iosr-Jm   Volume-10 ~ Issue-1 ~ Jan-Feb 2014

Abstract: The object of the present paper is to study generalized projective -recurrent Sasakian manifolds. Here we find a relation between the associated 1-forms A and B. We also proved that the characteristic vector field and vector field associated to the 1-forms A and B are co-directional. Finally we proved that generalized projective -recurrent Sasakian manifold is of constant curvature.
Key Words: Generalized projective -recurrent, Sasakian manifold, Sectional curvature.

[1] Blair, D.E., Contact manifolds in Riemannian geometry, Lecture Notes in Math. Springer 509(1976).
[2] Bhagwat Prasad, A pseudo projective curvature tensor on a Riemannian manifolds Bull.Cal.Math.Soc., 94:3(2002), 163-166.
[3] Asli Basari, Cengizhan Murathan, Generalized -recurrent kenmotsu Manifolds, Sdu fen debiyat fakultesi, 3(1)(2008), 91-97.
[4] M.C.Chaki, On Pseudo Symmetric manifolds, Analele Stiintifice Ale Univeritatti. 33(1987), 53-58.
[5] U.C.De, N.Guha, On generalized recurrent manifolds, J.National Academy of Math. India, 9(1991), 85-92.

Abstract: The idea of difference sequence spaces was introduced by Kizmaz [1] and then this subject has been studied and generalized by various mathematicians. In this paper we define some difference rate sequence spaces by Orlicz space of bounded sequences and establish some inclusion relations. Some properties of these spaces are studied.
Keywords: Difference sequence, Bounded sequence, Orlicz function.

[1] H.Kizmaz, On certain sequence spaces, Canad. Math. Bull., 24 (2) (1981), 169-176.
[2] M.Et and R. Colak, On some generalized difference sequence spaces, Soochow J. Math., 21 (4) (1995), 377 – 386.
[3] M. Et, On some topological properties of generalized difference sequence spaces, Int. J. Math. Math. Sci., 24 (11) (2000), 785 – 791.
[4] M. Et and F. Nuray, – Statistical convergence, Indin J. Pure Appl. Math., 32 (6) (2001), 961 – 969.
[5] R. Colak, M. Et and E. Malkowsky, Some Topics of Sequence Spaces, Lecture Notes in Mathematics. Firat University Press, Elazig, Turkey, 2004.

Abstract: The approximate solutions for the Kuramoto – Sivashinsky Equation are obtained by using the Adomain Decomposition method (ADM). The numerical examples show that the approximate solution comparing with the exact solution is accurate and effective and suitable for this kind of problem.

Keywords: Adomain Decomposition method (ADM); Kuramoto – Sivashinsky Equation.

[1] S.T. Mohyud-Din, On Numerical Solutions of Two-Dimensional Boussinesq Equations by Using Adomian Decomposition and He's Homotopy Perturbation Method,J. Applications nd Applied Mathematics,1932-9466, 2010, 1-11.
[2] Kuramoto, Y., Tsuzuki, T., Persistent propagation of concentrationwaves in dissipative media far from thermal equilibrium,Pron. Theor. Phys. ,55, 1976, 356.
[3] Hooper, A.P., Grimshaw, R., Nonlinear instability at theinterface between two viscous fluids. Phys. Fluids ,28, 1985, 37–54.
[4] Sivashinsky, G.L., Instabilities, pattern-formation, and turbulencein flames. Ann. Rev. Fluid Mech. ,15, 1983, 179–199.
[5] Akrivis, Georgios, Smyrlis, Yiorgos-sokratis, Implicit-explicitBDF methods for the Kuramoto-Sivashinskyequation,Appl.Numer. Math. 51, 2004, 151–169.
[6] Manickam, A.V., Moudgalya, K.M., Pani, A.K., Second-ordersplitting combined with orthogonal cubic spline collocation methodfor the Kuramoto–Sivashinsky equation, Comput. Math. Appl. 35, 1998, 5–25.

Abstract: In this paper, an application of homotopy perturbation method (HPM) is applied to finding the approximate solution of nonlinear diffusion equation with convection term, We obtained the numerically solution and compared with the exact solution.The results reveal that the homotopy perturbation method is very effective, simple and very close to the exact solution.

Keywords: Diffusion equation with convection term,homotopy perturbation method.

1] J.H.He, Variational iteration method: a kind of nonlinear analytical technique: some examples,International Journal of Non-Linear Mechanics, 34, 699-708,1999.
[2] He J.H., Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computation, 135, 73-79, 2003.
[3] J.H. He, Homotopy perturbation technique,Computer Methods in Applied Mechanics and Engineering, 178, 257-262,1999.
[4] J.H.He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, International Journal of Non-Linear Mechanics, 35, 37-43, 2000.
[5] J.H.He,Comparison of homotopy perturbation method and homotopy analysis method,applied Mathematics and Computation, 156, 527-539,2004.
[6] J.H. He, A review on some new recently developed nonlinear analytical techniques, International Journal of Nonlinear Sciences and Numerical Simulation,1, 51-70,2000.

Abstract: This paper examined the queueing situation in Shehu Mohammed Kangiwa Medical Center Kaduna Polytechnic. The complaints of patients on delays were corroborated by the 9minutes mean queue time and mean queue length of 3persons in the existing structure. A new multy -channel queueing model which yielded a mean queue time of 1minute and a mean queue length of 0persons was formulated. This multy-channel queueing model gave optimal results and is proposed for adoption.

Key words: Medical Center, Multy-Channel Queueing Model, Patients, Queue length, Queue time.

[1] Wagner .H.M principle of management science
[2] Russell l. Ackoff and Maurice w. Sasieni fundamentals of operations research. ( Wiley Easter ltd ,1986)
[3] Frederick S.H. and Gerald J.L (2007), Introduction to Operations Research. Concept and Cases 8th Edition. Tata (Mcgraw-Hill Publishing Company Ltd. New Delhi ,2007).
[4] Kothary C,R An Introduction to Operations Research, (Vikas Publishing House, New Delhi ,2008).
[5] Ivo Adan and Jaques Resing queueing theory department of maths & comp. sc Eudhoven university of technology Netherlands (2002)

Abstract: Nicholson Bailey model (NB-1930) was developed to describe the population dynamics of host parasite system. Host parasite models are similar to host parasitoid model except that the parasite does not kill the host [1]. The NB model does not allow for stable host-parasitoid interactions due to potential fecundity of parasites is not limited [7]. In this paper the modified NB model is applied to host parasitoid system and the stability criteria were analysed and illustrated.

Keywords: Host-parasitoid system, Nicholson-Bailey model, Stability analysis.

[1] Cheryl.J.Briggs and Martha.F.Hoopes: Stabilising effects in spatial parasitoid-host and predator – prey models: a review, 300, 299-
315 (2003).
[2] David Eberly: Stability analysis for system of Differential equations: 1-14, (2008).
[3] Elaydi.S: An introduction to difference equations. Springer, Berlin (2000)
[4] Hassell MP: Insecticides in host-parasitoid interactions. Theoretical population Ecology, 26(3), 378-386 (1984).
[5] Hassell. MP, comins. HN: Discrete time model for two-species competition, Theor. Population Biology 9, 202-221 (1976)

Abstract: In this paper we have to study on the problem of 'Corruption' in different ways by using mathematical modelling. The problem of corruption is everywhere, so we will try to find the solution for the problem of 'removing corruption' in the society. Therefore, how to measure the corruption in the society of any field or any country in the world? So, we have found the formula that is Mathematical corruption model for measuring the corruption in the society of any field or any country of the world. When we measure the corruption in the society then there will be no difficult to remove the corruption from the society of any country in the world. So we have to take some illustrations for measuring the corruption in various fields of the country India.

Keywords: mathematical thinking, corruption mentality, modelling, applied.

[1]. Andriole SJ (1983) Handbook of Problem Solving: An Analytic Methodology Princeton, NJ: Petrocelli Books.
[2]. Blum, W., Niss, M. (1991). Applied Mathematical Problem Solving, Modeling, Applications and links to other subjects- state, trends and issues in mathematics instruction. In: Educational studies in Mathematics, 22(1), 37-68.
[3]. BhaskarDasgupta, Applied Mathematical Methods published by Darling Kindersley (India) Pvt. Ltd. Delhi.
[4]. Bender EA (1978) An Introduction to Mathematical Modeling New York: John Wiley and Sons.
[5]. Daniel A. Murray, Introductory Course in Differential equations, Orient Longman ltd. Harlow and London (1993).
[6]. De Lange, J. (1996). Real Problems with Real world Mathematics. In L. Alsina& al. (Eds.), proceeding of the 8th Int. Congress on Math.1 Education (pp. 83-110). Seville: Thales.

Abstract: In this paper, we have established a theorem on approximation of function belonging to Lip( ( class by Matrix-Cesaro summability method of Fourier series.

Keywords: Degree of approximation, Lip( ( class of function, Matrix-Cesaro summability method, Fourier series, Lebesgue integral.

[1]. Chandra P., On the degree of approximation of function belonging to the Lipschitz class, Nanta Math. 8 (1975), No.1, 88-91.
[2]. Chui C.K. and Holland A.S.B., On the order of Approximation by Euler and Taylor means, J. Appro. Theory 39(1983), 24-38.
[3]. Khan H.H., On the degree of approximation of functions belonging to the class Lip( Indian J. Pure Appl. Math.5(1974), No.2, 132-136.
[4]. Nigam H.K., Degree of approximation of a class of function by product summability means, IAENG Int. J. of Appl. Math., 41:2, IJAM_41_2_07.
[5]. Qureshi K., On the degree of approximation of functions belonging to the Lipschitz class by means of a conjugate series, Indian J. Pure Appl. Math.12-(1981), No. 9, 1120-1123.
[6]. Qureshi K., On the degree of approximation of functions belonging to the class Lip( Indian J. Pure Appl. Math. 13(1982), No. 4, 466-470.

Abstract: In this thesis we consider four multivariate models (i.e. three multiple regression models respectively) that captures the forecast mechanism of yearly total observation (YTO) of Man-Hour Worked for accident, man-hour lost for cost reduction, maintenance trend and Cost Reduction Linear Programming (LP) Model at the Kaduna Refining and Petrochemical Company (KRPC). Data were collected from Health, Safety and Environment Department (HSED), Planning Budget and Monitoring Department (PBMD) of KRPC records and classified into purposeful and logical categories for analysis. Multiple regression model was adopted as the suitable model for predicting the yearly total observation of man-hour worked as a result of accident in the system, man-hour lost as a result of accident which will assist the management in putting resources in place that will reduce cost in the system and maintenance models that will inform progressive routine maintenance plan in the system.

Keywords: KRPC, Safety, Accident, Maintenance, Man-hour Loss, Man-hour worked, Fire incident, Oil spillage, work permit.

[1]. Abdulkadir, Bara-Hart (2008:6): "Work Permit and Accident Rate in KRPC Plant Operations". NNPC Chief Officers MDP Course 055 (Unpublished)
[2]. Aguba, Peterson (2006): "Work Permit System and Accident Prevention" NNPC Chief Officers MDP Course 054 (Unpublished). PP.9
[3]. Aguba, James (2006): "Safety Audit Compliance and Accident Prevention in KRPC" ABB Lumus Survey Report. NNPC Chief Officers MDP Course 054 (Unpublished). PP. 8
[4]. Dan H. Barber and Robert E. Donovan (2004): Industry Safety Engineering and Management Hand Book. Zub-Chord Publishers.
[5]. Dupont (1950): A world Leader in Industrial Safety Management "Causes of Industrial Accident" www.dupont.com/safety1 (1950)

Abstract: Császár in [4] introduce a weak structure as generalization of general topology. The aim of this paper is to give basic concepts of the measure theory in weak structure.

Keywords: weak structure,  - algebra ,  - additive function, Measures

[1] A. Császár, Generalized open sets, Acta Math. Hungar 75 (1997), 65-87.
[2] A. Császár, Generalized topology, generalized continuity, Acta Math. Hungar 96 (2002), 351-357.
[3] A. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar 106 (2005), 53-66.
[4] A. Császár, Weak structures, Acta Math. Hungar 131(1-2) (2011), 193-195.
[5] J. Umehara H. Maki and T Noiri, Every topological space is pret1/2, Mem. Fac. Sci.Kochi.Univ. Ser. A Math. 17 (1996), 33-42.

Abstract: The Holy Bible has said  value is equal to 3. Mathematicians were not satisfied with the value. They thought over. Pythagorean theorem came in the mean time. A regular polygon with known perimeter was inscribed in a circle and the sides doubled successively until the inscribed polygon touches the circumference, leaving no gap between them. Hence this method is called Exhaustion method. The value of the perimeter of the inscribed polygon is calculated applying Pythagorean theorem and is attributed to the circumference of the circle. This method was interpreted, first time, on scientific lines by Archimedes of Syracuse, Greece. He has said  value is less than 3 1/7.

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