iosr-Jm   Volume-11 ~ Issue-2 ~ Mar-Apr 2015

Abstract: An arbitrary ring with unity can be thought of as a category with one object. In this paper we have shown how an arbitrary ring with unity can be thought as a category with one object. Also we have defined quotient category of a ring. The categorical approach to the fundamental theorem of homomorphism of ring theory has been provided. Moreover the isomorphism theorems of ring have been proved categorically.

Keywords: Category , Cokernel, Congruence relation, Functor, Kernel, Morphism , Quotient category, Ring (category of rings)..

[1]. Anderson,Frank W.& Fuller,Kent R., Rings and Categories of Modules,Springer-Verlag New York berlin Heidelberg London paris Tokyo Hong Kong Barcelona Budapast.
[2]. Mac Lane, S.,1971: Categories for the Working Mathematician, Springer-Verlag New York Berlin.
[3]. Mitchel, Barry.1965: Theory of Categories, Academic Press New Yorkand London.
[4]. Krishnan,V.S.,198TH1: An introduction to Category Theory,North Holland NewYork Oxford.
[5]. Schubert, Horst,1972: Categories, Springer-Verlag Berlin Heidelberg New York.
[6]. Popescu,N.,1973: Abelian Categories with Applications to Rings and Modules, Academic Press, London & New York.
[7]. Awodey, Steve.,2006: CategoryTheory,Second Edition, Clarendon Press,Oxford.

Abstract: In this article some of the interesting results on prime numbers are surveyed which made prime numbers very fascinating. Keywords - prime numbers, Dirichlet theorem, Prime number theorem

[1] Benjamin Fine, Gerhard Rosenberger, Number Theory, Birkhauser, (2007)
[2] David M. Burton, The History of Mathematics: An Introduction, Mc Graw Hill Company, Fifth edition, 2003.
[3] Niven, Zuckerman, An Introduction to the theory of of numbers.

Abstract: A general method to find complete solution of the equation x2 + y2 = Z2 in whole numbers in the form of formulae, with proof and resolution of Birch and Swinnerton-Dyre conjecture with respect to the solutions of the equation x2 + y2 = Z2 in whole numbers

[1]. Principles of mathematical analysis third edition, by Walter Rudin
[2]. Millennium prize problems in mathematics, announced and published by Clay Mathematics Institute of Cambridge Massachusetts (CMT)

Abstract:In the present paper, we introduce the class of p - valent functions in the unit disc We obtain coefficient estimate, distortion and closure theorems, radii of close-to-convexity and  - neighborhood for this class.

Keywords and phrases: multivalent function, distortion theorems, radius theorems,  - neighborhood.
2000 Mathematics Subject Classification: 30C45.

[1]. Aouf M. K., El-Ashwah and Ahmed M Abd Eltawab, On certain subclass of p-valent functions Journal of classical Analyis, 4,
1(2014), 63 - 68.
[2]. Liu, Jin-Lin; Owa, Shigeyoshi. Properties of certain integral operator. Int. J. Math. Sci. 3 (2004), no. 1, 69 - 75.
[3]. Jung, Il Bong; Kim, Yong Chan; Srivastava, H. M. The Hardy space of analytic functions associated with certain one-parameter
families of integral operators. J. Math. Anal. Appl. 176 (1993), no. 1, 138 - 147.
[4]. Bernardi, S. D. Convex and starlike univalent functions. Trans. Amer. Math. Soc. 135, 1969, 429 - 446.
[5]. Libera, R. J. Some classes of regular univalent functions. Proc. Amer. Math. Soc. 16 1965, 755 - 758.

Abstract: In this paper , we elaborate some existing result of fixed point theorem, that fulfill the nature of G-metric space and satisfy the ∅-maps. Previously Erdal Karapinar and Ravi Agrawal [20]have modified some existing result of fixed point theory of Samet et al Int.J.Anal(2013:917158,2013) [38]and Jleli-Samet (Fixed point theory application.2012:2010,2012) [39]in a different way.

[1]. Abbas, M, Sintunavarat, W, Kumam, P: Coupled fixed point of generalized contractive mappings on partially ordered G-metric spaces. Fixed Point Theory Appl. 2012, Article ID 31 (2012)
[2]. Abbas, M, Nazir, T, Vetro, P: Common fixed point results for three maps in G-metric spaces. Filomat 25(4), 1-17 (2011)
[3]. Agarwal, R, Karapınar, E: Remarks on some coupled fixed point theorems in G-metric spaces. Fixed Point Theory Appl.2013, Article ID 2 (2013)
[4]. Aydi, H, Shatanawi, W, Vetro, C: On generalized weak G-contraction mapping in G-metric spaces. Comput. Math.
[5]. Appl. 62, 4223-4229 (2011)
[6]. Aydi, H, Karapinar, E, Shatnawi, W: Tripled fixed point results in generalized metric spaces. J. Appl. Math. 2012, ArticleID 314279 (2012)
[7]. Aydi, H, Karapinar, E, Mustafa, Z: On common fixed points in G-metric spaces using (E.A) property. Comput. Math.Appl. 64(6), 1944-1956 (2012)

Abstract:In this paper introduces a novel non-linear ten-dimensional autonomous system which has ten quadratic nonlinearities and twelve positive real constant parameters , complex chaotic dynamics behaviors and gives analysis of novel system. More importantly. We analyze the novel system by eans of phase portraits , equilibrium points , calculated Lyapunov exponents, fractional dimension and attractors of the system. The qualitative properties and the phase portraits of the novel chaotic system have been described in detail.
Numerical simulations using MATEMATICA are provided to illustrate phase portraits and the qualitative
properties of the novel chaotic system.

Keywords:numerical simulation, ten-dimensional chaotic system, chaotic attractor andLyapunov exponents.

[1]. C. W. Chang-Jian and S. M. Chang, "Bifurcation and chaos analysis of spur gear pair with and without nonlinear suspension",
Nonlinear Analysis: Real World Applications, vol. 12, (2011), pp. 979-89.
[2]. G. Qiang, Y. Hua and Y. Hongye. The Research of Chaos-based M-ary Spreading Sequences. TELKOMNIKA. Vol. 10, (2012);
pp.2151-2158.
[3]. J. Lv, S. M. Yu, H. Leung and G. Chen, "Experimental verification of multi-directional multi-scroll chaotic attractors", IEEE Trans.
Circuits Syst. I, vol. 53, no. 1, (2006), pp. 149-165.
[4]. S. M. Yu, J. Lv, H. Leung and G. Chen, "Design and implementation of n-scroll chaotic attractors from a general Jerk circuit",
IEEE Trans. Circuits Syst. I, vol. 52, no. 7, (2005), pp. 1459-1476.
[5]. J. Lv, G. Chen, X. H. Yu and H. Leung, "Design and analysis of multi-scroll chaotic attractors from saturated function series", IEEE
Trans. Circuits Syst. I, vol. 51, no. 12, (2004), pp. 2476-2490.

Abstract: A study has been made of the disturbances produced by a normal line load moving along the boundary surface of a perfectly conducting magnetoelastic semi-space. The displacement on the boundary has been obtained. The stress distribution shows how both the normal stress and tangential stress varies with depth, and with the increase in the magnetic field intensity.

Key words: Magnetoelastic, Moving Load, Perfect Conductor

[1]. I. N. Sneddon,Stress produced by a pulse of pressure moving along the surface of a semi-infinite solid, Rc. Cric.mat.Palermo, 2(1952), 57-62.
[2]. S. K. Chakraborty,Stresses produced by a line load moving over the boundary of a semi-infinite transversely isotropic solid,Bull.Calcutta math.Soc(Supplement),(1958), 30-34.
[3]. M. Mitra,Note on the disturbance produced in an elastic half-space by transient pressure applied over a portion of the boundary,Pure and Applied Geophysics,28,A(1)(1961), 199-205.
[4]. J. Cole, J. Huth,Stresses produced in a half-plane by moving loads,J.Appl.Mech., 25(1958), 433-436.
[5]. Y. C. Fung,Foundation of solid mechanics, Pentice Hall,New Delhi, (1968).

Abstract:In this paper we introduce new domination parameter with real life application called neighborhood triple connected two out degree equitable domination number of a graph. A subset D of V of a nontrivial graph G is said to be a neighborhood triple connected two out degree equitable dominating set if D is a two out degree equitable dominating set and the induced sub graph <N(D)> is triple connected. The minimum cardinality taken over all neighborhood triple connected two out degree equitable dominating set is called neighborhood triple connected two out degree equitable domination number and is denoted by 𝛾𝑛𝑡𝑐2𝑜𝑒. We investigate this number for some standard graphs

Key words: dominating set, equitable, neighborhood Triple connected, two out degree,

[1]. T.W. Haynes, S.T. Hedetniemi and P.J. Slater, "Fundamentals of Domination in Graphs" Marcel Dekker Inc., 1998.
[2]. T.W. Haynes, S.T.Hedetniemi andP.J.Slater, Domination in Graphs Advanced Topics, Marcel DekkarInc 1998.
[3]. A. Sahal and V. Mathad "Two-out degree equitable Domination in graphs" Transactions on Combinatorics, Vol. 2 No. 3 (2013),
pp. 13-19.
[4]. Arumugam, S. and Sivagnanam. C."Neighborhood connected domination in graphs", J. Combin. Math, Combin, Comput., Vol.73,
PP.55-64, 2010.

Abstract: Ever since fuzzy sets were introduced by Lotfi Zadeh in the year 1965 [1], many algebraic structures were introduced by many authors. One such structure is fuzzy groups introduced in [2]and [3]. In [4] the authors introduced a novel definition of fuzzy group homomorphism between any two fuzzy groups and gave element wise characterization of some special morphisms in the category of fuzzy groups. In this article we prove the existence of the intersection of a family of fuzzy subgroups, and also study some
properties of pullbacks.
Keywords: Injective, Intersection, Equalizer, Fuzzy morphism, Fuzzy group homomorphism, Morphism, Monomorphism, Strong monomorphism,

[1]. L.A. Zadeh, Fuzzy sets, Information and control, 1965, 8: 338 - 353.
[2]. J.M. Anthony and Sherwood, Fuzzy Groups Redefined, Journal of Mathematical Analysis and Applications 69, 124-130 (1979).
[3]. Azriel Rosen Feld, Fuzzy Groups, Journal of Mathematical Analysis and Applications 35, 512-517 (1971).
[4]. P.Vijayalakshmi, P. Geetha, A. Kalaivani, Category of Fuzzy Groups, Two day International conference on Algebra and its Applications (December 14 and 15 2011, Pp 337-343).
[5]. George Boj Adziev And Maria Boj Adziev Fuzzy Sets, Fuzzy Logic, Applications, Advances in Fuzzy Systems-Applications and Theory,Vol5, World Scientific Publishing Company, 1995.

Abstract: A graph G with p vertices and q edges is a mean graph if there is an injective function f from the vertices of G to {0,1,2,….q} such that when each edge is labeled with is even and is odd then the resulting edges are distinct. In this paper we investigate vertex odd and even mean labeling of Umbrella graph , Mongolian tent and 𝐾1+𝐶𝑛.

Keywords: Mean labeling, Mongolian tent, Umbrella graph, vertex odd mean labeling, vertex even mean labeling.

[1]. J.A.Bondy and U.S.R.Murthy, Graph Theory and Applications (North-Holland).Newyork (1976)
[2]. J. A. Gallian, A dynamic survey of labeling, The Electronics Journal of Combinatorics17(2014).
[3]. F. Harary, Graph theory, Addison Welsey, Reading, Massachusetts, 1972.
[4]. Manickam. K and Marudai. M, odd mean labeling of graphs, Bulletin of Pure and Applied sciences. Vol. 25E. No.1(2006), 149-153.
[5]. S. Somasundaram and R. Ponraj, Mean labeling of graphs, Natl. Acad, Sci. Let.,26 (2003) 210-213

Abstract: The aim of this paper is to introduce the notion of sequentially compact intuitionistic fuzzy metric spaces and prove a generalized common fixed point theorem for pairs of weakly compatible self mappings in this newly defined space .
Keywords: Intuitionistic fuzzy metric space, sequentially compact intuitionistic fuzzy metric space , compatible mappings , weakly compatible mappings , common fixed point .

[1]. Alaca, C., Turkoglu, D. and Yildiz, C., Fixed points in intuitionistic fuzzy metric spaces ,Chaos, Solitons and Fractals , 29(2006),
1073 – 1078 .
[2]. Atanassov , K., intuitionistic fuzzy sets , Fuzzy sets and systems 20(1986) 87-96.
[3]. Dubois , D. and Prade , H., Fuzzy sets : Theory and Applications to Policy Analysis and Information Systems Plenum Press , New
York , 1980 .
[4]. George , A. and Veeramani , P ., On some results in fuzzy metric space , Fuzzy sets and Systems , 64(1994) , 395-399 .
[5]. Grabiec , M ., Fixed points in fuzzy metric spaces , Fuzzy Sets and Systems 27(1988),385-389.

Abstract:In this paper, we presented modification of variational iteration method for solving partial differential equation. Tested for some examples and the obtained results demonstrate efficiency of the proposed method. he results were presented in tables and figure using the MathCAD 12 and Matlab software package.
Keywords: Modified variational iteration method, partial differential equation, lagrange multiplier.

[1]. K. Diethelm and A. D. Freed, ―On the solution of nonlinear fractional order differential equations used in the modeling of viscoelasticity,‖ in Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, F. Keil, W. Mackens, H. Voss, and J. Werther, Eds., pp. 217–224, Springer, Heidelberg, Germany, 1999.
[2]. R. Metzler, W. Schick, H. G. Kilian, and T. F. Nonnenmacher, ―Relaxation in illed polymers: a fractional calculus approach,‖ he Journal of Chemical Physics, vol. 103, no. 16, pp. 7180–7186, 1995.
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[5]. I. Podlubny, ―Fractional diferential equation,‖ in Mathematics in Science and Engineering, vol. 198, Academic Press, San Diego, Calif, USA, 1999.

Abstract: In the present paper, the multi-objective solid transportation problem with fuzzy coefficients for the objectives and constraints is modelled and then solved. Fuzzy goal programming is used to the linear multi-objective solid transportation problem, and an optimal compromise solution is obtained. Firstly, expected values of the fuzzy objective functions are considered to derive crisp values. In this method, a defuzzification model, which is an application of fuzzy linear programming and conditions for a solid transportation problem are imposed. Fuzzy programming technique and goal programming approach are applied to derive optimal compromise solutions of multi-objectives. Three numerical examples are presented using the above mentioned methodology and the appropriate comparative study is also included. Obtained concluding remarks are given in the last section.

Keywords: Solid transportation problem, Fuzzy sets, Expected value fuzzy programming technique, Goal programming approach.

[1]. E.D. Schell, Distribution of a product by several properties, Proc. 2nd Symposium in Linear Programming, DCS/comptroller, HQ
US Air Force, Washington DC, 1955, 615-642.
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