iosr-Jm   Volume-12 ~ Issue-5 ~ Sep-Oct 2016

Abstract: In this paper, we consider the unsteady hydrodynamic flow of an incompressible Oldroyd-B fluid in a parallel plate channel, initially induced by a constant pressure gradient. The pressure gradient is suddenly withdrawn and the upper plate moves with a uniform velocity while the lower plate continues to be at rest. The arising flow is referred to as run up flow. The unsteady governing equations are solved as initial value problem using Laplace transform technique. The expressions for velocity, shear stresses on both plates and discharge are obtained. The behaviour of the velocity, shear stresses and mass flux has been discussed in detail with respect to variations in different governing flow parameters and is presented through graphs.

Keywords: Run-up flow, Oldroyd-B fluid, Laplace transforms and parallel plate channels.

[1] Naduvinamani. N.B., P.S. Hiremath, G. Gurubasavaraj, Squeeze film lubrication of a short porous journal bearing with couple
stress fluids, Tribol. Int., 34(11), pp. 739–747, 2001.
[2] Naduvinamani. N.B., P.S. Hiremath, G. Gurubasavaraj, Surface roughness effects in a short porous journal bearing with a couple
stress fluid, Fluid Dyn. Res., 31(5–6), pp. 333–354, 2002.
[3] Naduvinamani. N.B., P.S. Hiremath, G. Gurubasavaraj, Effects of surface roughness on the couple stress squeeze film between a
sphere and a flat Plate, Tribol. Int., 38(5), pp. 451–458, 2005.
[4] Naduvinamani. N.B., Syeda Tasneem Fathima, P.S. Hiremath, Hydrodynamic lubrication of rough slider bearings with couple stress
fluids, Tribol. Int., 36(12), pp. 949–959, 2003.
[5] Naduvinamani N.B., Syeda Tasneem Fathima, P.S. Hiremath, Effect of surface roughness on characteristics of couplestress squeeze
film between anisotropic porous rectangular plates, Fluid Dyn. Res., 32(5), pp. 217–231, 2003.

Abstract: In this paper, He's Variational Iteration Method (HVIM) is used to study the nonlinear timeinvariant and time-varying singular systems. The results obtained using He's Variational Iteration Method and the methods taken from the literature [18] were compared with the exact solutions of the nonlinear timeinvariant and time-varying singular systems. It is found that the solution obtained using the He's Variational Iteration Method is closer to the exact solutions of the nonlinear time-invariant and time-varying singular systems. Error Calculations for discrete and exact solutions are presented in a table form to highlight the efficiency of this method.

Keywords:Singular systems, nonlinear singular time-invariant, time-varying, He's Variational Iteration Method, Leapfrog Method.

[1] J. C. Butcher, "The Numerical Methods for Ordinary Differential Equations", 2003, John Wiley & Sons, U.K.
[2] S. L. Campbell, Singular systems of differential equations, Pitman, London, (1980).
[3] S. L. Campbell, Singular systems of differential equations II, Pitman, London. (1982).
[4] L. Dai, Singular Control Systems, Springer-Verlag, London, (1989).
[5] N. Declaris and A. Rindos, Semistate analysis of neural networks in Apysia Californica, Proc. 27th MSCS, (1984), 686–689.

Abstract: This paper presents the design and construction of a faculty course timetable. The system uses an Integer Linear Programming model which attempts to assign groups of course units to time periods where each group is a result of a graph coloring approach. Limited number of lecture halls, large number of subject combinations and growing number of student registration have made the problem very tight which results thousands of variables and constraints to the model..................

Keywords: Course Timetabling, Graph Coloring, Integer Linear Programming

[1]. E.K. Burke, S. Petrovic, Recent research directions in automated timetabling, European Journal of Operational Research 140 (2002), pp 266-280.
[2]. Enzhe Yu, Ki Seok, A genetic algorithm for a university weekly course timetabling problem, international transaction in operational research, 9(2002), pp 703-717.
[3]. F. Zibran, A multi phase approach to university course timetabling, M.Sc.Thesis , 2007.
[4]. J. Rickman, J. Yellen, Course Timetabling Using Graph Coloring and A.I. Techniques, 10th International Conference of the Practice and Theory of Automated Timetabling, (PATAT), 26-29, 2014.
[5]. M. Dimopoulou , P. Miliotis, Theory and Methodology - Implementation of a university course and examination timetabling system, European Journal of Operational Research 130 (2001), pp 202-213.

Abstract: In this paper we propose to obtain a factorization via a modular difference of squares , where the squares arise due to binary quadratic forms. To obtain the quadratic forms we adapt Zhang's method of parametrization used in his special quadratic sieve method. A certain linear parametrization in two variables leads to quadratic form in ambiguous forms..................

Keywords: Quadratic Forms, Factorization, Ambiguous Forms.

[1]. M. Zhang, Factorization of the Numbers of the form 1 0 2 2 3 m  c m  c m c , 1998, Springer-Verlag, London, UK, ISBN 3-
540-64657-4.
[2]. Seth Viren Neel, Binary Quadratic Form and The Ideal Class Group.
[3]. D.H. Lehmer and E. Lehmer, A New Factorization Technique Using Quadratic Forms.
[4]. Benzamin Bakker, Lecture Notes: Quadratic Forms.
[5]. Eric Landqusit, An implementation of Zhang's Special Quadratic Sieve and Possible Extension, Math 488: Integer Factorization,
Dec 20, 2002.

Abstract: In this paper, we made an attempt to study the algebraic nature of intuitionistic (T, S)-fuzzy subfield of a field.

Keywords: T-norm, S-norm, fuzzy subset, intuitionistic fuzzy subset, fuzzy subfield, intuitionistic (T, S)-fuzzy subfield, Product.

[1] Akram. M and Dar.K.H, On fuzzy d-algebras, Punjab University Journal of Mathematics, 37, 61-76, (2005).
[2] Anthony.J.M. and Sherwood.H, Fuzzy groups Redefined, Journal of mathematical analysis and applications, 69,124 -130 (1979 ).
[3] Asok Kumer Ray, On product of fuzzy subgroups, Fuzzy sets and sysrems, 105 , 181-183 (1999 ).
[4] Atanassov.K.T., Intuitionistic fuzzy sets, Fuzzy sets and systems, 20(1), 87-96 (1986).
[5] Atanassov.K.T., Intuitionistic fuzzy sets theory and applications, Physica-Verlag, A Springer-Verlag company, April 1999, Bulgaria.

Abstract: The topological Markov chain A  on the Golden Mean Lookalike Shift of order m [GMLSm] is a very typical topological discrete system possessing rich dynamical properties. In this paper we establish some results in connection with the chaotic properties of this Markov chain. In particular, we prove that it is Devaney chaotic (DevC), Auslander-Yorke chaotic and generically  -chaotic. Further, it has been shown that A  has chaotic as well as modified weakly chaotic dependence on initial conditions. Moreover, the zeta function for this Markov chain has been derived.

Keywords:Shift Space, Shift Map, Devaney Chaos, Topological Transitivity, Topological Mixing, Topological Markov chain, Topological Conjugacy, Sensitivity Dependence.

[1]. Lind, Douglas, and Marcus, Brian, Introduction to Symbolic Dynamics and Coding, Cambridge University Press, Cambridge, New
York, 1995.
[2]. Katok, Anatole and Hasselblatt, Boris, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, New York, 1999.
[3]. Alligood, Kathleen T. et al, CHAOS-An Introduction to Dynamical Systems, Springer-Verlag New York, Inc., 175 Fifth Avenue,
New York, 2008.
[4]. Brin, Michael and Stuck, Garret, Introduction to Dynamical Systems, Cambridge University Press, New York, USA, 2002.
[5]. Kitchens, B.P., Symbolic Dynamics: One-sided, Two-sided and Countable State Markov Shifts, Universitext, Springer Verlag,
Berlin, 1998.

Abstract: A[p/2]-cordiallabeling of a graph G with p verticesisabijection..................

Keywords: [p/2]-cordial, path, complete bipartite, star.

[1]. J. A. Bondy and U. S. R. Murty, Graph Theory with applications, Macmillan press, London (1976)
[2]. J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of combinatorics (2014).
[3]. F. Harary, Graph Theory Addison – Wesley, Reading Mars., (1968)

Abstract: In [8], the electronic algorithm has allowed to find the optimal solutions for the travelling salesman problem. In this article, I demonstrate that the same algorithm will allow to find the optimal solutions for the knapsack problem.

Keywords: Graph, Hamilton cycles, P=NP, the knapsack problem, the travelling salesman problem, TSP, KP.

[1]. Lizhi Du. A polynomial time algorithm for hamilton cycle. IMECS, I: 17–19, March 2010. Hong Kong.
[2]. L.Lovasz. Combinatorial problems and exercises. Noth-Holland, Amsterdam, 1979.
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Abstract: In this paper we present another variation of Latin square design called Graeco 3RR - Latin Square design. This design adds one more restriction on randomization to the existing 3RR - Latin square by superimposing two orthogonal 3RR – Latin squares. The existence of a Graeco 3RR– Latin square is proved and illustrated by considering Latin squares of order 4 and 9. A statistical model for the design is presented, the estimators of parameters in the model are derived and the Analysis of Variance procedure is developed

Keywords: Latin square, Graeco Latin square, 3RR – Latin Square, Graeco 3RR - Latin square, randomization, experimental error, ANOVA.

[1]. Alvan, D. (2014): "STAT 507". Department of Statistics, Pennsylvania State University; http:/ /onlinecourse .science. psu. edu/sta507/node/34
[2]. Bose, R. C. and Shrikhande, S. S. (1960). Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler‟s Conjection. Transactions of the American Mathematical Society, vol 12, p. 189 – 203
[3]. Cochran, W. G. and Cox M. (1957). Experimental Design. John Wiley and Sons Ltd, New York.
[4]. Colton, J. A. (2012): "Avoiding Mean Square Error Bias in Designed Experiment" published under MiniTab Inc.
[5]. Effanga, E. O. and Offong, N. E. (2016). International Journal of Innovative research and advanced studies. Vol. 3 Issue 9, Pp 84 – 87.

Abstract: In some categories, certain subgroups of Hom(A,A) for some groups of morphisms A→A are ver useful and interesting. In this paper, the author's main aim is to study some such groups. Specifically, the automorphism groups of A, A being a group or a topological space, have been studied in certain cases.

Keywords: Category, morphism, homomorphism, homeomorphis, free product, structure

[1]. M. A. Hossain, The automorphism group of special semigroups. Journal of Math.and Mathematical Sciences 25(2010):9-12.
[2]. M. A. Hossain and S. Majumdar, On some characterizations of special semigroups, Rajshahi University Journal of Sciences 35
(2007): 119-125.
[3]. M. A. Hossain and S. Majumdar, On automorphism groups of some particular groups,
Submitted to J. Bangladesh Acad. of sci. 2016.
[4]. S. Majumdar, K.K. Dey and M. A. Hossain, Direct product and Wreath productof transformation semigroups,GANIT J.
Bangladesh Math. Soc. 31(2011): 1-7.
[5]. S. Majumdar and M.A.Hossain, The endomorphism semigroup of a special semigroup. J.Bangladesh Acad. of sci. 32(1) (2008): 55-
60

Abstract: In the present paper learn thermal energy communication by unsteady MHD Run Precedent a perpendicular absorbent laminate captivated in a absorbent average.. a moment needy suction to the plate into a time dependent , parameter and the corresponding momentum and energy equations have been solved numerically the non linear governing partial differential equation obtained are converted into PDE.non –dimensional rate and high temperature profiles be next in presence graphically for different value of the parameter entering into the problem

Keywords: Thermal radiation, MHD, Unsteady, Suction, Porous medium

1] Alabraba, M. A., Bestman, A. R. and Ogulu, A. (1992): Laminar Convection in Binary Mixer of Hydromagnetic Flow with Radiative Heat Transfer. Astophys. Sapce Sci., Vol.195, pp. 431-445.

[2] Alam, M. S. and Rahman, M. M. (2005): Dufour and Soret Effects on MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Flat Plate Embedded in a Porous Medium. J. Nav. Arc. Mar. Eng., Vol.2(1), pp.55-65.

[3] Ali, M. M., Chen, T. S. and Armaly, B. F. ( 1984): Natural Convection Radiation Interaction in Boundary Layer Flow Over Horizontal Surfaces. AIAA Journal., Vol.22(12), pp. 797-1803.

[4] El-Arabawy, H. A. M. (2003): Effect of Suction/Injection on a Micropolar Fluid Past a Continuously Moving Plate in the Presence of Radiation. Intl. J. Heat Mass Trans., vol.46, pp.1471-1477.

[5] Ferdows, M., Sattar, M. A. and Siddiki, M. N. A. (2004): Numerical Approach on Parameters of the Thermal Radiation Interaction with Convection in a Boundary Layer Flow at a Vertical Plate with Variable Suction. Thammasat Intl. J. Sci. Tech., Vol.9(3), pp.19-28.

Abstract: I give in this article one proof to the famous conjecture of Ulam about the (-1)-reconstruction of the symmetrical graphs.Résumé : Je donne dans cet article une preuve à la célèbre conjecture d' Ulam sur la (-1)-reconstruction des graphes symétriques.

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[3]. J. Fisher. A counterexample to the countable version of a conjecture of ulam. Journal of combinatorial theory, 7:364–365, 1969.
[4]. Bondy J.A. and R.L. Hemminger. Graph reconstruction. J. Graph Theory1, pages 227–268, 1977.
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Abstract: The study of mathematical model of two phase blood flow in artery presented here. P.N. Pandey and V. Upadhyay have considered the blood flow has two phased, one of which is that of red blood cells and other is plasma. They have also applied the non-Newtonian power law model in bio fluid mechanical set-up. We have collected a clinical data in the case of Hepatitis A. The overall presentation is in tensorial form and solution technique adapted is analytical as well as numerical. The role of Hematocrit is explicit in the determination of blood pressure in case of Hepatitis A infection. The graphical presentation for particular parametric value is much closer to the clinical observation

Keywords: Hepatitis A, Hematocrit, Hepatic Blood Flow, non-Newtonian power law model, circulatory system, Liver.

[1] Berry A.K.,Kapoor A.S., NagabhushanamR , Animal physiology, 1981
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[4] Rappaport AM. Hepatic blood flow: morphologic aspects and physiologic regulation. Int Rev Physiol 1980; 21: 1-63
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Abstract: Let G be a molecular graph. A graph G=(V(G),E(G) ) consists of the vertex set V(G) and the edge set E(G) such that each edge e in E is assigned an unordered pair of vertices (u, v), called the end vertices of e. The skeleton of an organic molecule (usually, of a hydrocarbon) represents simple graph. Thus the vertices of molecular graph represent the carbon atoms, and edges the carbon-carbon bonds. In molecular graph we have many topological indices. In this paper, we are computing some topological indices values of butane isomers.

Keywords: Graph, Molecular graph, Topological indices.

[1]. K.C.Das, Atom-bond connectivity index of graphs, Discr.Appl.Math.158 (2010) 1181-1188.
[2]. K.C.Das, I.Gutman, B.Furtula, On atom-bond connectivity index, Chem.Phys.Lett.511 (2011)452-454.
[3]. Estrada, Atom-bond connectivity and the energetic of branched alkanes, Chem.Phys.Lett.463 (2008) 422-425.
[4]. B.Furtula, A.Graovac, D.Vukicevic, Atom-bond connectivity index of tree, Discrete Appl.Math.157 (2009)2828-2835.
[5]. K.C.Das, N.Trinajstic, Comparison between first geometric-arithmetic index and atom-bond connectivity index,
Chem.Phys.Lett.497 (2010)149-151.