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

Abstract: The concept of graceful labeling was introduced by Solomon Wolf Golomb (May 30, 1932). In this paper we discuss graph and its graceful labeling. Finally we show that V*2Fn is graceful for an n.
Keywords: Graceful tree, graceful labeling, root, stem, branch, leaf, flower.

[1] Douglas B. West., Introduction to Graph Theory, Second edition, Dorling Kindersley (India) Pvt. Ltd. (2001).
[2] Edmonds. J., Paths, trees, and flowers,Can.J.Math.17(1965),449-467.
[3] Frank Harary., Graph Theory, Narosa Publishing House, 1969.
[4] Golomb. S.W., How to number a graph in Graph Theory and computing (ed. R.C. Road) l, Academic Press, 1972.
[5] Graham. R.L and Sloane. N.J.A.,An Additive Bases and Harmonious Graph, SIAMJ. Alg. Discrete. Math., 1 (1980) 382 - 404.

Abstract: In this paper , I have invented the first new type of a scalene quadrilateral and also developed the two new formulae for finding the area of that's new type of quadrilateral. My finding are based on phthagoras theorem.

[1]. Geometry concept & Pythagoras theorem.

Paper Type	:	Research Paper
Title	:	On Restrained 2-Domination Number of the Join and Corona of Graphs
Country	:	Philippines
Authors	:	Esamel M. Paluga, Rolando N. Paluga
	:	10.9790/5728-10241722

Abstract: Let G be a graph. A subset S of V(G) is a restrained 2-dominating set if every vertex of V(G) \ S is adjacent to at least two vertices of S and every vertex of V(G) \ S is adjacent to at least one vertex in V(G) \ S . The restrained 2 -domination number of G , denoted by ( ) 2 G r  , is the smallest cardinality of a restrained 2 -dominating set G . In this paper, we characterize the graphs obtained in the join of two graphs having ( ) = 2,3,4 2 G r  . We also characterize restrained 2 -dominating sets in the corona of two graphs and give a formula for computing the restrained 2 -domination number.

[1]. I.P. Kelkar, J.J. Mohan . Restrained 2-Domination in Graphs. IOSR Journal of Engineerin, Vol 2, Issue 8, August 2010, pp. 06-09.
[2]. Wai Chee Shiu, et.al. On the total restrained domination number of direct product of graphs. Discussiones Mathematicae: Graph
Theory 2012, Vol 32, Issue 4 page 629.
[3]. M.H.Muddebihal, D. Busavarajappa, A.R. Sedamkar Restrained Domination in Graphs. Canadian Journal on Science and
Engineering Mathematics. Vol 2 No.5, Dec 2011
[4]. J.A. Telle and A. Proskurowski. Algorithms for vertex partitioning problems on partial k-trees. SIAM J. Discrete Mathematics,
10(1997), 529-550.
[5]. F. Harary, Graph Theory. Addison-Wesley, Reading MA (1969).

Paper Type	:	Research Paper
Title	:	Availability Analysis of a Standby System with Three Types of Failure Categories
Country	:	India
Authors	:	Dr. Upasana Sharma, Jaswinder kaur
	:	10.9790/5728-10242328

Abstract: The present paper is an attempt to analyze the availability of an operating compressor unit working in a milk plant. In a milk plant's refrigeration system compressor plays an important role. Any major failure or annual maintenance brings the operating unit to a complete halt. It has been observed that the unit can fail due to various types of failures which can be categorized as- serviceable type, repairable type and replaceable type. For availability analysis of the unit real failure as well as repair time data from a milk plant have been collected and measures of unit effectiveness i.e. availability and mean time to unit failure has been computed graphically as well as numerically by using semi-Markov process and regenerative point technique.
Keywords: Compressor unit, Regenerative point technique, Refrigeration system, Semi-Markov process .

[1] R.K. Tuteja, and G.Taneja, "Profit analysis of one server one unit system with partial failure and subject to random inspection",Mi-croelectron. Reliab,vol 33,pp 319-322.1993.
[2] R.K.Tuteja, G.Taneja, and U.Vashistha, " Two-dissimilar units system wherein standby unit in working state may stop even without failure", International Journal of Management and Systems, vol 17 no 1,pp 77-100,2001
[3] M.E.S Khaled, . and S.E.S Mohammed, "Profit evaluation of two unit cold standby systemwith preventive and random changes in units."Journal of Mathematics and Statistics. vol 1, pp. 71-77. 2005
[4] G.Taneja, V.K.Tyagi, and P. Bhardwaj,. "Profit analysis of a single unit programmable logic controller (PLC)", Pure and Applied Mathematika Sciences, vol. LX no (1-2),pp 55-71,2004
[5] G.Taneja, "Reliability and profit analysis of a system with PLC used as hot standby". Proc.INCRESE Reliability Engineering Centre, IIT, Kharagpur India, pp: 455-464.,2005(Conference proceedings).

Paper Type	:	Research Paper
Title	:	Study of Visco-Elastic Fluid Flow and Heat Transfer over a Stretching Sheet with Variable Viscosity and Thermal Radiation
Country	:	India
Authors	:	M. Ramya, K. Sangeetha, M. Pavithra
	:	10.9790/5728-10242934

Abstract: This dissertation deals with the boundary layer flow and heat transfer in a visco-elastic fluid flow a stretching sheet in the presence of radiation. Two different temperature are studied here, (i) PST, that is the sheet with prescribed surface temperature (ii)PHF, that is the sheet with prescribed heat flux. The basic boundary layer equations for momentum and heat transfer which are non-linear parital differential equation is converted into non-linear ordinary differential equation using similarity transformation. The resulting non-linear equation is solved using numerical shooting method for three unknown initial conditions with fourth order Runge-Kutta method. To know the physics of the problem, numerical results are discussed with the help of graphs for various of parameters, such as fluid viscosity parameter, visco-elastic parameter, Prandtl number, Eckert number, heat source/sink parameter and radiation parameter.

[1]. Andersson,H.I., MHD flow of a visco-elastic fluid past a stretching surface, Acta. Mech., 95, 1992, 227-232
[2]. Abo-Eldahab Emad,M and EI AZIZ mohammed,A., Blowing suction effect on hydromagentic heat transfer by mixed convection from an inclined continuously stretching surface with internal heat generation/absorption, Int. J. Therm science, 45, 2004, 709-719
[3]. Bataller, P ., Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet, computer and maths with Appl., 35, 2007, 305-316
[4]. Chen, C.K and Char, M.I ., Heat transfer on a continuous stretching surfaces with suction or blowing, J. Math .Anal. Appl., 33, 1988, 568-580
[5]. Carragher, P and Crane L.J ., Heat transfer on a continuous stretching sheet, ZAM P, 12, 1982, 564-565

Paper Type	:	Research Paper
Title	:	On generalized Weyl's type theorem
Country	:	Morocco
Authors	:	A. Babbah, M. Zohry
	:	10.9790/5728-10243541

Abstract: It is shown that if a bounded linear operator T or its adjoint T* has the single-valued extension property, then generalized Browder's theorem holds for f(T) forevery f ∈ H(σ(T)). We establish the spectral theorem for the B-Weyl spectrumwhich generalizes [21, Theorem 2.1] and we give necessary and sufficient conditionsfor such operator T to obey generalized Weyl's theorem.
Keywords: Single-valued extension property, Fredholm theory, generalizedWeyl's theorem, generalized Browder's theorem.

[1]. B. A. Barnes, Riesz points and Weyl's theorem, Integr. Equ. Oper. Theory, 34 (1999), 187-196.
[2]. M. Berkani, Index of B-Fredholm operators and generalization of a Weyl theorem, Proc. Amer. Math. Soc., 130 (6) (2001), 1717-
1723.
[3]. M. Berkani, On a class of quasi-Fredholm operators, Integ. Equ. Oper. theory,34 (1999), 244-249.
[4]. M. Berkani, B-Weyl spectrum and poles of the resolvent, J. Math. Anal., 272 (2002), 596-603.
[5]. M. Berkani and J. J. Koliha, Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged), 69 (2003), 359-376.

Paper Type	:	Research Paper
Title	:	Positivity Preserving Interpolation of Positive Data by Rational Quadratic Trigonometric Spline
Country	:	India
Authors	:	M. Dube, P. S. Rana
	:	10.9790/5728-10244247

Abstract: In Computer Aided Geometric Design it is often needed to produce a positivity preserving curve according to the given positive data. The main focus of this work is to visualize the positive data in such a way that its display looks smooth and pleasant. A rational quadratic trigonometric spline function with three shape parameters has been developed. In the description of the rational quadratic trigonometric spline interpolant, positivity is preserved everywhere. Constraints are derived for shape parameters to preserve the positivity thorough positive data. The curves scheme under discussion is attained C1 continuity.
Keywords: Interpolation, positivity, Rational quadratic trigonometric spline, Shape parameters.

[1] Butt, S. and Brodlie, K.W., Preserving positivity using piecewise cubic interpolation. Comput. Graphics, vol. 17, no. 1, 1993, pp. 55-64.
[2] Sarfraz, M., Hussain, M.Z. and Nasar, A., Positive data modeling using spline function. Applied Mathematics and Copmputation. 2010, vopl 216, pp. 2036-2049.
[3] Hussain, M.Z. and Ali, J.M., Positivity preserving piecewise rational cubic interpolation. Mathematika, vol, 22, 2006, pp. 147-153.
[4] Gregory, J.A. and Sarfraz, M., A rational cubic spline with tension. Computer Aided Geometric Design, vol. 7, no. 1-4, 1990, pp. 1-13.
[5] Schmidt, J. and He , W., Positivity of cubic polynomial on intervals and positive spline interpolation. BIT 1988, vol. 28, pp. 340-352.

Paper Type	:	Research Paper
Title	:	The Co-action of Lie group on Hom Space
Country	:	Iraq
Authors	:	Abid A.. Al-Ta'ai, Hoor M. Hussein
	:	10.9790/5728-10244854

Abstract: let G be a Lie group, and is a dual representation of G, In this paper we will present and study the concepts of co-action of Lie group on Hom space, we recall the definition of tensor product of two representations of lie groups and construct the definition of co-action of Lie group, and also study the properties of this action. we use the co-action of Lie group on Hom space combining with another Hom space having the same structure with different vector space, .so we have new co-action which called double co-action of Lie group G, denoted by Co-AAC_Lie group which acting on .
Keywords: Action Group, CO-AC-Lie group, CO-AAC-Lie group, Tensor space, Hom space.

[1] Hall, B. C., "Lie Groups, Lie Algebras and Representations, An Elementary Introduction", Springer, USA, May, 2004.
[2] Usenko, V. and Lev, I. B., "Spinor Representation of Lie Algebra for Complete Linear Group", Uktaine, 46, Nauky. Ave, NAS, Vol.50, Part 3, pp.1202-1206.
[3] Wan, Z. X., "Lie Algebras", Translated by Lee, Che-Young, ISBN, Volume 104, 1975.
[4] Keith Jones,"Notes on Lie Groups",December 25, 2007, kjones@math.binghamton.edu
[5] Wolfgang Ziller," Lie Groups. Representation Theory and Symmetric Spaces" University of Pennsylvania, Fall 2010.

Paper Type	:	Research Paper
Title	:	Wilcoxon signed rank test for imprecise observations
Country	:	India
Authors	:	V. S. Vaidyanathan
	:	10.9790/5728-10245559

Abstract: This article extends the Wilcoxon signed rank test for testing whether the median of a population is a specified constant by treating the observations as imprecise values. The test procedure is developed by using the concepts of "Credibility Theory" for studying the behavior of fuzzy phenomena. Numerical illustration of the proposed test is provided by representing the observations as trapezoidal fuzzy numbers.
Keywords: Credibility measure, fuzzy number, fuzzy ordering, Wilcoxon test.

[1] Lehmann, E.L. and Romano, J.P., Testing statistical hypothesis (Springer, 2005).
[2] Gibbons, J.D. and Chakraborti, S., Nonparametric statistical inference (Marcel Dekker, New York, 2003, 4th edition).
[3] Zadeh, L.A., Fuzzy sets, Information and Control, 8(3), 1965, 338-353.
[4] Kruse, R., Statistical estimation with linguistic data, Information Sciences, 1984, 197-207.
[5] Kruse, R. and Meyer, K.D., Statistics with vague data (Reidel, Dordrecht, 1987).

Paper Type	:	Research Paper
Title	:	Radiation Effect on Mixed Convection Flow of a Micropolar Fluid over an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation
Country	:	India
Authors	:	M. Suryanarayana Reddy, S. Vijaya Lakshmi
	:	10.9790/5728-10246072

Abstract: The unsteady, two dimensional, mixed convection flow of an viscous incompressible electrically conducting micropolar fluid over a vertical and impermeable stretching surface in the presence of Heat source/sink and radiation when the buoyancy force assists and opposes the flow has been studied. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, forth order Runge-Kutta method along with shooting technique has been used for solving it. Numerical results are obtained for the skin-friction coefficient, the couple wall stress and the local Nusselt number as well as the velocity, microrotation and temperature profiles for different values of the governing parameters, namely, material parameter, unsteadiness parameter, heat source/sink parameter, radiation parameter and Eckert number.
Keywords: unsteady flow, mixed convection, Heat Transfer, micropolar fluid, Stretching surface, heat generation, radiation and viscous dissipation.

[1]. Eringen, A.C., (1960), Theory of micropolar fluids, J. Math. Mech., Vol. 6, pp. 1-18.
[2]. Eringen, A.C., (1972), Theory of thermomicropolar fluids, Math. Anal. Appl. J., Vol. 38, pp.481-496.
[3]. Willson, A.J., (1970), Boundary-layer in micropolar liquids, Proc. Cambridge Philos. Soc., Vol. 67, pp.469–476.
[4]. Bergholz, R.F., (1980), Natural convection of a heat generating fluid in a closed cavity, ASME J. Heat Transfer, Vol.102, pp.242–247.
[5]. Chandra Shekar, B., Vasseur, P., Robillard, L., Nguyen, T.H., (1984), Natural convection in a heat generating fluid bounded by two horizontal concentric cylinders, Can. J. Chem. Eng., Vol. 62, pp.482–489.

Paper Type	:	Research Paper
Title	:	Multidimensional integral transform involving I-function of several complex variables as kernel
Country	:	India
Authors	:	Prathima J., Vasudevan Nambisan T. M.
	:	10.9790/5728-10247380

Abstract: The theory of integral transforms is very useful in solving various types of boundary value problems. By giving various values to the kernel k(x; s) and considering the interval (0, 1) generally, a number of integral transforms have been introduced and studied by several authors from time to time. In the present paper we have introduced multidimensional I-function transform involving I-function of r variables as kernel. In our earlier paper we have established the multiple Mellin transform of product of two I-functions. With the help of that result, in the present paper we have discussed some theorems on multidimensional I-function transform. Special cases include the results involving H-function of several complex variables, I-function of two variables and Hfunction of two variables. The special case also includes the results given by V.C.Nair.
Keywords: Mellin-Barnes integral, H-function, H-function transform, I-function, Multidimensional I-function transform

[1]. K. Rathie, A new generalization of generalized hypergeometric functions, Le Matematiche, vol. 52, no. 2, 1997, pp. 297-310.
[2]. I.S.Ansari, F.Yilmaz, M.S.Alouni and O.Kucur, On the sum of gamma random variates with application to the performance of
maximal ratio combining over Nakagami-m fading channels,Signal Processing Advances in Wireless Communications (SPAWC),
2012 IEEE 13th International Workshop, 2012, 394 398.
[3]. I.S.Ansari,, F.Yilmaz, and M.S.Alouni,On the Sum of Squared eta- Random Variates with Application to the Performance of
Wireless Communication Systems, Vehicular Technology Conference (VTC Spring), 2013 IEEE 77th, 2013, 1-6.
[4]. Xia Minghua, Wu Yik-Chung and Aissa Sonia, Exact Outage Probability of Dual-Hop CSI- Assisted AF Relaying Over
Nakagami-m Fading Channels, IEEE Transactions on Signal Processing,60(10), 2012, 5578-5583.
[5]. K.Shanthakumari,T.M.Vasudevan Nambisan,K. Arjun Rathie, A study of the I-function of two variables,To appear in Le
Matematiche. Also see arXiv:1212.6717v1 [math.CV].30Dec2012.

Paper Type	:	Research Paper
Title	:	A Study of Psychological Morbidity among Female Sex Workers
Country	:	India
Authors	:	Kasthuri. Pandiyan, H. Chandra Shekar, N. R. Prashanth, A. Gangadara
	:	10.9790/5728-10248188

Abstract: The psychological distresses are higher in women in sex industry. The confluence of drug use, mental stressors, poverty, sexually transmitted diseases, low self-esteem and high-risk partners forms a fertile ground for psychological morbidity. Prostitution is associated with a host of psychosocial vulnerabilities and disadvantages [1]. Socio-demographic disadvantages like minority, ethnic status, low income, homelessness, low education level are linked with commercial sex workers [2,3]. This study was undertaken to assess the psychiatric morbidity in female commercial sex workers likely to be involved in sexual high risk taking behavior. 30 consecutive female sex workers attending the psychiatric OPD at Victoria hospital were assessed clinically after informed consent and relevant investigation.
Key words: psychological morbidity; female sex workers.

[1]. Mandi L, Burnette, Lucas M, Ilgen M, Frayne SM, Mayo J, Julie C, Weitlauf. Prevalence and Health Correlates of Prostitution Among Patients Entering Treatment for Substance Use Disorders. Arch Gen Psychiatry 2008; 65: 337-344
[2]. Medrano MA, Hatch(1 ) JP, Zule WA, Desmond DP. Childhood trauma and adult prostitution behaviour in a multiethnic heterosexual drug-using population. Am J Drug Alcohol Abuse. 2003; 29: 463-486
[3]. Gilchrist G, Gruer L, Atkinson J. Comparison of Drug Use and Psychiatric Morbidit between Prostitute and Non-Prostitute Female Drug Users In Glasgow, Scotland. Addict Behav. 2005; 30(5):10194. El-13Bassel N, Schilling RF, Irwin KL, Faruque S, Gilbert L, Von Bargen J, Serrano Y, Edlin BR. Sex trading and psychological distress among women recruited from the streets of Harlem. Am J Public Health. 1997; 87(1):66-70.
[4]. Kelly JA, Murphy DA, Baker GR. Factors associated with severity of depression and high risk sexual behaviour among persons diagnosed with HIV infection. Health Psychol (1993) 12:215–219
[5]. Vanwesenbeeck I. Burnout among female indoor sex workers. Arch Sex Behav (2005) 34:627.[CrossRef]