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

Abstract: In this paper we have constructed stiff fluid cosmological models by considering five dimensional Kaluza-Klein space-time based on Lyra geometry in the frame work of scalar tensor theory of gravitation proposed by Saez and Ballester, which are obtained for two different cases: constant displacement vector and time dependent displacement vector. Also some physical and kinametical properties of the models are discussed.

Key words: Five dimensional cosmological models, stiff fluid, Lyra geometry.

[1]. Alvarez, E., BelenGavela, M.: Phys. Rev. Lett., 51, 931 (1983)
[2]. Chodos, A., Detweiler, S.: Phys. Rev. D., 21, 2167 (1980)
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[7]. Rahaman, F., Chakraborty, S., Begum, N., Hossain, M., Kalam, M.: FIZIKA B, 11, 57 (2002)

Abstract: We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.

Keywords: steady hydro magnetic flows, three dimensional flows, parallel plate channel, porous medium, radiative heat, optically thin fluid.

[1]. Cogley, A. C. L., Vincenti, W. G., Gilles, E. S (1968), Differential approximation for radiative heat transfer in a non grey gas near
equilibrium, Am. Inst. Aeronat. Astronaut. J 6: 551 – 553.
[2]. Crammer, K., Pai, S. I (1973), Magnetofluid dynamics for engineers and applied physicists. McGraw-Hill Book Company.
[3]. Grief, R., Habib, I. S., Lin, J. C (1971), Laminar convection of a radiating gas in a vertical channel, J Fluid Mech.46: 513 – 520.
[4]. Israel – cookey, C., Nwaigwe, C., (2010), Unsteady MHD flow of a radiating fluid over a moving heated porous plate with time –
dependent suction, Am. J. Sci. Ind. Res. 1(1): 88 – 95.
[5]. Kearsley, A. J (1994), A steady state model of Couette flow with viscous heating, Int. J. Engng Sci. 32: 179 – 186

Abstract:Circle, square and triangle are basic geometrical constructions.  constant is associated with the circle. In this paper, circle-triangle interlationship chooses the real value of  and calculating the area of the triangle involving  of the inscribed circle. The alternate formula to find the area of the triangle is 2 3 3 d 14 2         . This formula has a geometrical backing.
Keywords: Altitude, base, circle, diameter, perimeter, triangle

[1]. Lennart Berggren, Jonathan Borwein, Peter Borwein (1997), Pi: A source Book, 2nd edition, Springer-Verlag Ney York Berlin
Heidelberg SPIN 10746250.
[2]. Alfred S. Posamentier & Ingmar Lehmann (2004), , A Biography of the World's Most Mysterious Number, Prometheus Books,
New York 14228-2197.
[3]. RD Sarva Jagannada Reddy (2014), New Method of Computing Pi value (Siva Method). IOSR Journal of Mathematics, e-ISSN:
2278-3008, p-ISSN: 2319-7676. Volume 10, Issue 1 Ver. IV. (Feb. 2014), PP 48-49.
[4]. RD Sarva Jagannada Reddy (2014), Jesus Method to Compute the Circumference of A Circle and Exact Pi Value. IOSR Journal of
Mathematics, e-ISSN: 2278-3008, p-ISSN: 2319-7676. Volume 10, Issue 1 Ver. I. (Jan. 2014), PP 58-59.
[5]. RD Sarva Jagannada Reddy (2014), Supporting Evidences To the Exact Pi Value from the Works Of Hippocrates Of Chios, Alfred
S. Posamentier And Ingmar Lehmann. IOSR Journal of Mathematics, e-ISSN: 2278-3008, p-ISSN:2319-7676. Volume 10, Issue 2
Ver. II (Mar-Apr. 2014), PP 09-12

Abstract: We have established in this paper, that the set of solutions of a system of Ordinary Differential Equations obtained using the exponential of a Matrix Method, can form a Fundamental Matrix. We also discussed when the diagonalizable matrix is not idempotent. Keywords: Diagonalizable, Exponential matrix, matrix, fundamental matrix, idempotent, Ordinary Differential Equations, set of solutions, Wronskian.

[1]. Jervin Zen lobo and Terence Johnson,
[2]. Solution of Differential Equations Exponential of a Matrix, IOSR Journal of Mathematics, e-ISSN 2278 – 5728, volume 5, Issue 3, (Jan – Feb 2013) pp 12 – 17.
[3]. Erwin Kreyszig,
[4]. Advanced Engineering Mathematics, 10th Edition, pp 75- 78.
[5]. Dennis G. Zill,

Abstract: Treatment is of great importance in fighting against infectious diseases. Backward bifurcation of SIR epidemic model with treatment rate is proposed and analyzed by Wang W. We have reinvestigated the above model by considering a backward bifurcation of SIR epidemic model with non-monotone incidence rate under treatment. It is assumed that the treatment rate is proportional to the number of patients as long as this number is below a certain capacity and it becomes constant when that number of patients exceeds this capacity. Mathematical models have become important tools in analyzing the spread and control of infectious diseases. It is shown that this kind of treatment rate leads to the existence of multiple endemic equilibria where the basic reproduction number plays a big role in determining their stability. Moreover, numerical calculations are support to analyze the global stability of unique endemic equilibrium. Keywords: Backward Bifurcation, Basic reproduction number, Endemic, Epidemic, Incidence rate, Treatment function.

[1] Wang W., 2006. Backward Bifurcation of an Epidemic Model with Treatment, J. Math. Bio. Sci., 201:58-71

[2] Capasso V. and G. Serio., 1978. A Generalization of the Kermack-Mckendrick Deterministic Epidemic Model. Mat,. Bio. Sci., 42:43-61.

[3] Derrick W.R. and P. Van Der Driessche ., 1993. A Disease Transmission Model in a Non- constant Population, J. Math. Biol., 31:495-512.

[4] Esteva L. and M. A. Matias., 2001. Model for Vector Transmitted Diseases with Saturation Incidence, Journal of Biological System, 9(4):235-245

[5] Gajendra Ujjainkar, V. K. Gupta, B. Singh, R. Khandelud., 2012. An Epidemic Model with Modified Non-monotonic Incidence Rate under Treatment, 6:1159-1171.

[6] Hethcote H.W. and P. Van Den Driessch., 1991. Some Epidemiological models with Non- linear Incidence, J. Math. Boil., 29:271-287.

Abstract: This study unifies square, circle, Golden Ratio, arbelos of Archimedes and  value. The final result,
in this unification process, the real  value is identified, and is,
14 2
4

= 3.14644660942…
Key words: Arbelos, area, circle, diameter, diagonal, Golden Ratio, Perimeter,  value, side, square

[1]. Lennart Berggren, Jonathan Borwein, Peter Borwein (1997), Pi: A source Book, 2nd edition, Springer-Verlag Ney York Berlin
Heidelberg SPIN 10746250.
[2]. Alfred S. Posamentier & Ingmar Lehmann (2004), , A Biography of the World‟s Most Mysterious Number, Prometheus Books,
New York 14228-2197.
[3]. RD Sarva Jagannada Reddy (2014), New Method of Computing Pi value (Siva Method). IOSR Journal of Mathematics, e-ISSN:
2278-3008, p-ISSN: 2319-7676. Volume 10, Issue 1 Ver. IV. (Feb. 2014), PP 48-49.
[4]. RD Sarva Jagannada Reddy (2014), Jesus Method to Compute the Circumference of A Circle and Exact Pi Value. IOSR Journal of
Mathematics, e-ISSN: 2278-3008, p-ISSN: 2319-7676. Volume 10, Issue 1 Ver. I. (Jan. 2014), PP 58-59.
[5]. RD Sarva Jagannada Reddy (2014), Supporting Evidences To the Exact Pi Value from the Works Of Hippocrates Of Chios, Alfred
S. Posamentier And Ingmar Lehmann. IOSR Journal of Mathematics, e-ISSN: 2278-3008, p-ISSN:2319-7676. Volume 10, Issue 2
Ver. II (Mar-Apr. 2014), PP 09-12

Abstract: In the present paper, we introduce the theory of four dimensional Finsler space and define geodesic equation with the basis of Finsler space. We also try to define geodesic equation to useful significance

[1]. Berwald, L, (1947):Uber Finslersche und Cartansche Geometries IV. Projective Krummungallgemeneraffiner Raume and Finselersche Raume skalarer Krummunrg, Ann. of Math. (2), 48 , 755-781
[2]. Cartan, E(1934).:Les Espaces de Finsler. Actualities ScientifiquesIndustrilles no.79, Paris, Hermann .
[3]. Finsler, P. (1918):UberKurven and Flachen in allgemeinen Dissertation, Gottingen,
[4]. Hombu, H.(1934):KonformeInvariatenimFinslerschen Raume, J. Fac. Sci.Hokkaido Univ.12, 157-168.
[5]. H. Rund(1959).; The differential geometry of finsler spaces, spcingerKerlag.
[6]. Matsumoto, M. and Miron R. (1977) :On an invariant theory of The Finsler Spaces, Period.Math.Hungary, 8,73-82.
[7]. Matsumoto, M. and Shimada, H.(1977) :On Finsler spaces with the curvature

Abstract: Let T be open, nonempty subset of
 n and f :T  be a function onT . In general if f is
concave, every local maximum of f is also a global maximum and first order conditions are sufficient to
identify global of concave or convex optimization problems and they are so strict and quite restrictive as an
assumption.
In this paper we present characterizations of optimization problems under a weakening of the condition of
concave functions, called "quasi-concave" functions. Some of the characterizations of these functions as a
generalization of concave functions and proves are discussed in terms of its contour sets (level sets), derivatives
and extreme properties of the functions on line segment. It also discuses its optimality conditions
Key words: Concave functions, quasi-concave functions, Semi-strict, Upper and lower contour.

[1]. D.T.Luc, Generalized convexity and some Applications to vectors optimization, vietnam journal of Mathematics 26:2(1998).
[2]. D. T. Luc, characterizations of quasi-convex functions, Bulletin of Australia mathematical society 48 (1993).
[3]. Rangarajan, K. Sundaram, A first course in optimization theory, Cambridge, United States; University Press, (1976).
[4]. Schaible S. and Ziemba W.T,Generalized concavity I optimization and Economics,Academic Press,New York, (1981)
[5]. Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge, Syndicate of the University Press, (2006).
[6]. W.E. Diewert, A.Avriel, and I. Zang, Generalized concavity (2010).
[7]. I.Ginchev and V.I. Ivanov, Second order characterizations of convex and pseudo-convex functions,Journal of Analysis vol.9,No 2
(2003) .

Abstract:A deterministic model was proposed to study the spread and control of asthma disease and treatment. The model is a system of first order ordinary differential equations. The model equations were analyzed to obtain the characteristics equation and equilibrium states. Stability analysis of the free and endemic equilibrium states was carried out. From our stability analysis, we observed that the free equilibrium state will always be stable if the birth rate 𝛽 is less than the death rate 𝜇 of the population (where 𝛽𝜇, is number of susceptible individuals produced).
Key words: Disease free equilibrium state, endemic equilibrium, asthma, infectious disease, stability analysis

[1]. Benyah, F, (2005); Introduction To Mathematical Modeling; 7th Regional College On Modeling, Simulation And Optimization, University Of Cope Coast, Ghana.
[2]. Eykhoff, P. (1974).System Identification-Parameter and State Estimation. Willey New
[3]. York.
[4]. Microsoft Corporation (2009).Treatment and Infection, Encarta Premium, U.S.A
[5]. World Health Organization, (2006)."Frequently asked questions about HIV and TB", WHO Report, Geneva Switzerland

Abstract: Logistic regression is widely used as a popular model for the analysis of binary data with the areas of applications including physical, biomedical and behavioral sciences. In this study, the logistic regression model, as well as the maximum likelihood procedure for the estimation of its parameters, are introduced in detail. The study has been necessited with the fact that authors looked at the simulation studies of the logistic models but did not test sensitivity of the normal plots. The fundamental assumption underlying classical results on the properties of MLE is that the stochastic law which determines the behaviour of the phenomenon investigated is known to lie within a specified parameter family of probability distribution (the model). This study focuses on investigating the asymptotic properties of maximum likelihood estimators for logistic regression models. More precisely, we show that the maximum likelihood estimators converge under conditions of fixed number of predictor variables to the real value of the parameters as the number of observations tends to infinity.We also show that the parameters estimates are normal in distribution by plotting the quantile plots and undertaking the Kolmogorov -Smirnov an the Shapiro-Wilks test for normality,where the result shows that the null hypothesis is to reject at 0.05% and conclude that parameters came from a normal distribution.
Key Words: Logistic, Asymptotic, Normality, MRA(Multiple Regression Analysis)

[1] T. Amemiya. Advanced Econometric. Havard University Press, Cambridge, 1985.
[2] M. Beer. Asymptotic properies of the maximum likelihood estimator in [1] dichotomodi logistic regression model. 2001.
[3] David Collett. Modelling Binary Data. Chapman & Hall/CRC, New York, USA, second edition, (2002).
[4] Jerome Cornfield. Joint dependence of risk of coronary heart disease on serum cholesterol and systolic blood pressure: A
discriminant function analysis. In Federation Proceedings, volume 21, page 58, 1962.
[5] D. R. Sir Cox and E. J. Snell. Analysis of Binary Data. London.Chapman & Hall, 1989

Abstract: In this paper, we introduce the concept of KS-graph of commutative KS-semigroup. We also introduce the notion of L-prime, zero divisors of commutative KS – semigroup and investigated its related properties. We also discuss the concept of KS-graph of commutative KS-semigroup and provide some examples and theorems.

Keywords: commutative KS-semigroup, connected graph, KS- graph, L- prime of commutative KS- semigroup P- ideal, zero divisors.

[1] J. Mong and Y.B.Jun, BCK-Algebras, kyung moon sa ca., Seoul Korea, 1994.

[2] Y.Imai, K. Iseki, on axiom system of propositional calculi, XIV, japan Acad. 42 (1996), 19-22

[3] K. Iseki, An algebra related with a propositional calculus, Japan Acad. 42 (1996), 26– 29

[4] Y.B. Jun, K. J. Lee, Graph based on BCK / BCI – algebras, IJMMS (2011)

[5] J. Meng, Y. B. Jun, BCK – algebras, Kyung Moonsa. Seoul, Korea (1994)C

[6] O.Zahari, R. A. Borzooei, graph of BCI – algebras, International Journal of Mathematics and Mathematical Sciences, Volume 2012 Article ID 126835, 16 pages.

Abstract: Various risks and uncertainties exist in construction projects. These may not only prevent the projects to be completed within budget and time limit, but also threaten the quality, safety and operational needs. In making decisions involving multiple objects we have to consider conflicting goals and weigh them against each other. Fuzzy decisions making is a suitable method used by decision makers in uncertain situations in this work. A case study is used to demonstrate the concept of general contractor choice on the basis of multiple attributes of efficiency with fuzzy inputs applying convexity proportional assessment graph method.
Keywords: Fuzzy graph, multi-attribute, decision-making model, Fuzzy number

[1]. Zavadskas,E.K., A.Zakarevicius and J.Antuchevi cien e(2006).Evaluation of ranking accuracy in multi-criteria decisions. Informatica, 17(4), 601 – 618
[2]. Zavadskas, E.K., A.Kaklauskas, F.Peldschus and Z.Turskis(2007b).Multi-attribute assessment of road design solutions by using the COPRAS method. The Baltic Journal of Road and Bridge Engineering,2(4), 195 – 203
[3]. G.Nirmala and N.Vanitha, Risk of Construction project with Fuzzy Characteristics, Narosa Publication, 2010
[4]. G.Nirmala and N.Vanitha, Fuzzy Graph in Geology, International Journal of Scientific Research, May 2013, ISSN No. 2277-8179
[5]. G.Nirmala and N.Vanitha, Risk analysis of river- type hydropower plants, Aryabhatta Journal of Mathematics and informatics, May 2014, Volume I

Abstract:The Diophantine equation of degree six with four unknowns given by
4 4 2 1 5 x y 2 zT k   
has been analyzed for its non-zero integral solutions.A few interesting relations between the solutions and
special numbers are given.
Keywords: Sextic equation with four unknowns, integral solutions, polygonal numbers

[1]. L.E.Dickson, History of Theory of Numbers Vol.11, Chelsea Publishing Company, New York (1952).
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[4]. Carmichael ,R.D.,The theory of numbers and Diophantine Analysis,Dover Publications,New York (1959)
[5]. M.A.Gopalan and Sangeetha, On the sextic equations with 3 unknowns
2 2 2 6 x xy y (R 3) z n     , Impact
J.Sci.tech.Vol 4 No 4,2010,89-93.
[6]. M.A.Gopalan, Manju Somnath and N.Vanitha, Parametric Solutions of
2 6 2 x  y  z ,Acta ciencia indica,XXXIII,3,2007,1083-
1085..