iosr-Jm   Volume-4 ~ Issue-3

Abstract :In this paper we extend theorem of existence and uniqueness of fractional differential equations to n system of fractional differential equations.

[1] Sabatier, J. ;Agrawal, O.P.; Tenveiro Machado, J. A; Advances in Fractional Calculus: The oretical Developments and application
in physics and Engineering, springer, 2007.
[2] Heymans, N.; Podlubny, I.; Physical Interpretation of Initial Conditions of Fractional Differential Equations with Reimann-
Liouville Fractional Derivatives. RheoLAcla, 45, 2006.
[3] Juan Bisquert, Albert compt. Theory of Electrochemical Impedance of an Amatous Diffusion, J of Electroanalytical chemistry 499,
2001.
[4] Barcenaetal, Discrete Control for Computer Hard Disc by Fractional Order Hold Devise. University of paisvais spain, 2000.
[5] Shantana Das, B. B. Biswas, Total Energy Vtitization From Nuclear Sources PORT. 2006 Nuclear Energy for New Europe
Slovenia, 2006.
[6] Shantana Das, etal. Ratio Control with Logarithmic Logies in new P and P control algorithm for a true fuel-efficient reactor. Int. J.
Nuclear Energy science and Technology. Vol.3, No.1, 2007.
[7] V. Lakshmikantham, S. Leela and J. vasundhara; Theory of Fractional Dynamic Systems, Cambridge Academic publishes,
Cambridge, 2009.
[8] Al-Tabakchaly, M. A., on the existence and uniqueness for fractional differential Equations, Msc. Thesis, University of Musol.
[9] Dr. Ahmed Zain-Abdin, Maha Ahd-Wahab, Theorem on Certain Fractional Functions and Derivative, Eng. and Tech. Journal.
Vol.30, No.2, 2012.
[10] Spanier Keith B. Oldham and Jerome, The Fractional Calculus, Theory and Application of Differentiation to Arbitrary Order
Manufactured in the United State by Courier Corporation: ISBN-13: 978-0-486-45001-8, 2006.

Abstract :This researchpaper examines a computational approach to solving the Verhulst–Pearl Model (often called the Logistic Model). The paper also examines the applications of such a model in some related fields. The aim of this research paper is to put forward the integrator derived by Odekunle, Adesanya and Sunday (2012B) as an alternative tool for solving Logistic Models. The results obtained from the integrator show that it is computationally reliable.

Keywords:Block Integrator, Computationally Reliable, IVPs, Models, Verhulst-Pearl Equation

[1] D. N. Burghesand A. D. Wood, "Mathematical models in the Social, Management and Life Sciences", Ellis Harwood Limited, 1980.
[2] G. Elert, "Measuring Chaos", The Chaos Hypertext book, 2007.
[3] W. J. Meyer, "Concepts of Mathematical Modeling", Mc Grow–Hill Book Company, 1995.
[4] R. E. Mickens, "Nonstandard Finite Difference Models of Differential Equations", World Scientific, Singapore, 1994.
[5] O. D. Ogunwale, O. Y. Halid, and J. Sunday, (2010), "On an Alternative Method of Estimation of
[6] PolynomialRegression Models",Australian Journal of Basic and Applied Sciences,vol. 4, no. 8, pp. 3585-3590, 2010.
[7] E. A. Areo, R. A. Ademiluyi and P. O. Babatola, "Three Steps Hybrid LinearMultistep Method for the Solution of First-Order Initial Value Problems in Ordinary Differential Equations",Journal of Mathematical Physics,vol. 19, pp. 261-266, 2011.
[8] D. O. Awoyemi, R. A. Ademiluyi and W. Amuseghan, "Off-grids Exploitation in the Development of More Accurate Method for the Solution of ODEs", Journal of Mathematical Physics, vol. 12, pp. 379-386, 2011.
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Abstract :We focused attention on the Quantitative techniques and its significance roles in transport management. Emphasis is on the parametric statistics tests that are commonly used in transport management. The parametric statistics Z-test, t-test and F-test were fully discussed in this paper and its applications in transport management when testing for one sample means, two sample means and three or more sample means. The paper also reveals that parametric tests are more powerful than their non-parametric counterpart. Finally, the condition(s) for using t, z and F-test were fully discussed.

Keywords:Parametric, non-parametric, scaling ordinal, nominal, inductive, deductive, homoscedasticity

[1] Button, K. J. (1973): "Motor car ownership in the West Riding of Yorkshire. Some findings" Traffic Engineering and control.
[2] Boxton, M. J. and D.G. Rhys (1972): "The demand for car ownership: A note" Scottish Journal of Political Economy.
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Transportation, vol.2.
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[5] Asogwa, S.E, Obionu C. N. (1985): Urban Pedestrian accidents and the efficacy of a counter-measure. Centre. African J. medicine.
1985, 31: 62-65

Abstract :The failure of many projects, be it, Federal, states or local government is due in many cases, to poor design. Design can be defined as the formal framework that establishes, in advance, what the intention of the project is; a logical plan of activities, with the means to measure progress, taking into consideration the environmental factors and other socio-political factors that could affect the assumptions on which the project is based. The matrix method is primarily a device of project planning which define the project inputs, outputs and the intermediate and higher objectives in measurable terms.

[1] ANON (1984), Design and Evaluation for UNIDO Executed Projects and Programmes UNIDO USA.
[2] ANON (1981), Guidelines on Logical Framework Planning and Project Benefit Monitoring Evaluation Agricultural and Rural
Development Asian Development Bank, Indonesia.
[3] CASLEY, D.J and LURRY, D.A (1982), Monitoring and Evaluation of Agricultural Development IBRD, UK.
[4] CHAMBERS, R: (1980), Repaid Rural Appraisal, IDS Discussion Paper No 155, UK.

Abstract :Shannon inequalities are well known in information theory. In this paper, we have proposed some generalized inequalities in terms of relative AG divergence of type s and 2  - divergence. The result obtained in particular lead us to some known divergence measure.

Keywords:Csiszar's f- divergence, Relative Arithmetic Geometric divergence, 2  divergence, AG divergence of type s, Triangular discrimination, Information inequalities.

[1] I.Csiszar, Information type measures of differences of probability distribution and indirect observations, Studia Math. Hungarica
2(1967) 299-318.
[2] I.Csiszar, J.korner, Information theory: Coding theorems for discrete memoryless systems, Academic press, New York, 1981.
[3] S.S Dragomir, Some inequalities for the Csiszar f –divergence in information theory. Available from
<http://rgmia.vu.edu.au/monographs/Csiszar.htm>
[4] S.S Dragomir, A Converse inequality for the Csiszar  -divergence, Inequality for Csiszar f divergence in information
theory.Available from http://rgmia.vu.edu.au/monographs/Csiszar.htm
[5] S.S Dragomir, v. Gluscevic and C.E Pearce, Approximations for the Csiszar f- divergence via Mid points inequalities, In inequality
theory and applications-Volume 1, Y.J Cho, J.K Kim and S.S Dragomir (Eds), Nova science publishers, Inc. Huntington, New york,
2001, pp 139-154.
[6] K.Pearson, On the criterion that a given system of deviations from the probable in the case of correlated system of variables is such
that it can be reasonable supposed to have arisen from random sampling, Phil. Mag., 50(1900), 157-172.
[7] A.Sgarro, Information divergence and the dissimilarity of probability distribution, Estratto da calcolo, vol. XVII (3) (1981), 293-302.
[8] R. Sibson, Information radius, Z. wahrs.und verw Geb., (14) (1969), 149-160.
[9] I.J Taneja, Relative divergence measures and information inequalities-To appear: inequality theory and applications, volume 4, Y.J
Cho, J. K Kim and S. S Dragomir(Eds), Nova Science publishers, Inc. Huntington, New york, 2004.

Abstract :In the present paper, an inventory model without shortages has been considered in a fuzzy environment. Our goal is to determine the optimal total cost and the optimal order quantity for the proposed inventory model. The Trapezoidal fuzzy numbers have been introduced in order to achieve this goal. The computation of economic order quantity (EOQ) is carried out through defuzzification process by using signed distance method. The signed distance method is more applicable than the other methods of defuzzification. To illustrate the results of the proposed model, we have given two model examples and presented the computational results. Sensitivity for this model is also studied, which shows a linear relation between demand, EOQ, and total cost. The advantage of the proposed approach is that it is simple, gives a better result in relatively less computational work.

Keywords:Trapezoidal Fuzzy Numbers, Fuzzy Inventory Model, Defuzzification.

[1] Harris, F., Operations and cost, AW Shaw Co. Chicago, (1915).
[2] Wilson, R., A scientific routine for stock control. Harvard Business Review, 13, 1934, 116–128,
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8, 1982, 117-132.
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1082-1084.

Abstract :No manual method exists to divide a circular arc into equal numbers of division. This paper presents a method of dividing a circular arc into equal numbers of division using the method of arc rectification. The manual method of dividing a circular arc presented in this paper is completely a new method developed by the author, and will be very useful in graphics.

Keywords:Circular arc, Chord, Bisection, Rectification

[1] Chandra, A. M. and Chandra, S. (2003): Engineering Graphics, Narosa Publishing House, New Delhi, 2nd ed., PP. 65-66, 2003.

Abstract :Let M be a simple gamma ring with an involution I. In this paper, we develop some characterizations of these gamma rings with involution. We also obtain some properties of Lie and Jordan ideals with involutions.

Keywords:Simple gamma rings, Involution, Symmetric elements, skew symmetric elements, Jordan ideals, Lie ideals.

[1] W.E. Barnes :"On the gamma rings of Nobusawa", Pacific J. Math 18 (1966) 411-422.
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Technology Vol.4(2) (2011), 63-70.