iosr-Jm   Volume-12 ~ Issue-4 ~ Jul-Aug 2016

Abstract: The aim of this research paper is to establish some bilateral generating relations involving I-function of two variables.

[1]. Rainville, E. D.: Special Functions, Macmillan, NewYork, 1960.
[2]. Sharma C. K. and Mishra, P. L.: On the I-function of two variables and its certain properties, ACI, 17 (1991), 1-4.
[3]. Shrivastava, H. M. and Manocha, H. L.: A treatise on generating functions, Ellis Horwood Limited England.

Abstract: In existing literature the inventory models are developed under supply chain model of a volume agile manufacturing process for the deteriorating items. In this study, a model for the producer by assuming production to be stock dependent and exponentially increasing and demand rate to be linear and quadratic simultaneously with constant deterioration rate and holding cost is developed. Shortages are not allowed. This whole study is studied in the inflationary environment. The mathematical expression for the total cost is derived and it is minimized. A numerical example has been illustrated using MATLAB to describe the model.

Keywords: Constant deterioration; production exponentially increasing, linear and quadratic Simultaneous demand rate; Inflation; Inventory; holding cost

[1]. Chang, J.H. and Lin, F.W. 2010 "A partial backlogging inventory model for non-instantaneous deteriorating items with stock
dependent consumption rate under inflation" Yugoslav Journal of Operation Research, 20(1), 35-54.
[2]. Datta, T.K. and Pal, A.K. 1991. Effects of inflation and time value of money on an inventory model with linear time dependent
demand rate and shortages. European Journal of Operation Research, 52(3), 326-333.
[3]. Padmanabhan, G. and Vrat, P. 1990. An EOQ model for items with stock dependent consumption rate and exponential decay.
Engineering Costs and Production Economics, 18(3), 241-246.
[4]. Hong, J.D., Sandrapaty, R.R. and Hayya, J.C. 1990 "A production policy for linearly increasing demand and finite uniform
production rate Computers Industrial Engg., 18(2), 119-127.
[5]. Khouja, M. and Mehrez, A. 1994. "An economic production lot size model with variable production rate and imperfect quality"
Journal of operational Research Society, 45(12), 1405-1417.

Abstract: Swine flu (H1N1) is prevalence due to increased infection rate around the world, as specially in India. A large number of humans die or have serious effects on the different states of India. In this paper we present an initial model with disease in different size population for the evolution of the infected people with Swine flu (H1N1).We explore the dynamics of the Swine flu disease at the population level using an epidemiological model. Data of Statistic are used to estimate some of the parameters of the model and we will see spread of the disease in different scenarios.

Keywords: Swine flu Disease, Epidemiological model, H1N1, Pandemic, Mathematical model

[1]. Safety Precautions to Deal with H1N1 Swine Flu: Symptoms of Swine Flu (http://www.thefitindian.com/h1n1-virus-swine-flu/) [Accessed: Feb.27, 2015].
[2]. Swine Flu and You" (http://www.cdc.gov/swineflu/swineflu_you.htm) CDC. 2009-04- 26. [Accessed: Feb. 27, 2015].
[3]. Pandemic Influenza A H1N1: Directorate General of Health Services Ministry of Health and Family Welfare Government of India, (http://karhfw.gov.in/H1N1/5.%20Clinical%20Management%20Protocol Pan-
demic%20influenza%20A%20H1N1.pdf) [Accessed Feb. 26, 2015].
[4]. M. Martcheva, C. Castillo Chavez, Diseases with chronic stage in population with varying size, Math. Biosci. 182 (2003) 1–25.
[5]. J. Mena-Lorca, H.W. Hethcote, Dynamic model of infectious diseases as regulators of population size, J. Math Biol. 30 (1992) 693–716.

Abstract: In this paper, an attempt has been made to discuss frailty models and their further developments under the Bayesian approach. The modeling of baseline hazard function with parametric and semiparametric approach, distribution of frailty variable along with derivation of posterior distribution with the help of the data likelihood and the prior distribution of the parameters of the frailty distribution with examples are also discussed here. Based on this review work it is observed that the Bayesian analysis of frailty models in survival analysis attains vast attention by the researchers..............

Keywords: Survival modeling, unobserved random effect, shared and correlated frailty models, Markov Chain Monte Carlo methods, Baseline Hazard function

[1] Aalen, O.O. Heterogeneity in survival analysis, Statistics in Medicin 7.1988. 1121-1137
[2] Aalen, O.O. Modelling Heterogeneity in Survival Analysis by the Compound Poisson Distribution, Annals of Applied Probability 4(2), 1992. 951-972.
[3] Aalen , O.O., Tretli, S. Analysing incidence testis cancer by means of a frailty model,Cancer Causes and Controll, 1999. 285-292.
[4] Andersen, P.K., Klein, J.P., Zhang, M. J. Testing for centre effects in multi-centre survival studies: A Monte Carlo Comparison of Fixed and Random Effect, Tests Statistics in Medicine 18, 1999.1489-1500 [5] Arjas, E. and Gasbarra, D., Nonparametric Bayesian inference from right censored survival data, using the Gibbs sampler. Statistica Sinica, 1994.505-524.

Abstract: It is worth repeating that if data are approximately normally distributed then parametric tests (as in the modules on hypothesis testing) are more appropriate. However, there are situations in which assumptions for a parametric test are violated and a nonparametric test is more appropriate. This study was aimed to investigates the strength and Limitation of independent t-test, Mann Whitney U test and Kolmogorov Smirnov test procedures on independent samples from unrelated population, under situations where the basic assumptions of parametric are not met for different sample size.........

Keywords: Independent Sample, Independent t-test, Mann Whitney U test, Kolmogorov Smirnov test,Type I error and Power of the test

[1]. J. D. Gibbons and S. Chakraborti, Nonparametric Statistical Inference, 4th edition. CRC Press. ISBN 0-8247-4052-1. 2003
[2]. G. W. Corder and D. I. Foreman, Nonparametric Statistics: A Step-by-Step Approach. John Wiley & Sons New York:. ISBN 978-1118840313. 2014
[3]. T. P. Hettmansperger and J. W. McKean, Robust Nonparametric Statistical Methods. Kendall's Library of Statistics 5 (First edition). London: Edward Arnold. New York: John Wiley & Sons. ISBN 0-340-54937-8.MR 1604954. 1998
[4]. G. M. Clarke and D. Cooke, A Basic Course in Statistics 4th Edition Nicki Dennis London NW1 3BH. 1998
[5]. P. Sprent, Applied Non-parametric Statistical Methods. 2nd Edition. Chapman and Hall 1993

Abstract: The unsteady (MHD) thin film flow of an incompressible Oldroyd –B fluid over an oscillating inclined belt making a certain angle with the horizontal through a porous mediumis analyzed .The analytical solution of velocity field is obtained by a semi-numerical technique optimal homotopy asymptotic method (OHAM) .Finally the influence of various dimensionless parameters emerging in the model on velocity field is analyzed by graphical illustrations

[1]. Anakira , NP. , Alomari AK. and Hashim . ; "Optimal homotopy asymptotic method for Solving Delay Differential Equations, , " Hindawi Pub Corp Math Problems in Eng. 1 (2013) 1-13 .
[2]. Burdujan , L. ; " The flow of a particular class of Oldroyd-B fluids" , J. Series on Math and its Applications. 3 (2011) 23-45.
[3]. Fetecau , C. , Hayat T. and Fetecau C. ; " Starting solutions for oscillating motions of Oldroyd-B fluids in cylindrical domains" , Journal of Non-Newtonian fluid Mechanics. 153 (2008) 191-201.
[4]. Fetecau , C. , Sharat C. , Prasad SC. and Rajagapal , KRA. ; " A note on the flow iducad by a constantly accelerating plate in an Oldroyd-B fluid " , Applied Mathematical Modeling . 31 (2007) 647-654.
[5]. Haitao , Q. and Mingyu , X. ; " Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative " , Applied math .Modeling . 33 (2009) 4184-4191.

Abstract: This paper deals with the construction of minimum spanning tree of city – to – city network in Nigeria. Nodes in our network are the 36 state capitals in Nigeria and the FCT, and the arcs are the proposed major roads that link the state capitals. The distances between states are computed using the Lad/Long converter software which makes use of the latitude and longitude of each state capital. We employed Prim's algorithm to determine the minimum spanning tree with Yenagoa as the starting point. The result gives a total distance of 5, 128.5 km.

Keywords: Spanning tree, Network, Prim's algorithm, Latitude and Longitude

[1]. Agarwal,D.(2010). Kruskal Algorithm .Technicalcollection. http://sites.google.com/ site /mytechnicalcollection/ algoritms/graphs/minimum - spanning- tree/kruskal's algorithm.
[2]. Ahuja, R. K., Magnantic, L. T., Orlin, J. B. and Reddy, R. M. (1992). Applications for NetworkOptimization. http://dspace.mit.edu/bitstream/handle/1721.1/5097/OR-3?Sequence=1.
[3]. Brimberg, J. N., Mladenovic, H., Pierre, L. K., and Breton, M. (2003). An oil pipeline design problem. Operations Research, Vol. 51, No. 2, Pp228 – 239. http://www.jstor.org/stable/4132402?Origin=JSTORpdf
[4]. Dippon, M. C. and Kenneth, E. T. (1999). The cost of local Telecommunication Network. A comparison of Minimum Spanning Tree and the HAI model. National Economic Research Associates, Enthropy Estimation Workshop.
[5]. Donkor, E. K., Amponsah, S. K. and Darkwa, F. K. (2010). Optimal connection for theWest African Gas Pipeline Project. http://Maxellsci.com/print/rjaset/v3-67-73pdf.

Abstract: In this paper we introduce and study the new class of sets, namely Regular Mildly Generalized Open (briefly, RMG-open) sets, Regular Mildly Generalized neighborhoods (briefly, RMG-nhd), RMG-interior and RMG-closure in topological space and also some properties of new concept has been studied

Keywords: RMG-closed sets, RMG-open sets, RMG-neighborhoods, RMG-interior, RMG-closure.

[1] D. Andrijevic, Semi-preopen sets, Mat. Vesnik, 38(1986), 24-32.
[2] S. S. Benchalli and R.S. Wali, On RW-closed sets in topological spaces, Bull.Malaysian.Math. Sci. Soc. (2) 30(2) (2007), 99-110.
[3] J. Dontchev and T. Noiri, Quasi-normal spaces and π-g-closed sets,Acta Math. Hungar.,89(3)(2000), 211-219.
[4] T.Kong, R. Kopperman and P. Meyer, A topological approach to digital topology,Amer. Math. Monthly, 98 (1991), 901-917.
[5] A.S. Mashhour, M.E. Abd. El-Monsef and S.N. El-Deeb, On pre continuous mappings and weak pre-continuous mappings, Proc Math, Phys. Soc. Egypt, 53(1982), 47-53.

Abstract: In this current article generalized common fixed point theorem in intuitionistic fuzzy metric space using occasionally converse commuting maps .we prove two common fixed point results for assure an embedded family member.

Keywords: Intuitionistic fuzzy metric space; occasionally converse commuting (occ); occasionally weakly compatible.

[1] C.Alaca, D.Turkoflu, and C.Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitions and Fractals, 29 (2006), 1073-1078.

[2] K.Atanassov, Intuitionistic fuzzy sets, fuzzy sets and Systems 20 (1986), 87-96.

[3] D.Coker, An introduction to Intuitionistic Fuzzy topological Spaces, Fuzzy sets and System, 88 (1997), 81-89.

[4] A.George and p.Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399.

[5] G.Jungck, Common Fixed Points for Non-continuous non-self Mappings on a non-numeric Spaces, Far East J.Math. Sci. 4(2) 1996, 199-215.

Abstract: In this paper, we study a fuzzy implicative ideal of a BH-algebra. We give some properties of this fuzzy ideal and link it with other types of fuzzy ideals and fuzzy subset of a BH-algebra.

Keywords: fuzzy completely closed ideal, fuzzy ideal, fuzzy implicative ideal, fuzzy set, fuzzy sub-implicative ideal, fuzzy p- ideal, implicative BH-algebra, implicative BH-algebra.

[1] D. Dubois and H. Prade, "Fuzzy Sets and Systems", Academic Press. INC. (London) LTD, fifth Avenue, New Yurk, 1980.
[2] E. M.kim and S.S. Ahn," On Fuzzy n-fold Strong Ideals of BH-algebras", J. Appl. Math. & Informatics. 30,(No.3) – 4,pp. 665 - 676,2012
[3] H. H. Abbass and H. A. Dahham,"Some Types of Fuzzy Ideals with Respect to an Element of a BG-algebra", M.S.c thesis, Kufa University, 2012.
[4] H. H. Abbass and H. M. A. Saeed, "The Fuzzy Closed BCH-algebra with Respect to an Element of a BH-algebra", M.S.c thesis, Kufa University, 2011.
[5] H. H. Abbass and S. A. Neamah, " On Fuzzy Implicative Ideal with Respect to an Element of a BH-algebra ", M.S.c thesis, Kufa University, 2014.

Abstract: Analytical and computational studies on transient peristaltic heat flow through a finite length porous channel are presented in this paper. the expression for temperature field, axial velocity , volume flow rate, pressure difference, local wall shear stress, stream function are obtained under the assumption of long wavelength and low Reynolds number. Effects of different physical parameters ,reflecting couple-stress parameter, permeability parameter, Hartman number, constant heat radiation factor and Grashof number, as well as amplitude ration on pumping characteristics and frictional force, stream lines pattern and trapping of peristaltic flow pattern studied with particular emphasis........

Keywords: Transient peristaltic flow ,Heat transfer, Pressure gradient , Local wall shear stress , Couple stress , Magnetic field , Porous Medium

[1]. A.H. Shapiro, M.Y. Jaffrin, S.L. Weinberg, (1969).Peristaltic pumping with long
wavelengths at low Reynolds number, Journal of Fluid Mechanics 37 ,799-825.
[2]. A.R. Rao, M. Mishra, Peristaltic transport of a power-law fluid in a porous tube, (2004). Journal of Non-Newtonian Fluid
Mechanics121,163-174.
[3]. B. Jeffrey, H.S. Udaykumar, K.S. Schulze,(2003).Flow fields generated by peristaltic reflex in isolated guinea pig ileum: impact of
contraction depth and shoulders ,American Journal of Physiology-Gastrointestinal and Liver Physiology 285 , G907 – G918 .
[4]. D. Tripathi,O. A. Beg ,(2012). A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length
channel by peristaltic pumping Proceedings of the Institution of Mechanical Engineers ,Part H: Journal of Engineering in Medicine
226, 631-644.
[5]. D. Tripathi ,(2012). A mathematical model for swallowing of food bolus through the oesophagus under the influence of heat
transfer, International Journal of Thermal Science 51, 91 – 101

Abstract: In this paper we add a physical meaning to the Riesz potential by using Newtonian force fields due to a body and velocity fields of any fluid. To do this, we firstly give some properties of Newtonian force fields and correspondingly Newtonian potentials. Then, we introduce the Riesz potentials which is arised from fractional order a / 2 Poisson differential equations like Newton potentials and by using these notions we give a physical interpretation of Riesz potential. Finally, we cite the flow velocity of a fluid and add a physical meaning to Riesz potential by using velocity potential of a fluid that is irrotational in some simply connected region in the same way

Keywords: Vector Fields-Flows, Potentials, Laplace's Equations

[1] Oliver Dimon Kellogg, Foundations of Potential Theory ( Berlin: Verlag Von Julius Springer, 1929)
[2] Lester L. Helms, Introduction To Potential Theory (New York: Wiley-Interscience, 1969)
[3] Richard J. Blakely, Potential Theory in Gravity and Magnetic Applications ( Cambridge University Press, 1996)
[4] İnan Çınar, On Some Properties of Generalized Riesz Potentials, Intern. Math. Journal, Vol. 3,2003, no. 12, 1393-1397
[5] C. Martinez, M. Sanz, F. Periogo, Distributional Fractional Powers of Laplacian, Riesz Potential. Studia Mathematica 135 (3) 1999

Abstract: In many applications of Risk Management nature, Credit Migration Matrices or Transitional matrices are the main Cardinal inputs and the accuracy of their estimation is very critical. Three approaches namely Cohort, time homogeneous, non homogeneous are explored in this paper and the differences resulting statistically highlighted. Using techniques of bootstraps, a testing procedure is developed for assessing statistically the migration matrices differences. We find that using the Frequentist (Cohort) approach can yield huge discrepancies than the two duration methods namely Homogeneous and Non-Homogeneous duration methods...............

Keywords: Risk management, Credit Migration, Credit Risk, Transitional Matrices, Bootstrap

[1] Aalen O.O and S Johansen 1978 "An Empirical Transition matrix for non-homogeneous
[2] Markov chains based on Censored observations". Scandinavian journal of Statistics.
[3] Altman E.I and D.L kao 1992, "Rating Drift of High Yield Bonds"3. Arvinitis, A,J Gregory and J-P Laurent 1999, "Building Models for Credit Spreads. journal of Banking and finance.
[4] B. Belkin, S. Suchower and L.Forest Jr. (1998), "A one parameter presentation of Credit Risk and Transitional Matrices"
[5] Bahar R. Nagpal. K, 2000, "Rating Transitions: Modelling the dynamics"'

Abstract: In this paper we will convert weighted bipartite graph to intersection graph. Also we introduce the variation of the algorithm of bipartite graph and intersection graph

Keywords: Graph, Contingency table, bipartite graph, intersection graph, clique, algorithms.

[1]. Cook ,D.J.,Holder,L.,B.,2006.Mining graph data. New York :john.
[2]. Intersection graph –based representation of contingency tables,Valter Martins Vairinhos.
[3]. Anderson,T.W.(1984).An introduction to multivariate statistical Analysis,John Wiley.
[4]. Intersectiongraph :an introduction ,Madhumangal Pal 2013.
[5]. SatuElisa,:graph clustering, Computer Science Review, (2007),27-64.

Abstract: In the present paper the closed form analytical expressions for the displacement and stresses at any point of an infinite irregular orthotropic elastic medium as a result of normal line-load have been obtained by using eigen-value approach. The irregularity of rectangular and parabolic shape has been considered. To examine the effect of different type of irregularities the variation of displacement and stresses with horizontal distance have been shown graphically by taking different sizes of irregularities. Also to study the effect of irregularities present in the medium the comparison between the displacement due to with and without irregularities have been made. Contour maps showing the displacement field for each type of irregularities are presented.

Keywords: Orthotropic medium, Normal line-load, Irregularity, Rectangular, Parabolic, Eigen value

[1]. J. D. Noyer, The effect of variations in layer thickness of love waves, Bull. Seism. Soc. Am.51, 1961 227-235.
[2]. A.K Mal, On the frequency equation for love waves due to abrupt thickening of crustal layer, Geofis .Pure Appl.52, 59, 1962, 59-68.
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[5]. D P Acharya and Indrajit Roy, Effect of surface stress and irregularity of the interface on the propagation of SH-waves in the magneto- elastic crustal layer based on a solid semi space;, Sadhana 34 (2), 2009, 309-330.

Abstract: In this article, we devoted to study about the n-dimensional Finsler 𝐹𝑛=(𝑀𝑛,𝐿) with an (𝛼,𝛽)-metric 𝐿 𝛼,𝛽 to be projectively flat, where 𝛼 is Riemannian metric and 𝛽 is differential 1-form under some geometric conditions on the basis of Matsumoto results.

Keywords: Finsler space, (𝛼,𝛽)-metrics, Projective flatness

[1]. M. Matsumoto, Projective flat Finsler space with (𝛼,𝛽)- metric, Rep. On Math. Phys., 30 (1991), 15- 20.
[2]. M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaishima Press., Saikawa, Otsu, 520, Japan, (1986).
[3]. L. Berwald, Ueber Finsersche und Cartanscher geometric, IV, Projectiv Krummung allegemeiner affine raume und Finslerscher Raume skalarer krummung, Ann. Of Math., 48, No. 03,(1947), 755-781.
[4]. M. Matsumoto, Projective changes of Finsler metric and projectively flat Finsler spaces, Tensors, N. S., 34(1980), 303-315.
[5]. Gauree Shankar and Ravindra Yadav, On some projectively flat (𝛼,𝛽)- metrics, Gulf Journal of Mathematics, 1 (2013), 72-77.

Abstract: This paper considered statistical calibration models. It focused on Eiesinhart s calibration model for two tests X & Y where X is an exact but expensive and slow test and Y is less expensive but quick and cheap test. The objective was to investigate through a simulation experiment the effect of the degree of linear dependency between X & Y as well as sample size on confidence interval estimation of the forecasted value of X .It is shown that changes on these factors have no significant effect on the degree of confidence Keywords: Absolute calibration, comparative calibration, Jaundice, Inverse Predictions, Linear model, classical estimator

[1]. Christine Osborne . (1991). Statistical Calibration: A Review. School of Mathematical Sciences, University of Bath, Bath BA2 7A
Y, England
[2]. Aitchison, J. & Dunsmore, I.R. (1975). Statistical Prediction Analysis. Cambridge University Press. Ali, M.A. & Singh, N. (1981).
[3]. John Neter &William Wasserman & Michael H. Kunter. Applied linear regression models. Richard D. Irwin, ink(1983) ,172-173
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Abstract: This paper hosts a comparison between logistic regression model and calibration linear model . Both models were applied on random sample of 120 people , 100 are infected with blood cancer and 20 are fit . And we have 3 independent variables , age , pcv , mch . When applying both models we discovered that the values of standard errors in calibration regression model are less than the value of standard errors in logistic regression model , meaning that calibration regression method was better . Some other results were reached , like when applying logistic all variables mentioned above have significant influence on cancer infection , we also found that pcv variable is the most influential in cancer infection , followed by the rest age and msh

Keywords: Linear model, classical estimator, calibration model,vce(robust) ,efficiency, Blood cancers.

[1]. MARIE-ANNE GRUET,(1996) , A non Parametric Calibration Analysis
[2]. Christine Osborne . (1991). Statistical Calibration: A Review. School of Mathematical Sciences, University of Bath, Bath BA2 7A Y, England
[3]. AITCHISON, J., and DUNSMORE, I. R. (1975), Statistical Prediction Analysis, London: Cambridge University Press.
[4]. DUNSMORE, I. R. (1968), "A Bayesian Approach to Calibration," Journal of the Royal Statistical Society.
[5]. Cox, D. R. (1981). Theory and general principle in statistics: the Address of the President (with Proceedings). J. R. Statist.

Abstract: This paper introduces a two-step iterative process for finding a solution of a variational inequality problem for accretive operators in Banach spaces. The result obtained in this paper is motivated by the result given by Koji Aoyama et al [3]. Further, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space

Keywords: Accretive operators, sunny non-expansive retractions, Banach spaces, variational inequality problem.

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