iosr-Jm   Volume-13 ~ Issue-3 ~ May-June 2017

Abstract: Exact extreme value distribution is one of the most important compound distributions which is based on the theory of the maximum of random variable of random numbers. This distribution uses partial duration series (PDS) data to analyze extreme hydrological. This distribution is presented with its properties and graphical representations. Moments (MOM), maximum likelihood (ML) and Bayesian - based on non-informative and informative prior- methods are used to estimate the unknown parameters of the distribution. Markov Chain Monte Carlo (MCMC) technique is used to compute the Bayesian estimates.........

Keywords: Exact extreme value distribution, maximum likelihood, Bayesian estimation, MCMC

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1970, p. 1059-1063.
[2] Todorovic, P. and Zelenhasic, E., A stochastic model for flood analysis, Water Resources Research, 6(6) 1970, p. 1641-1648.
[3] Kotb, N.S.A., El-Gohary, M.M. and El-Helbawy, A.T. , Analysis of Flood Frequency Distribution, Journal of Faculty of
Commerce Al-Azhar University Girls Branch, 19,2001, p. 5-25.
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[5] Bhunya, P.K., Singh, R.D., Berndtsson, R. and Panda, S.N.,Flood analysis using generalized logistic models in partial duration
series,. Journal of hydrology, 420,2012, p. 59-71.

Abstract: Unsteady natural convection laminar flows in a square cavity formed by insulated bottom and top walls, uniformly heated left wall and cooled right wall has been investigated. The governing equations are transformed into a non-dimensional form and the resulting partial differential equations are solved numerically applying upwind finite difference method together with Successive Over-Relaxation (SOR) scheme. The effect of the heat generation and the Rayleigh number on streamlines and isotherms as well as on the local rate of heat transfer in terms of the local Nusselt number and the average Nusselt number from the heated wall of the cavity are presented.

Keywords: Natural convection, Unsteady laminar flow, Heat generation, Square cavity

[1] S. Ostrach, Natural convection in enclosures. ASME J. Heat Transfer 110 (1988) 1175-1190.
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Abstract: The present study deals with an Unsteady MHD free convective Heat and Mass transfer flow over an inclined plate embedded in porous medium, which moves with time dependent velocity in a viscous, electrically conducting incompressible fluid, under the influence of uniform magnetic field, applied normal to the plate. The presence of thermal radiation, heat source and Soret effect are considered. The dimensionless governing equations i.e. momentum equation which is coupled with the energy and mass diffusion equations are analytically solved in closed form by Laplace transform technique. The expressions for velocity, temperature, concentration, skin friction, rate of heat and mass transfer are studied graphically for different physical parameters.

Keywords: MHD, Free convection, Heat and Mass transfer, Radiation, Thermal diffusion, Heat source, inclined porous plate and Laplace transform technique

[1]. Soundalgekar .1979, free convection effects on the flow past a vertical oscillating plate. Astrophysics and Space Science 64, 165- 172.
[2]. Revankar.2000, Free convection effect on the flow past an impulsively started or oscillating infinite vertical plate., Mechanics Research Comm.27, 241-246.
[3]. Soundalgekar et al.1995, Mass Transfer effects on flow past a vertical oscillating plate with variable temperature. , Heat and Mass transfer 30(5), 309-312.
[4]. Das et al.1996, Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux – an exact solution. , Heat and mass transfer 31, 163-167.
[5]. Muthukumaraswamy 2003, Effects of chemical reaction on moving isothermal plate with variable mass diffusion. Theory Appl. Mech. 30(3), 209-220.

Abstract: The present paper addresses diffusion-reaction equation describing the dynamics of both dissolved oxygen and biochemical oxygen demand in case of river pollution. Numerical solutions are obtained and some important inferences are drawn through simulation study. The diffusion – reaction equation is characterized by the reaction term whenever it depends on concentration of the contaminants and in this case the original single diffusion – reaction equation will evolve to be a system of equations. This system of equations develops problem in finding analytical solution. In order to tackle this kind of problem one needs to consider numerical approximation. Hence, we employed numerical methods here in. For that purpose we first separated diffusion term from non-linear reaction term using splitting method...........

Keywords: River pollution, Dissolved oxygen, Biological oxygen demand, Diffusion-Reaction equation, Splitting method, Finite element method, Improved Runge-Kutta method of order six transform technique

[1]. Brain J. McCartin, Sydney B. and Forrester Jr. (2002), A Fractional Step-Exponentially Fitted Hopscotch Scheme for the Streeter-Phelps Equations of River Self-Purification, Engineering Computations, Vol. 19, Pp. 177-189.
[2]. Butcher J. C. (2009), On Fifth and Sixth Order Explicit Runge-Kutta Methods: Order Conditions and Order Barriers, Canadian Applied Mathematics Quarterly, Vol. 17, No. 3, Pp.1-14.
[3]. Chertock A., Kurganov A. and Petrova G. (2006), Fast explicit operator splitting method for convection–diffusion equations, International Journal for Numerical Methods in Fluids, doi: 10.1002/fld.1355, http://www.interscience.wiley.com.
[4]. Geiser J. (2016), Multicomponent and Multiscale Systems Theory, Methods and Applications in Engineering, Springer International Publishing Switzerland, doi 10.1007/978-3-319-15117-5_2, http://www.springer.com/978-3-319-15116-8.
[5]. Hasadsri S. and Maleewong M. (2012), Finite Element Method for Dissolved Oxygen and Biochemical Oxygen Demand in an Open Channel, Procedia Environmental Sciences, Vol. 13, Pp. 1019 – 1029, doi:10.1016/j.proenv.2012.01.095.

Abstract: The article proves another two new symmetric properties of odd numbers. The new properties are helpful to know odd numbers in a deep level, especially in knowing the distribution of an odd number's multiples and divisors.

Keywords: Odd numbers, symmetric property, multiple numbers, divisors

[1] WANG Xingbo, Valuated Binary Tree: A New Approach in Study of Integers, International Journal of Scientific and Innovative Mathematical Research (IJSIMR), 4(3), 2016, 63-67

[2] Xingbo WANG, Amusing Properties of Odd Numbers Derived From Valuated Binary Tree, IOSR Journal of Mathematics, 12( 6,Ver.V),2016,53-57

[3] Xingbo WANG, Genetic Traits of Odd Numbers With Applications in Factorization of Integers, Global Journal of Pure and Applied Mathematics,13(1),2017,318-333

Abstract: The aim of this study is to compare between chi-square test and Mantel-Haenszel test and to assess the potential risk factors for prostate cancer incidence in order to set priorities for public heath interventions and to reduce the incidence of the disease. This study included patients with prostate cancer who were being treated at the National Center for Radiotherapy and Nuclear Medicine in Khartoum State, Sudan. 250 patients were chosen by interviews and from their medical history. The potential risk factors that significantly related to the incidence of prostate cancer were identified by using chi square test, Fisher exact test and Mantel-Haenszel test. These variables relative to their odds ratios were: prostate specific antigen...........

Keywords: Incidence, PSA, Risk factor, Odds Ratio, Fisher, Mantel-Haenszel

[1] https://www.healthknowledge.org.uk/public-health-textbook/disease-causation-diagnostic/2b-epidemiology-diseases-phs/cancers/prostate-cancer. http://globocan.iarc.fr/old/Factsheets/cancers/prostate-new.asp.
[2] Report of the Sudanese Federal Ministry of Health for 2016
https://pcafrica.wordpress.com/site-map/sudan/data/ http://training.seer.cancer.gov/prostate/intro/ [National cancer institute & SEER Training Modules]
[3] John Ludbrook, Is there still a place for Pearson's chi-square test and Fisher exact test in surgical research, ANZ journal of surgery, 81(12), 2011; 923-926.
[4] Wayne W. Daniel, Biostatistics (United States Of America, Wiely, 2009), 9th edition.
[5] Saumya Panda, Module on Biostatistics and research methodology for the Dermatologist, IJD, 61(1), 2016; 385-392.

Abstract: Fuzzy sets and soft sets are two different tools for representing uncertainty and vagueness. We introduce the notions of fuzzy soft digraphs, fuzzy soft walk, fuzzy soft trail in digraph and some operations in fuzzy soft in fuzzy soft digraph

Keywords: fuzzy soft graph, fuzzy soft digraph, walk in fuzzy soft digraph, trail in fuzzy soft digraph, union and intersection in fuzzy soft digraph.

[1] D.A. Molodtsov , Soft set theory -f irst results , Computers and Mathematics with Applications 37 19 – 31.
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[5] M. Akram, S. Nawaz, On fuzzy soft graphs , Italian Journal of Pure and Applied Mathematics 34 (2015) 497 – 514.

Abstract: Fuzzy Matrix (FM) is a very important topic of Fuzzy algebra. In FM, the elements belong to the unit interval [0, 1]. When the elements of FM are the subintervals of the unit interval [0,1], then the FM is known as Interval-Valued Fuzzy Matrix [ IVFM ] . In IVFM, the membership values of rows and columns are crisp ie. Rows and columns are certain. But, in many real life situations they are also uncertain. So to model these type of uncertain problems, a new type of Interval-Valued Fuzzy Matrices (IVFMs) are called Interval-Valued Fuzzy Matrices with Interval-Valued Fuzzy Rows and Columns (IVFMFRCs). In this paper, some new elementary operators on α-cuts of IVFMFRCs are defined. Using these operators, some important theorems are proved.

Keywords:α-cut, α-cuts of interval valued fuzzy matrix, Fuzzy matrix, Fuzzy rows and columns, Interval valued fuzzy matrix.

[1] A.Kalaichelvi, K.Janofer, α-cuts of Triangular fuzzy Numbers and α-cuts of Triangular Fuzzy Matrices, Int. Journal of Mathematics Sciences and Applications, Vol 2, No 2, May 2012 635-643.
[2] Madhumangal Pal, Interval-Valued Fuzzy Matrices with Fuzzy Rows and Columns, Fuzzy Information and Engineering (2015): 335-368.f
[3] M.Pal, Fuzzy Matrices with Fuzzy Rows and Columns, Journal of intelligent and Fuzzy Systems to appear.
[4] A.Pal, M.Pal, Some results on Interval-Valued Fuzzy Matrices, The 2010 International conference on E-Business Intelligence Org by Tsinghua University, Kunming, China, Atlantis Press(2010) 554-559,doi;2991/icebi. 2010.39.
[5] A.K.Shyamal, M.Pal, Interval-Valued Fuzzy Matrices, The journal of Fuzzy Mathematics 14(2006) 583-604.2.

Abstract: In This Paper We Introduce Octagonal Intuitionistic Fuzzy Numbers With Its Membership And Non-Membership Functions. A New Method Is Proposed For Finding An Optimal Solution For Intuitionistic Fuzzy Transportation Problem, In Which The Supplies And Demands Are Octagonal Intuitionistic Fuzzy Numbers. The Procedure Is Illustrated With A Numerical Example

Keywords: Intuitionistic Fuzzy Transportation Problems, Initial Basic Feasible Solution, Modi Method, Ranking Method, Octagonal Intuitionistic Fuzzy Numbers, Optimal Solution

[1] Fuzzy sets and K.Atanassov.1989. More on Intuitionistic Fuzzy sets, Fuzzy sets and systems, 33, pp.37-46.
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[3] A.Thamaraiselvi and R. Santhi,"On Intuitionistic Fuzzy Transportation Problem Using Hexagonal Intuitionistic Fuzzy Numbers", International Journal of Fuzzy Logic systems (IJFLS) Vol.5, No.1, January 2015.
[4] Thangaraj Beaula – M. Priyadharshini, " A New Algorithm for Finding a Fuzzy Optimal Solution for Intuitionistic Fuzzy Transportation Problems, International Journalof Applications of Fuzzy Sets and Artificial Intelligence ( ISSN 2241-1240), Vol.5(2015),183- 192.
[5] Dr.S.Ismail Mohideen, K.Prasanna Devi, M. Devi Durga, "Fuzzy Transportation Problem of Octagon Fuzzy Numbers with -Cut and Ranking Technique", Dr.Ismail Mohideen et al, Journal of Computer – JoC, Vol.1 Issue.2, July-2016, pg-60-67..