iosr-Jm   Volume-10 ~ Issue-3 ~ May-June 2014

Abstract: Suppose C and D are permutation groups on Γ and Δ respectively. The wreath product of C by D denoted by C wr D is the semi – direct product of C by Δ so that W = {( , with multiplication in W defined as; (f1,d1) (f2,d2) = [(f1f2d1-1), (d1d2)] for all f1, f2 P and d1d2 D. These communication (paper) provides with clarity the conditions under which wreath products of such permutation groups are transitive, primitive and faithful and also provides a very good example to demonstrate such conditions.
Keywords: Group actions, Transitive Permutation groups, Primitivism and faithfulness of W on ΓXΔ, wreath product, stabilizer and centre of wreath products.

[1]. Audu, M.S. "On Transitive Permutation Groups". African Matimatika,Journal of African Mathematical Union, series 2, Vol.5 (155-160)
[2]. Ali, B. (1992): "On Transitive and Permutation Groups" University of Jos.
[3]. Rose, J.S. (1978). "A Course on Group Theory" Cambridge University Press.
[4]. [4]Apine, E. (1991). "On Permutation Groups of Prime-Power Order"University of Jos.
[5]. Ezenwanne, I.U. "Transitive, Primitivism and Wreath Product of Permutation Group" University of Jos

Abstract: The paper aims to develop solutions from a pre-determined solution to the 8 knight's problem with the aid of linear transformation termed as' Shifting Techniques'. The term 'Shifting Technique' implies displacement of the position of the two knights while maintaining a definite number of gaps between them. The employment of: 'Vertical, Horizontal, Alternate, Diagonal & L-shaped shifting techniques has been effectively generated limited number of solutions to the 8 knights problem due to symmetric pattern constraints.. The use of symmetry & parallelism illustrates the generation of missing solutions on the board. Further cases devised in the paper have been discussed to imbibe the reader with the concept of 'Shifting Techniques'. The latter parts of the paper discuss the applications of these shifting techniques in the generation of fractals that are an important class in image development. These have been extensively used in image construction. Figure Solutions generated via MATLAB coding at the end of the paper elucidates the generation of solutions to illustrate the idea of fractal generation

[1]. Realization of 8 queens problem(www.linkspringer.com)
[2]. Self Experimentation of chess techniques.
[3]. Self Experimentation of Game Shifting Techniques.
[4]. Permutation Arrays under Chebyshev distance, Information Theory Te Tsung Lin,; Shi-Chun Sai ; Wen-Guen-Zeng ,IEEE Transactions
[5]. Fractal Geometry methods
[6]. Image Processing techniques in MATLAB (www.stackoverflow.com)

Abstract: A retrial queue with general retrial times, modified vacation policy and Bernoulli feedback is analyzed in this paper. If the server is busy or on vacation, an arriving customer either enters on orbit with probability b, or balks with probability 1-b. Otherwise the service of the arriving customer commences immediately. At the service completion epoch, the test customer may either enter the orbit for another service with probability p or leave the system with probability q (=1-p). If the orbit is empty, the server takes at most J vacations until at least one customer is recorded in the orbit when the server returns from a vacation. By applying supplementary variable technique some analytical results for the system are derived. The effects of various parameters on the system performance are analyzed numerically.
Key words: Retrial queues, balking, Bernoulli feedback, supplementary variable technique, Laplace Stieljes< transform.

[1]. Artalejo J.R. and Lopez-Herrero M.J. (2000) 'On the single server retrial queue with balking' INFOR 38, pp 33-50.
[2]. I.Atencia, P.Moreno,(2005) 'A single server retrial queue with general retrial times and Bernoulli schedule' Applied Mathematics and Computation, 162, pp 855-880.
[3]. Falin G.I. and Templeton J.G.C. (1997) Retrial queues, London, Chapman and Hall.
[4]. Gomez-Corral A(1999) 'Stochastic analysis of a single server retrial queue with general retrial times', Naval Research Logistics, 46, pp 561-581.
[5]. Jan-Chnan Ke, Fu-Min Chang, (2009) 'Modified vacation policy for M/G/1 retrial queue with balking and feedback' , Computers and Industrial engineering 57,pp 433-443.

Abstract: The analysis of the phenomenon of extreme values of climate, especially rainfall is very important for government to reduce the negative impacts. Global circulation model (GCM) is an important data in the climate system because it can provide information about the climate in the future on a large scale. Techniques to reduce the size of the spatial scale using statistical downscaling (SD). SD modeling method requires a more flexible alternative to the assumption that the resulting models can be used to describe the climate events. Generalized additive model (GAM) is a method that accommodates the influence of linear and nonlinear in extreme rainfall events. The methodology is applied to forecast montly extreme rainfall in Indramayu District.
Keywords: extreme rainfall, generalized additive model, global circulation model, statistical downscaling

[1]. J.D. Prang, Sebaran Nilai Ekstrim Terampat Dalam Fenomena Curah Hujan, Bogor Agricultural University, Indonesia, 2006.
[2]. A. Busuioc, D. Chen, C. Hellstrom, Performance of statistical downscaling models in GCM validation and regional climate
change estimates (Application for Swedish Publiched date 09June 2014, precipitation), International Journal of Climate, 21,
2001, 557-578.
[3]. N. Beck, S. Jackman, Getting The Mean Right is a Good Thing: GAMs (San Diego: University of California, 1997)
[4]. S. Hidayat, Iklim Lokal (Indonesia: Mercubuana University, 2008).
[5]. M. Gilli M, E. Kellezi, An Application of Extreme Value Theory for Measuring Risk, Department of Econometrics, University of
Geneva, Switzerland, 2003.
[6]. U. Haryoko, Pendekatan Reduksi Dimensi Luaran GCM untuk Penyusunan Model SD, Bogor Agricultural University, Indonesia,
2004.

Abstract: We consider an extension to the lost sale recapture model in a newsvendor framework developed earlier by the authors. As in real practice, we have considered that there may be an opportunity to backlog the lost sales, by offering some incentive for waiting. The back log fill rate is modelled as a log function of adding one to the proportion of rebate relative to the price. The retailer's decision includes selling price, order quantity and the rebate that will maximize its expected profit. Sensitivities of the demand errors in the form of normal distribution rather than the uniform distribution serve as an extension to the previous work by the authors.

Keywords: newsvendor problem, lost sales, rebates, price dependent demand

[1]. Alford, B.L., Biswas, A. (2002). The effects of discount level, price consciousness and sale proneness on consumers' price
perception and behavioral intentions. Journal of Business Research 55, 775-783.
[2]. Arcelus, F.J, Ravi Gor, Srinivasan, G. (2012): Price, rebate and order quantity decisions in a newsvendor framework with rebate
dependent recapture of lost sales, International Journal of Production Economics, Vol. 140, No. 1. (November 2012), 473-482.
[3]. Arcelus, F.J., Srinivasan, G. (1987). Inventory policies under various optimizing criteria and variable markup rates. Management
Science 33, 756-762.
[4]. Arcelus, F. J., Kumar, S., Srinivasan, G. (2005). Retailer's response to alternate manufacturer's incentives under a single period,
price-dependent, stochastic-demand framework. Decision Sciences 36, 599-626.
[5]. Aydin, G., Porteus, E.L. (2009). Manufacturer-to-Retailer versus Manufacturer-to-Consumer Rebates in a Supply Chain. In N.
with the left-skewed (right-skewed) the next lowest (highest) and the symmetrical, Agrawal & S. Smith (Eds.), Retail Supply Chain
Management. New York: Kluwer.

Abstract: Splines, which were invented by Schoenberg, constitute a smooth curve between given data points. They are widely used in computer-aided designs, geometric modeling, graphics, and aerodynamic designs. This paper gives a new technique for efficient mathematical modeling of prestressing cable using B-spline curve. In prestressed concrete structures, cable profile plays an important role in reducing tension from concrete. So far, this cable was modeled, as of parabolic shape but the actual cable profile is a smooth curve. A new approach has been used in this paper for efficient modeling of cable using B-spline. This gives various other added advantages, which is not possible by any other curve. This is implemented in finite element analysis of 9-node Lagrangian element for concrete and cable model by 3-node bar element. Based on vector calculus formulation reaction of the cable on the concrete is obtained and applied on finite element nodes. Effects of friction and cable stiffness are taken into accounts. A finite element software has been developed incorporating these features. Various prestressed concrete beams of different spans have been successfully analysed and validated. It is observed, this formulation is very powerful in accurate analysis of the prestressed concrete structures.

[1]. Bangesh M.Y.H. "Concrete and concrete structures: Numerical modeling and Application", Elsevier, London (1989).
[2]. Gerald Farin, Curves and Surfaces for Computer Aided Geometric Design, Academic Press,(1988)
[3]. Jain M.K., S.R.K.Iyenger and R.K. Jain, " Numerical Methods Problem and solutions", New Age Publications, New Delhi, 166-168.
[4]. Qing S.B. and Liu Ding Yuan, Computational Geometry – Curve and Surface Modeling, Academic Press, London(1989)
[5]. Rogers D.F., and Adams J.A., Mathematical Elements for Computers Graphics, Second Edition, McGraw Hill, New York, (1990)
[6]. Zienkiewicz,O.C., and Taylor, R.L., The Finite Element Method Vol.1&2, Forth Edition,McGraw Hill Book Company, London, (1991)

Abstract: This paper demonstrates the application of Markov chain model with non-stationary transition probabilities to study data of the Reservoir elevation of Shiroro dam in the dry and raining seasons. The result indicates an optimal of 40% and 49% transition probabilities at equilibrium for dry season and wet season respectively. The result confirms the reality on the ground that higher reservoir elevation is obtained more during the raining season. Conversely, the lower reservoir elevation is experienced largely in the dry season. The variation of the reservoir elevation directly affects the hydro electric power generation and the availability of the other dam resources. Markov chain model could be used as a predictive device for studying reservoir elevation of Shiroro dam. These predictions might be used for the management of the dam resources.
Keywords: Markov chain, non-stationary, transition, probability, dam, reservoir, elevation.

[1]. Akyuz D.E, Bayazit M and Onoz B (2012): Markov chain models for hydrological drought characteristics, American Meteorological Society. (AMMS) journal, vol.13 (1),pp25-29.
[2]. Piantadosi, J. (2004), Optimal policies for storage of urban storm water, PHD Thesis, University of South Australia.
[3]. Sule B.F. (1988), Reservoir operation policy for optimizing energy generation at Shiroro dam, water reservoir management vol. 2(3), 125-132
[4]. Abubakar U.Y., Mohammed A., Lawal A. (2013). An Evaluation of a Reservoir Elevation with Markov Model in Continuous Time. Asian Journal of Fuzzy and Applied Mathematics. Vol.1(1), pp 21-27.
[5]. Ross S.M. (1989), Introduction to Probability Models. Academic Press, Inc.New York.

Abstract: Let M be a -near ring. An element aM is called a dependent element on a mapping f if
f(x)αa= ax for all xM, α. In this paper we study and investigate concerning dependent elements of M by certain mappings on prime and semi prime -near rings using certain assumption (A), and also we study the generalized -derivation F of -near ring M and -derivations D which are free action.
KeyWords: -near ring, generalized -derivation, reverse centralizer, dependent element, free action.

[1]. A.Laradji and A.B.Thaheem, On Dependent Elements in Semiprime Ring, Math.Japonica, 47 (1998), No.1, 576-584. F. J. Murray and von Neumann J., On Rings of Operators, , 37, 116-229, Ann. Math.,(1936).
[2]. M. S. Samman and Anwar M., Dependent Element of Left Centralizer of Semiprime Rings, 33, 313-319, The Arabian Journal for Science and Engineering (2008).
[3]. J.Vakman, On Dependent Elements and Related Problems In Ring, Internationsl Math. Journal, 8 (2005), No.2, 93-112.
[4]. J.Vakman, Free Actions of Semiprime Rings with Involution Induced by Aderivation, Demenstratio Mathematica, 38 (2006), No.4, 811-817.
[5]. J.Vakman and I.Kosi-UIbI, On Dependent Elements in Rings, International Mathematical Journal, 6 (2005), No.2, 93-112.

Abstract: In the present paper we have discuss finite element method for the partial differential equation governing one dimensional unsteady flow through unsaturated porous media. Finite element method is a numerical method for finding an approximate solution of differential equation in finite region or domain. In FEM, we generate difference equation by using approximate method such as Weighted residual method, Variational method with piecewise polynomial solution.
Keywords: Finite Element Method, Unsteady Flow, Unsaturated Porous Media, Variational Method

[1]. Scheidegger, A. E. Physics of flow through porous media, (Revised Ed.). Univ. Toronto P., 1974.
[2]. Greenskorn, R.A. Flow phenomena in porous media, Marcel Dekkar Inc., Newyork, 1983.
[3]. Anderson, Computational Fluid Dynamics.
[4]. Chung T.J., Computational Fluid Dynamics.
[5]. Jain M.K., Numerical solution of differential equations.2nd edition, Wiley Eastern, 1984.
[6]. Jain M.K., Iyengar S.R., Jain R.K., Computational Methods for Partial Differential Equations, Wiley Eastern.

Abstract: The aim of this paper is to apply Galerkin weighted residual method for solving eleventh-order BVPs. In this method, we exploit Bernstein and Legendre polynomials as basis functions which are modified into to a new set of basis functions to satisfy the corresponding homogeneous form of boundary conditions where the essential types of boundary conditions are mentioned. The method is formulated as a rigorous matrix form. Examples of both linear and nonlinear BVPs are presented to illustrate the reliability and efficiency of the proposed method. It is observed that the present method is a more effective tool and yields better results.
Keywords: Galerkin Method, Eleventh-order Linear and Nonlinear BVPs, Bernstein and Legendre Polynomials.

[1]. R.P. Agarwal, Boundary value problems for higher order differential equations (World Scientific, Singapore, 1986).
[2]. J.N. Reddy, Applied functional analysis and variational methods in engineering (Krieger Publishing Co. Malabar, Florida, 1991).
[3]. K.E. Atkinson, An Introduction to Numerical Analysis (John Wiley & Sons, NY, 2nd Edition, 1989).
[4]. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Clarendon Press, Oxford, 1961, Reprinted: Dover Books, New York, 1981).
[5]. S. S. Siddiqi and E. H. Twizell – Spline solutions of linear eighth-order boundary value problems, Comput. Methods Appl. Mech.
Engrg., 131, 1996, 309-325.

Abstract: A System in which employees leave the organization during busy period and new employees are recruited after the busy period is treated. After the busy period, recruitment starts. In Model-A busy period has general distribution and the inter departure time of employees has Erlang Phase two distribution and in Model-B General Departure time and Erlang operation time is also treated. Joint Laplace stieltjes Transforms of busy period and recruitment time and their means are obtained.
Key Words: Manpower system, Loss of Manpower and Recruitment, Joint transform, Erlang Phase two

[1]. J.Barthlomew,Statistical technique for manpower planning,John Wiley,chichester(1979)
[2]. D.R.C.Grinold and K.T.Marshall, Manpower Planning models.North Holl, New York (1977)
[3]. G.W.Lesson and Wastage and Promotion in desired manpower structures.J.Opl.Res.Soc,33(1982),433-442.
[4]. C.Mohan and R.Ramanarayanan,An Analysis of Manpower,Money and Business with Random Environments,International Journal of Applied Mathematics,Vol 23,No.5(2010) 927-940
[5]. K.Setlhare,Modeling of an intermittently busy manpower system,Botswans(2007)

Abstract: A new hybrid conjugate gradient method for unconstrained optimization by using homotopy formula we computed the parameter as aconvex combination of (Polak-Ribiere (PR))[9] and (Al-Bayat and Al-Assady (BA))[1].
Keywords: Unconstrained optimization , line search , conjugate gradient method . homotopy formula

[1]. A.Y. Al-Bayati, and N.H. Al-Assady, Conjugate Gradient Method,Technical Research report, No. 1,school of computer studies , Leeds Uuiversity .
[2]. N. Andrei, Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization , J.Optim. Theory Appl., 141, 2009, 249-264.
[3]. Y.H. Dai, and Y.Yuan, A nonlinear Conjugate Gradient Method With a Strong Global Convergence Property, SIAM J. Optimization, 10,1999, Pp. 177-182.
[4]. R. Fletcher, Practical Methods of Optimization,(Vol. 1: Unconstrined Optimization , John Wiley and Sons, New York, 1987).
[5]. R. Fletcher, and C. Reeves, Function Minimization by Conjugate Gradients, Comput. J.,7, 1964, Pp. 149-154.
[6]. M.R. Hestenes, and E.L.Stiefel, Methods of Conjugate Gradients for Solving Linear Systems, J.Research Nat. Bur. Standards, 1952,Pp. 409- 436,49 .

Abstract: In this article, it will be shown that the set of Real numbers is uncountable in four different ways. The first one uses the least upper bound property of the set of real numbers (sometimes called the completeness property of ), the second one uses the nested intervals property of , the third one uses Cantor's diagonal argument and the fourth one by proving that a non- empty perfect subset of is uncountable.
Keywords: Uncountable set, monotone sequences, bounded above, bounded below, perfect set , neighbourhood of a point, limit point of a set.

[1]. W. Rudin, Principles of Mathematical Analysis, Third Edition, 1976.
[2]. C.G. Denlinger, Elements of Real Analysis, First Indian Edition, 2011.
[3]. N.L.Carothers, RealAnalysis, First South Asian Edition, 2006
[4]. Bartle & Sherbert, Introduction to Real Analysis, Third Edition
[5]. G.F. Simmons, Introduction to Topology and Modern Analysis, Sixteenth reprint, 2011.
[6]. S.Kumaresan, Expository Articles, Notes and Exercise Sets.

Abstract: In this paper, we introduce the concept of (T , ξ; η)-invex function of second kind .Fur- ther,we establish the equivalence between the problems (GNV I P ) and (DGN V I P ) using (T , ξ; η)-invex function of second kind.
Key Words: and Phrases. Nonlinear variational ineqality problems, Invex set,η − invexset,η−preinvexf unction,(T , ξ; η)-invex function and η−hemicontinuous,η-monotone function.

[1] M. A. Hanson: "On Sufficiency of the Kuhn-Tucker Conditions," Journal of Mathe- matical Analysis and Applications, 80 (1981), 545 - 550.
[2] A. Ben-Israel, J. Mond: "What is Invexity ?," J. Australian Mathematical Society. Series B, 28 (1986), 1 - 9.
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Abstract: Membership function of a fuzzy set is the generalization of the characteristic function of a crisp set. Membership functions can be generalized using distributions or generalized functions. Distributed fuzzy sets are defined using distributions. In this paper we introduce the concept of Practical Distributed Fuzzy sets and extend the operations of usual fuzzy sets to practical distributed fuzzy sets
Keywords: distributed fuzzy sets, fuzzy sets, generalized function , membership functions, practical distributed fuzzy sets

[1] I.M. Gelfand , and G.E. Shilov, "Generalized functions ", Academic press,1964.
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Abstract: Deformation of a uniform half-space with rigid boundary caused by a long inclined strike-slip fault of finite width is studied analytically and numerically. Closed-form expressions for the displacement and stresses at any point in a homogeneous, isotropic, perfectly elastic half-space with rigid boundary caused by a long inclined strike-slip fault of finite width are derived. The variation of the displacement and stresses at the interface with the distance from the fault and depth from the fault is studied numerically. It is found that the displacement and stress field is heavily dependent on the dip-angle.
Keywords: Inclined strike-slip fault; Half-space; finite width.

[1]. Steketee, J.A, On Volterra's Dislocations in a Semi-infinite Elastic Medium, Can. J. Phys., vol. 36,1958a, 192-205.
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Abstract: Deterministic inventory model is developed for deteriorating products when the demand rate is considered as quadratic function of time, further incorporating two parameter Weibull rate of deterioration with inflation . The model is solved for when shortages are not allowed. A numerical example and sensitivity of the models is also studied at the end.
Key words: Weibull deterioration, Quadratic demand, salvage value, Inflation

[1] Buzacott J.A.,(1975) Economic Order Quantity with Inflation, Operations Research Society, Vol 26,553-558
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Abstract: Climate change is one of the environmental challenges currently facing Man, Plant and Animal existence globally. Awareness of its effect on some of the climatic factor is important; as this will tell the need for urgent abatement action, especially for developing countries who might be nonchalant given the level of their economic activities. This research therefore considered data on climatic factors collected from 18 States out of the 36 state; covering the six geopolitical zones of Nigeria. These factors were analyzed using Path analysis; with correlation coefficient as the path coefficients. The effect of climate change on these factors was measured by the path coefficients obtained from the correlation analysis. Path modeling shows the order in which these factors are affected. The regression result shows some effect of multicolinearity among the variables used. However the R2 value of 0.668 indicates that the variables used accounted for 66.8% approximately 67% of the total variability in the values of the response variable; that is accounted for by the fitted regression model. Therefore the model can be said to have a good fit, hence the variables were used for Path modeling.
Keywords: Climate change, Effects, Factors, Global warming, Path Analysis

[1] I.N Nwachukwu, C.I Ezeh and C.O Emerole, The effect of Climate Change on Cocoa Production in Nigeria. African Crop Science Journal, Vol. 20(2012) 487 - 491
[2] Global Warming and Climate Change Threats and Impacts http://www.nature.org/ourinitiatives/urgentissues/global-warming-climate-change/threats-impacts/ Acessed April 25, 2014
[3]. Consequences of climate change. http://ec.europa.eu/clima/policies/brief/consequences/index_en.htm Acessed April 25, 2014.
[4]. C. Lleras, Path Analysis. Encyclopedia of Social measurement vol 3 Assessed 23th April, 2014
[5] G. J. William, Standardizing and Relative Importance. Regression III: Advanced Methods http://polisci.msu.edu/jacoby/icpsr/regress3 Accesses 9th, May, 2014