iosr-Jm   Volume-10 ~ Issue-4 ~ July-August 2014

Abstract: This study is aimed at employing the methodology of concomitant order statistics in the analysis of poultry feeds data. The purpose is directed toward finding the distribution of maximum and minimum concomitant order statistics of the cholesterol level given the egg weight. It was estimated on the basis of sample of 96 chickens, which were classified into two groups of 48 chickens each. One group was fed with in-organic copper salt combination while the second group with organic copper salt combination. The estimate of the probability of obtaining both the highest and the lowest are given using numerical approach to solve the integral obtained.

[1]. Balakrishnan, N and Kim, J.A. (2005). Point and Interval Estimation for bivariate normal distributionbased on progressively Type-II censored data. In Communication In Statistics Theory and Methods, Special issue in memory of Milton Sobel.
[2]. Bhattacharya, P.K. (1974). Convergence of sample paths of normalized sums of induced order statistics.Annals of Statistics, 2, 1034-1039.
[3]. David, H.A. (1973): Concomitants of Order Statistics, Bulletin of the International Statistical Institute,45, 295-300.
[4]. David, H.A. and Nagarajah, H.N.(1998): Concomitants of Order Statistics, In Handbook of Statistics16: order statistics theory and methods. pp.487-513, North-Holland Academic Publishers, Amsterdam.
[5]. Ihaka, R., and Gentleman, R. (1996) R. A Language for Data Analysis and Graphics. Journal Com-putational and Graphical Statistics 5, 299-314.

Abstract: This paper concerns with the study of constructing a special family of 3-tuples (a,b,c) such that the product of any two elements of the set added with k-times their sum increased by 4 2 k  is a Perfect square.
Keywords: Diophantine triple, Gaussian integer.2010 Mathematics Subject Classification: 11D99

[1]. I.G.Bashmakova(ed.), Diophantus of Alexandria, "Arithmetics and the Book of Polygonal Numbers", Nauka, Moscow,1974.
[2]. N.Thamotherampillai, "The set of numbers {1,2,7}", Bull. Calcutta Math.Soc.72(1980),195-197.
[3]. E.Brown,"Sets in which xy+k is always a square", Math.Comp.45(1985), 613-620
[4]. H.Gupta and K.Singh, "On k-triad Sequences", Internet.J.Math.Sci., 5(1985),799-804.
[5]. A.F.Beardon and M.N.Deshpande, "Diophantine triples",The Mathematical Gazette, 86 (2002),253-260.
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[7]. M.N.Deshpande,"Families of Diophantine Triplets",Bulletin of the Marathawada Mathematical Society, 4(2003),19-21.
[8]. Y.Bugeaud,A.Dujella and Mignotte,"On the family of Diophantine triples ( 1, 1,16 4 ) 3 k  k  k  k ",Glasgow
Math.J.49(2007),333-344.

Abstract:In this article, we consider the perturbed controlled linear system described by the difference equation , and the corresponding output , we suppose that ω is a disturbance which infects the system. Obliged to take into account the undesirable perturbation ω, we investigate also in this work a feedback control which allows to eliminate or to attenuate the effects of ω. To illustrate the obtained results, various examples are presented.
Keywords: Discrete-time systems, perturbation analysis, stability, pole placement controllability, Ackermann's theorem, Milman's theorem, tolerance

[1] J. Ackermann, A. Bartlett, D. Kaesbauer, W. Sienel, and R. Steinhauser, Robust Control, Systems with Uncertain Physical Parameters. London, U.K.: Springer-Verlag, 1993
[2] A. Abdelhak, M. Rachik and E. Labriji. On the tolerable perturbed initial states: Discret systems. Journal of Applied Mathematical Sciences, 3(9), (2009) 429-442.
[3] M. Derouich and A. Boutayeb. Dengue Fever, A mathematical model with immunization program. In Handbook of Research on Systems Biology Applications in Medicine Daskalaki (eds) Medical Information Science Reference, (2009) 805-819.
[4] Jean-Baptiste Hiriart-Urruty, Claude Lemarechal, Convex Analysis and Minimization Algorithms I, Springer-Verlag, 1996
[5] DeaOjme, Sylvie Delabriere and Yves Raynaud. ConvexAnalysis-Universit ´e Pierre et Marie Curie - Paris 6, 2000/2001.
[6] L. Afifi, A. El Jai and M. Magri. Compensation problem in finite dimension linear dynamical systems. International Journal of ApplieMathematical Sciences, 2(45), (2008) 2219-2228

Abstract: This research was set to examine the effect Multicollinearity has, on the standard error for regression coefficients when it is present in a Classical Linear Regression model (CLRM). A classical linear regression model was fitted into the GDP of Nigeria ,and the model was examined for the presence of Multicollinearity using various techniques such as Farrar-Glauber test, Tolerance level, Variance inflation factor, Eigen values etc and the result obtained shows that Multicollinearity has contributed to the increase of the standard error for regression coefficients, thereby rendering the estimated parameters less efficient and less significant in the class of Ordinary Least Squares estimators. Tolerance levels of 0.012, 0.005, 0.002 and 0.001 for𝛽1, 𝛽2, 𝛽3 ,and 𝛽4 respectively clearly shown a very low tolerance among all the explanatory variables with very high Variance Inflation Factors of 84.472, 191.715,502.179 and 675.633 respectively. A Coefficient of determination (R- Square) of 99%, though signaled a very high validity for the CLRM but it is equally an indications of a very high degree of Multicollinearity among the explanatory variables. The Eigen values of 0.431, 0.005, 0.002 and 0.000 for 𝛽0, 𝛽1, 𝛽2, 𝛽3 ,and 𝛽4 respectively clearly shown a very low Eigen value among the explanatory variables, which are closer to zero with very high Condition index of 30.983, 49.759 and 100.810 for 𝛽2, 𝛽3 ,and 𝛽4 respectively which indicate that the Multicollinearity present is due greatly to the influence of regressors X2, X3, and X4..

Keywords: Eigen values, Multicollinearity, Standard Errors , Tolerance Level ,Variance Inflation Factor

[1] Belsley, D.A., Kuh, E. &Welsch, R.E.(1980), "Regression Diagnostics: Identifying influential Data and Sources of Collinearity". John Wiley & Sons., New York.
[2] Bowerman, B.L and O‟ Connell, R.T (2006), "Linear Statistical Models an Applied Approach" Boston: PWS-KENT Publishing
[3] Farrar and Glauber (1967), "Multicollinearity in regression analysis" review of economics and statistics, 49, pp. 92-107
[4] Greene (2000), "Econometric Analysis" .Fourth edition, Upper Saddle River, NJ:Prentice- Hall.
[5] Gujarati, D.N. and Porter, D.C. (2009): Basic Econometrics. 5th ed. Mc Graw-Hill, New York. Pp 320-351Haitovsky (1969), "Multicollinearity in Regression analysis Comment," review of economics and statistics, 50, pp. 486-489

Abstract: We consider the unsteady flow of a conducting optically thin visco-elastic fluid through a rotating channel filled with saturated porous medium and non-uniform walls temperature has been discussed taking hall current effects. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. The analytical solutions are obtained for the problem making use of perturbation technique. The effects of the radiation and the magnetic field parameters on velocity profile and shear stress for different values of the visco-elastic parameter with the combination of the other flow parameters are illustrated graphically, and physical aspects of the problem are discussed.

Keywords: Radiation effects, heat transfer, visco-elastic fluids, MHD flows, porous medium, rotating parallel plate channels

[1]. McWhirter, J. D., Crawford, M. E. and Klein, D. E., "Magneto hydro dynamic Flows in Porous Media II: Experimental Results,"
Fusion Technol., Vol. 34, pp.187-197 (1998).
[2]. Geindreau, C. and Auriault, J. L., "Magneto hydro dynamic Flows in Porous Media," J Fluid Mech., Vol. 466, pp. 343-363 (2002).
[3]. Seth, G. S., Jana, R. N. and Maiti, M. K., "Unsteady hydro magnetic Couette Flow in a Rotating System," Int J Engng Sci., Vol. 20,
pp. 989-999 (1982).
[4]. Singh, A. K., Sacheti, N. C. and Chandran, P., "Transient Effects in Magneto-Hydrodynamic Couette Flow with Rotation:
Accelerated Motion," Int J Engng Sci., Vol. 32, pp. 133-139 (1994).
[5]. Chauhan, D. S. and Vyas, P., "Heat Transfer in hydro magnetic Couette Flow of Compressible Newtonian Fluid," ASCE J of Engng
Mech., Vol. 121, pp. 57-61 (1995).

Abstract: Research on "Estimation of Confidence Interval on the Continuous Time Parameter" aims to know the distribution of the parameter on the continuous time especially using structural equation model and the shortest of the confidence interval length. CT model is important to solve some problem on the time series data or some longitudinal data because this method can analyze incomplete data. Beside that CT model can estimate the parameter with other time interval. Due to the importance of the CT model, this article analyzes the estimation of confidence interval for knowing the distribution of the parameter; it is used to test the hypothesis of the significance parameter likely on the regression model. The data that are used are the assessment of mathematic and the experience of the teacher from Trends International Mathematics and Science Study (TIMSS) since 1995 until 2011.
Keywords: continuous time model, structural equation model, confidence interval, bootstrap, TIMSS

1] Baltagi, Econometric Analysis of Panel data. John Wiley, England,2005.
[2] B. Efron , R.J.Tibsirani, An Introduction to The Bootstrap,Chapman Hall, New York,1993.
[3] J.H.L Oud, Continuous time modeling of the cross-lagged panel design, Kwantitatieve Methoden , 2002, 69:1-27.
[4] K. A Bollen, Structural Equation Modelling with Latent Peubah, John Wiley &Son,Inc , New York, 1989.
[5] J.H.L Oud , H.Singer, Continuous time modeling of panel data: SEM versus filter techniques , Statistica Neerlandica, 2008,
62(1):4-28.
[6] J.H.L Oud, R.A.R.G Jansen, Continuous time state space modeling of panel data by means of SEM., Psychometrika, 2000, 65:199-
215.

Abstract: The purpose of the paper is to introduce the notion of generalized recurrent Lorentzian trans-Sasakian manifold and study some of the properties of generalized recurrent and Ricci recurrent Lorentzian Trans-Sasakian manifolds.

Keywords: Local differential geometry, weakly symmetric, weakly Ricci symmetric, α-Sasakian, β-Kenmotsu, Lorentzian Trans-Sasakian manifold

[1]. A. Gray and L.M. Harvella, The sixteen classes of almost Hermitian manifolds and their linear invariants,Ann.Math.Pura Appl, 123(4)(1980), 35-58.
[2]. Ahmed Yildiz, On Lorentzian α- Sasakian manifolds,Kyungpock Math.J. 45 (2005), 95-103.
[3]. A.Y. Mine Turan and Eftal Acet A,On three dimensional Lorentzian α- Sasakian manifolds, Bulletin of Mathematical Analysis and Applications, ISSN 1821-1291 (2009), 90-98.
[4]. G.T. Srinivas, Venatesh and C.S. Bagewadi, On Lorentzian β- Kenmotsu manifolds, General Mathematics, 18(4)(2010), 61-69.
[5]. Hakan Ozturk, et.al. (2010) On α-Kenmotsu manifolds Satisfying Certain conditions pl.sciences vol. 12. , 115-126.

Abstract: Pi value equal to 3.14159265358… is derived from the Exhaustion method of Archimedes (240 BC of Syracuse, Greece. It is the only one geometrical method available even now. The second method to compute 3.14159265358… is the infinite series. These are available in larger numbers. The infinite series which are of different nature are so complex, they can be understood and used to obtain trillion of decimals to 3.14159265358… with the use of super computers only. One unfortunate thing about this value is, it is still an approximate value. In the present study, the exact  value is obtained. It is 14 2 4  = 3.14644660942… A different approach is followed here by the blessings of the God. The areas of constituent rectangles of the superscribed square, are estimated both arithmetically, and in terms of  of the inscribed circle. And  value thus derived from this study of correct relationship among superscribed square, inscribed circle and constituent rectangles of the square, is exact.
Keywords: Circle, diagonal, diameter, area, radius, side, square

[1]. Lennart Berggren, Jonathan Borwein, Peter Borwein (1997), Pi: A source Book, 2nd edition, Springer-Verlag Ney York Berlin Heidelberg SPIN 10746250.
[2]. Alfred S. Posamentier & Ingmar Lehmann (2004), , A Biography of the World's Most Mysterious Number, Page. 25 prometheus Books, New York 14228-2197.
[3]. RD Sarva Jagannada Reddy (2014), New Method of Computing Pi value (Siva Method). IOSR Journal of Mathematics, e-ISSN: 2278-3008, p-ISSN: 2319-7676. Volume 10, Issue 1 Ver. IV. (Feb. 2014), PP 48-49.
[4]. RD Sarva Jagannada Reddy (2014), Jesus Method to Compute the Circumference of A Circle and Exact Pi Value. IOSR Journal of Mathematics, e-ISSN: 2278-3008, p-ISSN: 2319-7676. Volume 10, Issue 1 Ver. I. (Jan. 2014), PP 58-59.
[5]. RD Sarva Jagannada Reddy (2014), Supporting Evidences To the Exact Pi Value from the Works Of Hippocrates Of Chios, Alfred S. Posamentier And Ingmar Lehmann. IOSR Journal of Mathematics, e-ISSN: 2278-3008, p-ISSN:2319-7676. Volume 10, Issue 2 Ver. II (Mar-Apr. 2014), PP 09-12

Abstract: The development of data analysis is still predominanlty use linear statistics. Whereas the research world there are other types of data is data direction. One type of data direction is the data circular. Statistical analysis aimed at modeling the causal relationship between the independent variable and the dependent variable is regression analysis. So as to model the relationship between wind direction and cloud direction against rainfall is circular circular – linear multiple regression analysis. The purpose of this research it to build a model circular circular – linear regression analysis of order m in circular variable α and β against linear variable (Y). Data used in this research is the simulation data and secondary data obtained from the Meteorology, Climatology, and Geophysics in Bogor a cityof West Java, Indonesia. The data is the result of observations of wind direction, coulds direction, and rainfall in february 2014 and march 2014. From the analysis of the data showed that the best model to see the effect of wind direction and could direction against rainfall is circular circular – linear regression analysis to the order four better of the linear multiple regression analysis. It is seen from the sum square of error, p-value, and r-square.
Keywords: data circular, circular circular – linear regression, rainfall.

[1]. Martin GK. 2008. Circular Statistics. Article Alley. http://www.articlealley.com/ circular-statistics-657388.html [17 February 2014]. [2]. Mardia, K.V. dan Jupp, P.E. 2000. Directional Statistics. New York: John Wiley & Sons.
[3]. Jammalamadaka S.R, Sarma Y.R. 1988. A Correlation Coefficient for Angular Variables. In Matusita, K. editor, Statistical Theory and Data Analysis II, pages 349—364. North Holland, Amsterdam.
[4]. Fisher N.I. 1993. Statistical Analysis of Circular Data. Cambridge: Cambridge University Press.
[5]. Jammalamadaka, S.R. dan A. SenGupta. 2001. Topics in circular Statistics. London: World Scientifics Publishing. [6]. Mardia KV. 1976. Linier-Circular Correlation Coefficients and rythmometry. Biometrika, 63, 403-405.

Abstract:The Purpose Of This Paper Is To Introduce Strongly And Perfectly  *Continuous Maps And Basi Properties And Theorems Are Investigated. Also, We Introduced  * Open And Closed Maps And Their Properties Are Discussed. Mathematics Subject Classifications: 54ao5
Keywords : and phrases: strongly  * continuous functions, perfectly  * continuous functions,  *open maps and  *closed maps.

[1]. Y. Beceren. On strongly  - Continuous functions, Far East J. Math. Sci (FJMS) Part I,(2000), 51-58.
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[3]. Levine N.Strong continuity in topological spaces,Amer.Math.Monthly 67(1960)269
[4]. A.S.Mashhour, I.A.Hasanein and S.N.E.L Deeb,  -Continuous and  -open mappings, Acta Math.Hung., Vol.41,(1983), 213-
218.
[5]. Malghan S.R , Generalized closed maps, J.Karnatk Univ. Sci., 27(1982) 82-88

Abstract:Let T be the class of analytic functions of the form:

Keywords and phrases: Analytic function, Univalent function, Starlikeness, Convexity, Coefficient inequalities.

[1]. M. Acu, S. Owa. On some subclass of univalent functions, J. Inequalitity in Pure and Appl. Math., 6 (3) 70(2005), 1-14.
[2]. M. K. Aouf, R.M. El-Ashwali, S.M. El-Deeb, Certain classes of Univalent functions with negative coefficient and n-starlike with
respect to certain points, Malemankn Bectink, 62(3) (2010), 215-226.
[3]. M.K Aouf, A.Shamandy, A.O Mostafa, and S.M Madian, A subclass of m  starlike functions, Acta Universitation
Apulensis No 21 (2010), 135-142.
[4]. J. Dziok, On the convex combination of the Dziok-Srivastava operator, Appl. Math. Comput., 188(2006), 1214-1220.
[5]. R.M. El-Ashwah, D.K. Thomas, Some subclass of close-to-convex functions, J. Ramaunjan. Math. Soc., 2(1987), 86-100.

Abstract:For functions f (z) of the form: which are starlike and convex of order  in the open unit disk U , the authors derive a new subclass of normalized analytic functions in the open unit U . The results presented in this paper generalize many existing results in the literature. Mathematics Subject Classification: Primary 30C45
Keywords: Analytic, Univalent, Close-to-convex, Starlike, Convex, Coefficient inequalities

[1] M. Acu, S. Owa, On some subclass of univalent functions, J. Inequalitity in Pure and Appl. Math., 6 (2005), 1-6.
[2] M.K. Aouf, On a certain class of meromorphic univalent function with positive coefficient Rend. Math., 7 No. 11 (1991), 209-219.
[3] N.E. Cho, S.H. Lee, S. Owa, A class of meromorphic univalent function with positive coefficicent, Kobe J. Math., 4 (1987), 43-50.
[4] J. Clunie, On meromorphic schlicht functions, J. London Math. Soc, 34 (1995), 205-216,
[5] P.L. Duren, Univalent functions, Grundlehren Der Mathematischen Wissenschafen, volume 259, Springer -Verlag, Newyork-Berlin-
Heidelberg-Tokyo (1983).
[6] B.A. Frasin. M. Darus, On certain meromorphic functions with positive coefficients, South East Asian bulletin of Math., 28 (2004),
615-623.

Abstract:A module M is said to be weakly projective iff it has a projective cover  : P (M) M and every mapping P(M) into a finitely generated module can be factored through M via an epimorphism. In particular, if M and N are two R-modules and assume M has a projective cover  : P  M, We say that M is pseudo weakly N-projective if for every map  : P  N there exists an epimorphism  : P  M and a homomorphism g : M  N such that  = g .. In this paper we generalize the basic properties of pseudo weakly projective modules.
Keywords: Pseudo projective module, pseudo weakly projective module, Projective cover.

[1]. Dinguuo Wang and Jinqui Li: Characterization of rings using weakly projective module. Vietnam journal of mathematics.vol.25.(1998)
[2]. Quasi weakly projective and quasi weakly injective module: M.R. Aloney S. Jat. Ultra scientist journal of physical sciences.(2011)
[3]. A.K.Tiwary and B.M.Pandeya: Pseudo projective and pseudo injective modules. B.H.U. Vol.9 No.9(1978)
[4]. S. K. Jain, Lopez - Permouth, K. Oshiro and M. A. Saleh : "Weakly Projective and Weakly Injective Modules." Can. J. Math. Vol 46(5) (1994) 971-981.
[5]. S. R. Lopez - Permouth : Ring Characterized by their Weakly Injective Modules, Glasgow Math. J. 34 (1992) 349-353.

Abstract: Time series analysis is one of statistical procedures in time series data which is applied to predict the conditions that will come in the context of decision making. Generally, the huge size of data not only non linear but also non stationary and it is difficult to be interpreted in concrete. This problem can be solved by performing the decomposition process, the process of changing into a simpler form. Decomposition method that is Ensemble Empirical Mode Decomposition (EEMD). Decomposed time series data can also be used for prediction of the initial data. The ensemble methods can be used such as Fourier analysis used because IMF patterned sinusoid and ARIMA is used because this method is very popular in time series data. The methodology is applied to forecast weekly rice prices in Jakarta province from January 2002 to August 2013.

Keyword: ARIMA, EEMD, Ensemble, Fourier Analysis, Time Series data..

[1]. Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH. 1998. The empirical mode decomposition
and the Hilbert spectrum for nonlinear and nonstationary time series analysis. Proc. Roy. Soc. Lond., A(454):903–995.
[2]. Nursyifa C. 2013. Identifikasi Pola Pergerakan Harga Beras Melalui Dekomposisi Deret Waktu Secara Ensemble. Bogor : IPB.
[3]. Huang NE, Wu Z. 2005. Ensemble empirical mode decomposition: A noise assisted data analysis method. Advances in Adaptive
Data Analysis. 1(1):1-41.
[4]. Zhu M. 2008. Kernels and ensembles: Perspectives on statistical learning. The American Statistican 62 (2): 97-109.
[5]. Wu Z, Huang NE. 2004. A study of the characteristics of white noise using the empirical mode decomposition method. Proc. Roy.
Soc. Lond., A(460):1597-1611

Abstract: A model for the interaction of HIV with the CD T  4 cells was examined in which an optimal treatment parameter was introduced to control the infectivity termin the HIV dynamic model. The control class was chosen to be a measurable function defined with an objective functional which maximizes the T cell count and minimizes the systemic cost based on the percentage effect of the antiretroviral therapy drug. Optimal control was characterized by applying pontryagin's maximum principle. The values of the objective function at the optimal control shows that the greatest effect do occur when treatment is initiated earliest. Also, results of the numerical simulations indicate that the rate of uninfected CD T  4 increased and virus population decreased due to treatment parameter.
Keywords: Drug threrapy, Immunological model,Optimal control, Objective function, Pontryagin's principle

[1]. S. Alan and W. Patrick,Mathematical Analysis of HIV-1 Dynamics in Vivo-Society, Industrial and Applied Mathematics, Vol. 41,
No. 1,1999, pp 3–44.
[2]. H. Ghiasi and N. Chahkandi, Presentation of a Fast Solution For Solving HIV-Infection Dynamics and chemotherapy optimization
based on fuzzy AVK Method, Journal of AIDS and HIV Research Vol4(3),2012, pp.60-67.
[3]. D. Kirschner, S. Lenhart and S. Serbin,Optimal control of the chemotherapy of HIV, Journal of Mathematical Biology,1997,pp 35
775–792.
[4]. D.Kirschner and G.F. Webb,A model for Treatment Strategy in the chemotherapy of AIDS, Bullettin of Mathematical Biology.
1996.
[5]. H. Zarei, A.V Kamyad and S. Effati, Multiobjective Optimal control of HIV Dynamics, Hindawi publishing corporation,
Mathematical problem in Engineering, 2010, pp.1-29.

Abstract: Heat and mass transfer effects on an unsteady MHD flow of a chemically reacting micropolar fluid over an infinite vertical porous plate through a porous medium with Hall effects and thermal radiation in the presence of radiation absorption and heat sink are studied. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using the perturbation technique to obtain the expressions for velocity, microrotation, temperature and concentration. With the help of graphs, the effects of the various important parameters entering into the problem on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed. Also the effects of the pertinent parameters on the skin friction coefficient and rates of heat and mass transfer in terms of the Nusselt number and Sherwood number are presented numerically in a tabular form.

Keywords: Micropolar fluid, Perturbation technique, Heat and mass transfer, Hall effect, Porous medium, radiation absorption and heat sink.

[1]. Eringe, A. C., (1964), "Heat Simple micropolar fluids," International Journal of Engineering Science, Vol. 2, pp. 205-217.
[2]. Eringen, A. C., (1966), "Theory of micropolar fluids," Vol. 16, pp. 1-18.
[3]. Eringen, A. C., (1972), "Theory of thermomicrofluids," Journal of Mathematical Analysis and Applications, Vol. 38, No. 2, pp. 480-496.
[4]. Ariman, T., Turk, M. A., and Sylvester, N. D., (1973), "Microcontinuum fluid mechanics-a review," International Journal of Engineering Science, Vol. 11, No. 8, pp. 905-930.
[5]. Ariman, T., Turk, M. A., and Sylvester, N. D., (1974), "Applications of microcontinuum fluid mechanics," International Journal of Engineering Science, Vol. 12, No. 4, pp. 273-293.

Abstract: In this paper, We introduce a new Class of Closed set namely 𝑃 g Closed Sets . We give characterizations for 𝑃 g Closed Sets and Open sets Further We investigate some of their Fundamental properties.
Keywords: P g -Closed sets, P g -Open sets , Closed sets,Open set , P g Closure, P g Interior.

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