iosr-Jm   Volume-3 ~ Issue-5

Abstract :In this paper, fuzzy L-open sets due to Abd El-Monsef et al. [4] are used to introduce a new separation axiom and new type of function in fuzzy topological ideals spaces . Some the basic properties of fuzzy L-irresolute functions, as well as the connections between them, are investigated. Possible application to superstrings and   space–time are touched upon.

1] M.E. Abd El-Monsef and M.H. Ghanim , On semi open fuzzy sets, Delta , J. Sci.5 (1981) 30-40.
[2] M.E. Abd El-Monsef; A.A. Nasef and A. A. Salama, Extensions of Fuzzy Ideals, Bull.Cal.Maths.Soc., 92, (3) ( 2000 ) 181 –188
[3] M.E. Abd El-Monsef; A.A.Nasef and A.A.Salama, Some Fuzzy Topological operators via Fuzzy ideales Chaos, Solitons &
Fractals.(12)(13),(2001) , 2509-2515.
[4] M.E. Abd El-Monsef; A.A. Nasef and A.A.Salama, Fuzzy L-open Sets and Fuzzy L-continuous Functions, Analele Universitatii
din Timisoara .XL,fasc.Seria Matematica - Informatica(2),(2002),3-12
[5] K.K. Azad, On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal App. 82 (1981) 1432.
[6] C.L. Chang, Fuzzy Topology Spaces, J. Moths. Anal – Apple 24 (1968) 128-189.
[7] R.A.Mahmoud, Fuzzy Ideals, fuzzy local functions and *-fuzzy topology, the Journal of Fuzzy Mathematics Vol.5, No.1, 1997
Los Angeles.
[8] Pu Pao – Ming and Liu Yang, Fuzzy Topology .1. Neighbour – hood structure of fuzzy point and Moore smith convergence, J.
Math Anal. App. 76 (1980) 571-599.
[9] A.A.salama, Fuzzy Ideals on fuzzy topological spaces, Ph.D in Topology ,Tanta Univ., Egypt( 2002).
[10] D.Sarkar,Fuzzy ideal theory, Fuzzy local function and generated fuzzy topology , Fuzzy Sets and Systems 87 (1997) 117 – 123

Abstract :This paper presents a non parametric measure of association between k populations, and a method of testing for its significance. Analysis of variance technique is employed to developa test statistic for the measure of the association. An illustrative example is provided and the method compares equally well with the Friedman's two way analysis of variance by rank.

[1] Gerald, K. and Warrack , B. (2003): Statistics for Management and Economics, Curt Hinrichs, USA
[2] Gibbons, J.D. (1971): Non Parametric Statistical Inference, McGraw Hill, New York
[3] Legendre, P. (2005): Species Associations: The Kendall Coefficient Revisited, American Statistical Association and International
Biometric Society, Journal of Agricultural, Biological, and Environmental Statistics, Vol 10, 2
[4] Oyeka, C.A. (2009): An Introduction to Applied Statistical Methods (5theds), Nobern Avocation Pub. Coy., Enugu
[5] Scheaffer, R.L. and McClave, J.T. (1982): Statistics for Engineers, PWS, Publishers, USA
[6] Sheskin, D.J (1997): Handbook of Parametric Statistical Procedures, CRC Press, Inc, Boca Raton, New York
[7] Zar, J.H (1999), Biostatistical Analysis (4theds), Prentice Hall, Upper Saddle River, New Jersey

Abstract :This paper developed a Ties adjusted non parametric statistical method for the analysis of ordered repeated measures that are related in time, space or condition that takes account of all possible pairwise combinations of treatment levels. A test statistic is developed to determine whether subjects are increasingly performing better or worse over time or space. The proposed method also enables the researcher to have a bird's eye view of the proportions of subject who are successively improving, experiencing no change or worsening overtime, space or condition to guide the introduction of any desired interventionist measures. The method is illustrated with some data and shown to be more powerful than Friedman test and shown to beeasier to use than the Bartholomew procedure.

[1] Bartholomew DJ (1959a): A Test of Homogeneity for Ordered Alternatives. Biometrika, 46, 36-48
[2] Bartholomew DJ (1959b): A Test of Homogeneity for Ordered Alternatives 11. Biometrika, 46, 328-335
[3] Freidlin B and Gastwirth JL.(): Should the Median Test be Retired from general Use? American Statistician, 54, 161-164
[4] Gibbons JD(1971): Non- Parametric Statistical Inference. McGraw Hill, New York,
[5] Gibbons JD(1993): Non- Parametric Statistical. An Introduction; Newbury Park: Sage Publication
[6] Oyeka, C. A., Ebuh, G.U., Nwankwo, C.C., Obiora- Ilouno, H. Ibeakuzie, P. O., Utazi, C.(2010) : A Statistical Comparison of Test
Scores: A Non- Parametric Approach. Journal of Mathematical Sciences, 21(1) 77-87
[7] Siegel S() : Non- Parametric Statistics for the Behavioural Sciences. McGraw- Hill, Tokyo
[8] Hollander, M. and Wolfe, D.A.(1999): Non-Parametric Statistical Methods (2nd Edition). Wiley Interscience, New York

Abstract :This paper aims to forecast the inflation rate in Nigeria using Jenkins approach. The data used for this paper was yearly data collected for a period of 1961-2010. Differencing method were used to obtain stationary process. The empirical study reveals that the most adequate model for the inflation rate is ARIMA (1,1,1). The model developed was used to forecast the year 2011 inflation rate as 16.27%. Based on this result, we recommend effective fiscal policies aimed at monitoring Nigeria's inflationary trend to avoid the consequences in the economy
Keywords -ARIMA models, Box-Jenkins, Differencing method, forecasting, Inflation rate

[1] S. Arthra and S.M. Sheffarin, Economic: Principle in action (Upper Saddle River, New Jersey, Pearson Prentice Hall, 2003 pp:340)
[2] Bayo Fatukasi, Determinants of inflation in Nigeria: An Empirical Analysis, International Journal of Humanities and Social
Science 1(18).
[3] Central Bank of Nigeria , "Money supply, inflation and the Nigerian economy" ,Bullion Publication of CBN, 21(3), 1996.
[4] P. I. Nwosa et al, Monetary policy, exchange rate and inflation rate in Nigeria, research Journal on Finance and Accounting (3)
(3), 2012.
[5] C. K. Lee, H. J. Song & J. W. Mjelde , The forecasting of international expo tourism using quantitative and qualitative techniques,
Tourism Management, 29(6), 1084-1098, 2008
[6] S. E. Alna and F. Ahiakpor, ARIMA (autoregressive integrated moving average) approach to predicting inflation in Ghana.
Journal of Economics and International Finance 3(5), pp. 328-336, May 2011
[7] K.. Wong, H. Song, S. F. Witt & D. C. Wu , Tourism forecasting: to combine or not to combine? Tourism Management, 28, 1068-
1078, 2007
[8] Meyer, B. H.Meyer & M. Pasaogullari, "Simple Ways to Forecast Inflation: What Works Best?" Federal Reserve Bank of
Cleveland: Economic Commentary. Retrieved from http://www.clevelandfed.org/research/commentary/2010/2010-17.cfm, 2010
June
[9] D. Wessel, "Tinker Bell Economics Colors Inflation Predictions." The Wall Street Journal. Retrieved from
http://online.wsj.com/article/ SB10001424052748704520504576162322026133298.html, 2011. February
[10] A. Carrick, "January Inflation Remained under Control in Both Canada and US" Reed Construction Data Retrieved from
http://www.reedconstructiondata.com/contruction -forecast/news/2012/02/january-inflation-remand-under-control-in both-theUSand-
Canada/, 2012

Abstract :nonlinear stability analysis is performed for a triple- diffusive convection in a magnetized ferrofluid with magnetic field –dependent viscosity (MFD) for stress- free boundaries. The major mathematical emphasis is on how to control the non-linear terms caused by magnetic body force and inertia forces. A suitable generalized energy functional is introduced to perform the nonlinear energy stability analysis. It is found that nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of linear instability, and thus indicate that the subcritical instabilities are possible. However, it is noted that in case of non-ferrofluid global nonlinear stability Rayleigh number is exactly same as that of linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter 𝑀3 , solute gradients 𝑆 1 & 𝑆2and MFD viscosity parameter 𝛿 , on the subcritical instability region have also been analyzed.
Keywords -nonlinear stability, magnetized ferrofluid, triple- diffusive convection, MFD viscosity , magnetization

[1] A. Abraham, Rayleigh–Be´nard convection in a micropolar ferromagnetic fluid, Int. J. Eng. Sci. 40 (4), 2002,449–460.
[2] A. J. Pearlstein et.al., The onset of convective instability in a triply diffusive fluid layer, Journal of Fluid Mechanics, 202, 1989,
443-465.
[3] B.A. Finlayson, Convective instability of ferromagnetic fluids, J. Fluid Mech.40 (4), 1970, 753–767.
[4] B. Straughan and D.W. Walker, Multi component diffusion and penetrative convection,Fluid DynamicsResearch, Vol. 19,
1997,77-89.
[5] B. Straughan , A sharp nonlinear stability threshold in rotating porous convection, Proc. Roy. Soc. London. A. vol. 457,
2001,87-93.
[6] B. Straughan , The energy method, Stability, and Nonlinear Convection, New York, Springer Verlag , 2004.
[7] B. Straughan , Global nonlinear stability in porous convection with a thermal non-equilibrium model ,proc. R. soc. A. vol.462,
2006, 409-418.
[8] C .Oldenberg and K. Pruess, Layered thermohaline convection in hypersaline geothermal systems.Transport in Porous Media,
vol. 33 , 1998,29-63.
[9] D.A.Nield and A. Bejan, Convection in Porous Media, New York, Springer,1998.
[10] D. D. Joseph , On the stability of the Boussinesq equations, Cambridge University Press, 1965.

Abstract :This analysis examines the problem of oscillatory flow of a viscoelastic fluid and heat transfer along a porous oscillating channel with radiative heat transfer. Here we consider the flow through a channel in which the fluid is injected on one boundary of the channel with a constant velocity, while it is sucked off at the other boundary with the same velocity. The two boundaries are considered to be in close contact with two plates parallel to each other. The plates are supposed to be oscillating with a given velocity in their own planes. The analytical expressions for the velocity, the temperature and the wall shear stress have been obtained. The effects of viscoelastic parameter on the velocity profile, shear stress are presented graphically with the combinations of the other flow parameters. It is also observed that the temperature field is not significantly affected by the viscoelastic parameter.
Keywords -Viscoelastic fluid, radiative heat transfer, porous wall, oscillating channel

[1] C. Y. Wang, Pulsatile flow in a porous channel, Journal of Applied Mathematics, 38, 1971, 553-555.
[2] B.C. Bhuyan and G.C. Hazarika, Effect of magnetic field on pulsatile flow blood in a porous channel, Bio-Science Research
Bulletin, 17, 2001, 105-112.
[3] A Raptis, Unsteady free convective flow and mass transfer through a porous medium bounded by an infinite vertical limiting
surface with constant suction and time-dependent temperature, International Journal of Energy Research, 7, 1983, 385-389.
[4] P.C.Ram, Effect of Hall current and wall temperature oscillation on convective flow in a rotating fluid through porous medium,
Heat and Mass Transfer, 25, 1990, 205-208.
[5] O.D. Makinde and P.Y. Mhone, Heat transfer to mhd oscillatory flow in a channel filled with porous medium, Romanian Journal of
Physics, 20, 2005, 931-938.
[6] J. Prakash and A. Ogulu, A study of pulsatile blood flow modeled as a power law fluid in a constricted tube, International
Communications in Heat and Mass Transfer, 34, 2007, 762-768.
[7] A. Mehmood and A. Ali, The effect of slip condition on unsteady mhd oscillatory flow of a viscoelastic fluid in a planar channel,
Romanian Journal of Physics, 52, 2007, 85-91.
[8] S.D. Adhikary, J.C.Misra, Unsteady two-dimensional hydromagnetic flow and heat transfer of a fluid, International Journal of
Applied Mathematics and Mechanics, 7(4), 2011, 1-20.
[9] S.K. Ghosh, Hydromagnetic fluctuating flow of a viscoelastic fluid in a porous channel, Journal of Applied Mechanics, 74, 2007,
177-180.
[10] B.D. Coleman and H. Markovitz, Incompressible second-order fluids, Advances in Applied in Mechanics, 8, 1964, 69-101.

Abstract :The use of the double integral is the topic of the paper. The link of the double integral and the single integral is mentioned and the splitting of the double integral in two simple single integrals is involved. Also the equation of the curve formed when the double integral is converted to a single in integral is mentioned. The paper deals with the question that if the double integral is solved and it is converted to single integral then what is ment by it, also the equation of the curve formed of that single integral function is discussed and the relation between the surface of that double integral function and the single integral function is discussed.

[1] www. tutorial.math.lamar.edu
[2] www. people.rit.edu
REFERENCE AUTHORS :
[3] PROF. RAMANNA, M.SC. MATHEMATICS (HONS), ENGINEERING MATHEMATICS.
[4] PROF. ALGONDA DESAI , M.SC. MATHEMATICS
[5] PROF. P. WARTIKER, HIGHER ENGINEERING MATHEMATICS.
[6] Dr. B. S. GAREWAL, HIGHER ENGINEERING MATHEMATICS, KHANNA PUBLISHERS, DELHI.
[7] DR. SRIVASTAVA, ENGINEERING MATHEMATICS -2.

Abstract :Using Deissler's approach, the decay for the concentration of a dilute contaminant undergoing a first-order chemical reaction in dusty fluid homogeneous turbulence at times prior to the ultimate phase for the case of multi-point and multi-time is studied. Here two and three point correlations between fluctuating quantities have been considered and the quadruple correlations are ignored in comparison to the second and third order correlations. Taking Fourier transform the correlation equations are converted to spectral form. Finally, integrating the energy spectrum over all wave numbers we obtained the decay law for the concentration fluctuations in a homogeneous turbulence prior to the final period in presence of dust particle for the case of multi-point and multi-time.
Keywords -Deissler's method, Dust particle, First order reactant, Navier-Stock's equation, Turbulent flow.

[1] R. G. Deissler, On the decay of homogeneous turbulence before the final period. Phys. Fluids 1(2), 1958, 111-121.
[2] R. G. Deissler, A theory of decaying homogeneous turbulence, Phys. Fluids 3(2), 1960, 176-187.
[3] A.L. Loeffler, and R.G. Deissler, Decay of temperature fluctuations in homogeneous turbulence before the final period, Int .J. Heat
Mass Transfer, 1, 1961, 312-324.
[4] P. Kumar, and S.R. Patel, First-order reactant in homogeneous turbulence before the final period of decay. Phys .Fluids, 17, 1974,
1362-1368.
[5] P. Kumar, and S.R. Patel, On first-order reactants in homogeneous turbulence, Int. J. Eng. Sci., 13,1975, 305-315.
[6] M .S. A. Sarker, and N. Kishore, Decay of MHD turbulence before the final period, Int.J. Engeng. Sci., 29, 1991, 1479-1485.
[7] S., Chandrasekhar, The invariant theory of isotropic turbulence in magneto-hydrodynamics, Proc. Roy.Soc., London, A204, 1951,
435-449.
[8] M. S. A. Sarker, and M. A. Islam, Decay of MHD turbulence before the final period for the case of multi-point and multi-time,
Indian J. pure appl. Math.,32,2001,1065-1076.
[9] M.A.Aziz, M.A.K Azad, and M.S. Alam Sarker, First Order Reactant in MHD turbulence before the final period of decay for the
case of multi-point and multi-time in a rotating system in presence of dust particle. Res. J. Math. Stat., 2, 2010, 56-68.
[10] S., Corrsin, On the spectrum of isotropic temperature fluctuations in isotropic turbulence.J.Apll.Phys, 22, 1951, 469-473.

Abstract :The superimposition of infinite number of intervals [a1, b1], [a2, b2], [a3, b3],......., [an, bn] follows two laws of randomness if (a) ai ≠ aj; i,j= 1, 2,......, n, (b) bi ≠ bj; i,j= 1, 2,......, n, (c) max(ai) ≤ min(bi); i= 1, 2,..., n, where n→ ∞
Keywords -Superimposition of sets, Probability distribution function, Glivenko – Cantelli Lemma.

[1] Hemanta K. Baruah, Construction of Normal Fuzzy Numbers Using the Mathematics of Partial Presence, Journal of Modern
Mathematics Frontier, Vol. 1, No. 1, 2012, 9 – 15
[2] Hemanta K. Baruah, The Randomness–Fuzziness Consistency Principle, International Journal of Energy, Information and
Communications, Vol. 1, Issue 1, 2010, 37 – 48
[3] Hemanta K. Baruah, The Theory of Fuzzy Sets: Beliefs and Realities, International Journal of Energy Information and
Communications, Vol. 2, Issue 2, 2011, 1 – 22
[4] Hemanta K. Baruah, In Search of the Root of Fuzziness: The Measure Theoretic Meaning of Partial Presence, Annals of Fuzzy
Mathematics and Informatics, Vol. 2, No. 1, 2011, 57 – 68
[5] Hemanta K. Baruah, Set Superimposition and Its Applications to the Theory of Fuzzy Sets, Journal of the Assam Science Society,
Vol. 40, No. 1 & 2, 1999, 25-31