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.