823–1829.

[20]. Njah, A. N. & Vincent, U. E. (2008). Chaos synchronization between single and double wells Duffing Van-der Pol oscillators using active control, Chaos, Solitons and Fractals 37, 1356–1361.

[21]. Njah, A. N. (2006). Synchronization of forced damped pendulum via active control, Journal of the Nigerian Association of Mathematical Physics 10,143–148.

[22]. Ucar, A., Bai, E. W. & Lonngren, K. E. (2003). Synchronization of chaotic behavior in nonlinear Bloch equations, Physics Letters A 314, 96–101.

[23]. Lei, Y. , Xu, W. , Shen, J. & Fang, F. (2006). Global synchronization of two parametrically excited systems using active control, Chaos, Solitons and Fractals 28 ,428–436.

[24]. Ucar, A., Lonngren, K. E. & Bai, E. W. (2006). Synchronization of the unified chaotic systems via active control, Chaos, Solitons and Solitons 27, 1292–1297.

[25]. Ucar, A., Lonngren, K. E. & Bai, E. W. (2007). Chaos synchronization in RCL-shunted Josephson junction via active control, Chaos, Solitons and Fractals 31,105–111.

[26]. Vincent, U. E. & Laoye, J. A. (2007). Synchronization and control of directed transport in inertia ratchets via active control, Physics Letters A 363, 91–95.

[27]. Khan, A. & Shahzad, M. (2013). Synchronization of a circular restricted three body problem with Lorenz hyper chaotic system using robust adaptive sliding mode controller. Complexity, 18(6), 58-64.

[28]. Bhardwaj, R. & Kaur, P. (2006). Satellite's Motion Under the effect of magnetic Torque. American Journal of Applied Sciences: 3(6), 1899-1902.

[29]. Cai, G. & Zheng S. (2008). Anti-synchronization in different hyperchaotic systems, Journal of Information and Computing Science: 3,181-188.

[30]. Shahzad, M. (2011). Synchronization and anti-synchronization of planar oscillation of a satellite in an elliptic orbit via active control. Journal of Control Science & Engineering, article id: 816432.

[31]. Khan, A. & Shahzad, M. (2012). Computational study of synchronization & anti-synchronization in Mimas-Tethys system. i' manager's Journal on mathematics, 1(2), 26-33.

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Research Paper

ICE Math: Geometric Software Illustrating Concentric Circles In Figure Skating

Diana Cheng* , Tetyana Berezovski**

* Assistant Professor, Towson University, Maryland, USA.

** Associate Professor, St. Joseph's University, Pennsylvania, USA.

Cheng, D., and Berezovski, T. (2013). ICE Math: Geometric Software Illustrating Concentric Circles In Figure Skating. i-manager’s Journal on Mathematics, 2(4), 14-20. https://doi.org/10.26634/jmat.2.4.2611

Abstract

In light of the upcoming Winter Olympic Games, a mathematical modeling problem involving algebra and geometry is presented via dynamic geometry software in the context of pairsfigure skating. The death spiral involves a lady's and man's forming concentric circles with their blades on the ice. In-service elementary, middle and high school teachers used knowledge of rates and circumference to solve problems involving the death spiral. Teachers' work is analyzed and discussed.

References

[1]. Akyuz, Didem. (2012). “The Value of Debts and Credits.” Mathematics Teaching in the Middle School, 17(6): 332-8.

[2]. Ball, Deborah L., Thames, Mark H. and Phelps, Geoffrey. (2008). “Content Knowledge for Teaching: What makes it special?” Journal of Teacher Education, 59: 389-406.

[3]. Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/assets/CCSI_Math%20Standards.pdf

[4]. Fennema, E., Franke, M. L., Carpenter, T.P., & Carey, D. A. (1993). Using children's mathematical knowledge in instruction. American Educational Research Journal, 30(3): 403-34.

[5]Greeno, J. G. (1993). For research to reform education and cognitive science. In L.A. Penner, G.M. Batsche, H.M. Knoff, & D.L. Nelson (Eds.), The challenge in mathematics and science education: Psychology's response. 153-92. Washington, DC: American Psychological Association.

[6]. Kerrigan, Nancy & Spencer, Mary. (2003). Artistry on Ice: Figure Skating Skills and Style. Human Kinetics: Champaign, IL.

[7]. Posamentier, Alfred S. (2003). Math Charmers: Tantalizing Tidbits for the Mind.Prometheus Books.

[8]. United States Figure Skating. (2013). http://usfsa.org/content/FactSheet.pdf

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Research Paper

Proximalpositive Parallel Notation: A Novel Method Of Expressing Mathematical Complements, Collaborations, and Combinations

James Edward Osler II*

North Carolina Central University

Osler, J. E., II. (2013). Proximal Positive Parallel Notation: A Novel Method of Expressing Mathematical Complements, Collaborations, And Combinations. i-manager’s Journal on Mathematics, 2(4), 21-32. https://doi.org/10.26634/jmat.2.4.2612

Abstract

This monograph provides anepistemological rational for the mathematical “Proximal Positive Parallel Notation” as a novel mathematical operation. This innovative mathematical notation is used to define the relationship between values that construct the Standard Tri–Squared Test 3 × 3 Table used in the transformative process of qualitative data into quantitative outcomes. The Tri–Squared Test was introduced in an earlier Journal on Mathematics article by the author. The mathematical notion of “Unlimitation” is also introduced as an explicative part of the definition of the Proximal Positive Parallel formulae. Integrated into this new parallel notation is the neoteric “Coextensive” sign as a symbol of the relationship between terms. The Proximal Positive Parallel as a unique and inventive mathematical notation that may be applied to other areas and arenas of mathematics, statistics, and other sciences. Its broader application in diverse academic fields (such as the social sciences) will aid in building and strengthening the connections between mathematics and other academic disciplines.

References

[1]. Coxeter, H. S. M. (1961). Introduction to Geometry.John Wiley & Sons.p. 192. Encyclopedic Dictionary of Mathematics Volumes I–VI.(2000). MIT Press.pp. 1330–1331.

[2]. Evans, N. (1995). “A–Quantifiers and Scope”. In Bach, Emmon W. Quantification in Natural Languages. Dordrecht, The Netherlands; Boston, MA: Kluwer Academic Publishers. p. 262.

[3]. Iyanaga, S. (1977). Encyclopedic dictionary of mathematics, Volumes I, II, hardback, translated from the 2nd Japanese edition (1st ed.), MIT Press, pp. 1–1750.

[4]. Jacobson, N. (2009). Basic Algebra 1 (2nd ed.), Dover.

[5]. Koblitz, Neal (1984). P–adic numbers, p–adic analysis, and zeta–functions (2nd ed.). New York: Springer–Verlag.p. 1.

[6]. Levy, A. (1979). Basic Set Theory, Perspectives in Mathematical Logic, Springer–Verlag. Reprinted in 2002, by Dover.

[7]. Osler, J. E. (2010). Visualus ™ © Visioneering Volumetrically: The Mathematics of the Innovative Problem–Solving Model of Inventive Instructional Design (First Edition).Lulu Publishing, Morrisville NC.

[8]. Osler, J. E. (2013a). Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test. April–June Journal on Mathematics,2 (2), pp. 10–16.

[9]. Osler, J. E. (2013b). The Triangulation Algorithmic: A Transformative Function for Designing and Deploying Effective Educational Technology Assessment Instruments. April–June Journal of Educational Technology,10 (1), pp. 46–54.

[10]. Suppes, P. (1972). Axiomatic Set Theory. Dover. Originally published by D. van Nostrand Company in 1960.

[11]. Szmielew, W.(1983). From Affine to Euclidean Geometry.Springer, p. 17.

[12]. Wolf, R. S. (1998). Proof, Logic and Conjecture: A Mathematician's Toolbox. W. H. Freeman.

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Research Paper

On Some Properties Of Closability Of FarthestPoint Maps In Fuzzy n-Normed Spaces

Muhammed Recai Turkmen * , Hakan EFE**

* Department of Mathematics, Faculty of Science and Arts, Mus Alparslan University, Guzeltepe, Mus, Turkey.

** Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, Ankara, Turkey.

Turkmen, M.R., and Efe, H. (2013). On Some Properties of Closability Of Farthest Point Maps in Fuzzy N-Normed Spaces. i-manager’s Journal on Mathematics, 2(4), 33-38. https://doi.org/10.26634/jmat.2.4.2613

Abstract

In this paper, we study farthest point map in fuzzy n - normed spaces. Firstly, we give some definitions about fuzzy n - normed space and we present some examples by using this definitions. Secondly, we study farthest point map in fuzzy n - normed spaces and we redefine some some definitions by using previous definitions. Moreover, we abtain fuzzy uniquelly remotal associated singleton. Additionally, we give some relations about - convergent sequences in fuzzy n - normed spaces. Finally, we show that fuzzy - farthest point map is closable and characterize some properties of the closability of farthest point map in fuzzy n - normed spaces and prove some theorems. 2010 Mathematics Subject Classification: 46A30, 46A70, 54A40.

References

[1]. Bag, T. and Samanta, S. K., Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (3) (2003), 687-705.

[2]. Bag, T. and Samanta, S. K., Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), 513-547.

[3]. Mirmostafaee, A.K. and Mirzavaziri, M., Closability of farthest point map in fuzzy normed spaces ,Bulletin of Mathematical Analysis and Applications, 2 (4) (2010), 140-145.

[4]. Gähler, S., Lineare 2-normierte Räume, Math.Nachr. 28 (1964), 1-43.

[5]. Gähler, S., Untersuchungen über verallgemeinerte m -metrische Räume, I, Math.Nachr. 40 (1969), 165-189.

[6]. Gunawan, H. and Mashadi, M., On n-normed spaces, Int. J. Math. Math. Sci. 27 (10) (2001), 631-639.

[7]. Al. Narayanan and Vijayabalaji, S., Fuzzy n-normed linear space, Int. J. Math. Math. Sci. 24 (2005), 3963-3977.

[8]. Vijayabalaji, S., and Thillaigovindan, N., Complete fuzzy n-normed linear space, Journal of Fundamental Sci. 3 (1) (2007), 119-126.

[9]. Malceski, R., Strong n-convex n-normed spaces, Mat. Bilten 21 (47) (1997), 81-102.

[10]. Misiak, A. , n-inner product spaces, Math.Nachr. 140 (1989), 299-319.

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 12 Issue 1

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Most Cited

Volume 2 Issue 4 October - December 2013

Remarks On Four-Dimensional PseudosymmetricKahlerian Manifolds

Beldjilali Gherici* , Mohamed Belkhelfa**, Hasni Abdelbasset***

*-**-*** Laboratoire de Physique Quantique de la matière et de Modélisation Math_ematique, (LPQ3M), Université de Mascara, Mascara, Algeria.

Gherici, B., Mohamed, B., and Abdelbasset, H. (2013). Remarks on Four-Dimensional Pseudosymmetric Kahlerian Manifolds. i-manager’s Journal on Mathematics, 2(4), 1-6. https://doi.org/10.26634/jmat.2.4.2609

Abstract

References

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Synchronization and Anti-Synchronization Of A Chaotic Satellite Under The Effect Of Magnetic Torque Via Active Control

Mohammad * , Mohammed Raziuddin**

* Department of General Requirements, College of Applied Sciences, Nizwa, Oman. ** Department of Information Technology, Nizwa College of Technology, Nizwa, Oman.

Mohammad Shahzad and Mohammad Raziuddin (2013). Synchronization and Anti-Synchronization of A Chaotic Satellite Under The Effect of Magnetic Torque via Active Control. i-manager’s Journal on Mathematics, 2(4), 7-13. https://doi.org/10.26634/jmat.2.4.2610

Abstract

References

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ICE Math: Geometric Software Illustrating Concentric Circles In Figure Skating

Diana Cheng* , Tetyana Berezovski**

* Assistant Professor, Towson University, Maryland, USA. ** Associate Professor, St. Joseph's University, Pennsylvania, USA.

Cheng, D., and Berezovski, T. (2013). ICE Math: Geometric Software Illustrating Concentric Circles In Figure Skating. i-manager’s Journal on Mathematics, 2(4), 14-20. https://doi.org/10.26634/jmat.2.4.2611

Abstract

References

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Proximalpositive Parallel Notation: A Novel Method Of Expressing Mathematical Complements, Collaborations, and Combinations

James Edward Osler II*

North Carolina Central University

Osler, J. E., II. (2013). Proximal Positive Parallel Notation: A Novel Method of Expressing Mathematical Complements, Collaborations, And Combinations. i-manager’s Journal on Mathematics, 2(4), 21-32. https://doi.org/10.26634/jmat.2.4.2612

Abstract

References

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On Some Properties Of Closability Of FarthestPoint Maps In Fuzzy n-Normed Spaces

Muhammed Recai Turkmen * , Hakan EFE**

* Department of Mathematics, Faculty of Science and Arts, Mus Alparslan University, Guzeltepe, Mus, Turkey. ** Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, Ankara, Turkey.

Turkmen, M.R., and Efe, H. (2013). On Some Properties of Closability Of Farthest Point Maps in Fuzzy N-Normed Spaces. i-manager’s Journal on Mathematics, 2(4), 33-38. https://doi.org/10.26634/jmat.2.4.2613

Abstract

References

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Beldjilali Gherici* , Mohamed Belkhelfa, Hasni Abdelbasset*

-- Laboratoire de Physique Quantique de la matière et de Modélisation Math_ematique, (LPQ3M), Université de Mascara, Mascara, Algeria.

* Department of General Requirements, College of Applied Sciences, Nizwa, Oman.

** Department of Information Technology, Nizwa College of Technology, Nizwa, Oman.

* Assistant Professor, Towson University, Maryland, USA.

** Associate Professor, St. Joseph's University, Pennsylvania, USA.

* Department of Mathematics, Faculty of Science and Arts, Mus Alparslan University, Guzeltepe, Mus, Turkey.

** Department of Mathematics, Faculty of Science, Gazi University, Teknikokullar, Ankara, Turkey.