iosr-Jm   Volume-12 ~ Issue-6 ~ Nov-Dec 2016

Abstract: Let G  (V,E,F) be a simple, finite, plane graph with |V (G)| number of vertices, |E (G)| number of edges and |F (G)| number of faces. A labeling of type (1,1,0) is a bijective mapping from the vertex set and edge set of G to the set {1, 2,…, |V (G)| + |E (G)|}. Moreover, the labeling is called super if the vertices are labeled with the smallest numbers. The weight of a face under the labeling is the sum of labels of edges and vertices surrounding that face. In this paper we study face bimagic labeling of type (1,1,0) for wheels, cylinders and disjoint union of m copies of prism graphs.

Keywords - Wheel, cylinders, prism, face bimagic labeling

[1]. A. Ahmad, M. Bača, M. Lascsáková, and A. Semaničová-Feňovčíková, Super magic and antimagic labelings of disjoint union of
plane graphs, Science International, 24, 2012, 21-25.
[2]. M.A. Ahmed, and J.B. Babujee, Bimagic labeling for strong face plane graphs, International Conference on Mathematical
Computer Engineering, VIT University, Chennai, India, 2015.
[3]. K. Ali, M. Hussain, A. Ahmad and M. Miller, Magic Labelings of type (a,b,c) of families of wheels, Math. Computer Sci, 7, 2013,
315-319.
[4]. J.B. Babujee, Bimagic labeling in path graphs, The Mathematics Education, 38, 2004, 12-16.
[5]. J.B. Babujee, On edge bimagic labeling, J. Combin. Inf. Syst. Sci, 28, 2004 , 239-244.

Abstract: The concept of intuitionistic fuzzy set and intuitionistic fuzzy topological space were defined by Atanssov. Later Coker introduced the concept of intuitionistic set and intuitionistic points. He also introduced the concept of intuitionistic topological space and investigated basic properties of continuous function and compactness. In a recent paper, the concept of intuitionistic  -open, intuitionistic -closure and intuitionistic -interior in intuitionistic topological space were defined by Singaravelan. Also some basic properties of intuitionistic -open set were discussd. The purpose of this paper is to introduce and study the concept of intuitionistic -continuous functions in intuitionistic topological space and studied its relation with other existing intuitionistic continuous functions.

Keywords - Iβ-open sets, Iβ-closed sets, Iβ- closure, Iβ- interior, Iβ- continuous.

[1]. M.E.Abd EI-Monsef, S.N. EI-Deeb and R.A.Mahmoud, -open sets and -continuous mappings, Bull.Fac.Sci.Assiut Univ. 12(1)(1983), 77-90.
[2]. D.Andrijevic, Some properties of the topology of α-sets, Mat.Vesnik 36(1984), 1-10.
[3]. D.Andrijevic, Semi-preopen sets, Mat.Vesnik, 38(1986), 24-32.
[4]. K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, No.1 (1986), 87-66.
[5]. A. Csaszar( Budapest), Generalized open sets, Acta Math. Hungar, 75(1-2)(1997), 65-87.

Abstract: Canonical correlation is a multivariate tool that measures the strength of association between two sets of variables. It extends bivariate correlation, allowing more than two independents variables with more than two dependent variables to be analyzed together at once. This correlation tells us how the best linear combinations of predictor variables related to the best linear combinations of the dependent variable. Canonical correlation analysis determines a set of canonical variates, orthogonal linear combinations of the variables within each set that best explain the variability both within and between sets.

[1]. Onyenanu O.A. (2007). Canonical correlation analysis on the comparison of Jamb results and post jamb result 2006-2007 session,
Unpublished B.Sc research project, Nnamdi Azikiwe University, Awka, Nigeria.
[2]. Akinboade- Orire L. (2016).Why FG of Nigeria Scrapped post UMTE tests, Vanguard News June 3, Follow@vanguardngrnews,
http://www.vanguardngr.com/2016/06/fg-scrapped-post-utme-tests/
[3]. Borga M. (2001). Canonical correlation a Tutorial, www.imt.liu.se/ magnus/ cca / tutorial/ tutorial.pdf
[4]. Hair J. F, Anderson Jr. R.E, Tatham R. L, and Black W. C (1995). Canonical correlation a supplement to multivariate data analysis,
Multivariate Data Analysis, Pearson Prentice Hall Publishing, 1-44.

Abstract: In interference theory of reliability, reliability expressions for multi-component systems are not simple enough to facilitate analytical estimation of reliability and its other characteristics. Here, we have shown how reliability R = P(X<Y<Z) can be estimated by Monte-Carlo simulation (MCS) for n-standbys when stressstrength both follows a particular continuous distribution

Keywords - Reliability, Stress-Strength(S-S); Monte-Carlo Simulation (MCS)

[1]. Ahmad, K.E., Fakhry, M.E. and Jaheen, Z.F., (1997): "Empirical Bayes Estimation of P(X>Y) and Characterizations of Burr-type X model‟, Journal of Statistical Planning and Inference, Vol. 64, Issue: 2. pp. 297-308.
[2]. Aldrisi, M. M., (1987): "A Simulation Approach for Computing System Reliability‟, Microelectronics Reliability, Vol. 27, Issue: 3,
pp. 463-467.
[3]. Church, J.D. and Harris, V., (1970): "The Estimation of Reliability from Stress-Strength Relationship‟, Technometrics, Vol.12,
Issue: 1, pp.49-54.
[4]. Dutta, K. and Sriwastav, G.L., (1986): "An n-Standby System with P (X < Y < Z)‟, Indian Association of Productivity , Quality
and Reliability Trans. Vol. 12, No. 1-2, pp. 95-97.
[5]. Guangming, P., (2013): "Non Parametric Statistical Inference for P(X<Y<Z)‟, Sankhya: Indian Journal of Statistics, Vol.75-A,
pp.118-138.

Abstract: In this paper, the notions of ,q -Q-fuzzy subgroup and normal subgroup are introduced and some of their properties are investigated.

Keywords - Q-fuzzy subgroup and normal subgroup, Fuzzy point, ,q -Q-fuzzy subgroup

[1]. A. Rosenfield, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971), 512-517.
[2]. A. Solairaju and R. Nagarajan, A New Structure and Construction of Q-fuzzy groups, Advances in Fuzzy Mathematics, Vol. 4(1),
(2009), pp 23-29.
[3]. A. Solairaju and R. Nagarajan, Q-fuzzy left R-subgroups of near rings w.r.t. T-norms, Antarctica Journal of Mathematics. 5, (1-2),
2008.
[4]. K. H. Kim, Y. B. Jun, Normal fuzzy r-subgroups in near rings, Fuzzy Sets and Systems, 121 (2001) 341-345.
[5]. K. H. Kim, Y. B. Jun, On fuzzy R-subgroups of near rings, J. fuzzy math. 8 (3) (2000) 549-558

Abstract: The present paper deals with the study of magneto hydrodynamics boundary layer flow of nanofluid past a stretching sheet. Here second order velocity slip boundary condition is considered. The governing equations are transformed into nonlinear coupled ordinary differential equations with the help of suitable similarity transformations. These equations were then solved numerically by using an implicit finite difference well known method as Kellerbox scheme.............

Keywords - Nanofluid, magnetohydrodynamic, boundary layer flow, stretching sheet, slip condition.

[1]. S. Kakac, A. Pramuanjaroenkij. (2009) " Review of convective heat transfer enhancement with nano fluids" Int. J. Heat Mass Transfer 52 ,pp3187–3196.
[2]. H.S. Takhar,A.J. Chamkha,G. Nath.(2001)"Unsteady three-dimensional MHDboundary-layer flow due to the impulsive motion of a stretching surface" ,Acta Mech.146 pp59–71.
[3]. J.Vleggaar.(1977)"Laminar boundary layer behaviour on continuous acceleratingsurface", Chem. Eng. Sci. 32 pp 1517–1525.
[4]. L.J. Crane.(1970) "Flow past a stretching plate", J. Appl. Math. Phys. (ZAMP) 21 pp 645–647.
[5]. K.N.Lakshmisha, S.Venkateswaran, G.Nath.(1988) "Three-dimensional unsteady flow with heat and mass transfer over a continuous stretching surface", ASME J. Heat Transfer 110 pp 590–595.

Abstract: right near – ring N is called weak commutative if xyz = xzy for every x,y,z ϵ N (Definition 9.4 [10]). A right near – ring N is called pseudo commutative (Definition 2.1 [11] ) if xyz = zyx for all x,y,z ϵ N.A right near – ring N is called quasi – weak commutative (Definition 2.1 [7]) if xyz = yxz for all x,y,z ϵ N. We call a right near – ring N to be weak m – power commutative if xym z = xzm y for all x,y,z ϵ N. N is said to be weak (m,n) power commutative near – ring ifxymzn = xzmyn for all x,y,z ϵ N.In this paper we study and establish various results of weak m – power commutative near – ring and weak (m,n) power commutative near -- ring.

[1]. .H.E.Bell,Quasi Centres,Quasi Commutators, and Ring Commutativity,Acta Maths,Hungary4( 1 – 2 )(1983), 127 – 136.
[2]. L.O.Chung and Jiang Luh,Scalar Central elements in an algebra over a Principal ideal domain,Acta Sci.Maths 41,(1979),289 – 293.
[3]. G.Gopalakrishnamoorthy and R.Veega, On Quasi – Periodic,Generalised Quasi-Periodic Algebras,Jour.of Inst. of Mathematics and Computer Sciences,Vol 23,No 2 (2010).

Abstract: This paper proposes a semiparametric non-linear (SPNL) model that incorporates the relationship between individual independent variable and unobserved heterogeneity variable. Five different estimation techniques namely; Least Square (LS), Generalized Method of Moments (GMM), Continuously Updating (CU), Empirical Likelihood (EL) and Exponential Tilting (ET) Estimators were employed for estimation, for the purpose of modelling the independent variables non-linearly on metrical response variable. The performances of these estimators were examined at different levels of multicollinearity..........

Keywords - Panel data; Multicollinearity; Non-Linear; Model; Estimator.

[1]. Akeyede and B.L. Adeleke (2015). Nonlinear time series model. Unpublished Ph. D dissertation, University of Ilorin, Nigeria.
[2]. Chandra R. Bhat (2000). Duration Modeling, The University of Texas, Austin Press
[3]. Damodar N. Gujarati (2009). Basic Econometrics, Fifth Edition. Mc Graw Hill,Singapore
[4]. Doug Walker (2008). "Incorporating Competitor Data into Customer RelationshipManagement". Published Ph.D. dissertation, Iowa State University.
[5]. Degui Li, Jia Chen And Jiti Gao (2011). Non-parametric time-varying coefficient panel data models with fixed effects. Econometrics Journal, volume 14, Pp. 387–408.

Abstract: The objective of this paper is to study the behaviour of the server breakdown and repair in an / ( , )/1 [ ] M G a b X queueing system with two heterogeneous service, multiple vacation, closedown, balking and stand-by server. After a first stage of service to a batch of customers the main server serves the second stage of service to the same batch of customers. The main server may breakdown at any stage of service with exponential rate '  , then the main server go for a repair service which follows exponential with rate ' and the interrupted stage of service to a batch of customers is transferred to the stand-by server and he starts a interrupted stage service to that batch of customers a fresh...........

Keywords - Bulk service, Two heterogeneous service, Multiple vacation, Stand-by service.

[1]. M.F. Neuts, A general class of bulk queues with poisson input, The Annals of Mathematical Statistics 38(3) (1967) 759-770.
[2]. F. Downton, Waiting time in bulk service queues, Journal of the Royal Statistical Society. Series B (Methodological) 17(2) (1955)
256-261.
[3]. N.K. Jaiswal, Bulk-service queuing problem, Operations Research 8(1) (1960) 139-143.
[4]. K.C. Madan, Walid Abu-Dayyeh, Steady State Analysis of two / ( , )/1 [ ] M M a b X queue models with random
breakdowns,Information and Management Sciences 14(3) (2003) 37-51.
[5]. K.C. Madan, A bulk input queue with a stand-by, South African Statistical Journal 29 (1995) 1-7.

Abstract: This is a qualitative descriptive study by applying learning media with Lesson Study in the learning process. The learning process in this research included the implementation of learning, students activities and students responses. However, it did not exclude learning outcomes. The target product in this study were (1) Media/props used in learning; (2) learning tools that suit the media used; (3) The Lesson Study is expected to become input for schools as a reference for educators to be more innovative in the use of media that can be used by any educators both in Palopo and in other regions.

Keywords - Learning Media, Lesson Study, Learning Process

[1]. Arsyad. Media Pembelajaran. Jakarta : PT. Raja Grafindo Persada.2002
[2]. Mulyana. Mengembangkan Soal Terbuka (Opend-Ended) Dalam Pembelajaran Matematika. Proseding Seminar Nasional (457-479). Yogyakarta: Universitas Negeri Yogyakarta. 2007
[3]. Suwarsono. Topik-Topik Penelitian Dalam Bidang Pendidikan Matematika dan Klasifikasi Penelitian (Jenis-jenis Penelitian), Bahan Kuliah, Program Pascasarjana S3 Pendidikan Matematika. UNESA. Tidak dipublikasikan. 2015

Abstract: In this paper, we proposed two efficient algorithms to minimizing the fuzzy cost. First we obtained the optimal value of fuzzy assignment problem using one's termination method. Next, we separate the Fuzzy assignment cost into lower and upper bound of the  cut interval and we analyzed the range of certainty of FAP by statistical approach. A numerical example is included............

Keywords -  α- cut, Triangular Fuzz Number (TFN), T- test, One Termination Method

[1]. AbhinavBansal, Trapezoidal Fuzzy Numbers Arithematic Behavior, International journal of Physical and Mathematical Sciences,
2011, 39-44.
[2]. A.Bogomolnaia and A.MoulinA. A New solution to the Random Assignment Problem, Journal of Economic Theory,100, 2001,
295- 328.
[3]. N.Belacela and M.R. Boulasselb , Multicriteria Fuzzy Assignment Method, Artificial Intelligence in Medicine, 21, 2001, 201- 207
[4]. D. Coppersmith and G.B. Serkin, Constructive Bounds and Exact Expectation for the Random Assignment Problem, Random
Structure and Algorithm, 15(2), 1999, 113 -144.
[5]. E. Gillett Billy, Introduction to Operations Research A Computer Oriented Algorithmic Approach, Tata Mc-Graw Hill, New Delhi.
2000

Abstract: In this paper we study invariant submanifolds of (k, μ) -contact manifold. Here we investigate the conditions for invariant submanifolds of................

Keywords - Invariant submanifold, (k, μ) - contact manifold, totally geodesic.

[1]. Avijit Sarkar, On Submanifolds of Sasakian Manifolds, Lobachevskii Journal Of Mathematics, 32 (1) (2011), 88-94.
[2]. Avik De, A note on invariant submanifolds of -contact manifolds,Ukranian Mathematical J. 62, 11(2011), 1803-1809.
[3]. D.E. Blair, Contact manifolds in Riemannian geometry, Lecture notes in Math., 509, Springer-Verlag, Berlin (1976).
[4]. D.E. Blair, T. Koufogiorgos and B. J. Papantoniou Contact metric manifolds satisfyng a nullity condition,Israel J. Math., 91 (1995),
189-214.
[5]. E. Boeckx, A full classification of contact metric -spaces,Illinois J. Math. 44 (2000), 212-219.

Abstract: This article includes a technique to derive shape functions in global co-ordinates for general quadrilateral finite elements. It identifies clearly the element geometry for which the shape functions in global co-ordinates cannot be derived and explains the way to overcome such situation. Finally, it presents formulae based on array multiplication for exact computation of different types of element matrices needed for the employment of the said element in finite element solution procedure. The computation process of element matrices require only..............

Keywords - Global co-ordinates, shape functions, Quadrilateral elements, inverse and monomials.

[1]. Zienkiewicz, O.C.and Cheungy.K.,The Finite Element in the Solution of Field Problems.(The Engineer, 220: pp. 507-510, 1965).
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[3]. Okabe, M., Analytical Integration Formulae related to Convex Quadrilateral Finite Elements, Comput. Methods Appl. Mech. Engg. 29, 1981, 201-218.
[4]. Zienkiewicz, O.C.and Morgan, K., Finite Element and Approximation. (John Wiley & Sons, Inc., New York, 1983).
[5]. Babu, D. and Pinder, G.F., Analytical integration formulae for linear isoparametric finite elements, Int. J. Num. Meth. Engg., 20, 1984, 1153-1166.

Abstract: Multivariate data depth functions are designed to provide a center- outward ordering (and thus a ranking) of points in p R . Three multivariate depth functions are studied in this article and used to test the equality of mean vectors. The depth of three different datasets were found and used as rank in Kruskal-Wallis non-parametric test to test the hypothesis of equality of means. The three data depth functions were compared based on the results of our analysis and we found Mahalanobis data depth to be the best among the three

Keywords - Spatial depth, Projection depth, Mahalanobis depth, Kruskal-Wallis test, Metric space, Norn and Mahalanobis distance

[1]. Chakraborty, A. and Chaudhuri, P. (2014). On data depth in infinite dimensional spaces. Annals of the Institute of Statistical
Mathematics, 66,303-324. DOI10.1007/s10463-013-0416-y
[2]. Folorunso, S. A., Chukwu, A. U. and Oluwasola, T. A. (2015). The cox regression model with application to predict admission
lifetime of female genital cancer, Conference Proceedings of Nigerian Statistical Association Osun State Secretariat, Osogbo, 375- 386.
[3]. Ghosh, A.K. and Chaudhuri, P. (2005). On maximum depth and related claaifier. Scandinavian Journal of Statistics, 32, 327-350.
[4]. Jornsten, R. (2004). Clustering and classificsation based on the L1 data depth. Journal of Multivariate Analysis, 90, 67-89.
[5]. Kruskal, W.H. and Wallis, W.A. (1952).Use of rank in one criterion variance analysis, Journal of the American Statistical
Association, 47, 583-621.