iosr-Jm   Volume-11 ~ Issue-4 ~ July-Aug 2015

Abstract: Motivated by some results on Semiprime Gamma Rings with Orthogonal Reverse Derivations, in [4], the authors defined the notion ofReverseDerivations on Gamma Ringsand investigated some results on the Reverse Derivations in Gamma Rings. In this paper, we also introduce the notion of Orthogonal Reverse Derivations of SemiprimeSemirings and derived some interesting results.

[1]. Bresar.M and Vukman.J, Orthogonal derivation and extension of a theorem of Posner, RadoviMatematicki 5(1989), 237-246.
[2]. Chandramouleeswaran, Revathy, Orthogonal Derivations on Semirings, M.Phil.
[3]. Dissertation submitted to Madurai Kamaraj University (2012), 20-47 [4] Jonathan S.Golan,Semirings and their Applications, Kluwer Academic Press(1969).
[4]. KazimierzGlazek, A Guide to the literature on Semirings and their applications inMathematics.

Abstract: Shewhart S-control chart is one of the widely used charts to control process dispersion. Presence of outliers may extremely affect this control charting procedure. More- over, if the quality characteristic is not following normality assumption, one has to look for a robust control chart. A robust control chart is a better choice to overcome it. This article presented a Shewhart type robust dispersion control chart based on Modified Maximum Likelihood Estimator (MMLE) which is robust to the presence of outliers as well as the change in assumptions on distribution.

[1]. H. Shahriari1, A. Maddahi, and A. H. Shokouhi, A Robust Dispersion Control Chart Based on M-estimate, Journal of Industrial and Systems Engineering, 2(4), 2009, 297-307.
[2]. M.A. Mahmoud, G.R. Henderson, E. K. Epprecht and W. H. Woodall, Estimating the standard deviation in Quality Control Applications, Journal of Quality Technology, 42(4), 2010, 348-357.
[3]. Zhang Guoyi, Improved R and s control charts formonitoring the process variance, Journal of Applied Statistics, 41(6), 2014, 1260–1273.
[4]. P. Langenberg, and B. Iglewicz, Trimmed Mean X bar and R chart, Journal of Quality Technology, 18, 1986, 152-161.
[5]. D.M. Rocke, Robust Control charts, Technometrics, 31(2), 1989, 173-184.

Abstract: In this paper, we have discussed imbibition phenomenon in double phase flow through porous media. Numerical solution of non linear partial differential equation governing the phenomenon of imbibition in a homogeneous medium with magnetic fluid has been obtained by finite element method. Finite element method is a numerical method for finding an approximation solution of differential equation in finite region or domain. A Matlab code is developed to solve the problems and the numerical results are obtained at various time levels.
Keywords: Porous media, fluid flow, magnetic fluid, finite element method.

[1]. Scheidegger, A. E. Physics of flow through porous media, (Revised Ed.). Univ., Toronto Press.,1974.
[2]. Jain M.K., Numerical solution of differential equations.2nd edition, Wiley Eastern, 1984.
[3]. Reddy J.N., An introduction to the finite element method, 3rd edition, McGraw-Hill, Inc., Newyork, 2006.
[4]. Brownscombe, E.R. and Dyes, A.B., Amer. Petrol Inst. Drill. Prod. Pract. , P. 383
[5]. Enright, R.J., Oil gas J, 53,954,104.
[6]. Graham, J.W. and Richardson, J.G., J. Petrol. Tech., 11,65.
[7]. Rijik, V.M., Izv. Akad. Nauk. SSSR, Utd. Tech. Nauk Mekhan Mashinostor, 2.

Abstract: Let 𝑀 be a 2-torsion free prime 𝛤-ring. Then we prove that every Jordanhigher left (𝜎,𝜏)- centralizer on 𝑀 is higher left (𝜎,𝜏)- centralizer on M. We also prove that with certain conditions every Jordan higher left (𝜎,𝜏)- centralizer on 𝑀 is a Jordan triple higherleft(𝜎,𝜏)- centralizer of 𝑀.

Keywords: prime 𝛤–ring, higher left (𝜎,𝜏)- centralizer, Jordan higher left (𝜎,𝜏)- centralizer.

1]. B.Zalar" On Centralizers of Semiprime Ring", Comment. Math.Univ. Carolinae,Vol. 32 ,(1991), 609-614.
[2]. K.KDey. and A.C.Paul,"commutativity of prime gamma rings with left centralizers " , J. Sci.Res. ,Vol.6 ,No.1,(2014) , 69-77 ,
[3]. M.F.Hoque and A.C.Paul, "On Centralizers of Semiprime Gamma Rings", International Mathematical Forum,Vol . 6No.13 ,(2011), 627- 638
[4]. M.F.Hoque ,F. S. Alshammariand A.C.Paul, "On Centralizers of Semiprime Gamma Rings withInvolution" , Applied Mathematical Sciences, Vol.8 No.95,(2014), 4713- 4722 .
[5]. N.Nobusawa," On a Generalization of the Ring Theory", Osaka J. Math., (1964), 81-89.

Abstract: This paper attempts to study the effect of home environment on the academic achievement in Mathematics of 10th standard students. This study was conducted for a sample of 1007 students belongs to two districts of Taminadu, to identify the influence of home environment that can affect students achievement. The researcher have tabulated certain data obtained from the test conducted, and suitable analysis were carried out on the same using descriptive and inferential statistics. This study reveals a positive correlation between the home environment and academic achievement of the students towards mathematics.

Keywords: Home Environment, Academic Achievement, Mathematics.

[1]. Adesehinwa, O. A. (2013). Effects of family type (monogamy or polygamy) on students' academic achievement in Nigeria. Intl J. of
Psychology and Counselling, 5 (7), 153 – 156 DOI 10.5897/IJPC10.012 ISBN 2141 - 2499
[2]. Babara, K.T. (1982). Home environment and learning quantitative synthesis. Journal of Experimental Education, 50(3): 120 128.
[3]. Adesehinwa O. A. and Aremu, A. O. (2010). The relationship among predictors of child, family, school, society and the government and academic achievement of senior secondary school students in Ibadan, Nigeria. Procedia Soc. Behav. Sci. 5, 842 – 849.
[4]. Akinsanya, O. O., Ajayi, K. O. and Salomi, M. O. (2011). Relative effects of parentaloccupation, qualification and academic motivation of wards on students achievement in senior secondary school mathematics in Ogun State. British J. of Arts and Soc. Sc., 3(2), 242 – 252. ISBN: 2046 - 9578
[5]. Diaz, A. L. (2004). Personal, family, and academic factors affecting low achievement in secondary school. Electronic J. of Res. in Ed. Psychology and Psychopedagogy, 1 (1), 43 – 66. ISBN 1696-2095

Abstract: In this paper a new parallel Hybrid algorithm is introduced which is based on the Bisection algorithm and Newton-Raphson algorithm. The proposed Hybrid algorithms helps in finding real roots of single non-linear equations in less number of iterative operations and reduce the time of solving. These methods have been applied in parallel environment. A description of the algorithms details and comparison between them is included in this work.

Keyword: Parallel Numerical Algorithm, bisection Method, Newton-Raphson Method, HybridAlgorithm, Parallel Hybrid Algorithm, parallel finding roots.

[1]. A.J.Maeder and S.A.Wynton, Some Parallel for Polynomial Root-Finding, Journal of Computation and Applied Mathematics 18, 71-81, North Holland, 1987.
[2]. IoananChiorean, Parallel Numerical Methods for Solving Nonlinear Equations, StudiaUniy. "BABES-BOLYAI", Mathematica, Vol.XLVI, NO.4, 53-59, Dec. 2001.
[3]. Khalid A. Hussein, Abed Ali H. Altaee and Haider K. Hoomod,A new Approach to Find Roots of Nonlinear Equations by Hybrid Algorithm to Bisection and newton-Raphson Algorithms, Iraqi journal for Information Technology , Vol.7th No.1, 2015.
[4]. Guy E. Blellochand Bruce M. Maggs , Parallel Algorithms , Carnegie Mellon University, ACM Computing Surveys (CSUR),1996.
[5]. Guy E. Blellochand Bruce M. Maggs , Parallel Algorithms , Carnegie Mellon University, ACM Computing Surveys, CRC Press, Vol.28 ,No.1 , 1996.

Abstract: In this paper, we considered a generalized class of Szegő polynomials arising from Gauss hypergeometric function using the approach of three term recurrence relation. Formulas for moments and weight function are given explicitly. [2000] Orthogonal polynomials; Hypergeometric Functions; Recurrence relation

[1]. Andrews G. E., Askey R. and Roy R., 1999, Special functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge
Univ. Press, Cambridge.
[2]. Erdélyi T., Nevai P., Zhang J., 1991, A simple proof of "Favard's theorem" on the unit circle, Atti Sem. Mat. Fis. Univ. Modena 39,
no. 2, 551–556.
[3]. Geronimus L. Ya., 1961, Orthogonal polynomials: Estimates, asymptotic formulas, and series of polynomials orthogonal on the unit
circle and on an interval, Authorized translation from the Russian Consultants Bureau, New York.
[4]. Hendriksen E. and van Rossum H., 1986, Orthogonal Laurent polynomials, Nederl. Akad. Wetensch. Indag. Math. 48, no. 1, 17–36.
[5]. Jones W. B. and Njåstad O., 1991, Applications of Szegő polynomials to digital signal processing, Rocky Mountain J. Math. 21,
no. 1, 387–436.

Abstract: We have obtained Ruban's cosmological model with wet dark fluid in general theory of relativity. For solving the Einstein field equations the relation between metric coefficients is used. Also, some physical and Kinematical properties of the model are discussed.
Key words: Ruban's space time, Wet dark fluid..

[1]. Tait, P. G. : The Voyage of HMS Challenger ( H. M. S. O., London,) ( 1988).
[2]. Hayward, A. T. J., Brit. J. Appl. Phys. 18, 965, (1967).
[3]. Holman, R. and Naidu, S., ar Xiv: Astro-phy/0408102 (preprint) (2005).
[4]. Singh, T. and Chaubey, R. : Pramana Journal of Physics, Vol. 71,No. 3 (2008).
[5]. Adhav et al :Adv.studies Theor.Phys.Vol.4,No.19,917-922(2010).
[6]. Adhav et al.:Int.J.TheoryPhys,50,164(2011a).
[7]. Adhav,K.S.,Nimkar,A.S.,Ugale,M.R.,Pund,A.M.:JVR 6,1,23-28(2011b).

Abstract: In this paper we aimed at defining a concatenation of rotations of the Rubik's cube and one finite group of scrambling of facets. Through observations of Rubik's Cube and group theoretic arguments we describe the positioning and the orientation of the edge and the corner cubies. Since the cube has 54 facets, it has a subgroup of 𝑆54 3 . We have seen that the permutation of the corner cubies must have the same sign as the permutation of the edge cubies. We have also seen that we cannot change the orientation of a single cubie without changing the orientation of another cubie of the same kind.

Keywords: Homomorphism, permutation, orientation, position, edge, corner.

[1]. C. Whitehead, Guide to Abtract Algebra, (second edition), Palgrave Macmillan, 2003.
[2]. I. N. Henstein, Topics in Algebra, Wiley & Sons, New York, 1975
[3]. O. Bergvall, et al, Note on Rubik's Cube, 2010.
[4]. P. Masawe, et al, Note on Rubik's Cube, 2010.
[5]. W. D. Joyner, Mathematics of the Rubik's cube. internet www page
[6]. http //www.nadn.navy.mil/MathDept/wdj/rubik.html, 1996.

Abstract: The aim of this paper is to introduce and investigate Generalized Double Star Closed set in Interior Minimal spaces. Several properties of these new notions are investigated.

Keywords: M-g** Separationspace, Maximal M-g**closed, Maximal M-g**open, Minimal M-g**closed, Minimal M-g** open

[1]. F. Nakaoka and N. Oda, On Minimal Closed Sets, Proceeding of Topological spaces Theory and its Applications, 5(2003), 19-21.
[2]. F. Nakaoka and N. Oda, Some Properties of Maximal Open Sets, Int. J. Math. Sci. 21,(2003)1331-1340.
[3]. A. Vadivel and K. Vairamanickam, Minimal rgα-open Sets and Maximal rgα-closed Sets, Submitted to Journal of Tripura Mathematical Society
[4]. S. Balasubramanian, C. Sandhya and P. A. S. Vyjayanthi, On v-closed sets (In press) ActaCienciaIndica.

Abstract: This paper deals with the boundary and initial value problems for the fractional dispersion equation model by using the modified variational iteration method. The fractional derivative is described in Caputo's sense. Tested for some examples and the obtained results demonstrate efficiency of the proposed method. The results were presented in tables and figure using the MathCAD 12 and Matlab software package.
Key words: Modified variational iteration method, Fractional dispersion equation, Lagrange multiplier

[1]. Podlubny I.," Fractional Differential Equations", San Diego: Academic Press, 1999.
[2]. Miller KS, Ross B. ''An Introduction to the Fractional Calculus and Fractional Differential Equations'', NewYork: Wiley, 1993.
[3]. Shimizu N, Zhang W. ''Fractional calculus approach to dynamic problems of viscoelastic materials'', JSMESeries C–Mechanical Systems, Machine Elements and Manufacturing,42:825-837, 1999.
[4]. Iman. I. Gorial," Modified Variational Iteration Method of Solution the Fractional Partial Differential Equation Model", IOSR Journal of Mathematics (IOSR-JM), Volume 11, Issue 2 Ver. IV (Mar - Apr. 2015), PP 84-87.
[5]. J. H. He, "Variational iteration method for delay diferential equations," Communications in Nonlinear Science and Numerical Simulation, vol. 2, no. 4, pp. 235–236, 1997.

Abstract: Mathematical models for the spread of HIV infection have made a considerable contribution on the understanding of HIV/AIDS dynamics. In this paper, an HIV/AIDS epidemic model in a heterosexual population is analyzed through modification of Susceptible-Infective-Removed (SIR) model by incorporating time lags (delay) for one to become infective and the other to become fully blown in a given population.By application of the next generation matrix, the reproduction number R0 is determined.

[[1]. Abbas A.K., Lichman A.H.,Pober J.S, (1994). In: Cellular and Molecular Immunology 2nd (Ed) Philadelphia, W.B Sounders, pp. 419-442 and 425-426.
[2]. Anderson, R., May, R., (1991). Infectious diseases of humans. Oxford Univesity Press, London/New York.
[3]. Bangham, C.R.,(2000). The immune response for HTLV-1.Curr Opin. IMmunol.,12,397-402.
[4]. Bellman, R., Cooke K. L.,(1963). Differential-Difference Equations. Academic Press, New York.
[5]. Boese, F. G. (1989).Stability conditions for the general linear difference-differential equation with constant coefficients and one constant delay. Journal of mathematical analysis and applications 140, 136-176.
[6]. CDC Global Health, (2013).Kenya Demographic Profile. CIA World fact book, website: http://countryoffice.unfpa.org/kenya/drive/FINALPSAREPORT.pdf.

Abstract: A model for HIV transmission with treatment is formulated for a heterosexual population of varying size. The dynamics of the spread of HIV is completely determined by the Basic Reproduction Number (BRR) 0 R .The model exhibits two equilibria, viz. a disease-free equilibrium and the endemic equilibrium. The diseasefree equilibrium is globally stable if 0 R ≤ 1 and the endemic equilibrium is locally stable when 0 R > 1. Numerical analysis of the model is presented to determine the role of some key epidemiological parameters of the model.
Keywords: HIV/AIDS, Epidemic model, Treatment, Basic Reproduction Number, Stability

[1]. World Health Organization Report on HIV/AIDS (November 2014) (available at http://www.who.int/mediacentre/factsheets/fs360/en/).
[2]. May R. M. and Anderson R. M., Transmission dynamics of HIV infection, Nature, 326, 137-142(1987).
[3]. Anderson R. M. and May R. M., Epidemiological parameters of HIV transmission, Nature, 333, 514-519 (1988).
[4]. Isham V., Mathematical modeling of the transmission dynamics of HIV infections and AIDS: a review, J. Roy. Stat. Soc. (Ser. A) 151, 5-30 (1988).
[5]. Dietz K. and Hadeler K. P., Epidemiological models for sexually transmitted diseases, J. Math. Biol., 26, 1-25 (1988).