#### Version-2 (Mar-Apr 2014)

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**Version-2**
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**Version-6**
**Version-7**

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**Abstract:** We investigate the nature of the singularity in the non-spherical gravitational collapse of the strange quark null fluid. The interesting feature that emerges is that the non-spherical gravitational collapse of charged strange quark matter leads to a naked singularity whereas the gravitational collapse of neutral monopole quark matter gives the singularity is covered in an event horizon, i.e. it produces a black hole. In the present paper we have shown that the monopole spacetime does not play any fundamental roll in the formation of naked singularity.

**Keywords:** Cosmic censorship, event horizon, gravitational collapse, naked singularity.

[1] D M Eardley and L Smar, Time function in numerical relativity: Marginally bound dust collapse, Phys. Rev,D 19, 1979, 2239-2259.

[2] D Christodoulou, Violation of cosmic censorship in gravitational collapse of a dust cloud, Commun. Math. Phys., 93, 1984, 171-195.

[3] R P A C Newman, Strength of naked singularities in Tolman-Bondi space-times, Class. Quantum Grav.,3, 1986, 527.

[4] K D Patil and U S Thool, Spherical and non-spherical gravitational collapse in Husain space-time,Int. J. Mod. Phys., D 14(6), 2005, 873-882.

[5] K D Patil, Structure of radial null geodesics in higher-dimensional dust collapse, Phys. Rev. D 67, 2003, 024017.

[6] A Papapetrou, in A Random Walk in Relativity and Gravitation, eds. N Dadhich, J K Rao, J V Narlikar and C V Vishveshwara (Wiley, New York, 1985)

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**Abstract:** Till very recently we believed 3.1415926… was the final value of .And no body thought exact
value would be seen in future. One drawback with 3.1415926…is, that it is not derived from any line-segment
of the circle. In fact, 3.1415926… is derived from the line-segment of the inscribed/ circumscribed polygon in
and about circle, respectively. Surprisingly, when any line-segment of the circle is involved two things
happened: they are 1. Exact value is derived and 2 that exact value differs from 3.1415926… from its 3rd
decimal onwards, being 3.1464466… Two geometrical constructions of Hippocrates of Chios, Greece (450
B.C.) and Prof. Alfred S. Posamentier of New York, USA, and Prof. Ingmar Lehmann of Berlin, Germany, are
the supporting evidences of the new value. They are detailed below.

**Keywords:** value, lune, triangle, area of curved regions

[2]. P. Dedron and J. Itard (1973). Mathematics and Mathematicians, Vol.2, translated from French by J.V. Field, The Open

University Press, England.

[3]. Alfred S. Posamentier&Ingmar Lehmann (2004). A Biography of the World‟s Most Mysterious Number. Prometheus Books,

New York, Pages 178 to 181.

[4]. RD Sarva Jagannadha Reddy (2014), Pi of the Circle, a Canto on-line edition, in the free website: www.rsjreddy.webnode.com

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Paper Type |
: | Research Paper |

Title |
: | Solving n power class (Q) operators using MATLAB |

Country |
: | India |

Authors |
: | Dr. T. Veluchamy, K. M. Manikanadan, T. Ramesh |

: | 10.9790/5728-10221316 |

**Abstract:**In this paper we investigate the charactisation of n power class (Q) operators on Hilbert space using MATLAB.

Mathematics Subject Classification: 47B99, 47B15.

**Key words:**Normal operator, class (Q) operator, n power class (Q) operator, Hilbert space, Hadamard matrices ,MATLAB R2008a.

[2] A.A.S .Jibril , On Operators for which ( ) International Mathematical Forum, 5,2010, 46, 2255 – 2262.

[3] KrutanRasimi, LuigjGjoka, Some remarks on N – power class (Q) operators,International journal of Pure and Applied Mathematics, Volume 89, No. 2,2013, 147 – 151.

[4] A.A.S. Jibril , On n – power normal Operators, The Arabian Journal for Science and Engineering Volume 33, Number 2A.

[5] A.A.S Jibril, On 2 – normal Operators. Dirasat, Vol.23 , No 2(1996), 190-194.

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**Abstract:**The idea of difference sequences 0 ( ) ( ) : with , and k X x x x X X l c c was introduced by kizmaz. In this paper, using the sequence of moduli we define some generalized sequence spaces and give various topological properties of these spaces with some of their inclusion relations. Furthermore, we study some of their properties, such as solidity, symmetricity, convergence free and so on.

**Keywords:**Difference sequence space, Paranorm, Seminorm, Sequence of moduli.

[2]. M. Et, and R. Çolak, On some generalized difference sequence spaces, Soochow J Math, 21 (4), 1995, 377-386.

[3]. M. Et, and A. Esi, On Köthe-Toeplitz duals of generalized difference sequence spaces, Bull Malaysian Math Sci. Soc, 23 (1), 2000,

25–32.

[4]. C. Asma, , and M. Et, On v-invariant sequence spaces, Soochow J Math, 24 (4), 1998, 305–308.

[5]. C. A. Bektas, M. Et, and R. Colak, Generalized difference sequence spaces and their dual spaces, J Math Anal Appl, 292 (2), 2004,

423–432.

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**Abstract:**We study the steady state Magnetohydrodynamic (MHD) equations in the whole space Following the work of C. Bjorland and M. Schonbek [4] onNavier -Stokes equations in the whole space, we prove the existence of atleast one solution with finite Dirichlet Integral to steady state Magnetohydrodynamic equations in the whole space. Further, we show that these solutions are unique among all solutions with finite energy and finite DirichletIntegral .

[1] G. Duvaut and J.L. Lions, Arch. Rat. Mech. Anal., 46 (1972), 241-279.

[2] E. Sanchez Palencia, Journal de Mechanique, 8(4) (1969), 509-541.

[3] M. Sermange and R.Temam, Commu. Pure Appl. Math., XXXVI (1983),635-664.

[4] C. Bjorland and M. Schonbek, Nonlinearity, Vol. 22, (2009) 1615-1637.

[5] Yong Zhou, Ann. Inst. HenriPoincaré – AN 24 (2007) 491–505

[6] Jiahong Wu, J. Math. Fluid Mech. 13 (2011), 295–305

[7] QunyiBie, Qiru Wang and Zhengan Yao, Regularity criteria for the 3D MHD equations in term of velocity, arXiv: 1312.1012 v1 [math.AP] 4 Dec. 2013

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Paper Type |
: | Research Paper |

Title |
: | On α Generalized Closed Sets In Ideal Topological Spaces |

Country |
: | India |

Authors |
: | S. Maragathavalli, D. Vinodhini |

: | 10.9790/5728-10223338 |

**Abstract:**In this research paper, we are introducing the concept of α-generalized closed sets in Ideal topological space and discussed the characterizations and the properties of α-generalized closed sets in Ideal topological space.

**Keywords:**Ig closed sets, I ̂- closed set, αIg- closed sets, Semi- I closed set, Pre- I closed set, α- I closed set,b- I closed set.

[2]. A.S. Mashhour , I.N.Hasanein and S.N. El-Deeb,α-continuous and α-open mappings, Acta Math.Hungar.,41(1983),213-218.

[3]. R.Vaidynathaswamy, The localization theory in set topology, Proc. Indian Acad. Sci. Math.Sci., 20(1945), 51-61.

[4]. R.L.Newcomb, Topologies which are compact modulo an ideal Ph.D, Dissertation. Univ.Ca;.at Santa Barbara,1967.

[5]. D.V. Rancin, Compactness modulo an ideal, Societ Math.Dokl.,13,193-197.1972.

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Paper Type |
: | Research Paper |

Title |
: | Extended Generalized Mean Value Theorem for Functions of One Variable |

Country |
: | Zimbabwe |

Authors |
: | Phillip Mafuta |

: | 10.9790/5728-10223940 |

**Abstract:**In this manuscript, we state and prove a theorem of a similar flavour to the Generalized Mean Value Theorem for functions of one variable. For lack of a better term, we call the theorem ``Extended Generalized Mean Value Theorem'' and we abbreviate it EGMVT.In addition, we apply Rolle's Theorem to prove the theorem. Also, we deduce some corollaries for Mean Value Theorems. In addition, the EGMVT is verified by use of an example.

**Key words:**Rolle's Theorem; Functions of One Variable; Extended Generalised Mean Value Theorem.

[2] Rudin, W., Principles of Mathematical Analysis, McGraw-Hill, Inc, (1976) pp: 107-108.

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**Abstract:**The steady flow of Herschel-Bulkely fluid through a tube having overlapping stenosis has been investigated. Assuming the stenosis is to be mild, the flow equations have been linearised and the expressions for the resistance to the flow and wall shear stress have been studied. It is found that the resistance to flow increases with the height of the stenosis, power law index, wall shear stress andyield stress but decreases with stress ratio parameter. It is proved that the Hershcel-Bulkely fluid is more appropriate model to the stenosis than the Newtonian fluid.

**Key Words:**Herschel-Bulkely fluid, resistance to the flow, power law index, stress ratio parameter, stenosis

[2] Lee, J.S., Fung,Y.C 1970, Flow in Locally- constricted Tubes and Low RenoldsNumbers,J. Appl.Mech. Trans ASME. 37, 9-16

[3] Shukla, J.B., Parihar,R.S., Rao, B.R.P.,1980, Effects of stenosis on non-Newtonian flow through an artery with mild stenosis,Bull.Math.Biol. 42, 283-294.

[4] Chaturani, P., PonnalagarSamy,R., 1986, Pulsatile flow of Casson's fluid through stenosedarteries with applications to blood flow. Biorheol. 23, 499-511

[5] Radhakrishnamacharya,G., SrinavasRao,P., 2007, Flow of a magnetic fluid through a nonuniform wavy tube, Proc.Nat.Acad.Sci.,India 76(A),in press .

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**Abstract:**Sumathi and Rao (2008) proposed a cure model for the recurrent event count data. The proposed model was based on the zero inflated Poisson (ZIP) distribution. Several tests were proposed for testing the cured proportion for recurrent event count data (Sumathi and Rao (2010)). In any health related studies, whether epidemiological or long term follow up studies, it is very essential for an investigator to record the information of patients regarding their demographic and socio-economic status as well as their medical history, at the time of clinical examination. These factors, commonly known as covariates, do play a vital role in influencing the health status of the individuals. The present paper is an extension of the work of Sumathi and Rao (2010). It proposes tests for testing the cured proportion in the presence of covariates when the data are uncensored.

Unpublished Ph. D. thesis, Department of Statistics, Mangalore University, Karnataka, India.

[2]. Bhattacharya, A., Clarke, B.S. and Datta, G.S. (2008). A Bayesian test for excess zeros in a zero-inflated power series distribution.

IMS collections. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K Sen. Vol.1, 89-104.

[3]. Boag, J. W. (1949). Maximum likelihood estimates of the proportion of patients cured by

[4]. cancer therapy. Journal of the Royal Statistical Society, Series B 11, 15-44.

[5]. Broek, J. (1995). A score test for zero inflation in a Poisson distribution. Biometrics, 51, 738-743.

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Paper Type |
: | Research Paper |

Title |
: | On Solution to Traffic Flow Problem by Method of Characteristics |

Country |
: | Nigeria |

Authors |
: | James, Torudonkumo, Eze, Everestus Obinwanne |

: | 10.9790/5728-10226066 |

**Abstract:**Our main purpose in this paper is to use the method of characteristics to solve traffic flow problems involving the conservation of cars. The method of characteristics is a technique of solving partial differential equations (PDEs) by imposing new coordinates, that is to say, change of coordinates. Note the traffic flow equation is classified as hyperbolic equation. We also discussed the relationship between flow rate, density and velocity.

**Keywords:** Traffic flow problem, Method of Characteristics, Flow rate, Density, Velocity, Change of Coordinates.

ARIMA Process: Theoretical Basis and Empirical Results. Journal of Transportation Engineering © ASCE/November/December

2003/665. DOI: 10.1061/(ASCE)0733-947X(2003/129:6(664).

[2] Daganzo, C.F. (1999). "The lagged cell-transmission model." Proc., 14th Int. Symp. On Transportation and Traffic Theory, A.

Ceder, ed., Pergamon, New York, 81-106.

[3] Danielle L. Metcalf (2006) Mathematics Descipline University of Minnesota, Morris, MN 56267.

[4] Dr. Scott A. Sarra. The Method of Characteristics with applications to Conservation Laws. October 17, 2002.

[5] Haberman, Richard. Mathematical Models, Mechanical Vibrations, Population Dynamics, and Traffic Flow. Philadelphia: Society

of Industrial and Applied Mechanics, 1998. 275-382.

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**Abstract:**The notion of 'order' is introduced on the linear space ζ' of tempered generalized functions and the
topology of bounded convergence is assigned to ζ'. It is proved that the order topology and the topology of
bounded convergence on ζ' are the same. That the operations of convolution and direct product of comparable
elements in ζ' are compatible with the lattice operations in ζ' is also proved. Fourier Transform is applied to the
elements of ζ' and the properties of the transform and its inverse with the topology of bounded convergence
assigned to ζ' are studied. Illustrations of application of Fourier Transform to obtain fundamental solutions of
non-zero linear differential equations with constant coefficients are given. Comparison of various solutions is
also done.

**Key Words: **Fourier Transform, tempered generalized function, positive cone.
MSC (2010): 42A38, 46F12,46F05

Vol.4, No.2 (Dec 2007) pp 63-75.

[2] Limaye B.V., Functional Analysis (2nd Edition), New Age International Ltd., New Delhi, 1996

[3] Peressini, A.L., Ordered Topological Vector Spaces, Harper & Row, New York, 1967.

[4] Vladimirov V.S., Methods of the Theory of Generalized Functions, Taylor and Francis, New York, 2002

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Paper Type |
: | Research Paper |

Title |
: | The Drainage of Thin Liquid Films on an Inclined Solid Surface |

Country |
: | Iraq |

Authors |
: | Joseph G. Abdulahad, Salih A. Derbaz |

: | 10.9790/5728-10227380 |

**Abstract:**In this paper, we consider the thinning process of an inclined thin liquid film over a solid boundary
with an inclination angle to the horizontal in gravity driven flow. Throughout this work, we assumed that the
fluid thickness is constant far behind the front and we neglect the thickness of the film at the beginning of the
motion. The equation of the film thickness is obtained analytically, using the similarity method by which we can
isolate the explicit time dependence and then the shape of the film will depend on one variable only. The
solution of the governing equations of the film thickness is obtained numerically by the Rung-Kutta method with
the aid of Mat lab(ode45).

**Keywords:** Thin Liquid Films ,Navier-Stokes equations , continuity equation .

[2] Diez, J., Kondic L. and Bertozzi, A.L. (2001). Global models for moving contact lines, Phys. Rev., pp. 011208, 63.

[3] Kondic L. and Diez J. (1994). Contact line instabilities of thin fluid film flows: constant flux configuration, Phys. Fluids, pp. 224–234.

[4] Lin. T. S., Kondic, L. and Filippove, A.(2012). Thin films flowing down inverted substrated three dimensional flow, Physics of fluids, Vol.24, pp. 1-18.

[5] Karmina, K. A., (2013). Fluid flow and stability analysis in certain thin liquid films.M.Sc.thesis, University of Zakho.

[6] Drofler, F., Rauscher M. and Dietrich S.(2013). Stability of thin liquid films and sessile droplets under confinement,Eur. Phys. J. E.Vol.20, pp. 1-14.

[7] Kondic L (2003). Instabilities in gravity driven flow of thin fluid films, Siam Review, vol. 45, No. 1, pp. 95–115.

[8] Moriarty J.A., and Schwartz L.W.(1991). Unsteady spreading of thin liquid films with small surface tension,American institute of Physics, vol3, No.5, pp. 733-742.

[9] Zakariya, K., Sirweh, M. A. and Alkharashi, S. A.(2012), Non-linear analysis of creeping flow on the inclinedpermeable substrate plane subjected to an electric field. International Journal of Non-linear Mathematics, vol.47, pp. 577-598.

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**Abstract:**The theories of solutions of Differential Equations are way important because of their applicability to areas of physical science and modeling of some physical phenomena. The notion of their properties are quite revealing because of the cyclic relationship existing between them. In this paper, our objective is to x-ray the boundedness and continuity implications in a solution of an initial value problem of a first-order linear differential equation. We employed Arzela-Ascoli theorem and some other theorems from bounded linear maps to prove our assertions. The results obtained were quite revealing and shows the existence of a local solution to our equation if only is assumed to be continuous. Furthermore, that map continuity is equivalent to boundedness in Normed linear spaces. We concluded that our objectives were achieved based on our deductions.

**Keywords**: Boundedness, Continuity, Arzela-Ascoli Theorem, Normed linear map

[2] C. E. Chidume (2003): Foundations of Riemann Integration. International Centre for Theoretical Physics, Trieste, Italy

[3] C. E. Chidume (2006): Applicable Functional Analysis. International Centre for Theoretical Physics, Trieste, Italy

[4] Eze E.O, Ogbu H.M and Aja O.R (2013): On Application of Lyapunov and Yoshizawa's Theorems to Stability, Asymptotic Stability Boundedness and Periodicity of Solutions of Duffing's Equation. Book of Abstracts of the Nigerian Mathematical Society Conference Ile-Ife

[5] Eze E.O, Ogbu H.M and Aja O.R (2013): On the Uniform Convergence to the Solution of the Intial Value Problem of the Nth-Order Differential Equation. Journal of the Nigerian Mathematical Physics

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**Abstract:**In this Paper we are studding the polynomial approximation of entire functions of two complex
variables in Banach spaces; concept is depend on index-pair. The characterizations of ( ) order of entire
functions of two complex variables have been studied in terms of approximation errors. The results can be
extended to m-variables but to reduce the mechanical labour we have considered only two variables.

**Key Words**: Approximation error, order, type, entire function, index-pair.

[2] Ganti, R. and Srivastava, G.S., Approximation of entire functions of two complex variables in Banach spaces, J. Inequalities in Pure

& Applied Mathematics, 7, Issue 2, (2006), 1-11.

[3] Juneja, O.P., Kapoor, G.P. and Bajpai, S.K., On the ( p, q) order and lower ( p, q) order of an entire function, J. Reine

Angew. Math. 282 (1976), 53-67.

[4] Vakarchuk, S.B. and Zhir, S.I., On some problems of polynomial approximation of entire transcendental functions, Ukarainian

Mathematical Journal, (54) (9) (2002), 1393-1401.

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**Abstract:**Accurate, reliable, efficient, and robust simulation of groundwater flow in the unsaturated zone for the problems that characterized by sharp fronts in both space and time is computationally expensive. The accurate numerical solution of these problems by standard approaches with uniform spatial and temporal discretization usually inefficient and simulation is too costly. Moreover, it is very difficult to obtain explicit solution of Richards' equation by using standard time integration unless very small time steps are used in the integration process. Economical and robust solution may be achieved with variable time step size instead of constant time step size use. In this study,

[2] M. T. van Genuchten, A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils, Soil Sci. Soc. Am. J., 44, 1980, 892–898.

[3] G. A. Williams, and C. T. Miller, An evaluation of temporally adaptive transformation approaches for solving Richards' equation, Adv. Water Resources, 1999;22(8):831-840.

[4] R. J. Hanks, and S. A. Bowers, Numerical solution of the moisture flow equation for the infiltration into layered soils, Soil. Sci. Proc., 1962:530-534.

[5] N. Romano, B. Brunone, and A. Santini, Numerical analysis of one dimensional unsaturated flow in layered soils, Adv. Water Resources, 1998;21:315-324.

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Paper Type |
: | Research Paper |

Title |
: | Invariant Region, Endemic Equilibria and Stability Analysis |

Country |
: | Zimbabwe |

Authors |
: | P. Mafuta, J. Mushanyu, G. Nhawu |

: | 10.9790/5728-1022118120 |

**Abstract:**In this manuscript, the ideas of Lyapunov, Barbalat, Birkhoff and Rota have been explored on the deterministic model A that describes human population, whose state variables and parameters are assumed to be non-negative. This approach is ideally suitable for S.I models where there is no disease induced death rate, for instance chancroid and trichomoniasis. We have put forward and proved three conjectures, that is, the system of equations that describes model A is dissipative, for an endemic equilibrium point Q* of such a system there exist a strict Lyapunov function and that an endemic equilibrium point Q* is both globally and locally asymptotically stable whenever it exists.

**Key words:** Dissipative; Lyapunov function; Asymptotic Stability

[2] A.M. Lyapunov, The General Problem of the Stability of motion. (A. T. Fuller trans.) Taylor and Francis, London (1992).

[3] P. Mafuta, J. Mushanyu, S. Mushayabasa, C.P. Bhunu, Transmission Dynamics of Trichomoniasis in bisexuals. World Journal of Modelling and Simulations 9(2013) 302-320.

[4] J. Mushanyu, P. Mafuta, S. Mushayabasa, C.P. Bhunu, Assessing the Impact of Educational Cam- paigns and Condom use in Chancroid Transmission Dynamics. World Journal of Modelling and Simulations (2013) submitted.

[5] C.P. Bhunu, S. Mushayabasa, Transmission Dynamics of Trichomonas vaginalis: A mathematical approach. Journal of Mathematical Analysis and Applications 379(2011) 852-860.

[6] C.P Bhunu, S. Mushayabasa, Chancroid Transmission Dynamics: A Mathematical Approach. The- ory in Bio-sciences 130(2011) 289-298.

[7] G. Birkhorff, G.C. Rota, Ordinary Differential Equations. Needham Heights, Ginn (1982).

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Paper Type |
: | Research Paper |

Title |
: | "HCR‟s Series" |

Country |
: | India |

Authors |
: | Mr. Harish Chandra Rajpoot |

: | 10.9790/5728-1022121123 |

**Abstract:**This is a finite series which is the sum of first "n‟ natural numbers multiplied by their own respective factorials. The series has been derived from HCR‟s Rank formula which was proposed by the author. It is extremely useful in case studies & computations. Although HCR‟s Series is different from the Arithmetic, Geometric, Harmonic & Taylor‟s Series of simple functions, it is the expansion of factorial of any natural number in form of discrete summation thus it is also named as HCR‟s divergence series.

[2]. Manuscript ID: 004022014A (Website: www.researchpublish.com)Date: 19 Feb, 2014

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Paper Type |
: | Research Paper |

Title |
: | A study on Nonlinear Programming Problem in Fuzzy Environment |

Country |
: | India |

Authors |
: | M. Lalitha, Dr. C. Loganathan |

: | 10.9790/5728-1022124128 |

**Abstract:**In that paper, the fuzzy nonlinear programming problem is discussed. In order to obtain more accurate solution, the properties of fuzzy set and fuzzy number with linear membership function and fuzzy maximum decision maker is utilized to fuzzifying the crisp problem. In the illustration, we have given a refinement to obtain this solution.

**Keywords:**Fuzzy numbers, Nonlinear programming, Optimization problem, Fuzzy maximum decision making.

[2] D. Drinkov, H. Hellendoorn, and M. Reinfrank, An Introduction to Fuzzy Control, Springer, Berlin, etc., 1993.

[3] Iyengar. P, Non-Linear Programming; Introduction, IEOR, Handout 19, 16 October 2002.

[4] Z. A. Kanaya , An Interactive Method for Fuzzy Multi objective Nonlinear Programming Problems, JKAU Sci., Vol. 22, No. 1 (2010) pp. 103-112.

[5] B. Kheirfam F. Hasani. Sensitivity analysis for fuzzy linear Programming problems with Fuzzy variables, Advanced Model and Optimization, Vol. 12, No. 2, 2010.

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**Abstract:**In this paper, we devoted to study the existence of mild solutions for quasilinear integrodifferential equation in Banach spaces. The results are established by using Hausdorff's measure of noncompactness and the fixed point theorem. Application is provided to illustrate the theory.

**Keywords:**Mild solution, neutral differential equation, Hausdorff measure of noncompactness, fixed point theorem.

(2003), 359-367.

[2] K. Balachandran and E. R. Anandhi, Controllability of neutral functional integrodifferential infinite delay systems in Banach

spaces, Taiwanese Journal of Mathematics, 8 (2004), 689-702.

[3] E. Hernandez and H. R. Henriquez, Impulsive partial neutral differential equations, Applied Mathematics Letters, 19 (2006), 215-

222.

[4] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, Springer-Verlag, New York, 1993.

[5] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J.

Math. Anal. Appl. 162 (1992), 494-505.

[6] L. Byszewski, H. Akca, Existence of solutions of a semilinear functional-differential evolution nonlocal problem, Nonlinear Anal.

34 (1998), 65-72.

[7] L. Byszewski, V. Lakshmikanthan, Theorems about the existence and uniqueness of solutions of a nonlocal Cauchy problem in

Banach spaces, Applicable Anal. 40 (1990), 11-19.

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**Abstract:**Exchange rates are important financial problem that is receiving attention globally. This study investigated the volatility of daily Dollar/Naira exchange rate using GARCH (1, 1), GJR-GARCH (1, 1), TGARCH (1, 1) and TS-GARCH (1, 1) models by using daily data over the period June 1st, 2000 to July 26, 2011 consisting of 4083 observations. The results from all the models show that volatility was persistent (i.e. exceed 1) indicating GARCH (1, 1), GJR-GARCH (1, 1), and TS-GARCH (1, 1) models variances are not stationary but for TGARCH (1, 1) model (i.e. below 1) indicating the variance is stationary. The GJR-GARCH (1, 1) and TGARCH (1, 1) models show the existence of statistically significant asymmetry effect. The results from all the asymmetry models rejected the hypothesis of leverage effect. The TGARCH (1, 1) and TS-GARCH (1, 1) models are found to be the best models, they have all the parameters of the variance being significant and with lower information criteria.

**Keywords:**Volatility, GARCH, Exchange rate, Nigeria.

[2] Awogbemi Clement and Alagbe Samuel (2011) Empirical Modeling of Nigerian Exchange Rate Volatility. Mathematical Theory and Modeling, Vol.1(3): 8-15

[3] Black, F. (1976) Studies in Stock Price Volatility Changes, Proceedings of the 1976 Business Meeting of the Business and Economics Statistics section, published by American Statistical Association.

[4] Bollerslev, T. (1986) Generalised Autoregressive Conditional Heteroskedasticity, Journal of Econometrics. 51: 307-327.

[5] Dickey, D.A. and Fuller, W. A. (1979) Estimators for Autoregressive Time series with a unit root, Journal of the American Statistical Association. 74: 427 - 432.

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Paper Type |
: | Research Paper |

Title |
: | Isomorphism on Irregular Intuitionistic Fuzzy Graphs and Its Complements |

Country |
: | India |

Authors |
: | S. Yahya Mohamed, R. Jahir Hussain |

: | 10.9790/5728-1022149154 |

**Abstract:**In this paper, We study more results of Isomorphism on highly Irregular intuitionistic fuzzy graphs discussed. Isomorphism on neighbourly Irregular intuitionistic fuzzy graphs and its complement are established. Also we extend the isomorphic properties of Neighbourly total Irregular intuitionistic fuzzy graphs..

**Keywords:**Intuitionistic fuzzy graph, degree, total degree, neigbourly IFG, neighbourly Total IFG.

[2] Parvathi, R. and Karunambigai, M.G., Intuitionistic Fuzzy Graphs, Computational Intelligence, Theory and applications, International Conference in Germany, Sept 18 -20, 2006.

[3] A.NagoorGani and S.R. Latha, On Irregular Fuzzy Graphs, Applied Mathematical Sciences,Vol.6, 2012, no.11,517-523.

[4] A.NagoorGani and S.Shajitha Begum, Degree,Order and Size in Intuitionistic Fuzzy Graphs,International Journal of Algorithms, Computing and Mathematics,(3)3 (2010).

[5] Bhutani,K.R., On Automorphism of Fuzzy graphs, Pattern Recognition Letter 9:159-162,1989.

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Paper Type |
: | Research Paper |

Title |
: | Operational techniques upon certain single integral transform |

Country |
: | India |

Authors |
: | Darshowkat, Ab. Rashid Dar |

: | 10.9790/5728-1022155157 |

**Abstract:**The aim of this paper is to evaluate certain results on integral transform by using operational technique, Next the result obtained here are quite general in nature due to presence of operational technique which are basic in nature. A large number of new results and special cases have seen obtained by operational technique using proper choice of parameters.

**Keywords:**Laplace transform, Generalized Hypergeometric functions, integral Laplace transform, Inverse Laplace transform, Lagurre Polynomials, inverse Laplace transform integral.

west Sussex, po191Ed, England.

[2] Y. K. Luke (1969), Special function and there Approximations, Vol. 1 & ii. Academic press, Newyork and London.

[3] A. Erd lyi (1954), Tables of integral transforms, Vol's.1 and ii. McGraw-Hill, Newyork, Toronto, and London.

[4] E. D. Rainville (1960), Special function. Macmillan, Newyork, Reprint by cheses publ. Co., Bronx, Newyork, 1971.

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Paper Type |
: | Research Paper |

Title |
: | An Improved Self-Starting Implicit Hybrid Method |

Country |
: | Nigeria |

Authors |
: | E. O. Adeyefa |

: | 10.9790/5728-1022158163 |

**Abstract:**The paper presents the derivation a hybrid block method for the solutions of Initial Value Problems of Ordinary Differential Equations. This is achieved by using collocation and interpolation technique to contruct a self-starting method with continuous coefficients together with the additional methods from its first derivative which are combined to form a single block that simultaneously provide the approximate solutions for Initial Value Problem. The analysis of the properties of the method such as stability, consistency and convergence are discussed and the performance of the method is demonstrated on two test problems to show the accuracy and efficiency of the method. On comparison of the results obtained from numerical examples with some existing methods, we discovered that the method behaved favourably well.

**Keywords:**Chebyshev polynomial, Collocation, Hybrid, Interpolation.

[2] Awoyemi, D.O., A class of Continuous Methods for general second order initial value problems in ordinary differential equation. International Journal of Computational Mathematics, 72, 1999, 29-37.

[3] Bun, R.A. and Varsil'yer, Y.D., A numerical method for solving differential equations of any orders. Comp. Math. Phys. 32(3), 1992, 317 - 330.

[4] Lambert, J.D., Numerical Methods for Ordinary Differential Systems. John Wiley, New York, 1991.

[5] Kayode S.J., An improve numerov method for direct solution of general second order initial value problems of ODEs, National Mathematical Centre proceedings 2005.

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Paper Type |
: | Research Paper |

Title |
: | An Application of Graph Theory to the Electrical Circuit Using Matrix Method |

Country |
: | Nigeria |

Authors |
: | Samai'la Abdullahi |

: | 10.9790/5728-1022164166 |

**Abstract:**A graph is a pair of two set V and E so thatG (V,E) . A graph is a pictorial representation of a system using two basic element nodes and edges, a node is represented by a circle (either hallo shade) and edge is represented by a line segment connecting two nodes together. In this paper we present a circuit network in the concept of graph theory application and also circuit models of graph are represented in logical connection method were we formulate matrix method of adjacency and incidence of matrix and application of truth table.

**Key word:**Euler Circuit and Path, Graph representation of Circuit networks, Representation of Graph models, Representation Of circuit network using logical truth table.

[2] Y. Yao and W.J. Freeman, "Model of biological pattern recognition with spatially chaotic dynamics, '' Neural Networks, vol 2. No. 2 ,1990.pp. 153-170

[3] J.J. Hopfied "Neural Networks and physical systems with emergent collective computational abilities,'' proceeding of the National Academy ofscience, vol. 79,1982,pp.2554-2558.

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Paper Type |
: | Research Paper |

Title |
: | Mathematics in Hausa Culture: Some Examples from Kano State-Nigeria |

Country |
: | Nigeria |

Authors |
: | Dr. Garba Shuaibu |

: | 10.9790/5728-1022167171 |

**Abstract:**This paper is primarily concern with exploring and discussing Mathematics in Hausa culture with particular reference to some examples from kano state, Nigeria.The researcher survey the environment and observed that Hausa culture is rich with many aspects of mathematical study such as bee construction of their cells in regular n-gons design and the two Sallah Festivals. Itis recommended that mathematics and Hausa teachers should be prepared to face some very important area of concern such that there is different appropriate mathematics for different societies; hence teachers and students should strive hard to identify them for the sake of promoting what can be called mathematics for survival.

[2] Bekken, Otto B. [1990] Bees and Their Mathematics: A project Integrating Math and Science. Science and Technology Education Document Series No. 38. Paris. UNESCO.

[3] Berlin, C. P. [1998] When Student Imagines Numbers in Color; Is there a Relationship between Creativity and Mathematics ability? An Independent Studying Education Research.Harvard University, Graduate School of Education.

[4] Eshiwani [1979] In AMUCHMA-NEWSLETTER-9-August, 1991.

[5] Gardes, P. [1985] In AMUCHMA-NEWSLETTER-9-August,1991.