iosr-Jm   Volume-10 ~ Issue-2 ~ Mar-Apr 2014

Abstract: The present work contains an analytical method derived using Ghosh's Hypersonic similitude to predict the aerodynamic stability derivatives of a Planar Wedge in the Newtonian limit. It uses the strip theory developed by Ghosh's where span wise strips are independent of each other, to obtain the expressions for stiffness and damping derivatives in pitch for a planar wedge in the Newtonian limit. The present theory predicts the stability derivatives of a planar wedge for a wide range of geometrical and flow parameters. The knowledge of these stability derivatives is essential to freeze and arrive at the geometrical as well as the kinematic similarity parameters before we go for exhaustive computations and experimental studies. The present method predicts the stability derivatives in pitch for a planar wedge with remarkable computational ease, which is very handy at the design stage. The expressions derived for stability derivatives become exact in the Newtonian limit. It is found that stiffness derivative linearly varies with the pivot position. It is also observed that the centre of pressure moves towards the trailing edge and this shift is quite high at high angles of attack. Hence, this behavior could be utilized to stabilize the aerospace vehicle from the static stability point of view. In the case of damping derivative since the expression for the damping derivative is non-linear and the same has been reflected in the results. However, the behavior remains linear till angle of attack fifteen degrees, later the trend is non-linear.
Keywords: angle of incidence, Newtonian Limit, Strip theory, Planar wedge, pivot position.

[1] Carrier G. F., The Oscillating Wedge in a Supersonic Stream, Journal of the Aeronautical Sciences, Vol.16, March 1949, pp.150-152.
[2] Hui W. H., Stability of Oscillating Wedges and Caret Wings in Hypersonic and Supersonic Flows, AIAA Journal, Vol.7, August 1969, pp. 1524-1530.
[3] Hui. W. H., Supersonic/Hypersonic Flow past an Oscillating Flat plate at Large angles of attack, Journal of Applied Mathematics and Physics, Vol. 29, 1978, pp. 414-427.
[4] Liu D. D and Hui W. H., Oscillating Delta Wings with attached Shock waves, AIAA Journal, Vol. 15, June 1977, pp. 804-812.
[5] Hui W. H. et al, Oscillating Supersonic/Hypersonic wings at High Incidence, AIAA Journal, Vol. 20, No.3, March1982, pp. 299-304.

Abstract: Steady laminar natural convection of MHD flow over a semi-infinite moving vertical plate in the presence of internal heat generation and a convective surface boundary condition in a porous medium is examined in this paper. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface of the plate contains a heat source that decays exponentially with the classical similarity variable. The governing non-linear partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically by using the shooting techniques with the forth order Runga-Kutta method. The effects of physical parameters on the dimensionless velocity and temperature profiles are depicted graphically and analyzed in detail. Finally, numerical values of physical quantities, such as the local skin-friction coefficient and the local Nusselt number are presented in tabular form. It is observed that the velocity and thermal boundary layer thicknesses decrease with an increase in the intensity of radiation parameter.
Key words: moving vertical plate, internal heat generation, radiation, local Biot number, MHD, Porous medium.

[1] Abd-El-Naby M.A., Elasayed M.E., Elbarbary, Nader Y. and Abdelzem .(2003), Finite difference solution of radiation effects on MHD free convection flow over a mvertical plate with variable surface temperature, J.Appl .Math., Vol.2, pp. 65-86.
[2] Anwar Beg, O,Ghosh, S.K and Narahari, M.,(2011), Mathematical modeling on oscillatory MHD couette flow in a rotating highly permeable medium permeated by an oblique magnetic field, chemical engineering communications, Vol.198, pp.235-254.
[3] Anwar Hossain.M, Khalil Khanafer, Kambiz Vafai (2001), "The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate", International Journal of Thermal Science, vol.40, 2001,pp. 115-124.
[4] Aziz A. (2009), A Similarity Solution forLaminar Thermal Boundary Layer over a Flat Plate with a Convective Surface Boundary Condition, Communicatons in Nonlinear Science and Numerical Simulations, 14 (2009), 4, pp. 1064-1068.
[5] Baker L., Faw, R. E., Kalacki, F. A. (1976),Postaccident Heat Removal – Part I: Heat Transfer within an Internally Heated, Nonboiling Liquid Layer, Nuclear Science and Engineering, 61 (1976), 2, pp. 222-230.

Paper Type	:	Research Paper
Title	:	Existence of Steady State Solutions with Finite Energy for the Magneto hydro dynamic Equations in the Whole Space
Country	:	India
Authors	:	P. D. Raiter, R. V. Saraykar
	:	10.9790/5728-10231632

Abstract: We study the steady state Magnetohydrodynamic (MHD) equations in the whole space Following the work of C. Bjorland and M. Schonbek [4] on Navier -Stokes equations in the whole space, we prove the existence of at least one solution with finite Dirichlet Integral to steady state Magnetohydrodynamic equations in the whole space. Further, we show that these solutions are unique among all solutions with finite energy and finite Dirichlet Integral.

[1] G. Duvaut and J.L. Lions, Arch. Rat. Mech. Anal., 46 (1972), 241-279.
[2] E. Sanchez Palencia, Journal de Mechanique, 8(4) (1969), 509-541.
[3] M. Sermange and R. Temam, Commu. Pure Appl. Math., XXXVI (1983), 635-664.
[4] C. Bjorland and M. Schonbek, Nonlinearity, Vol. 22, (2009) 1615-1637.
[5] Yong Zhou, Ann. Inst. Henri Poincaré – AN 24 (2007) 491–505.

Paper Type	:	Research Paper
Title	:	An Application Of Queuing Theory To The TV Show Kaun Banega Crorepati ( KBC )
Country	:	India
Authors	:	Bhavin Patel, Pravin Bhathawala
	:	10.9790/5728-10233335

Abstract: The present paper explains the application of queuing theory to one episode of the TV show Kaun Banega Crorepati during a week. By analysis of one episode, we can understand the general scenario of the KBC. In one episode of this show, contestants or participants wait for their turn to go on the hot seat. At one time only one contestant can seat on the hot seat and other contestants are waiting in a queue. So, we can apply queuing theory to the TV show Kaun Banega Crorepati. We also seek to find the probability of one contestant to be selected for the hot seat and the expectation of contestants on each day of a week.
Keywords: Queue; Queuing Theory; Kaun Banega Crorepati (KBC); Hot seat.

[1]. J.D.C. Little, "A Proof for the Queuing Formula: ", Operations Research, vol. 9(3), 1961, pp. 383-387, doi:10.2307/167570.
[2]. Cooper RB (1972). Introduction to Queuing Theory. McMillan: New York.
[3]. Tijms HC (1986). Stochastic Modelling and Analysis. A Computational Approach. Wiley: Chichester.
[4]. K. Rust, "Using Little's Law to Estimate Cycle Time and Cost", Proceedings of the 2008 Winter Simulation Conference, IEEE Press, Dec. 2008, doi:10.1109/WSC.2008.4736323.
[5]. Worthington D and Wall A (1999). Using the discrete time modelling approach to evaluate the time-dependent behaviour of queuing systems. J Opl Res Soc50: 777-888.

Paper Type	:	Research Paper
Title	:	Some Properties of Fuzzy Soft Groups
Country	:	India
Authors	:	Dr. N. Sarala, B. Suganya
	:	10.9790/5728-10233640

Abstract: In this paper, the concept of fuzzy soft group is extended and some of their properties and structured characteristics are discussed and studied. Some important results are proved. Some important results are proved.
Keywords: Soft set, Fuzzy Soft Set, Soft Group, Fuzzy Soft Group, Fuzzy Subgroup, Soft Homomorphism.

[1] AbdülkadirAygüno_glu, HalisAygün,Introduction to fuzzy soft groups,computers and Mathematics with Applications 58,(2009) 1279_1286
[2] B.Ahmad and AtharKharal, "On Fuzzy Soft Sets", Advances in Fuzzy Systems,2009.
[3] Aktas. H and N. Cagman, Soft sets and soft group, Information Science 177 (2007), PP 2726-2735.
[4] G.J. Klir and B. Yuan, Fuzzy sets and fuzzy logic theory and applications, PretticeHelltic, New Jersey (1995).
[5] P.K.Maji, R.Biswas and A.R.Roy, "Fuzzy Soft Sets", Journal of Fuzzy Mathematics,9(3) , 2001, 589-602.

Paper Type	:	Research Paper
Title	:	Flow and Heat Transfer Analysis of a Nanofluid along a Vertical Flat Plate in Presence of Thermal Radiation Using Similarity Transformation Method
Country	:	India
Authors	:	Dr. K. Hemalatha, A. Krishna keerthi, Dr. G. Sambasiva Rao
	:	10.9790/5728-10233640

Abstract: In the present work effects of viscous dissipation and thermal radiationon convective heat transfer in nanofluid flow over a stretching sheet under the influence of applied magnetic field was analyzed. Three types of nanofluids, namely Cu-water, Al2O3-water and TiO2-water were considered. A similarity transformation was used to obtain a system of non-linear ordinary differential equation which was then solved numerically using MATLAB "bvp4c" function. Numerical results were obtained for Local Nusselt number as well as velocity and temperature profiles for selected values of parameters such as nanoparticle volume fraction Φ, Eckert number EC, Magnetic parameter M and thermal radiation parameter NR for fixed value of Prandtl number Pr=6.2(corresponding to water).It was shown that the Cu-water nanofluid exhibits higher heat transfer rate as compared to Al2O3-water and TiO2-water.
Keywords: Nanofluid flow, Heat transfer, Stretching sheet, Similarity Transformation,Thermal Radiation Parameter.

[1]. Stephen.U.S.Choi and J.A,Eastman.Enhancing thermal conductivity of fluids with NanoparticlesArgonne,#W-31-109-ENG-38(1995).
[2]. Ali.J.Chamka,Hydro magnetic three-dimensional free convection on a vertical stretching Surfacewith heat generation or absorption, 20,84-92(1999).
[3]. Khalilkhanfer,Kambizvafai,Marilyn light stone,Buoyancy-driven two-dimensional heat Transfer enhancement in a two-dimensional enclosure utilizing nanofluids,International Journal of heat and mass transfer 46, 3639-3653(2003).
[4]. Ahmed M Salem, Mohamed Abd EI-Aziz,Effect of hall currents and chemical reaction on Hydromagnetic flow of a stretching vertical surface with internal heat generation/ Absorption, 32, 1236-1254(2008).
[5]. HakanF. Oztop, Eiyad Abu-Nada.,2008,Numerical study of natural convection in partially Heated rectangular enclosures filled with nanofluids. International journal of heat and fluid Flow, 29, 1326-1336(2008).

Paper Type	:	Research Paper
Title	:	Modified Centroid Selection Method of K-Means Clustering
Country	:	Indonesia
Authors	:	Rose Mawati, I. Made Sumertajaya, Farit Mochamad Afendi
	:	10.9790/5728-10234953

Abstract: Clustering is a process of classifying object into groups which have similarity. The result of cluster-ing will show that objects in one cluster will be more homogeneous than others. There are two methods in clas-sic clustering analysis i.e. hierarchical cluster method and non-hierarchical cluster method. Determination of the member of clusters which formed by them is done subjectively. K-means is one of the algorithms that solve the well known clustering problem. The algorithm classifies object to a predefined number of clusters, which is given by the user. The idea is to choose random cluster centers, one for each other. The centroid initialization plays an important role in determining the cluster assignment in effective ways. This paper presents results of the simulated data of different datasets using original k-means and other modified algorithms implemented us-ing MATLAB R2010a. This results are calculated on some performance measures such as no. iterations, and accuracy.
Keywords: Clustering; K-Means; Centroid Selection.

[1] K. A. Abdul Nazeer and M. P. Sebastian, "Improving the Accuracy and Efficiency of the k-means Clustering Algoritm," Proceed-ings of the World Congress on Engineering 2009, Vol. I, WCE 2009.
[2] M. P. S. Bhatia and D. Khurana, "Experimental study of Data clustering using k-Means and modified algorithms," International Journal of Data Mining and Knowledge Management Process (IJDKP). Vol. 3. No. 3. 2013.
[3] M. R. Anderberg. "Cluster Analysis for Application," Academic Press. New York, 1973.
[4] S. Sujatha and A. S. Sona, "New Fast K-Means Clustering Algorithm using Modified Centroid Selection Method," International Journal of Engineering Reseach and Technology (IJERT), Vol. 2, Issue. 2, 2013. ISSN: 2278-0181.
[5] R. A. Johnson and D. W. Wichern, "Applied Multivariate Statistical Analysis," 6th Edition, Pearson Education.,New Jersey, 2007.

Paper Type	:	Research Paper
Title	:	Convergence Analysis of shifted Fourth kind Chebyshev Wavelets
Country	:	Iraq
Authors	:	Suha N. Shihab, Mohammed Abdulhadi Sarhan
	:	10.9790/5728-10235458

Abstract: The aim of this paper is to state and prove the uniform convergence theorem and accuracy estimation for shifted fourth kind Chebyshev wavelets.
Keywords: fourth kind Chebyshev polynomials, Chebyshev wavelets, uniform convergence.

[1] Yamg C. and Hou J., Chebyshev Wavelets Method for Solving Bratu's Problem, Yang and Hou boundary value problems, springer open journal, 2013.
[2] FariborziAraghi M. A. and Daliri S., Numerical Solution of Integro-Differential Equation by Using Chebyshev Wavelets Operational Matrix of Integration, International Journal of Mathematical Modeling & Computations, Vol. 02, No. 02 127-136, 2012.
[3] Ali A. and Iqbal M. A., Chebyshev Wavelets Method for Delay Differential equations, International Journal of Modern Mathematical Sciences Vol. 8, No. 2 , 102-110, 2013.
[4] Abd-Elhameed W. M, and Doha E. H., New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Non Linear Second –Order Differential Equations Involving Singular and Bratu Type Equations, Abstract and Applied Analysis Vol. 2013, Article ID 715756, 2013.
[5] Biazar J. and Ebraimi H.G., A Strong Method for Solving Systems of Integro-Differential Equations, Applied Mathematics, Vol.2, 1105-1113,2011.

Paper Type	:	Research Paper
Title	:	On I 2 -Cauchy Double Sequences in p-Adic Linear 2-Normed Spaces
Country	:	India
Authors	:	B. Surender Reddy, D. Shankaraiah
	:	10.9790/5728-10235969

Abstract: In this paper, we introduce the concept of   2 I convergence which is closely related to  2 I convergence and the concepts 2 I and   2 I Cauchy double sequences in p -adic linear 2-normed space. Also we investigate the relation between these concepts in p -adic linear 2-normed spaces.
Keywords: 2-normed space, p-adic linear 2-normed space,   2 I convergence,  2 I Cauchy double sequence,   2 I Cauchy double sequence.

[1] G.Bachman, Introduction to p-Adic Numbers and Valuation Theory (Academic Press, 1964).
[2] G. Bachman and L. Narici, Functional Analysis (New York and London, Academic Press, 1966).
[3] Balakrishna Tripathy and Binod Chandra Tripathy, On I-convergent double sequences ,Soochow Journal of Mathematics , 31, 2005
549-560,.
[4] P.Das ,P.Kostyrko,W.Wikzynski and P.Malik,I and I* -convergence of double sequences , Math. Slovaca, 58(5),2008,605-620.
[5] Erdinç Dündar and Bilal Altay, On Some Properties of  2 I Convergence and  2 I Cauchy of Double Sequences, Gen. Math.
Notes, Vol. 7, No.1, November 2011, pp.1-12.

Paper Type	:	Research Paper
Title	:	Weakly quasi-conformally symmetries of generalized (k, μ) space forms
Country	:	India
Authors	:	Shivaprasanna G. S., Y. B. Maralabhavi, Somashekhara G.
	:	10.9790/5728-10237078

Abstract:In this paper we study symmetries and weak symmetries of generalized (k, μ) space forms with
respect to Quasi-conformal curvature tensor. We establish relations regarding the associated 1-forms of weakly symmetric manifolds.
Keywords: generalized (k, μ) space forms, Quasi-conformal curvature tensor, Weakly Quasi-conformallysymmetric, Weakly Quasi-conformally Φ - Ricci symmetric, η -Einstein manifolds.

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012-0196-2, April(2012).
[3]. Alfonso Carriazo and Veronica Martin-Molina, Generalized (k, μ) -space forms and Da -homothetic deformations. Balkan
Journal of Geometry and its Applications, Vol.16, No.1, 2011, 37-47.
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