iosr-Jm   Volume-10 ~ Issue-4 ~ July-August 2014

Abstract: Image segmentation is an important task in the field of image processing. Medical image segmentation plays a vital role in assisting the radiologists to visualize and analyze the region of interest in medical images. Region growing is a very useful technique for image segmentation. Region growing method of segmentation which is based on the classification of pixels into connected components by selecting a seed and grouping its neighbours with the seed based on the gray levels of the neighbours. In this article, we propose a new seeded region growing segmentation algorithm based on metric topological - neighbourhoods of different metrics and grouping criterion for segmentation of region of interest from the medical images. The qualities of segmented images are measured by the evaluation measure 'Accuracy '.

Keywords: Metrics, Region Growing, Segmentation, Topological Neighbourhoods

[1] Jiang Guangyou and Kang Gewen, A threshold segmentation algorithm based on neighbourhood characteristics, The tenth International conference on Electronic Measurement and Instruments ,IEEE , 2011,328-331.
[2] Chantal Revol and Michel Jourlin, A new minimum variance region growing algorithm for image segmentation, Pattern Recognition Letters, 18, 1997, 249-258.
[3] Yi-Ta Wu , Frank Y. Shih , Jiazheng Shi and Yih-Tyng Wu, A top-down region dividing approach for image segmentation, Pattern Recognition, 41, 2008, 1948-1960.

[4] Maria Kallergi, Kevin Woods, Laurence P. Clarke, Wei Qian and Robert A. Clark, Image segmentation in digital mammography; Comparison of local thresholding and region growing algorithms, Computerized Medical Imaging and Graphics , Vol 16(5), 1992, 323-331.
[5] Pastore J., Bouchet A., Moler E. and Ballarin, V., Topological Concepts applied to Digital Image Processing, JCS&T, Vol. 6, No. 2, 2006, 80-84.

Abstract: All over the world, during the last decade or two a lot of of research activity is undertaken on the study of the oscillation of neutral delay difference equation. Such equations appear in a number of important appilcations including problems in population dynamics or in "cobweb" models in Economics. Further, they are frequently used for the study of distributed networks containing lossleds transmission lines see the Hale [11] . Upto now, many studies have been done on the oscillation problem of even order difference equations, and we refer the reader to the papers [2,3,4,5,8,13,14,15,18,20,21,24,25,26,27,29,30,31] and the references cited
there in.

[1]. Agarwal R.P., Difference Equation and Inequalities, Marcel Dekker, New York (1992).
[2]. Agarwal R.P., On the oscillation of higher order difference equation, Srochow. J.Math.31(2)(2005) 245-259.
[3]. Agarwal R.P. and Wong P.J.Y., Advanced Topics in Difference Equations, Klwer Academic Publishers, (1997).
[4]. Bolat.Y and Akin.O., Oscillatory behaviour of a higher order nonlinear neutral-type functional difference equation with an oscillating
coefficient., Appl. Math. Lett. 17(2004) 1073-1078.
[5]. Bolat.Y., Akin.O. and Yildirim.H., Oscillation criteria for a certain even-order neutral difference equation with an oscillating
coefficient. Appl.Math.Lett. 22(2009) 590-594.

Abstract: In this paper, we study the numerical solution of fuzzy differential equations by using modified twostep Simpson method. This method is adopted to solve the dependency problem in fuzzy computation. Examples are presented to illustrate the computational aspects of this method.
Keywords: Fuzzy initial value problem, Dependency problem in fuzzy computation, Modified two-step method.

[1]. S. Abbasbandy, T. Allahviranloo, Numerical solutions of fuzzy differential equations by Taylor Method, Computational Methods in Applied Mathematics 2 (2002) 113-124.
[2]. S. Abbasbandy, T. Allahviranloo, Numerical solution of Fuzzy differential equation by Runge-Kutta method, Nonlinear Studies 11 (2004) 117-129.
[3]. M. Ahamad, M. Hasen, A new approach to incorporate uncertainity into Euler method, Applied Mathematical Sciences 4(51) (2010) 2509-2520.
[4]. M. Ahamed, M. Hasan, A new fuzzy version of Euler's method for solving diffrential equations with fuzzy initial values, Sians Malaysiana 40 (2011) 651-657.
[5]. M. Ahmad, M. Hasan, Incorporating optimization technique into Zadeh's extension principle for computing non-monotone functions with fuzzy variable, Sains Malaysiana 40 (2011) 643-650.

Abstract: Scale free analysis has been developed recently and in this framework real number system is realized as an extended deformed real line R . This analysis is applied on a class of ordinary differential equations. We report in particular some simple but nontrivial applications of this nonlinear formalism leading to emergence of complex nonlinear structures even from a linear differential system. These emergent nonlinear phenomena from a linear system is argued to offer, a new non-perturbative method for computing solutions and estimate amplitude, frequency etc. for a specific nonlinear system, viz. the Van der Pol equation.
Keywords: Scale invariance, non-archimedean absolute value, relative infinitesimals, nonlinear increment, non-perturbative method.

[1] D.W. Jordan, P.Smith, Nonlinear Ordinary Differential Equations: An Introduction for scientists and Engineers (4th ed.), Oxford
University Press (2007).
[2] Kevorkian. J, Cole.J. D., Multiple scale and Singular Perturbative Methods, springer, (1996).
[3] S. Liao, Homotopy Analysis Method in Nonlinear Differential Equations, Springer Berlin Heidelberg (2012).
[4] D.P. Datta and A.Ray Chaudhuri, Scale free analysis and prime number theorem, Fractals,18,(2010),171-184.
[5] D.P.Datta and M.K.Bose, Higher derivative discontinuous solutions to linear ordinary differential equations: a new route to
complexity? Chaos, Solitons and fractals,22,(2004),271-275.

Abstract: In this paper I have extended a result of W.K.Hayman to Euler's gamma function which is known to
be a logarithmically Convex function.
Key Words: Euler's gamma function,convex function

[1]. HAYMAN W.K (1964):Meromorphic functions,Oxford Univ ,Press, London.
[2]. YANG LO,(1982): Value distribution theory,Science press,Beijing,.

Abstract: The multiple solitonsolutions of (1+1)-dimensional Hirota –Satsuma shallow water wave equation is studied usingPainlevé- Bӓcklundtransformation and the simplified Hirota's method.Also the hyperbolic and theExp-trigonometric function methods are used to obtain some more kind of solitary wave solutions.
Keywords: Hirota Satsuma water wave equation, multiplesoliton solution, SimplifiedHirota's method, hyperbolic and Exp-trignometric solutions.

[1]. Ablowitz, M. J, H. Segur (1981),.Solitons and the inverse scattering transform (Philadelphia: SIAM,
[2]. A-M,.Wazwaz. (2013) Multiple soliton solutions and rational solutions for the (2+1)-dimensional dispersive long water-wave
system OceanicEeng.60, 95-98
[3]. Freeman, N.C and Nimmo, J.J.C.(1983)The use of Backlund transformation in obtaining N-soliton solutions in Wronskian form.
Phys. lett. A 95, 1-3.
[4]. Hereman, W. Nuseir, A. (1997), Symbolic method to construct exact solution of nonlinear partial differential equation Math, Comp,
Simul., 43, 13-27
[5]. Hietarinta, J, (1987) A search for bilinear equation passing three-soliton condition I. KdV type bilinear equation, J. Math. Phys. 28,
1732-1742

Abstract: Mathematical models have been useful in the area of modeling of real life situations; its application can be found in virtually all spheres of scientific researches. As such, we adopt its use in the field of ecology where preys have to compete with other prey for survival. In this paper, we considered Lotka-Volterra type systems, consisting of two first order differential equations which were used to model the population size of prey–predator interaction. We also proposed a system of first order differential equations to model the population sizes of a prey and two predators. Under these conditions one of the predators dies out while the remaining predator and prey approach periodic behavior as time increases. Also we model the population size of two preys and one predator where there may be interaction between the preys. Under these conditions we found that one of the preys died out while the remaining preys and predators approached periodic behavior as time increased. For critical cases, each positive solution of the system was seen to be periodic in nature. Various examples and results were presented and further study was proposed.

Keywords: Mathematical Models, Lotka-Volterra, differential equation, habitat, predator, prey

[1] Chesson p., (2002), the interaction between predation and competition: a review and synthesis. Ecol. Lett. 5: 302-15
[2] Keddy(2001), Competition. Dordrcht: kluwer, 2nd edition.
[3] Abrams P. A., (2001), Positive indirect effects between prey species that share predators.
[4] Lokta A. J., (1924), Elements of physical biolog Williams & Wilkins, Baltimore.
[5] Barntt V. D., (1962), the monte carlo solution of a competing species problem.
[6] Cooke D., (1996), the mathematical theory of the dynamics of biological populations II, academic press Inc

Abstract: The present paper evaluates certain double integrals involving H -function of two variables [21] and Spherodial functions [23]. These double integrals are of most general character known so far and can be suitably specialized to yield a number of known or new integral formulae of much interest to mathematical analysis which are likely to prove quite useful to solve some typical boundary value problems.
Key words: H -function, H -function of two variables, Spheroidal function

[1]. Agarwal, R.P.; An extension of Meijer's G -function, Proc. Nat. Inst. Sci. India, 31A,(1965), 536-546.
[2]. Bromwich, T.J.I.A.; An Introduction to the Theory of Infinite Series, MacMillan, London, 1965.
[3]. Buschman, R.G. and Srivastava , H.M.; The H  function associated with a certain class of Feynman integrals, J.Phys.A:Math.
Gen. 23, (1990), 4707-4710.
[4]. Chu, L.J. and Stratton, J.A.; Elliptic and Spheroidal wave functions, J. Math. and Phys., 20(1941), 259-309.
[5]. Edwards. J.; A Treatise on the Integral Calculus, vol. II, Chelsea Publication, New York, 1954.
[6]. Erdelyi, A. et. al.; Higher Transcendental Functions, vol.I, McGraw-Hill Book Co., New York, 1953

Abstract: This paper proposes to develop the statistical method or measure for rank-ordering subjects relative to their performance or scores in a contest, test or condition in comparison with one another to enable guide decisions on preferential selection when opportunities or resources are scarce or limited.The methods which also provide appropriate modifications for their use when the population of research interest are numerical measurements, propose measures termed 'subject specific indices of relative performance' or 'subject specific relative performance indices' that are individual subject-specific rather loosely and globally-targeted, merely summary indices or averages.The proposed method using 'subject-specific relative performance indices' enables one easily and quickly estimate the median and other tiles of the distribution of the population.Test statistics based on the proposed indices are provided for testing desired hypotheses on patterns of relationship between performances or scores by subjects as well as about any percentiles of the population.The proposed methods are illustrated with some sample data and the method modified for use when the sampled population is numerical is shown to be relatively more powerful than the more generalized method used with measurements on at least the ordinal scale.

Key Words: and Phrases: One Sample Data, Measures of Central Tendency, Measures of Dispersion, One Sample T-test, Sign Test, Median Test, Relative Relationships, Performance or scores in a contest, Preferential Selection, Rank-order, Index and Decision.

[1]. Arua et al (1997): Fundamentals of Statistics for Higher Education. Fijac Academic Press, Nsukka, Nigeria.
[2]. Gibbons, J. D. and (1971): Nonparametric Statistical Inference. Mercel Dekker, Inc. New York.
[3]. Oyeka, I. C. A. (2012):Introduction to Applied Statistics. Nobern Avocacy Publishers, Enugu, Nigeria.
[4]. Oyeka, I. C. A. (2009): Introduction to Applied Statistics. Nobern Avocacy Publishers, Enugu, Nigeria.
[5]. Oyeka, I. C. A. (1996): Introduction to Applied Statistical Methods in the Sciences. Nobern Avocacy Publushers, Enugu, Nigeria.

Abstract: We present a single server with two heterogeneous service stages having different general (arbitrary) distribution, subject to random breakdowns and Bernoulli scheduled server vacation. The customers arrive in batches and the server provides service one by one. The second stage service must be provided after completing the first stage service by the server. On completion of the first phase of the service with FCFS schedule, the second phase starts. With probability p the customer feedback to the tail of original queue for repeating the service until the service be successful. With probability 1 - p = q the customer departs the system if service be successful. Upon the completion of the second stage service, the server will go for vacation with probability  or staying back in the system for providing the service to the next customer with probability 1 , if any. The vacation time follows general (arbitrary) distribution. The system may breakdown at random time and the breakdowns occur according to Poisson stream. Once the server breakdown, it could not be repaired immediately, so that there is a waiting time, called 'delay time' before the server getting repaired. Both the delay time and repair time follow exponential distribution. We obtain the time dependent probability generating functions in terms of their Laplace transforms and the corresponding steady state results explicitly. Also we derive the average number of customers in the queue and the average waiting time in closed form.
Keywords: / /1 [ ] M G X Queue, Heterogeneous Service, Bernoulli Vacation, Probability Generating Function, Delay Time, Mean Queue Length.

[1] R.F. Anabosi and K.C. Madan, A single server queue with two types of service, Bernoulli schedule server vacations and a single
vacation policy, Pakistan Journal of Statistics, 19(2003), 331 - 342.
[2] J.R. Artalejo and G. Choudhury, Steady state analysis of an M/G/1 queue with repeated attempts and two-phase service, Quality
Technology and Quantitative Management, 1(2004), 189 - 199.
[3] Y. Baba, On the / /1 [ ] M G X
queue with vacation time, Operations. Res. Lett., 5(1986), 93 - 98.
[4] A. BadamchiZadeh and G.H.A. Shahkar, Two Phases Queue System with Bernoulli Feedback and Bernoulli Schedule Server
Vacation, Information and Management Sciences, 19(2008), 329-338.
[5] P.J. Burke, Delays in single-server queues with batch input, Operations.Res., 23(1975), 830 - 833.

Abstract: In this paper, we develop the theoretical and computational per- spectives of tackling and calculating the concept of land equivalent ratio (LER). We apply this idea to discuss its application in a mutualistic interaction. Criteria for evaluating different intercropping situations are suggested also in this paper, and the land equivalent ration (LER) concept is considered for situations where intercropping has to be compared with growing each crop in pure stand. The need to use different standardizing sole crop yields in forming LERs is discussed, and a method of calculating an 'effective LER' is proposed to evaluate situations where the yield proportions achieved in intercropping are different from those that might be required by a farmer. The possible importance of effective LERs in indicating the proportions of crops likely to give biggest yield advantages is discussed.

Keywords: and phrases. LER, Mutualism, Numerical Simulation, ODE45, ODE23.

[1] R.B. Banks, Growth and Diffusion Phenomena Mathematical Frameworks and Applications, Springer-Verlag, 1994.

[2] E.N. Ekaka-a, Computational and Mathematical Modelling of Plant Species Interactions in a Harsh Climate, PhD Thesis, Department of Mathematics, The University of Liverpool and The University of Chester, United Kingdom, 2009.

[3] N.J. Ford, P.M. Lumb, E. Ekaka-a, Mathematical modelling of plant species interactions in a harsh climate, Journal of Computational and Applied Mathematics 234, (2010), 2732-2744.

[4] S. Giliessman, Agroecology: Ecological Processes in Sustainable Agriculture, Sleeping Bear Press, MI, 1998.

[5] P. Sullivan, Intercropping Principles and Production Practices, Appropriate Technology Trans- fer for Rural Areas (ATTRA), Fayetteville, AR, 1998.

Abstract: In this work, the deterministic model which describes the dynam- ics of interaction between two legumes has been defined. The motivation and benefits of stabilizing this system of complex model equations of continuous nonlinear first order ordinary differential equations in the field of agriculture has been clearly well posed. We will expect this pioneering research to form a bench mark collaboration between modellers and crop science experts.

Keywords: and phrases. Steady-State Solutions, Stability, Legumes.

[1] E.N. Ekaka-a, Computational and Mathematical Modelling of Plant Species Interactions in a Harsh Climate, PhD Thesis, Department of Mathematics, The University of Liverpool and The University of Chester, United Kingdom, 2009.

[2] N.J. Ford, P.M. Lumb, E. Ekaka-a, Mathematical modelling of plant species interactions in a harsh climate, Journal of Computational and Applied Mathematics 234, (2010), 2732-2744.

[3] N.J. Ford, S.J. Norton, Noise-induced changes to the behaviour of semi-implicit Euler methods for stochastic delay differential equations undergoing bifurcation, Journal of Computational and Applied Mathematics 229, (2009), 462-470.

[4] T.A. Troost, B.W. Kooi, S.A.L. M. Kooijman, Bifurcation analysis of ecological and evolu- tionary processes in ecosystems, Ecological Modelling 204, (2007), 253-268.

[5] Yubin Yan, Enu-Obari N. Ekaka-a, Stabilizing a mathematical model of population system, Journal of the Franklin Institute 348, (2011), 2744.-2758.

Abstract: In this paper, we introduce the concept of pairwise 0-completely regular filters on a pairwise completely regular ordered bitopological space; we define the category of bitopological ordered K-spaces, which is isomorphic to that found among both bitopological and ordered spaces.
Key words: & Phrases: A bitopological ordered space; a bitopological partially ordered space; a pairwise completely regular ordered space; a pairwise 0-completely regular filter; pairwise continuous isotone; a pairwise compact ordered space; pairwise Gk-set; pairwise k-compact; pairwise k-Lindelöf; bitopological Pspaces

[1]. Choe, T. H. and Hong, Y. H., Extensions of completely regular ordered spaces, Pacific J. of Mathematics, 66 (1) (1976), 37-48.
[2]. Kelley, J. C., Bitopological spaces, Proc. Landon Math. Soc. 13 (1963), 71-89.
[3]. Kim, Y. W., Pairwise compactness, Publicatione Mathematicae, 15 (1968), 87-90.
[4]. Kopperman, R. Asymmetry and Duality in topology, Topology and its Applications, 66 (1995)1-39.
[5]. Kopperman, R. and Lawson, J. D., Bitopological and topological ordered K- spaces, Topology and its Applications, 146-147 (2005)
385-396.

Abstract: In this paper a complete orthonormal family of Laguerre-Bessel functions is derived and certain spaces of testing functions and generalized functions are defined, whose members can be expressed in terms of a Fourier-Laguerre-Bessel series, which gives the inversion formula for Laguerre-Finite Hankel transform of generalized functions. The convergence of the series is interpreted in the weak distributional sense. An operational transform formula is derived which together with the inversion formula is applied in solving certain distributional differential equations. AMS Subject Classification: 44F12,44A15,46F10,41A58.

Key Words: Laguerre-Finite Hankel transform, Fourier-Laguerre-Bessel series,orthonormal series expansion of generalized functions

[1] A. H. Zemanian, Orthonormal series expansions of certain distributions and distributional transform calculus, J. Math. Anal. Appl. 14 (1966), 263–275.
[2] S. D. Bhosale and S. V. More, On Marchi-Zgrablich transformation of generalized functions, IMA J. Appl. Maths. 33 (1984), 33–42.
[3] S. K. Panchal and S. V. More, On modified Marchi-Zgrablich transformation of generalized functions, J. Indian Acad. Math 17(1) (1995), 13–26.
[4] S. K. Panchal, Laguerre-Finite Hankel Transform of Generalized Functions,Proceedings of the International Conference on Mathematical Sciences in honour of Professor A.M. Mathai, St. Thomas College Pala, Kottayam, Kerala, India.(Jan 3-5, 2011).
[5] A. H. Zemanian Generalized Integral Transformations, Interscience Publisher, New York, 1968

Abstract: The effect of Darcy dissipation on melting from a vertical plate with variable temperature embedded in porous medium is numerically studied. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equation which is solved numerically by Runge-Kutta-Gill methods. Dimensionless velocity, Temperature and concentration profiles are presented graphically for various values of physical parameter. During the course of integration, it is found that Increasing the values of melting result into the decrease in local nusselt number.

Keyword: Liquid phase;Mixed convection; Melting effect; and porous medium

[1]. Nield D A, Bejan A (2006) Convection in Porous Media, Springer-Verlag, New York.
[2]. Roberts L (1958). On the melting of a semi-infinite body of ice placed in a hot stream of air, J. Fluid Mech. 4: 505–528.
[3]. Tien C, Yen Y C (1965) The effect of melting on forced convection heat transfer, J. Appl. Meteorol. 523–527.
[4]. Epstein M, Cho DH (1976) Laminar film condensation on a vertical melting surface, ASMEJ. Heat Transfer 98: 108–113.
[5]. Sparrow E M, Patankar S V, Ramadhyani S (1977) Analysis of melting in the presence of natural convection in the melt region,
ASME J. Heat Transfer 99: 520–526.
[6]. Bakier AY. (1997) Aiding and opposing mixed convection flow in melting from a vertical flat plate embedded in a porous medium,
Transport in Porous Media. 29:127–139.

Abstract: In this paper, we will study the chaotic behaviour of the family of quadratic mappings fc (x) = x2 – x + c through its dynamics. In first few sections, we will take a review of some basic definitions and examples including a dynamical system, orbit, fixed and periodic, etc. Later, we will prove some results that analyse the nature and the stability of the fixed and periodic points of a dynamical system. Using these results, we will study the dynamics of the family of mappings fc (x) = x2 – x + c for various values of the real constant c.

Keywords: bifurcation, chaos, dynamical system, fixed points, orbits, periodic points, stability

[1]. Kathleen T Alligood, Tim D Sauer, James A Yorke, Chaos an Introduction to Dynamical Systems (Springer-Verlag New York, Inc.)
[2]. Devaney, Robert L, A First Course in Chaotic Dynamical System (Cambridge, M A : Persuse Books Publishing, 1988).
[3]. Edward R Scheinerman. Invitation to Dynamical Systems.
[4]. Cook P A (Nonlinear Dynamical Systems (Prentice-Hall International (UK) Ltd.1986.)
[5]. Denny Gulick, Encounters with Chaos( Mc-Graw Hill, Inc. 1992).
[6]. James Yorke and T-Y Li., Period three implies chaos. Amer. Math. Monthly, 82:985-992, 1975.