iosr-Jm   Volume-5 ~ Issue-2

Abstract: In all societies, women have claimed equal status with men. It is of a vital importance in modern social science studies, and involves serious research. Progress in attitude, behavior, pattern and legal system is inevitable in all civilized societies. In a progressive society the rights and obligations were determined on the basis of status of an individual. This paper examines historically the status of special reference to Tamil Nadu women.

[1] Mulladi Subbanma, women tradition and culture, sterling publishers pvt., Ltd., New Delhi 1982.
[2] Radhakrishnamoorthy, "Indian Women her position in society" Madras.
[3] Krishnakumari. N.S. Status of single women in India, Uppal Publishing House, New Delhi – 1987.
[4] Balasubramanian. C. The status of women in TamilNadu During the Sangam age, University of Madras, Madras 1976.
[5] Neelakanda Sastri. K.A. The culture and history of the Tamils, Tamil Publishing House, Madras 1964.
[6] Pillai K.K. The social History of the Tamils, University of Madras, 1975.
[7] Purnalingam. M.S. Tamil India, Saiva Sidhanta Publishing Society, Madras 1927.
[8] Otto Rahfeld, Women of India, R and R Clark Limited, Bombay 1928.
[9] Wilkins .W.J. Modern Hinduism, Cosmo Publications, New Delhi 1985.
[10] Sathiyanath Iyer, R. Cultural and Political History of India, Viswanathan Publishers, Madras.

Abstract: In this paper Reliability of Thermal stresses in simples bars whose body may be expand or contract due to some increase or decrease in the temperature of the body were computed. The thermal stresses or strains may also be found out first by finding out amount of deformation due to change in temperature, and then by finding out thermal strain due to the deformation. The thermal stress may be found out the thermal strain .For such thermal stresses in simple bars we are particularly interested in investigating the reliability by using the linear hazard Rate .It is also compared the results between the reliability of thermal stresses in bars if the ends of the bars are fixed to rigid supports and if the supports yield by an amount equal to Δ.it is observed that the reliability is depending on the coefficient of linear expansion ∝.This coefficient of linear expansion is different for each material.
Keywords: Thermal stresses, temperature, reliability, coefficient of linear expansion, hazard rate

[1] Kapur, K.C and L.R.Lamberson (1977): Reliability in Engineering Design, Jhon Wiley and Sons, In., NewYork
[2] T.S.Uma Maheswari (1991): Studies on some Stress-Strength reliability models, Ph.D.Thesis, Kakatiya University, Warangal.
[3] Abu-Bakr Iris (2007): Reliability Analysis of Simply Supported Steel Beams
[4] Australian Journal of Basic and Applied Sciences, 1(1): 20-29, 2007, INSInet Publication
[5] R.S. KHURMI, Strength of Materials [Mechanical of Solids], S. Chand Publications
[6] Lorenzo Bardella (2008): Reliability of First Order Shear Deformation Models for Sandwich Beams, Journal of Mechanics of
Materials and Structures, Vol. 3, No.7, 2008

Abstract: The purpose of this paper is to introduce and study the properties of (1,2) γ- open set in bitopological space .In this paper we also study (1, 2) γ-locally closed set, (1,2) γ-t-set, (1,2) γ-B-set and relationship between (1,2) b-open set and (1,2) γ-open set .
Keywords:(1, 2) b-open set , (1,2) B-set, (1,2) t-set (1,2) locally closed , (1,2) γ- open set .

[1] Ahmad Al- Omari and Mohd. Salmi Md., Noorani. , "Decomposition of continuity via b-open set.", Bol. Soc. Paran Mat., (3s.)
v. 26, 1-2 (2008):53-64.
[2] C. Janaki , Renu Thomas , ON (1,2)* -R*-CLOSED SETS , Asian Journal of Current Engineering and Maths 1:6 Nov-Dec
(2o12) 371-377.
[3] D. Andrijevic and M. Ganster, on PO-equivalent topologies, IV International Meeting on Topology in Italy (Sorrento, 1988), Rend.
Circ. Mat. Palermo (2) Suppl., 24(1990), 251-256.
[4] J. Tong, On Decomposition of continuity in topological spaces" Acta Math. Hungar 54(1-2) (1989), 51-55.
[5] Kelly, J.C., "Bitopological Spaces", Proc. London Math .Soc. 13 (1963) No 3, 71- 89.
[6] Lellis Thivagar, M., " Generalization of pairwise α –continuous Functions" ,Pure and Appl. Mathematika Sci. 28 (1991), 55- 63 .
[7] M. Lellis Thivagar and B. Meera Devi , "Bitopological B-open Sets " , International Journal of Algorithms , Computing and
Mathematics ,Volume 3 ,Number 3, August 2010.
[8] M. Lellis Thivagar , O. Ravi , On strong forms of (1,2)* -quotient mapping s in Bitopological Spaces , International .J. Math.
Game Theory and Algebra 14(6)2004, 481-492.
[9] R. Engelking , General topology vol 6 of sigma series in pure mathematics 1989.
[10] Yiezi Kadham Mahdi Semi -open and Semi-closed in Bitopological Spaces, 2007 19-18.

Abstract: In this paper the mathematical model of instability phenomenon occurs during secondary oil recovery process is formulated under the external magnetic effect which is due to injection of magnetic fluid into injection wells. Mathematical formulation of the present model leads tonon-linear partial differential equation of parabolic type which has been solved in form of power series with appropriate initial and boundary conditions for any time T > 0. The solution represents saturation of injected phase for different time T > 0. The graph shows that saturation of injected phase increases for distanceX increases for different time T. It is given by using MATLAB coding.
Keywords: Instability phenomenon, magnetic fluid, Power series solution 2010 Mathematics Subject Classification: 35Q35, 76S99

[1] Bali and Iyengar. A Text book of engineering mathematics, 6th Edition, Laxmi Publication Ltd, pp.592-593(2004).
[2] Bear J. Dynamics of fluids in porous media, American Elsevier, New York, (1972).
[3] Brailovsky I., Babchin A., Frankle M. and Sivashinsky G. Instability instability in water-oil displacement. Transport in porous media,
No.63, 380-393(2006).
[4] Lang A., Schroter M., Schere M., Engel A. and Rehberg I. Instability instability in water-sand mixture. The European Physical
Journal, No.4, 475-484,(1998).
[5] Mehta M. N. An asymptotic expansion in fluid flow through porous media; Ph.D. Thesis; S.G. University, Surat, India, (1978).
[6] Oroveanu T. ScurereaFluiidelorPrinMediPoeseaseNemogeme, EdituraAcadimiei R.P.R., Rumania, pp. 92 &328, (1963).
[7] Rosenweig R. E., Berkovsky B. M., et al. Thermo mechanics of magnetic Fluid, (Hemisphere, Washington DC),pp. 195, (1978).
[8] Scheidegger A. E. and Johnson E. F. The statistical behavior of instabilities in displacement processes in porous media, Canadian
Journal Physics, No. 39, 326-334(1961).
[9] Scheidegger A. E. Growth of instabilities on displacement fronts in porous media, Physics of Fluids, No. 3, 94(1960).
[10] Scheidegger A. E. The physics of flow through porous media, 3rd ed., University of Toronto Press, Toronto, (1974).

Abstract: This paper describes a new method for designing quadric patch and cubic patch of the surfaces and show how to use Mathematica programs for computations the equations of the patch of the surfaces. The surface with quadratic patches is defined through a given set of six points and the surface with cubic patches is defined through a given set of ten points
Keywords: Quadric surfaces, Cubic surfaces, Coons patches, Bezier surface Patches, Mathematica program

[1]. D. Hilbert & S. Cohn-Vossen , The Second-Order Surfaces, §3 in Geometry and the Imagination ( New York: Chelsea, 1999)
pp. 12-19.
[2]. B. Hunt, The 27 lines on a cubic surface and Cubic surfaces, Ch. 4 and appendix B. 4 in the geometry of some special arithmetic
quotients ( New York; Springer verlag, 1996) 108 – 67 and 302 – 10.
[3]. G. Alfred, Modern Differential Geometry of Curves and Surfaces (CRC Press, 1993).
[4]. L. Suresh and W. Joe, Bézier representation for quadric surface patches, Computer-Aided Design, Vol. 22, 1990, 574-579.
[5]. W. Boehm and D. Hansford, Parametric representation of quadratic surfaces, Mathematical Modeling and Numerical Analysis,
Vol. 26, 1992, 191– 200.
[6]. W. Boehm and D. Hansford, in G. Farin editor, Bezier patches on quadratics, NURBS for Curve and Surface Design (SIAM,
Philadelphia, 1991) 1 – 14.
[7]. I. D. Faux and M. J. Pratt, Computational geometry for design and manufacture, Mathematics and its Applications (Ellis
Horwood limited, New York-Chichester, 1979).
[8] R. B. M. Amer and M. A. Abd El- Mageed, Using Stirling's Interpolation to Find Gauss and Mean Curvature for the Surface,
IOSR Journal of Mathematics, 4 (2), 2012, 52-61.

Abstract: In this paper, a new class of size-biased Generalized Gamma distribution is introduced. The estimates of parameters of size-biased Generalized Gamma distribution are obtained by using new method of moments. A new distribution which contains as a special case is introduced. The characterizing properties of the model are derived. Also, other important property including Shannon entropy which is the measure of the uncertainty in this class of the distribution are derived and studied.
Keywords: Generalized Gamma distribution, Size-biased Generalized Gamma distribution, moment generating function, sample coefficient of variation, Shannon's entropy

[1]. Stacy,E.W., A Generalization of the Gamma Distribution, The Annals of Mathematical Statistics, Vol. 33, No.3,pp.1187-
1192,(1962)S
[2]. Diebold F. X., Rudebusch G.D. (1990). "A Nonparametric investigation of duration dependence in the American business cycle,"
Journal of Political Economy, 98, 596-616.
[3]. Kiefer N.M. (1984). "Simple test for heterogeneity in exponential models of duration," Journal of Labour Economics, 539 -549.
[4]. Eckstein Z., Wolpin K.I (1995). "Duration to first job and the return to schooling estimates from a search-matching model,"
Review of Economic Studies, 6, 6-6.
[5]. Lancaster T.(1979) " Econometric methods for the duration of unemployment," Econometrica, , 939-956.
[6] . Favero C. A., Pesaran M.H., Sharma S. (1994) "A duration model of irreversible oil investment: theory and empirical evidence,"
Journal of Applied Econometrics, 9, 95-112.
[7]. Jaggia S. (1991) "Specification tests based on the heterogeneous generalized gamma model of duration: with an application to
Kennan's strike data," Journal of Applied Econometrics, 6, 169-180.
[8] . Jamas Shannon C.E (1948) "A Mathematical theory of communication," Bell system Technical Journal, 27, 623-659
[9] . Prentice, R.L., A Log gamma model and its maximum likelihood estimation. Biometrika, 61(1974), 539-544.
[10]. Huang, P. H., Hwang , T.Y., On new moment estimation of parameters of the generalized gamma distribution using it's
characterization, Taiwanese Journal of Mathematics, Volume 10, No. 4, pp. 1083-1093, (2006).

Abstract: In this paper, we develop the Size-biased form of the weighted Generalized Beta distribution of first kind (WGBD1); a particular case of the weighted Generalized Beta distribution of first kind, taking the weights as the variate values has been defined. The structural property of Size-biased Generalized Beta distribution of first kind (SBGBD1) including moments, variance, mode and harmonic mean, coefficient of variation, skewness and kurtosis has been derived. The estimates of the parameters of Size- biased Generalized Beta distribution of first kind (SBGBD1) is obtained by employing a new method of moments. Also, a test for detecting the sizebaisedness is conducted.
Keywords: Generalized Beta distribution of first kind, Beta function, Size-biased generalized beta distribution of first kind, Structural properties and moment estimator.

[1] Barlow, R.E and Proschan, F.(1975). Statistical Theory of Reliability and Life Testing:Probobality Models. New York, Rinehart and
Winston.
[2] Johnson, N.L., Kotz, S. and Balakrishnan, N. 1995. Continuous Univariate Distributions, Volume 2(second edition). New York: John Wiley and Sons.
[3] Gupta, A.K. and Nadarajah, S.(2004). Handbook of Beta Distribution and its Applications.NewYork:Marcel Dekker.
[4] Fisher, R.A (1934).The effects of methods of ascertainment upon the estimation of frequencies. Ann. Eugenics, 6, 13-25
[5] Rao, C.R (1965). On discrete distributions arising out of method of ascertainment, in clasasical and Contagious Discrete, G.P. Patil
.ed ;Pergamon Press and Statistical publishing Society, Calcutta, pp-320-332.
[6] Rao, C. R(1985).Weighted distributions arising out of method of ascertainment , in A Celebration of Statistics,
A.C.Atkinson&S.E.Fienberg, eds, Springer-Verlag,New York, Chapter 24,pp.543-569
[7] Dennis, B. and Patil, G. 1984. The gamma distribution and weighted multimodal gamma distributions as models of population
abtidance.Math. Biosciences, 68,187-212.
[8] Gove,H.J.2003.Estimation and application of size-biased distributions in forestry, In Modeling Forest systems, A.Amaro,D. Reed and P.Soares CAB International Wallingford UK,201-212.
[9] Sandal C.E.1964. Estimation of the parameters of the gamma distribution, Technometrics,6, 405-414.
[10] Mir, K.A. 2009. Size-Biased Distributions and their Applications. Pakistan Journal of Statistics, 25(3), 283-294.

Abstract: In this paper, we develop the Size-biased form of the weighted Generalized Beta distribution of second kind (WGBD2); a particular case of the weighted Generalized Beta distribution of second kind, taking the weights as the variate values has been defined. The structural properties of Size-biased Generalized Beta distribution of second kind (SBGBD2) have been derived. The estimates of the parameters of Size- biased Generalized Beta distributions of second kind (SBGBD2) are obtained by employing a new method of moments. Also, a test for detecting the size-baisedness is conducted.
Keywords: Generalized Beta distribution of second kind, Beta function, Size-biased generalized beta distribution, Structural properties and moment estimator. Likelihood ratio test.

[1] Barlow, R.E and Proschan, F.(1975). Statistical Theory of Reliability and Life Testing:Probobality Models. New York, Rinehart and
Winston.
[2] Johnson, N.L., Kotz, S. and Balakrishnan, N. 1995. Continuous Univariate Distributions, Volume 2(second edition). New York: John
Wiley and Sons.
[3] Gupta, A.K. and Nadarajah, S.(2004). Handbook of Beta Distribution and its Applications.NewYork:Marcel Dekker.
[4] Fisher, R.A (1934).The effects of methods of ascertainment upon the estimation of frequencies. Ann. Eugenics, 6, 13-25
[5] Rao, C.R (1965). On discrete distributions arising out of method of ascertainment, in clasasical and Contagious Discrete, G.P. Patil
.ed ;Pergamon Press and Statistical publishing Society, Calcutta, pp-320-332.
[6] J.B.McDonald, Some Generalized functions for the size Distribution of Income,Econometrica,52(3), (1984), 647-663.
[7] J.B.McDonald and Y.J.Xu, A Generalized of the Beta distribution with Application, Journal of Econometrics, 69(2), (1995), 133-152.

Abstract: In this paper, a new class of size-biased Gamma distribution is derived. A size-biased gamma distribution, a particular case of weighted gamma distribution, taking the weights as the variate values has been defined. A new distribution which contains as a special case is introduced. The characterizing properties of the model are derived. A Baye's estimator of Size-biased gamma distribution (SBGMD) has also been obtained by using different priors. Also, other important properties including Shannon entropy and Fisher's information matrix which are the measure of the uncertainty in this class of the distribution are derived and studied.

Keys Words: Gamma distribution, Size-biased gamma distribution, Uniform prior, Non-Informative priors. Shannon's entropy and Fisher's Information matrix.

[1] Gupta.S.S and P.A.Groll, 1961.Gamma distribution in acceptance sampling based on life tests. J, Am.Stat.Assoc. 56:942-970.
[2] Engelardt, M. and L.J.Bain, 1978.Prediction intervals for the Weibull process.Technometrics, 20:167-69.
[3] Chao, M.and R.E.Glaser, 1978.The extract distribution of Bartlett‟s test statistic for homogeneity of variances with unequal sample
sizes.J.Am.Stat.Assoc. 73: 422-426.
[4] Jamali, A.S., L.J.Lin AND d.Yingzhuo, 2006.Effect of scale parameters in the performance of Shewhart control chart with
interpretation rules.J.Applied Sci., 6: 2676-2678.
[5] Lawless, J.F., 2003.Statistical Models and Methods for Lifetime data.Wiley-Interscience, UK.
[6] Kalbfleisch, J.D and R.L. The statistical analysis of failure time data.2nd Edn., Wiley-Interscience, New York,ISBN; 047136357X
Prentice, 2002..
[7] Ghafoor, A., F.Muhammad and I.A.Arshad, 2005. Bayesian regression with prior non-sample information on mash yield. J. Applied
Sci., 5: 187-191.
[8] Rahul, GP. Singh and O.P. Singh, 2009. Population project OF Kerala using Bayesian methodology .Asian J. Applied Sci., 2: 402-
413.
[9] Jamal Shannon C.E (1948) "A Mathematical theory of communication," Bell system Technical Journal, 27, 623 -659.
[10] Cover T. M., Thomas J.A., Elements of Information Theory, New York, Wiley, 1991.

Abstract: A lot of literatures characterize an extension of an order on a set (say, X) to a weak order on the set of all of its non- empty subsets (say, F). This extension makes use of the information contained in the primitive order on X. This paper considers the case where the subsets of X are formed by a compatibility relation defined on X. As its main contribution, the paper attempts to show that an ordering can be defined on the collection of compatible subsets of a finite set endowed with a compatibility relation. In particular, a necessary and sufficient condition is formulated that would guarantee when an ordering so defined turns out to be partial ordering.
Keywords: Compatibility relation, covering, ordering

[1] D. Singh, M.H. Dunari and J.N. Singh, A Note on Covering and Partition of a Finite Set, Math. Sci. Math. Edu. 5(2) (2010), 1- 5.
[2] N. Baigent and Y. Xu, Extending an Order on a Set to its Power Set: An Axiomatic Characterization of Average Borda Rule, Journal
of Economic Theory, 49(5) (2004), 43- 56.
[3] S. Moretti and A. Tsoukias, Ranking Sets of Possibly Interacting Objects Using Shapley Extensions, International Conference on
Principles of Knowledge and Reasoning, 12 (2010) 199- 207.
[4] S. Barbera and P.K. Pattanaik, Extending an Order on a Set to its Power Set: Some Remarks on Kannai and Peleg's Approach, Jou rnal of Economic Theory 49 (1989), 84- 92.