iosr-Jm   Volume-11 ~ Issue-1 ~ Jan-Feb 2015

Abstract: In this paper we investigate prime labelling of some new graphs. We prove that the graphs such as flower graph F, the splitting graph of Star , the bistar , the friendship graph the graph SF(n,1) are prime graphs.

Key Words: Prime Labelling, Splitting graph, Star, the bistar , the friendship graphthe graph SF (n, 1).

[1]. J.Gross and J.Yellen, " Graph Theory and Its Applications", CRC Press, Boca Raton, 1999.
[2]. J.A.Gallian, " A Dynamic survey of Graph Labelling", The Electronic Journal of Combinatorics, Vol.18,2011.
[3]. S K Vaidya and N H Shah, " Graceful and odd graceful labelling of some graphs", International Journal of Mathematics and Soft Computing, Vol.3,No.1(2013), 61-68.
[4]. Sami K.Vaidya, Udayam M.Prajapai, " Some New Results in Prime Graphs", Open Journal of Discrete Mathematics,2012,1,99-104.
[5]. S.K.Vaidya and N.H.Shah, " On Square Divisor Cordinal Graphs", Journal of Scientific Research 6(3), 445-455 (2014).

Abstract: In this paper we prove the existence of the solution for the second order nonlinear functional random differential equation in Banach Algebra under suitable condition. 2000 Mathematics Subject Classification: 47H10, 34F05.

Keywords and Phrases: functional Random differential equation, Existence theorem etc.

[1]. B.C. Dhage, Random Fixed Point theorems in Banach Algebras with applications to random integral equations, Tamkang J. Math. 34 (2003), pp. 29-43.
[2]. B.C. Dhage, A random version of Schaefer's fixed point theorem with applications to functional integral equations. Tamkang J. Math 35 (3) (2004), pp. 197-205.
[3]. C.J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), pp 53-72.
[4]. D.W. Boyd and J.S.W. Wong, On nonlinear contractions Proc. Amer. Math. Soc. 20 (1969), pp. 456-464
[5]. B.C. Dhage, On existence theorem for nonlinear integral equations in Banach algebras via fixed point technique, East Asian Math.J. 17 (1) (2001), pp. 33-45.

Abstract: An operator T B(H) is said to be absolute - (p, r) - paranormal operator if for all xH and for positive real number p > 0 and r > 0, where T = U |T| is the polar decomposition of T. In this paper, we prove that continuity of the set theoretic functions
spectrum, Weyl spectrum, Browder spectrum and essential surjectivity spectrum on the classes consisting of (p,
k) - quasihyponormal operators and absolute - (p, r) - paranormal operators.
Keywords: absolute - (p, r) - paranormal operator, Weyl's theorem, Single valued extension property, Continuity of spectrum, Fredholm, B – Fredholm

[1]. Aiena. P, Fredholm and Local Spectral Theory with Applications to Multipliers, Kluwer Acad. Pub., 2004.
[2]. Aiena. P and Monsalve. O, Operators which do not have the single valued extension property, J. Math. Anal. Appl., 250 (2000),
435 -- 438.
[3]. Apostol. C, Fialkow. L. A, Herrero. D. A, Voiculescu. D, Approximation of Hilbert space operators, Vol. II, Research Notes in
Mathematics., 102, Pitman, Boston (1984).
[4]. Berkani. M, On a class of quasi - Fredholm operators, Inter. Equat. operator Theory., 34 (1999), 244 -- 249.
[5]. Berkani. M, Index of B - Fredholm operators and generalization of the Weyl theorem, Proc. Amer. Math. Soc., 130 (2002), 1717 --
1723.
[6]. Burlando. L, Noncontinuity of the adjoint of an operator, Proc. Amer. Math. Soc., 128 (2000), 479 -- 486.

Abstract: The quality of learning and teaching Mathematics has been one of the major challenges and concern of the educators. Mathematics is often considered as a subject that a student either understand or doesn't with little in between. Now a days modeling is one of the central ideas in mathematics education. The concept of teaching is fundamental for the study of student cognitive action. In this paper we have developed a model for mathematics teaching and analyses the skill of teachers using fuzzy logic.

Keywords: Fuzzy sets and logic, Possibility, Probability, Uncertainty

[1]. Zadeh, L.A. Information and Control,8,338-353,1965.
[2]. Sutton, Jhon, Ed. Krueger, Alice Ed, ED Thoughts: What we know about mathematics teaching and learning.
[3]. Models of Mathematics teaching – CCSU. www.math.ccsu.edu/.../models of Mathematics Tea.
[4]. Michael Gr. Voskoglou, Fuzzy Measure For Students' Mathematical Modeling Skills, international journal of fuzzy logic system Vol. 2 No.2, 13-26, April 2012.
[5]. Michael Gr. Voskoglou, The Process Of Learning Mathematics: A Fuzzy Set Approach Http://Www.Ipv.Pt./Millenium/17_Ect4.Htm, March 2014. Page 1-7
[6]. Klir. G.J & Folger,T.A. (1988), Fuzzy Sets And Uncertainty And Information, Prentice Hall London.

Abstract:Analysis of count data is widely used in medical studies,epidemiology,ecology and many Researchof interest. The Bayesian approach is very useful in real world situation. In Bayesian estimation prior distribution and posterior distribution are the most important ingredients. The objective of this paper is to compare Blood Pressure in 20 places in Kanyakumari district using Gamma prior. The posterior probabilities have been calculated to find the risk of the Blood Pressure throughout the district.

[1]. Bhattacharjee A, Bhattacharjee D. A Bayesian Approach to Compare the Statewise Dengue Death Counts in India. International Journal of Collaborative Research on Internal Medicine & Public Health. 2011; 3(10):715-723.
[2]. Miller, R.B. (1980), "Bayesian analysis of the two-parameter gamma distribution", | Technometrics, vol. 22, 65-69
[3]. Glickman and van Dyk, Basic Bayesian Methods, Topics in Biostatistics, vol 404, 319-33
[4]. Carlin, B. P., and Louis, T. A. (2000) Bayes and Empirical Bayes Methods for DatAnalysis, 2nd ed. Boca Raton, Chapman & Hall.

Abstract:An operator T B(H) is said to be k - quasi - paranormal operator if for every xH , k is a natural number. This class of operators contains the class of paranormal operators and the class of quasi - class A operators. Let T or T* be an algebraically k -
quasi - paranormal operator acting on Hilbert space. Using Local Spectral Theory, we prove (i)Weyl's theorem holds for f(T) for every f H( (T)) ; (ii) a-Browder's theorem holds for f (S) for every S  T and f H( (S)) ; (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T.
Keywords: Paranormal operator, Weyl's theorem, k - quasi - paranormal operator, Riesz idempotent, generalized a - Weyl's theorem, B - Fredholm, B - Weyl, generalized Weyl's theorem, SVEP.

1]. P. Aiena, Fredholm and local spectral theory with applications to multipliers, Kluwer Academic Publishers (2004), Dordrecht,
Boston, London.
[2]. M. Berkani and A. Arroud, Generalized Weyl's theorem and hyponormal operators, J. Austra. Math. Soc., 76(2004), 291 - 302.
[3]. M. Berkani and J.J. Koliha, Weyl's type theorems for bounded linear operators, Acta. Sci. Math(Szeged)., 69(2003), 379 - 391.
[4]. M. Berkani and M. Sarih, On semi B - Fredholm operators, Glasgow Math. J., 43(2001), 457 - 465.
[5]. X. Cao, M. Guo and B. Meng, Weyl type theorems for p - hyponormal and M - hyponormal operators, Studia Math., 163(2004),
177 - 188.
[6]. M. Cho, M. Ito and S. Oshiro, Weyl's theorem holds for p - hyponormal operators, Glasgow Math. J., 39(1997), 217 - 220.

Abstract: The main purpose of this paper to solve two- dimensional an inverse steady state thermo elastic problem of thin rectangular plate to determine temperature distribution at any point of rectangular plate with given boundary condition by applying numerical technique , finite difference method.
Keywords: Finite difference method, Rectangular plate, Thermo elasticity, Temperature distribution.

[1]. Khobragade,N.W.and Lamba N.K. : An thermo elastic problem of a thin rectangular plate due to partially distributed heat supply, The journal of Indian Academy of Mathematics, (2011).
[2]. Deshmukh, K.C. and Ingle, S.G.: Analysis of thermal deflection of thin circular Plate due to partially distributed heat supply, Bull. of Pure and Appl. Sci , (2001).
[3]. Gaikwad, K.R. and Ghadle,K.P.: Three dimensional non-homogeneous thermo elastic problem in thick rectangular plate due to internal heat generation, Southern Africa Journal of pure and applied mathematics, Vol. (5), (2011).
[4]. Khobragade, N.W. and Wankhede, P.C.: An inverse unsteady-state thermo elastic problem of a thin rectangular plate, The journal of Indian Academy of Mathematics, Vol. (25), No. 2,(2003).
[5]. Mukhopadhyay, S.and Roshan kumar: "Solution of problem of generalized Thermo elasticity of annular cylinder with variable properties by finite difference method , computational method of science and technology 15 ( 2 ) 169-176 (2009).

Abstract: In this study, we formulate mixed integer and linear fractional program for manufacturer and retailer system of poultry firm in Bangladesh that is one of the most promising but unstable sectors in Bangladesh. This paper maximizes the profit, minimizes the cost and finally estimates the optimum selling prices of several the firms. In order to validate the model we have made a question survey on some main poultry firms in the district of Mymensingh and Gazipur of Dhaka. We try to figure out the actual situation of the unstable poultry market of Bangladesh. We have made a question survey on some poultry firm. From the survey, it has observed that the selling price of eggs and chicken fluctuate depending on the natural calamities. The formulated mixed integer linear fractional program model maximizes not only the ratio of return on investment but also optimize location, transportation cost, and the investment. In order to comparison, a mixed integer model has been derived for the same constraints.

[1]. Qin, Y., Tang, H. and Guo, C., Channel coordination and volume discounts with price- sensitive demand, Int. J.Production Economics, Vol. 105, 2007, 43-53.
[2]. Uddin, M. F., and Sano, K., Mixed Integer Linear Fraction Programming for Supply Integrated Supply Chain Network design and Optimization, International Journal of Business and Economics, ISSN 1906-5582, Vol.2, No. 1,2010, pp. 57-70.
[3]. Pourakbar, M., Farahani, R. Z. and Asgari, N., A joint economic lot-size model for an integrated supply Network using Genetic algorithm, applied mathematics and Computation, Vol. 189,2007, 583-596.
[4]. Wu, K.S. and Yen, H.F, On A note on the economic lot size of the integrated vendor buyer inventory system derived without derivatives, International journal of Information and Management Sciences, Vol. 20, 2009, 217-223.
[5]. Uddin, Islam and Kazi, A Two-Echelon Supply Chain and Facility Location Problem, International Journal of Basic & Applied Sciences IJBAS-IJENS Vol: 13 No: 04, 2013.

Abstract: The fractionalspace and time, as ageneralization of telegraph, diffusion and the waveequations, are considered. The (direct case and the modified cases) of Adomiandecompositionmethod are adopted to treat the certain space-time fractional partial differentialequations, in thispaper, four distinguished cases willbemodified and applied to solvedifferent certain space-timefractionalorder (homogeneous or inhomogeneous; linear or nonlinear), the steps of solutions willbegiven, sevendifferentexampleswillbesolved to show the powerful of thismethod to solvedifferentkinds of problems, finally figures and tables of resultswillbegiven by using programs of matlab.

Keywords: Adomian decomposition Method, Fractional Partial Differential Equations.

1]. G. Adomian, Nonlinear stochastic systems: Theory and applications to Physics, Kluwer Academic Press,1989.
[2]. G. Adomian, Solving Frontier problem of Physics: The Decomposition Method, Kluwer Academicpress, 1994.
[3]. G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135 (1988) 501–544.
[4]. A. Wazwaz, S. El-Sayed, A new modification of the Adomian decomposition method for linear and nonlinear operators, Appl. Math. Comput. 122 (2001) 393–405.
[5]. Y. Cherruault, "Convergence of Adomian's method," Kybernetes of Cybernetics and General Systems, vol. 18, no. 2, pp. 31–38, 1989.
[6]. D. Lesnic, "Convergence of Adomian's decomposition method: periodic temperatures," Computers & Mathematics with Applications, vol. 44, no. 1-2, pp. 13–24, 2002.

Abstract: This paper studies a continuous sampling plan to prevent entries of defective products for sale using theory of queues for bulk production and bulk sale systems. A machine produces random number of products at each production. Any product in a production lot may be good or defective. The sampling plan considered here to prevent defective products to go for sale has three inspection modes. Each lot of production is inspected in mode I and in modes II and III each lot is inspected with some probability c ≥ 0 and d > 0 respectively in order to avoid high cost of inspecting all the lots of products produced. Matrix methods are used to derive the stock level probabilities, the rate of entry of defectives, the expected defective products in the stock, the standard deviation and the coefficient of variation. Two models are treated. In one model, the maximum production size is greater than the maximum sale size and in the second model the maximum sale size is greater than the maximum production size. Numerical cases are treated to illustrate the significance of the continuous sampling plan in reducing the entry rates of defectives. The expected defective products in the stock for sale and all the risk measures are listed and discussed.

Keywords: Block Partitioned Methods, Continuous Sampling Plan, Expected Defective Products, Infinitesimal Generator, Rate of Entry of Defective Products.

[1]. H.F.Dodge (1943). A Sampling Inspection Plan for Continuous Production. Annals of Statistics, 14, 264-279.
[2]. G.K. Mytalas and M.A. Zazanis, (2007), Delay Analysis of Continuous Sampling Plans www.aueb.gr/pympe/hercma/ proceedings2007/H07-FULL-PAPERS
[3]. Albert H. Bowker, (1956) Proceedings of the Third Berkeley Symposium projecteuclid.org/download/pdf-1/euclid.bsmsp/1200511857
[4]. Sundar Viswanathan, (2015) Continuous Sampling Plan in Preventing Defects and Risk Evaluation in Production and Sales System, IJCA, accepted to appear in Jan.
[5]. Kenblock, (2012) Business Statistics for Contemporary Decision Making, John Wiley & sons Inc.
[6]. James c. Cox and Vjollca Sadiraj, (2009) On the Coefficient of Variation as a Measure of Risk of Sensitivity, http://excen.gsu.edu/ working papers /GSU_EXCEN_WP_2009-06.pdf.

Abstract: This paper studies two stochastic bulk demand (S, s) inventory models A and B with randomly varying environment. In the models the maximum storing capacity of the inventory is S units and the order for filling up the inventory is placed when the inventory level falls to s or below. Demands for random number of units occur at a time and wait for supply forming a queue when the inventory has no stock. The inventory is exposed to changes in the environment.

[1]. Thangaraj.V and Ramanarayanan.R, (1983), An operating policy in inventory system with random lead times and unit demands, Math.Oper and Stat.Series Optimization, Vol1 p111-124.
[2]. Daniel,J.K and Ramanarayanan.R, (1988) An S-s Inventory system with rest periods to the server, Naval Research Logistics Quarterly,Vol.35,pp119-123.
[3]. Ayyappan.G, Muthu Ganapathy Subramanian. A and Gopal Sekar. (2010). M/M/1 retrial queueing system with loss and feedback under pre- emptive priority service, IJCA, 2, N0.6,-27-34.
[4]. D. Bini, G. Latouche, and B. Meini. (2005). Numerical methods for structured Markov chains, Oxford Univ. Press, Oxford.
[5]. Chakravarthy.S.R and Neuts. M.F.(2014). Analysis of a multi-server queueing model with MAP arrivals of customers, SMPT, Vol 43, 79-95,

Abstract:In this paper, we obtain the characterization on pair of weights v and w so that the Hardy-Steklov
operator 2010 AMS Mathematics Subject Classification: 26D10, 26D15.
Keywords: Hardy-Steklov operator, Lorentz spaces, non-decreasing.

[1]. H.P.Heinig and G.J. Sinnamon, Mapping properties of integral averaging operators, Studia Math., 129(1998), 157-177.
[2]. A. Kufner and L.E. Persson, Weighted Inequalites of Hardy Type, World Scientific Publishing Co. Pte. Ltd, Singapore, 2003.
[3]. E. Sawyer, Weighted Lebesgue and Lorentz norm inequalites for the Hardy operator, Trans. of Amer. Math. Soc., Vol. 281(1984),
329-337 .