iosr-Jm   Volume-11 ~ Issue-5 ~ Sep-Oct 2015

Abstract: Diabetic mellitus is a chronic disease of pancreatic origin which is not fully curable once a person became diabetic. This paper treats the model with prophylactic treatment, considering a person who is exposed to diabetes and organ failure. In this model, time to diabetes is Erlang-2 where as organ failure process is general. In this paper we present the expected time to treatment and expected cure time with numerical examples.

Keywords: Chronic diseases, Prophylactic treatment,Preventivemaintenance, Erlang-2.

[1]. Bhattacharya S.K., Biswas R., Ghosh M.M., Banerjee P., A study of risk factors of diabetes mellitus, Indian Community Med., 18(1993), 7-13.
[2]. Esary J.D., Marshall A.W., and Prochan F., Shock models and wear processes. The Annuals of Probability, 1,4(1973), 627-649.
[3]. Foster D.W., Fauci A. S., Braunwald E., Isselbacher K.J., Wilson J.S., Mortin J.B., Kasper D.L., Diabetes Mellitus, Principles of International Medicines. 2(2002), 15th edition, 2111-2126.
[4]. Kannell W.B., McGee D.L., Diabetes and Cardiovascular risk factors – the Framingam study. Circulation,59(1979), 8-13.
[5]. King H, Aubert R.E., Herman W.H., Global bdrden of diabetes 1995-2025: prevalence, numerical estimates and projections, Diabetes care 21(1998), 1414-1431.
[6]. King H., and Rewers M., Global estimates for prevalence of diabetes mellitus and impaired glucose, tolerance in adults: WHO Ad Hoc Diabetes Reporting Group. Diabetes Care.16(1993), 157=177.

Abstract:This paper proposes a family of single step, fifth and fourth order continuous hybrid linear multistep methods (CHLMM). These methods are used to integrate the initial value problems of first order ordinary differential equations. The methods are obtained from the continuous schemes derived via interpolation and collocation procedure. The schemes are consistent, zero stable, convergent and accurate. Taylor's series approximation was adapted as simultaneous numerical integrators over non-overlapping intervals values and for the implementation of the methods. These methods compared favorably with some existing methods because they are efficient and simple in terms of derivation and implementation.

[1]. S. A. Odejide and A. O. Adeniran, A Hybrid Linear Collocation Multistep Scheme for Solving First Order Initial Value Problems. Journal of the Nigerian Mathematical Society 31, 229-241, 2012.
[2]. J. D. Lambert, Computational methods in ordinary differential equations. John Wiley and Sons, New York, 1973.
[3]. J. D. Lambert and A. Watson, Symmetric Multistep Method for Pardic Initial Value Problems. Journal of the Institute of Mathematics Application 18, 189-702, 1976.
[4]. D. O. Awoyemi, On some continuous linear multistep methods for initial value problems. Ph. D Thesis (Unpublished). University of Ilorin, Nigeria, 1992.
[5]. D. O. Awoyemi, A Class of Continuous Methods for General Second Order Initial Value Problem in Ordinary Differential Equation. Inter. J. Computer math, 72, 29-37, 1999.

Abstract:A family of functions is identified and all of its properties to be a complex continuous wavelet are verified and are applied in analyzing time series by using popular software Matlab. We discuss the cross wavelet spectrum and wavelet coherence using this new wavelet for examining relationships in time frequency space between two time series. We demonstrate how phase angle statistics can be used to gain confidence in causal relationships and test mechanistic models of physical relationships between the time series. The different graphical representation provided by the wcoher.m function in Matlab is used.
Keywords: One dimensional complex continuous wavelets, Wavelet cross spectrum and Wavelet coherence for Complex-valued Wavelets.

[1]. I. Daubechies: The wavelets transform, time frequency localization and signal analysis, IEEE Transactions on Information Theory, vol. 36, no. 6, Sept. 1990, pp. 9611005.
[2]. Daniel T. L. Lee, Akio Yamamoto, 1994. "wavelet analysis: Theory and applications", Hewlett –Packard Journal.
[3]. M.R. Azimi Digital Image Processing Lectures 15 & 16 Department of Electrical and Computer Engineering Colorado State University
[4]. Aguiiar-Conrariia,, Luíís e Mariia Joana Soares: "The Continuous Wavelet Transform:: A Priimer", NIPE WP 16/2011
[5]. Paul S Addison : The Illustrated Wavelet Transform Handbook, Introductory Theory and Applications in Science, Engineering, Medicine and Finance Napier University, Edinburgh, UK.
[6]. Significance tests for the wavelet cross spectrum and wavelet linear coherence Z. Ge Ecosystems Research Division, NERL, USEPA, 960 College Station Road, Athens, GA 30605, USA

Abstract:This presentation is based on a large study whose purpose was to explore the pedagogical practices in integration of ICT in teaching and learning mathematics in secondary schools in Nairobi County. The study adopted a descriptive survey design. Three instruments questionnaires', a structured interview schedule and an observation checklist were used to collect data. The study was carried out in twelve public secondary schools in Nairobi County. Data was analysed using descriptive statistics. Findings from the study indicated that, there were low levels of ICT integration, Mathematics teachers were not well prepared to integrate ICT in teaching Mathematics.

This presentation is based on a large study whose purpose was to explore the pedagogical practices in integration of ICT in teaching and learning mathematics in secondary schools in Nairobi County. The study adopted a descriptive survey design. Three instruments questionnaires', a structured interview schedule and an observation checklist were used to collect data. The study was carried out in twelve public secondary schools in Nairobi County. Data was analysed using descriptive statistics. Findings from the study indicated that, there were low levels of ICT integration, Mathematics teachers were not well prepared to integrate ICT in teaching Mathematics.

Abstract: Prime Minister voting tendencies are of interest every 5 years. By considering three party system generate a probabilistic transition matrix, or by the system of difference equation to solve the variables. Keywords: Probabilistic Transition Matrix, System of Difference Equation, Langrange's Interpolation, Markov Chain Process, Graphical Analysis.

[1]. G. Frank, W. Maurice and F. William,A First Course in Mathematical Modelling
[2]. J.N. Kapur, Mathematical Modelling(New Age International Publishers)
[3]. Kelly Walter G, Peterson Allan C,Theory of Difference Equations(New Delhi: Elsevier Publishers)
[4]. Mayer Walter J,Concepts of Mathematical Modelling(McGraw hill editions)
[5]. Mathematical Modelling (Staff of Research Association)
[6]. Fowler A.C,Mathematical Models in the Applied Sciences
[7]. Internet Site:encyclopedia.com / Indian general election/
[8]. Amos Gilat,MATLAB: An Introduction with Applications(John wiley Publishers)

Abstract:In this paper, He's Variational Iteration Method (HVIM) is used to study the linear time-invariant and time-varying singular systems. The results obtained using He's Variational Iteration Method and the methods taken from the literature [17] were compared with the exact solutions of the linear time-invariant and time-varying singular systems. It is found that the solution obtained using the He's Variational Iteration Method is closer to the exact solutions of the linear time-invariant and time-varying singular systems. Error graphs for discrete and exact solutions are presented in a graphical form to highlight the efficiency of this method.
Keywords: Singular systems, time-invariant, time-varying, He's Variational Iteration Method, Leapfrog Method.

[1] Abdou MA, Soliman AA. Variational iteration method for solving Burger's and coupled Burger's equations. J. Comput. Appl. Math. 2005, 181(2), 245–51.
[2] Abdou MA, Soliman AA. New applications of variational iteration method. Physica D 2005;211:1–8.
[3] Abdou MA. On the variational iteration method. Phys Lett A 2007;366:61–8.
[4] Ascher UM, Lin P. Sequential regularization methods for higher index differential-algebraic equations with constraint singularities: the linear index-2 case. SIAM J Anal 1996;33:1921–40.
[5] Babolian E, Hosseini MM. Reducing index, and pseudospectral methods for differential-algebraic equations. Appl Math Comput 2003;140:77–90.
[6] He JH. A new approach to nonlinear partial differential equations. Commun Nonlinear Sci Numer Simulat 1997;2(4):230–5.
[7] He JH. Variational iteration method for delay differential equations. Commun Nonlinear Sci Numer Simulat 1997;2(4):235–6.

Abstract: In this paper, we present analytical solutions of some system of non-linear partial differential equations using Reduced Differential Transform Method (RDTM). The solutions are considered as infinite series expansions which converge rapidly to their exact solutions. Solutions obtained by RDTM are in close conformity with the exact solutions. The results obtained show that the RDTM technique is accurate and efficient and require less effort in comparison to the other analytical and numerical methods. Keywords – Analytical solutions , Non-linear System, PDEs, RDTM.

[1] J.K. Zhou, Differential transformation and its application for electrical circuits, Huarjung University Press, Wuuhahn, China. (1986) [2] C.K. Chen and S.H. Ho, Application of differential transformation to eigenvalue problems, Applied Mathematics and Computation, 79(1996),173–188.

[3] C.L. Chen; S.H. Lin, and C.K. Chen, Application of Taylor transformation to nonlinear predictive control problem, Appl. Math. Model, 20(1996), 699–710.

[4] C.L. Chen and Y.C. Liu, Solution of two point boundary value problems using the differential transformation method, Journal of Optimization Theory and Applications, 99(1998), 23–35.

[5] M. Malik and H.H. Dang, Vibration analysis of continuous system by differential transformation, Applied Mathematics and Computation, 96(1998), 17–26. [6] C.K. Chen, and S. H. Ho, Transverse vibration of rotating twisted Timoshenko beams under axial loading, Int. Journal of Mechanical Science, 41(1999), 1339-1356.

Abstract: Completely Bounded Artex Spaces over bi-monoids contain the least and greatest elements namely 0 and 1. These elements play a good role in our study. Sum Combination of elements of a Completely Bounded ArtexSpace over a bi-monoid is defined. The sum span of a finite subset of a completely bounded Artex space over a bi-monoid is defined. Some propositions were found and proved. Examples are provided.

Keywords: Bi-monoids, Artex Spaces over bi-monoids, Completely Bounded Artex Spaces over bi-monoids, Sum Combination,Sumspan.

[1]. K.Muthukumaran And M.Kamaraj, "Artex Spaces Over Bi-Monoids", "Research Journal Of Pure Algebra", 2(5), May 2012, Pages 135-140.
[2]. K.Muthukumaran And M.Kamaraj, "Subartex Spaces Of An Artex Space Over A Bi-Monoid" ,"Mathematical Theory And Modeling"(With Ic Impact Factor 5.53), An Usa Journal Of "International Institute For Science, Technology And Education", Vol.2, No.7, 2012, Pages 39 – 48.
[3]. K.Muthukumaran And M.Kamaraj, "Bounded Artex Spaces Over Bi-Monoids And Artex Space Homomorphisms", "Research Journal Of Pure Algebra", 2(7), July 2012, Pages 206 – 216.
[4]. K.Muthukumaran And M.Kamaraj, "Some Special Artex Spaces Over Bi-Monoids", "Mathematical Theory And Modeling"(With Ic Impact Factor 5.53), An Usa Journal Of "International Institute For Science, Technology And Education", Vol.2, No.7, 2012, Pages 62 – 73.
[5]. K.Muthukumaran And M.Kamaraj, "Boolean Artex Spaces Over Bi-Monoids", Mathematical Theory And Modeling" (With Ic Impact Factor 5.53), An Usa Journal Of "International Institute For Science, Technology And Education", Vol.2, No.7, 2012, Pages 74 – 85.

Abstract:We consider a global supply chain consisting of one retailer and one manufacturer, both from different countries. As there is a time duration between the placement of the order and the order is acquired, there is a possibility in the exchange rate fluctuation between the two countries. This affects the optimal pricing and order quantity decisions of the retailer. In this paper we elaborate the derivations of analytic expressions involving the transaction exposure when the retailer or manufacturer undertakes to share the exchange rate risk
under the generalized hybrid demand in the news vendor framework.
Keywords: transaction exposure, exchange rate, global supply chain, newsvendor problem, optimal pricing and quantity, hybrid demand

[1] F.J. Arcelus, Ravi Gor, G. Srinivasan, Foreign exchange transaction exposure in a newsvendor setting, European Journal of Operational Research, 227(2013) 552-557
[2] Goel, M., 2012. Management of transaction exposure: a comparative analysis of MNCs in India. International Journal of Service Science,
Management, Engineering and Technology 3, 37–54.
[3] Eitemann, D.K., Stonehill, A.I., Moffett, M.H., 2010. Multinational Business Finance,12th ed. Prentice Hall, Boston.
[4] Shubita, M.F., Harris, P., Malindretos, J., Bobb, L.M., 2011. Foreign exchange exposure: an overview. International Research Journal of Finance and Economics 78, 171–177.
[5] Petruzzi, N.C., Dada, M., 1999. Pricing and the newsboy problem: a review with extensions. Operations Research 47, 183–194.

Abstract: The class of Volterra integral equation of second kind with smooth and weakly singular kernel is presented with the help of Taylor's series expansion method. Here we get approximate solution of the integral equation which can be expressed explicitly in a simple closed form. The method of solution of equations studied in the presented paper is very useful to solve the physical problems as radiative heat transfer, radiative equilibrium, potential theory and electrostatics. The numerical examples arising from radiative heat transfer and electrostatics which are accurate and in a good manner. Index Term: Volterra integral equation, Taylor's series, radiative heat transfer etc

[1] B Alpert, G Beylkin, R Coifman, V Rokhlin, Wavelet like bases for the fast solution of second kind integral equations, SIAM J. Sci. Comput., 14 (1993), pp. 159-184.

[2] K. E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, 1997.

[3] B. C. Choi, S. W. Churchill, A technique for obtaining approximate solutions for a class of integral equations arising in radiative heat transfer, Internat J. Heat Flow, 6 (1) (1985), pp. 42-48.

[4] L. M. Delves, J. L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, Cambridge, 1985.

[5] W. Hackbusch, Multigrid Methods and Applications, Springer, Berlin,1985.

[6] E. Hopf, Mathematical Problems of Radiative Equilibrium, Cambridge University Press, Cambridge, 1934.

[7] H. G. Kaper, R. B. Kellogg, Asymptotic behavior of the solution of the integral transport equation in slab geometry, SIAM J. Appl. Math., 32 (1977), pp. 191-200.

Abstract:This research paper deals with the optimality of Circular Neighbor Balanced Designs for total effects when the observation errors are correlated according to second order circular stationary autoregressive process. Few results pertaining to the optimality conditions under some specified conditions are provided and the efficiencies of circular neighbor balanced designs relative to the optimal continuous block designs are also investigated. The efficiency of the Circular Neighbor Balanced Designs is illustrated corresponding to the optimal continuous block designs.
Key Words: Auto regressive process, second order Block Design, Circular, Correlated observation, Total effect, Universal optimality.

[1]. AZA IS, J.M., BAILEY, R.A. and MONOD, H., (1993). Acatalogue of efficient Neighbor- designs with border plots. Biometrics 49.
[2]. AI, M.-y., GE, G.-n.andCHAN, L.-y. (2007). Circular neighbor-balanced designs universally optimal for total effects.Sci. China Ser. A 50 821–828.MR2353065
[3]. AI, M., YU, Y. and HE, S. (2009). Optimality of circular neighbor-balanced designs fortotal effects with autoregressive correlated observations. J. Statist. Plann.Inference 1392293–2304.MR2507991
[4]. BAILEY, R.A. and DRUILHET, P., (2004). Optimality of Neighbor-balanced designs for total effects. Ann. Statist. 32(4),1650-1661.
[5]. BOX, G.E.P., HUNTER, J.S. and HUNTER, W.G., (2005).Statistics for Experimenters. John Wiley & Sons, New Jersey.

Abstract: In this paper we introduce a new type of function called the **gα-continuous maps and **gα-irresolute maps and discuss their properties.

Key words: **gα-continuous maps, **gα-irresolute maps.

[1]. M.E.Abd El-Monsef, S.N.El-Deeb and R.A.Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12(1983), 77-90.
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Abstract:In the present paper, the effect of dimensionless parameter on mixed convection flow within a liddriven triangular cavity has been numerically investigated. The bottom wall of the cavity is considered as heated. Besides, the left and the inclined wall of the triangular cavity are assumed to be cool and adiabatic respectively. The cooled wall of the cavity is moving up in the vertical direction. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Rayleigh number, Prandtl number and the cavity aspect ratio.

[1]. Akinsete V.A., Coleman T.A., Heat transfer by steady laminar free convection in triangular enclosures, International Journal of Heat and Mass Transfer, 25(7), 1982, 991–998.
[2]. Aydin, O., Yang, W. J., Mixed convection in cavities with a locally heated lower wall and moving side walls, Numer. Heat Transfer, 37(7), 2000, 695-710.
[3]. Basak T., Roy S., Krishna Babu S., Balakrishnan A.R., Finite element analysis of natural convection flow in a isosceles triangular enclosure due to uniform and non-uniform heating at the side walls, International Journal of Heat Mass Transfer, 51(17), 2008, 4496–4505.
[4]. Braga, E. J., de Lemos, M. J. S., Laminar natural convection in cavities filed with circular and square rods, Int. Commun. in Heat and Mass Transfer, 32(10),2005, 1289-1297.

Abstract:In this paper, we derive the formula for Infinite Multi-Series generated by generalized backward alpha difference equation by equating the closed and infinite summation form solutions of higher order generalized i   backward difference equation for positive and negative variable. Suitable examples are inserted to illustrate the main results. Mathematics Subject Classification: 39A70, 47B39, 39A10.
Keywords: Generalized alpha difference equation, infinite multi-alpha series, Closed form solution.

[1] Bastos N R O, Ferreira R A C, and Torres D F M, Discrete-Time Fractional Variational Problems, Signal Processing, vol.91,no. 3,pp.
513-524, 2011.
[2] Britto Antony Xavier G., Sathya S. and Vasantha Kumar S.U., n-Multi-Series of the Generalized Difference Equations
to Circular Functions, International Journal of Mathematics Trends and Technology, 5 (2014), 97-107.
[3] Britto Antony Xavier G., Gerly T.G. and Nasira Begum H., Finite series of polynomials and polynomial factorials arising
from generalised _q difference operator, Far East Journal of Mathematical Sciences, 94(1) (2014), 47-63.
[4] Ferreira R A C and Torres D F M, Fractional h-difference equations arising from the calculus of variations, Applicable Analysis and
Discrete Mathematics, 5(1) (2011), 110-121.
[5] Grace S R, Oscillation of Certain Neutral Difference Equations of Mixed Type, Journal of Math Analysis Applications., 1998, 224:
241-254.
[6] Grace S R and Donatha S Oscillation of Higher Order Neutral Difference Equations of Mixed Type, Dynam Syst Appl., 2003, 12:
521-532.

Abstract:One of the techniques of studying the deterministic dynamics of the expected rate of inflation due to a changing duration of business in the unit of weeks depends on the process of mathematical modelling. The statistical measures of the impact of the actual rate of inflation on the stabilized steady-state expected rate of inflation were systematically calculated and discussed in this paper in the context of stabilizing this economic system. When the expected rate of inflation is 1.44, the statistical measures of the range, mean, variance, standard deviation and kurtosis are 0.44417472004, 0.27038055356, 0.01910049264, 0.13820453192 and 1.81433937992 indexed for the period of twenty (20) weeks when the initial expected rate of inflation is 0.035. We would expect this novel contribution to strength the other related knowledge-based results in numerical simulations, economic planning and economic policy on the control of the twin effects of inflation and unemployment on the social losses.

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Abstract: In this paper we have established fixed point theorem in 2-metric space which generalizes many previous results.
Key Words: Fixed point theorem, 2-metric space, Euclidean space, Rational expression.

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