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i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
Some Types of Generalized Closed and Generalized Star Closed Sets in Topological Ordered Spaces
Optimizing Capsule Endoscopy Detection: A Deep Learning Approach with L-Softmax and Laplacian-SGD
Kernel Ideals in Semigroups
Modeling the Dynamics of Covid-19 with the Inclusion of Treatment, Vaccination and Natural Cure
Calculation of Combined Vibrational Frequencies in Cl₂O using Lie Algebraic Method

Most Cited

Volume 2 Issue 2 April - June 2013

Article

Uniformly Stable Continuous Solutions Of A Functional Differential Inclusions

A.M.A. El-Sayed* , Fatma M.Gaffar, Nesreen F.M.El-haddad*

* Faculty of Science, Alexandria University, Alexandria, Egypt.

-* Faculty of Science, Damanhour University, Behera, Egypt.

El-SayedZ, A.M.A., Gaffar, F.M., and El-haddad, N.F.M. (2013). Uniformly Stable Continuous Solutions of A Functional Differential Inclusions. i-manager’s Journal on Mathematics, 2(2), 1-6. https://doi.org/10.26634/jmat.2.2.2310

Abstract

The authors concerned here with the concept and the existence of a uniformly stable continuous solution of the functional differential inclusion dx/dt∈ F(t, x(f(t))) a.e on I = [0, T], t > 0 with the initial condition x(0) = x0. The continuous dependence on the set of selections of the set-valued function F is also studied.

References

[1]. J. P. Aubin and A. Cellina, (1984). Differential Inclusions, Springer-Verlag.

[2]. A. M. A. El-sayed and Yassine Khouni, (2012). Measurable-Lipschitz selections and set-valued integral equations of fractional order, 1-8.

[3]. A. M. A. El-sayed and A. G. (1995). Ibrahim, Multivalued fractional differential equations, Applied Mathematics and Computation. 68, 15-25.

[4]. Rabha. W. Ibrahim, (2009). Existence of convex and non convex local solutions for fractional differential inclusions. 18, 1-13.

[5]. V. V. Chistyakov, A. Nowak, (2005). Regular Caratheodory-type selectors under no convexity assumptions, Journal of Functional Analysis 225 247-262.

[6]. M. Kisielewicz, (1991). Differential Inclusions and optimal control. Dordrecht, the Nether-Lands.

[7]. Georgi V. Smirnov, (2002). Introduction to the theory of Differential Inclusions. American Mathematical Society, providence.

[8]. M. Ailalioubrahim, (2010). Neumann boundary-value problems for Differential inclusions in Banach spaces, Electronic Journal of Differential Equations, Vol. 2010, No. 104, pp. 1-5.

[9]. P. Bettiol and H. Frankowska, (2007). Regularity of solution maps of differential inclusions under state constraints, Set-Valued Anal 15, 21-45.

[10]. A. I. Bulgakov and V. V. Vasilyev, (2002). On the theory of functional-differential inclusion of neutral type, 9, 33-52.

[11]. A.G. Ibrahim, (1991). On differential inclusion with memory, in Proc. Math. Phys. Soc. Egypt, 67.

[12]. Ravi P. Agarwal, Maria Meehan & Donal O’Regan, Fixed point theory and applications. Cambridge tracts in mathematics.141.

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Article

On The Dual Focal Curves With Dual Parameter In D3

Mustafa Yeneroglu* , Vedat Asil**

*-** Department of Mathematics, Faculty of Science, Firat University, Elaz ig, Turkey.

Yeneroðlu, M., and Asil, V. (2013). On The Dual Focal Curves with Dual Parameter in D3. i-manager’s Journal on Mathematics, 2(2), 7-9. https://doi.org/10.26634/jmat.2.2.2311

Abstract

In this paper, the authors study dual focal curves with dual parameters in the Dual 3-space D . They characterize focal curves of dual parameters in terms of their dual focal curvatures.

References

[1]. P. Alegre , K. Arslan, A. Carriazo, C. Murathan and G. Öztürk: (2010). Some Special Types of Developable Ruled Surface, Hacettepe Journal of Mathematics and Statistics 39 (3), 319 -- 325.

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[5]. W. Blaschke: (1948). Zur Bewegungsgeometrieauf der Kugel, Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Math-Natur. Wiss. Klasse. 2, Abhandlung 3.

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[9]. D. J. Struik: (1988). Lectures on Classical Differential Geometry, Dover, New-York.

[10]. R. Uribe-Vargas: (2005). On vertices, focal curvatures and differential geometry of space curves, Bull. Brazilian Math. Soc. 36 (3), 285--307.

[11]. A. Yücesan, N. Ayyildiz, and A. C. Çöken: (2007). On rectifying dual space curves, Rev. Mat. Complut. 20 (2), 497-506.

[12]. M.Yeneroglu and V. Asil: (2010). On rotation surfaces with pointwise 1-type Gauss map in the 3-dimensional dual space. World Applied Sciences Journal 12 (3) (2011), 354-357.

[13]. T. Körpinar, E. Turhan and S. Bas: (2013). Characterizing of Dual Focal Curves in D3, Bol. Soc. Paran. Mat. 31 (2), 76-81.

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Research Paper

Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test

James Edward Osler II*

North Carolina Central University

Osler, J. E., II. (2013). Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining The Application Process of The Tri–Squared Test. i-manager’s Journal on Mathematics, 2(2), 10-16. https://doi.org/10.26634/jmat.2.2.2312

Abstract

This monograph provides an epistemological rational for the transformative process of qualitative data into quantitative outcomes through the Tri–Squared Test introduced in an earlier i-Manager's Journal of Mathematics article. A research design geometric algorithmic model of the triangulation of the Transformative Trichotomy–Squared [Tri–Squared] Test as a means of informative inquiry is provided. This novel approach to data analysis simplifies the mixed methods approach to research design that involves the holistic combination and comparison of qualitative and quantitative data. A sequential mathematical model is provided that illustrates the entire process of Tri–Squared inquiry.

References

[1]. Apostol, T. M. (1967). Calculus, second edition, Vol. 1: One-variable calculus, with an introduction to linear algebra. Waltham, MA: Blaisdell.

[2]. Kant, I. (2007). Critique of pure reason (based on Max Müller's translation). P. Classics a Division of Pearson PLC. New York, NY.

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

[4]. Osler, J. E. (2013b). December–February i-manager's Journal on Educational Psychology, 8 (3), pp. 15–22.

[5]. Osler, J. E. (2012). Trichotomy–Squared – A novel mixed methods test and research procedure designed to analyze, transform, and compare qualitative and quantitative data for education scientists who are administrators, practitioners, teachers, and technologists. July – September i-manager's Journal on Mathematics, 1 (3). pp. 23–32.

[6]. Rust, J. & Golombok, S. (1989). Modern psychometrics: The science of psychological assessment (2nd ed.). Florence, KY, US: Taylor & Frances/Routledge. Sensagent: Retrieved, May 9, 2012: http://dictionary.sensagent.com/ trichotomy+(mathematics)/en-en/

[7]. Singh, S. (1997). Fermat's enigma: The epic quest to solve the world's greatest mathematical problem. A. Books a Division of Random House. New York, NY.

[8]. Singh, S. (2002). Fermat's last theorem. Hammersmith, London, UK: Harper Collins Paperback.

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Research Paper

Analysation of Super Strongly Perfectness in Ladder Graphs

Mary Jothi* , A. Amutha**

* Research Scholar, Department of Mathematics, Sathyabama University, Chennai.

** Associate Professor, Department of Mathematics, Sathyabama University, Chennai.

Jothi, R.M.J., and Amutha, A. (2013). Analysation of Super Strongly Perfectness in Ladder Graphs. i-manager’s Journal on Mathematics, 2(2), 17-21. https://doi.org/10.26634/jmat.2.2.2313

Abstract

A Graph G is Super Strongly Perfect Graph if every induced subgraph H of G possesses a minimal dominating set that meets all maximal cliques of H. In this paper, the authors have given a characterization of Super Strongly Perfect graphs. Using this characterization they have characterized the Super Strongly Perfect graphs in Ladder graphs. They have investigated the structure of Super Strongly Perfect Graphs in Ladder graphs. Also they have found the relation between domination number, co-domination number and diameter of Ladder Graphs.

References

[1]. Amutha A and Mary Jeya Jothi. R, (2012). “Characterization of Super Strongly Perfect Graphs in Bipartite Graphs”, Proceedings of an International Conference in Engineering and Business Management (ICMEB 2012), 1:183 - 185.

[2]. Bondy J. A and Murty U.S.R, (1976). “Graph Theory with Applications”, Elsevier Science Publishing Company Inc., New York.

[3]. Foulds. R, (1994). “Graph Theory Applications”, Springer, New York.

[4]. Hosoya. H and Harary, F. (1993). “On the Matching Properties of Three Fence Graphs” J. Math. Chem., 12:211-218.

[5]. Murty. U.S.R, (2006). “Open problems”, Trends in Mathematics, 381–389.

[6]. Rogers. D. G, (1982). “The Enumeration of a family of Ladder Graphs”, Information Processing Letters, 15:179-182.

[7]. Skiena. S, (1990). “Grid Graphs” In Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, Addison-Wesley publications, 147-148.

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Research Paper

Legendre Seudospectral Method For The Approximate Solutions Some Of The Fractional-Order Differential Equations

Zeliha Sariates Korpinar* , M??nevver TUZ**

*-** Firat University, Department of Mathematics, Elazig, Turkey.

Körpinar, Z.S., and TUZ, M. (2013). Legendre Seudospectral Method for The Approximate Solutions Some of The Fractional-Order Differential Equations. i-manager’s Journal on Mathematics, 2(2), 22-27. https://doi.org/10.26634/jmat.2.2.2314

Abstract

In this paper, the authors study Legendre Seudospectral Method (LSM) by using fractional ordinary diferential equations. They consider some different differential equations and we obtain numerical simulation with the exact solutions of FDEs.

References

[1]. R. P. Agarwal, B. de Andrade, and C. Cuevas, (2010). Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations, Nonlinear Analysis: Real World Applications, 11 (5), 3532--3554.

[2]. R. P. Agarwal, V. Lakshmikantham, and J. J. Nieto, (2010). On the concept of solution for fractional differential equations with uncertainty, Nonlinear Analysis: Theory,Methods & Applications, 72(6), 2859--2862.

[3]. R. Garrappa and M. Popolizio, (2011). On the use of matrix functions for fractional partial differential equations, Mathematics and Computers in Simulation, 81 (5), 1045--1056.

[4]. R. Hilfer, (2000). Applications of Fractional Calculus in Physics, World Scientific Publishing, River Edge, NJ, USA.

[5]. Y. Khan, N. Faraz, A. Yildirim, and Q. Wu, (2011). Fractional variational iteration method for fractional initial-boundary value problems arising in the application of nonlinear science, Computers & Mathematics with Applications, 62 (5), 2273-- 2278.

[6]. Z. Odibat, (2011). On Legendre polynomial approximation with the VIM or HAM for numerical treatment of nonlinear fractional differential equations, Journal of Computational and Applied Mathematics, 235 (9), 2956--2968.

[7]. I. Podlubny, (1999). Fractional Differential Equations of Mathematics in Science and Engineering, Academic Pres, San Diego, Calif, USA, (198).

[8]. S. G. Samko, A. A. Kilbas, and O. I. Marichev, (1993). Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland.

[9]. K. Diethelm, N. J. Ford, (2001). Analysis of fractional differential equations, Numerical Analysis Report, 377, 1360-1725.

[10]. S. Das, (2008). Functional Fractional Calculus for System Identification and Controls, Springer, New York.

[11]. K. Diethelm, (1997). An algorithm for the numerical solution of differential equations of fractional order, Electron. Trans. Numer. Anal., (5), 1-6.

[12]. M. Enelund, B.L. Josefson, (1997). Time-domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations, AIAA J., 35 (10), 1630-1637.

[13]. I. Hashim, O. Abdulaziz, S. Momani, (2009). Homotopy analysis method for fractional IVPs, Commun. Nonlinear Sci. Numer. Simul., 14, 674-684.

[14]. J.H. He, (1998). Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering, 167 (1-2), 57-68.

[15]. M.M. Meerschaert, C. Tadjeran, (2004). Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math., 172 (1), 65-77.

[16]. J.H. He, (1999). Variational iteration method -- A kind of non-linear analytical technique: Some examples, International Journal of Non-Linear Mechanics, 34, 699-708.

[17]. M. Inc, (2008). The approximate and exact solutions of the space- and time- fractional Burger's equations with initial conditions by variational iteration method, J. Math. Anal. Appl., 345, 476-484.

[18]. J.H. He, (1999). Homotopy perturbation technique, Comput. Methods Appl. Mech. Engng., 178 (3-4), 257-262.

[19]. N.H. Sweilam, M.M. Khader, R.F. Al-Bar, (2008). Homotopy perturbation method for linear and nonlinear system of fractional integro-differential equations, Int. J. of Computational Mathematics and Numerical Simulation, 1 (1), 73-87.

[20]. H. Jafari, V. Daftardar-Gejji, (2006). Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition, Appl. Math. and Comput., 180, 488-497.

[21]. M.M. Khader, (2011). On the numerical solutions for the fractional diffusion equation, Communications in Nonlinear Science and Numerical Simulation, 16, 2535-2542.

[22]. E.A. Rawashdeh, (2006). Numerical solution of fractional integro-differential equations by collocation method, Appl.

Math. Comput., 176, 1-6.

[23]. W.W. Bell, (1968). Special Functions For Scientists and Engineers, Great Britain, Butler and Tanner Ltd, Frome and London.

[24]. M.M. Khader, A.S. Hendy, (2012). The approximate and exact solutions of the fractional-order delay differential equations using legendre seudospectral method, International Journal of Pure and Applied Mathematics, 74 (3), 287-297.

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Most Read

Most Cited

Volume 2 Issue 2 April - June 2013

Uniformly Stable Continuous Solutions Of A Functional Differential Inclusions

A.M.A. El-Sayed* , Fatma M.Gaffar**, Nesreen F.M.El-haddad***

* Faculty of Science, Alexandria University, Alexandria, Egypt. **-*** Faculty of Science, Damanhour University, Behera, Egypt.

El-SayedZ, A.M.A., Gaffar, F.M., and El-haddad, N.F.M. (2013). Uniformly Stable Continuous Solutions of A Functional Differential Inclusions. i-manager’s Journal on Mathematics, 2(2), 1-6. https://doi.org/10.26634/jmat.2.2.2310

Abstract

References

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On The Dual Focal Curves With Dual Parameter In D3

Mustafa Yeneroglu* , Vedat Asil**

*-** Department of Mathematics, Faculty of Science, Firat University, Elaz ig, Turkey.

Yeneroðlu, M., and Asil, V. (2013). On The Dual Focal Curves with Dual Parameter in D3. i-manager’s Journal on Mathematics, 2(2), 7-9. https://doi.org/10.26634/jmat.2.2.2311

Abstract

References

Full Article (HTML)

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Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test

James Edward Osler II*

North Carolina Central University

Osler, J. E., II. (2013). Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining The Application Process of The Tri–Squared Test. i-manager’s Journal on Mathematics, 2(2), 10-16. https://doi.org/10.26634/jmat.2.2.2312

Abstract

References

Full Article (HTML)

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Analysation of Super Strongly Perfectness in Ladder Graphs

Mary Jothi* , A. Amutha**

* Research Scholar, Department of Mathematics, Sathyabama University, Chennai. ** Associate Professor, Department of Mathematics, Sathyabama University, Chennai.

Jothi, R.M.J., and Amutha, A. (2013). Analysation of Super Strongly Perfectness in Ladder Graphs. i-manager’s Journal on Mathematics, 2(2), 17-21. https://doi.org/10.26634/jmat.2.2.2313

Abstract

References

Full Article (HTML)

Pdf

Legendre Seudospectral Method For The Approximate Solutions Some Of The Fractional-Order Differential Equations

Zeliha Sariates Korpinar* , M??nevver TUZ**

*-** Firat University, Department of Mathematics, Elazig, Turkey.

Körpinar, Z.S., and TUZ, M. (2013). Legendre Seudospectral Method for The Approximate Solutions Some of The Fractional-Order Differential Equations. i-manager’s Journal on Mathematics, 2(2), 22-27. https://doi.org/10.26634/jmat.2.2.2314

Abstract

References

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A.M.A. El-Sayed* , Fatma M.Gaffar, Nesreen F.M.El-haddad*

* Faculty of Science, Alexandria University, Alexandria, Egypt.

-* Faculty of Science, Damanhour University, Behera, Egypt.

* Research Scholar, Department of Mathematics, Sathyabama University, Chennai.

** Associate Professor, Department of Mathematics, Sathyabama University, Chennai.