iosr-Jm   Volume-11 ~ Issue-3 ~ May-June 2015

Abstract:The two-dimensional magnetohydrodynamic boundary layer flow of non-Newtonian power-law nanofluids past a porous stretching sheet with linear hydrodynamic slip boundary condition in the presence of chemical reaction and temperature dependent slip boundary condition. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, bvp4c MATLAB solver has been used for solving it. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and Concentration profiles for different values of the governing parameters, namely, the power-law index parameter, Lewis number, Prandtl number, thermophoresis parameter, Brownian motion parameter, magnetic field parameter, linear momentum slip parameter, permeability parameter, temperature dependent slip parameter and chemical reaction parameter.

Keywords: Non-Newtonian nanofluids, MHD flow, Hydrodynamic slip, linear group transformations, porous medium, temperature dependent slip flow, chemical reaction.

[1]. Choi, S., Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Siginer, H.P.
[2]. Masuda, H., Ebata, A,Teramae, K., Hishinuma, N., (1993), Alteration of thermal conductivity and viscosity of liquid by dispersing
ultra-fine particles, NetsuBussei (Japan), Vol.7, No.4, pp.227–233.
[3]. Pearson, J. R. A., Tardy, P. M. J, (2002), Models for flow of non-Newtonian and complex fluids through porous media, J Non
Newton Fluid Mech, Vol.102, pp.447–473.
[4]. Ellahi R, Afza, S, (2009), Effects of variable viscosity in a third grade fluid with porous medium: an analytic solution, Commun
Nonlinear Sci Numer Simul., Vol.14(5), pp.2056–2072.
[5]. Ellahi, R, (2009), Effects of the slip boundary condition on non- Newtonian flows in a channel, Commun Nonlinear Sci Numer
Simul., Vol.144, pp.1377–1384.
[6]. Rama Subba Reddy Gorla and Mahesh Kumari, (2012), Mixed Convection Flow of a Non-Newtonian Nanofluid Over a Non-
Linearly Stretching Sheet, Journal of Nanofluids, Vol. 1, pp. 186–195.

Abstract: This study was to ascertain if gas flaring mediate upon gas production and climate change. This became necessary owing to the problems of climate change that has become very visible owing to crude oil drilling production in Nigeria and the south-south region of the country in particular. These climate changes ranges from high rainfall variability, temperature change, degradation of forest and forest resources as well as the aquatic habitat. This climate change was also observed in high volume of rainfall and the resultant flooding in the Niger delta region of Nigeria. These occurrences have caused several loss of lives and properties, hence the need for this study to ascertain if gas flaring mediates upon gas production and climate change in Nigeria.

[1]. Global Gas Flaring Reduction Initiative: Report No.1: Report on Consultations with Stakeholders, World Bank Group in collaboration with the Government of Norway, (c.2002)
[2]. Onyenechere, E.C (2010) Climate Change and Spatial Planning Concerns in Nigeria: Remedial Measures for More Effective Response, J Hum Ecol, 32 (3): 137-148 (2010
[3]. Albert, J.M. (2008). Mediation analysis via potential outcomes models. Statistics in Medicine, 27, 1282-1304.
[4]. Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182
[5]. Bollen, K. A., & Stine, R. (1990). Direct and indirect effects: Classical and bootstrap estimates of variability. Sociological Methodology, 20, 115-140.

Abstract: The aim of the present paper is to find the design variables which influence the tyre profile design. The scope of the present work is to parameterize these design variables so that we can easily optimize tyre profile. The relation between derivative of an arc length and radius of curvature is derived to find arc length of tyre and radius of curvatures were compared.

Keywords: Derivative of arc length, radius of curvature, tyre

[1]. Differential Calculus by Shanti Narayan, S. Chand
[2]. Automobile Tyres by L.J.K. Setright, Chapman and Hall, 1972
[3]. www.wikipedia.org
[4]. www.google.com
[5]. www.apollotyres.com

Abstract:Observing the environment and recoganizing patterns for the purpose of decision making are fundamental to any scientific enquiry. Pattern recognition is a scientific discipline so much so that it enables perception in machines and also it has applications in diverse technology areas. Among the scientific community, statistical pattern recognition has received considerable attention in recent years. The statistical pattern recognition challenges are mostly approached by Hidden Markov Models (HMMs). A Hidden Markov Model (HMM) is a probabilistic mathematical discrete structure with the state emission probabilities apart from consisting the components of a probabilistic finite state automaton (PFA). Over the years, researches have been carried out to study the relations between HMM and PFA. Probabilistic finite state automata are mathematical models constructed to generate distributions over a set of strings.

[1]. Paz. (1971). Introduction to Probabilistic Automata, New York: Academic Press.
[2]. L. Rabiner, A tutorial on hidden markov models and selected applications in speech recognition, Proc. IEEE. vol. 77,
(1989) pp. 257-286.
[3]. P. Dupont, F. Denis, and Y. Esposito, Links between probabilistic automata and hidden markov models: probability distributions,
learning models and induction algorithms, Pattern Recognition, vol. 38, (2004) pp. 1349- 1371.
[4]. R. Durbin, S. R. Eddy, A. Krogh and G. Mitchison. (1998). Biological sequence analysis: probabilistic models of proteins and nucleic
acids, Cambridge, UK: Cambridge University Press.

Abstract: In this paper we prove a common fixed point theorem for four weakly compatible self-mappings in fuzzy metric space by using (JCLR) property. An example is given which shows the validity of main theorem. We also extend the result to two finite families of self-mappings with pairwise commuting.

Key Words: Fuzzy Metric Space, Weakly Compatible Mappings, E.A Property, (CLR) Property and (JCLR) Property.

[1] M. Aamri - D. El Moutawakil, "Some New Common Fixed Point Theorems under Strict Contractive Conditions", J. Math. Anal., Appl., 270 (1) (2002), pp. 181-188.
[2] M. Abbas - I. Altun - D. Gopal, "Common Fixed Point Theorems for Non Compatible Mappings in Fuzzy Metric Spaces", Bull. Math. Anal. Appl. 1(2) (2009), 47-56.
[3] Y.J. Cho, "Fixed Points in Fuzzy Metric Spaces", J. Fuzzy Math. 5 (4) (1997), 949-962.
[4] Y.J. Cho - Sedghi - N. Shobe, "Generalized Fixed Point Theorems for Compatible Mappings with Some Types in Fuzzy Metric Spaces", Chaos, Solitons and Fractals, Vol.39, no.5, pp. 2233-2244, 2009.
[5] B. Deshpande, "Fixed Point and (DS)-Weak Commutativity Condition in Intuitionistic Fuzzy Metric Spaces", Chaos, Solitons and Fractals, Vol. 42, no. 5, pp. 2722-2728, 2009.

Abstract: In this paper we introduce Pythagorean matrices having column entries as odd or even, primitive or non-primitive Pythagorean triplets. We have classified these matrices and have shown fundamental characteristics. The second unit introduces certain square matrices which act on such Pythagorean matrices as operators converting their status and order. In the next unit we have represented each column of a matrix of a given class to represent an algebraic polynomial. Using integration, along with boundary condition on Libra values interesting properties of primitive polynomials are derived. Graphs of given matrix polynomial and primitive polynomial show important relations.

Key Words: Pythagorean Triplets, Odd Primitives Triplet, Even Primitive Triplet, Non-Primitive Triplet, Operator Matrix, Shift Operator Matrix: PJ1, Primitive matrices and Classes.

[1]. Hazra, A.K., Matrix: Algebra, Calculus and Generalized Inverse, Viva Books Pvt. Ltd. First Indian Edition 2009.
[2]. Shah, S.H., Prajapati, D. P., Achesariya, V.A. & Dr. Jha, P.J., Classification of matrices on the Basis of Special Characteristics, International Journal of Mathematics Trends and Technology, vol.19, pp.27-37, March,2015.
[3]. Trivedi, R .A., Bhanotar, S.A. and Dr. Jha, P.J.,Pythagorean triplets- views, analysis, and classification, IOSR journal of Mathematics, vol.11 pp 54-63, March-April 2015.

Abstract: The objects of the present paper is to characterize generalized Sasakian-space-form satisfying certain curvature conditions on T curavature tensor . In this paper we study T semisymmetric, T flat, T flat and T recurrent generalized Sasakian-space-forms. Generalized Sasakian-space-form satisfying T:S = 0 and T:R = 0 have also been studied.

Keywords: T curvature tensor, Generalized Sasakian manifold, T semisymmetric, T flat and T -flat .

[1]. P.Alegre, E.D. Blair and A.Carriazo, : Generalized Sasakian-space-forms, Israel Journal of Mathematics, vol. 141, 2004, 157-183.
[2]. P. Alegre and A.Carriazo, : Structure on generalized Sasakian-space-form, Differential Ge-ometry and its Applications, vol. 26, no. 6, 2008, 656-666.
[3]. ON THE T CURVATURE TENSOR OF GENERALIZED SASAKIAN SPACE FORM 12
[4]. P.Alegre, A.Carriazo, Y.H.Kim and D.W.Yoon, : B.Y.Chen's inequality for submanifolds of generalized space forms, Indian journal of Pure and Applied Mathematics, vol.38, no.3, 2007 ,185-201.
[5]. R. Al-Ghefari, R. Al-Solamy and H. M. Shahid, : Contact CR-warped product submanifolds in generalized Sasakian space forms, Balkan Journal of Geometry and its applications, Vol. 11, no. 2, 2006 ,1-10.
[6]. D.E.Blair, : Contact Manifold in Riemannian Geometry, vol. 509 of Lecture Notes in Math-ematics, Springer, Berlin, Germany, 1976.

Abstract: Techniques that improve on existing assumptions of normality and largeness of sample size would be of paramount interest as non normality increases with increasing complexity in data gathering techniques. An option of transformation could be either to carry out a normal transformation so as to improve on the normality of the data in other for the pearson and associated t-test to be applicable or to linearize the distribution so as to strengthen the linear relationship that exist between the data, the simulation study carried out on various transformations and sample sizes showed that the square root transformation fared consistently better than the other transformations and the sample size of n=80 proved to be the sample size that optimizes the pearson test.

Keyword: Pearson T-Test, Transformation, Discrete Data, Bivariate Correlation.

[1]. Beversdorf, L. M and Sa, P. (2011) Tests for Correlation on Bivariate Non-Normal Data. Journal of Modern Applied Statistical Methods, Vol. 10, No. 2, 699-709
[2]. Bishara, A. J., & Hittner, J. B. (2012). Testing the Significance of a Correlation with Non-Normal Data: of Pearson, Spearman, Transformation, and Resampling Approaches. Psychological Methods, 17, 399-417. doi:10.1037/a0028087
[3]. Duncan, G. T., & Layard, M. W. J. (1973). A Monte-Carlo study of asymptotically robust
[4]. tests for correlation coefficients. Biometrika, 60, 551-558
[5]. Ebuh, G.U. and Oyeka, I.C.A. (2012 ) A Non Parametric Method for Estimating Partial
[6]. Correlation Coefficient. J. BiomBiostat 3(8)http://dx.doi.org/10.4172/2155-6180.1000156.

Abstract: Following Agrawal and Sthapit [1], we have developed systems of exponential ratio-based and exponential product-based estimators. The proposed exponential ratio-based estimator of order 𝑘 and the proposed exponential product-based estimator of order 𝑘 are, under practical conditions, found to be more efficient than the customary exponential ratio and the mean per unit estimator and the customary exponential product estimator and the mean per unit estimator, respectively, when 𝑘 is optimally chosen. Under the optimal value of 𝑘, the 𝑘𝑡ℎorder exponential ratio-based and exponential product-based estimators are found to be as efficient as the linear regression estimator. With a view to establishing the supremacy of the proposed estimators over the existing estimators, numerical illustrations in respect of real populations have been considered.

Keywords: Simple random sampling, exponential ratio estimator, exponential product estimator, predictive estimation

[1]. M.C. Agrawal and A.B. Sthapit: "Hierarchic predictive ratio-based and product-based estimators and their efficiency", Journal of Applied Statistics, Vol. 24, No. 1, 1997, 97-104.
[2]. M. N. Murthy. Product method of estimation, Sankhya, A26, 1964, pp.69 -74.
[3]. S. Bahl and R.K. Tuteja: Ratio and product type exponential estimator, Information and Optimization Science, 12, 1991, 159-163 D.Basu . An essay on the logical foundations of survey sampling. In: V. P. Godambe & D. A.Sprott (Eds), Foundations of Statistical Inference, 1971, pp. 203 -233 (Toronto, Holt, Rinehart and Winston).
[4]. T. M. F. Smith .The foundations of survey sampling: a review, Journal of the Royal Statistical Society, Series A , 139, 1976, pp. 183 -204.

Abstract: Agrawal and Jain [1] employed a predictive framework to examine the predictive character of ratio, ratio-type and regression estimators in two-phase sampling. In this paper, an efficient predictive estimator, which is the fountainhead of a family of widely used estimators in two-phase sampling, is proposed. The newly proposed estimator has been shown to excel its competing estimators provided a weighting factor is appropriately chosen. In the absence of knowledge of the optimum weighting factor, performance-sensitivity of the proposed estimator has been carried out.

Keywords: Efficient predictive estimator in two-phase sampling; performance-sensitivity; ratio, ratio-type and regression estimators in two-phase sampling;

[1]. M.C.Agrawal and N.Jain.Predictive estimation in doublesampling procedures.American Statistician.42.1988.184-186.
[2]. M.C.Agrawal and N. Jain. A new predictive product estimator.Biometrika.76. 1989. 822-823.
[3]. S.K. Rayand ASahai. Efficient families of ratio and ratio-type estimators.Biometrika.67. 1980.211-215.
[4]. P. V. Sukhatme,B .V.Sukhatme,S.Sukhatme and C.Asok.Sampling theory of surveys with applications. (ISAS, New Delhi, India and Iowa State University Press, Iowa, U.S.A. 1980)

Abstract: The main purpose of this paper is to show that zero symmetric prime left near-rings satisfying certain identities are commutative rings

[1]. ArgaÇ.N. "On Prime And Semiprime Near-Rings With Derivations. Int .J. & Math .J.Sci.Vol.20 , No. 4 (1997)737-740 .
[2]. Ashraf.M. , Bouab .A. and Raji .A " On derivations and commutativity in prime near-rings" Science Direct Journal of Taibah University for Science ,V.8 ,(2014) 301–306
[3]. Asraf.M. and Siddeeque.M.A , "On permuting n-derivations in near-rings , Commun. Kor. Math. Soc. 28 (4) (2013)697–707.
[4]. Ashraf.M. , Sideeque.M.A and Parveen.N " On semigroup ideals and n-derivations in near-rings " Science Direct Journal of Taibah University for Science,V. 9 (2015) 126–132.
[5]. Bell.H.E. , "On Derivations in Near-Rings II ", vol. 426, Kluwer Aca-demic Publishers, Dordrecht, 1997, pp. 191–197.

Abstract: This paper analyses Oyo State crime data which consists of eighteen major crimes reported to the police between the periods of 1996 – 2014. The crimes consist of robbery, kidnapping, house and store breakings, theft/stealing, grievous hurt and wounding, murder, rape, assault etc. There is an average of 56 cases of Murder, 152 cases of Armed Robbery, 12 cases of Suicide, 541 cases of Grivious Harms/Wounding, 1196 cases of Assaults, 392 cases of Burglary/Stealing, 263 cases of Store Breaking, 544 cases of House Breaking, 1385 cases of Stealing/Theft, 99 cases of Rape/Indecent Assaults, 12 cases of Kidnapping, 442 cases of False Pretence/Cheating, 110 cases of Unlawful Possession, 16 cases of Arson, 327 cases of Breach of Peace, 23 cases of Forgery, 8 cases of Child Stealing and 29 cases of Unnatural Offences.

[1]. Gulumbe et al (2008); Analysis of Crime Data using Principal Component Analysis.
[2]. Alexandra Vaughn; Columbia University QMSS 5999 Thesis Spring 2012; Crime rate and concern for time series analysis.
[3]. International Journal of Academic Research in Business and Social Sciences;The Influence of Sport and Recreation upon Crime Reduction: June 2012, Vol. 2, No. 6 ISSN: 2222-6990
[4]. Brian Bell and Stephen Machin; Centre for Economic Performance, LSE; The Impact of Migration on Crime and Victimization.
[5]. Aaron Chalfin University of Cincinnati, Justin McCrary UC Berkeley, NBER; Criminal Deterrence: A Review of the Literature.

Abstract: This study investigated the effect of MHD flow in shock formation in one dimensional gas flow. A conducting gas has been considered with the flow occurring in the presence of varying magnetic field intensity H. The shock zone has been assumed to be a thin legume that is stationary. An analysis of the velocity profiles, density profiles and temperature distribution that have been obtained has been done. In addition, an investigation on how the Prandtl number, Hartmann number and Eckert number affect the velocity profiles and temperature distribution has been carried out. Differential equations that have been generated from this study are non-linear. The equations have been solved by finite difference method using the MATLAB software and results presented graphically. It has been noted that an increase in Hartmann number causes an increase in velocity profiles while an increase in Prandtl number leads to an increase in temperature distribution and an increase in Eckert number leads to an increase in temperature distribution.

Keywords: Magnetohydrodynamics, compressible flow, shock wave, normal shock, oblique shock, weak shock, strong shock.

[1]. Ames, W.F., (1997). Numerical solutions of Partial Differential Equations, second edition, Academic Press, New York.
[2]. Anand,R.K., (2013). Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow. Astrophysics Space Science. 343:713-733
[3]. Anand, R.K., and Harish, C.Y. (2013). On the Structure of MHD shock Waves in a Viscous Gas, High Energy Astrophysical Phenomena, Vol.4
[4]. Anderson, J.E.,(1963). Magnetohydrodynamical Shock Waves. MIT Press, Cambridge, Massachusetts.
[5]. Alfven, H.A., (1942). Existence of Electromagnetic hydrodynamic waves, Nature; (150):405.
[6]. Angail, A.S., (2004). State space formation of MHD free convection flow with two relaxation times, Journal of Applied Mathematics and Computation, 2(152):299-321

Abstract: A long surface breaking vertical strike slip fault is consider situated in a viscoelastic half space of Maxwell type. Tectonic forces due to mantle convection and other associated phenomena are acting on the system. The magnitude of the tectonic forces has been assume to be slowly increasing with time. When the stresses near the fault exceeds the frictional force across the fault it starts creeping. Expressions for displacement, stresses and strain are obtained using suitable numerical techniques involving integral transform, Green's function techniques and Correspondence principle for both before and after the fault movement. It is expected that such expression will give us more information on the mechanism of stress accumulation in the system during the aseismic period.

Keywords: Aseismic period; Creeping movement; Mantle convection; Strike slip fault; Viscoelastic half space

[1]. A.C. Fowler. On the Thermal State of the Earth's Mantle, J. Geophysics. 53, 1983,42-51.
[2]. L. Moresi et. al., Mantle convection modelling with viscoelastic/ brittle lithosphere : Numerical methodology and plate tectonic modelling, Pure and Applied Geophysics, 159, 2002, 2335-2356.
[3]. V.P.Trubitsyn, E.V. Kharybin, Rheological models of mantle convection reproducing the fragmentation of lithosphere in plates, Physics of the solid earth, Vol. 46, No. 4, , 2010, pp 275-280.
[4]. F. Fanucci et. al., A numerical study for convection in a cylindrical model with continuously varying viscosity, Annali Di Geofisica, Vol. xxxix, N. 3 May 1996.
[5]. T. Maruyama, On two dimensional dislocation in an infinite and semi-infinite medium, Bull. earthquake res. inst., tokyo univ., 44, part 3, 1966, pp. 811-871.
[6]. K. Rybicki, Static deformation of a multilayered half-space by a very long strike-slip fault, Pure and Applied Geophysics, 110, 1973, p-1955-1966..

Abstract: The main purpose of this paper is to show that zero symmetric prime left near-rings satisfying certain identities are commutative rings . As a consequence of the results obtained ,we prove several commutativity theorems about generalized n-derivatios for prime near-rings.

[1]. Ashraf,M., Ali,A. and Rani,R. ,On generalized derivations of prime rings, South east Asian Bull .Math. ,29 (2005) , 669−675.
[2]. Ashraf , M. and Siddeeque , M . A., On permuting n-derivations in near-rings, Commun.Korean.Math.Soc.,28(2013),No.4,pp.697–707.
[3]. Asraf.M. and Siddeeque.M.A , "On generalized n-derivations in near-rings , Palestine journal of mathematics ,V.3 (2014) 468 - 480.
[4]. Ashraf.M. , Sideeque.M.A and Parveen.N " On semigroup ideals and n-derivations in near-rings " Science Direct Journal of Taibah University for Science ,V. 9 (2015) 126 –132.